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		<title>Unveiling Hidden Patterns in the Cryptocurrency Market with Affinity Propagation and Python</title>
		<link>https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/</link>
					<comments>https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/#comments</comments>
		
		<dc:creator><![CDATA[Florian Follonier]]></dc:creator>
		<pubDate>Mon, 02 May 2022 18:34:02 +0000</pubDate>
				<category><![CDATA[Affinity Propagation (Clustering)]]></category>
		<category><![CDATA[Clustering]]></category>
		<category><![CDATA[Coinmarketcap API]]></category>
		<category><![CDATA[Correlation]]></category>
		<category><![CDATA[Covariance]]></category>
		<category><![CDATA[Crypto Exchange APIs]]></category>
		<category><![CDATA[Data Visualization]]></category>
		<category><![CDATA[Dimensionality Reduction]]></category>
		<category><![CDATA[Finance]]></category>
		<category><![CDATA[Python]]></category>
		<category><![CDATA[Scikit-Learn]]></category>
		<category><![CDATA[Seaborn]]></category>
		<category><![CDATA[Stock Market Forecasting]]></category>
		<category><![CDATA[Time Series Forecasting]]></category>
		<category><![CDATA[Advanced Tutorials]]></category>
		<category><![CDATA[AI in Finance]]></category>
		<category><![CDATA[Cryptocurrencies]]></category>
		<category><![CDATA[Financial Analysis]]></category>
		<category><![CDATA[Stock Market Cluster Analysis]]></category>
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					<description><![CDATA[<p>Affinity propagation is a powerful unsupervised clustering technique that can identify hidden patterns in large datasets. In the cryptocurrency world, where new coins are constantly emerging and prices can be highly volatile, affinity propagation can help investors simplify the chaos. By analyzing historical price data, affinity propagation groups coins into clusters based on their past ... <a title="Unveiling Hidden Patterns in the Cryptocurrency Market with Affinity Propagation and Python" class="read-more" href="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/" aria-label="Read more about Unveiling Hidden Patterns in the Cryptocurrency Market with Affinity Propagation and Python">Read more</a></p>
<p>The post <a href="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/">Unveiling Hidden Patterns in the Cryptocurrency Market with Affinity Propagation and Python</a> appeared first on <a href="https://www.relataly.com">relataly.com</a>.</p>
]]></description>
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<p class="wp-block-paragraph">Affinity propagation is a powerful unsupervised clustering technique that can identify hidden patterns in large datasets. In the cryptocurrency world, where new coins are constantly emerging and prices can be highly volatile, affinity propagation can help investors simplify the chaos.</p>



<p class="wp-block-paragraph">By analyzing historical price data, affinity propagation groups coins into clusters based on their past price fluctuations. Such a cluster analysis enables crypto investors to identify promising entry and exit points, ultimately helping them make smarter investment decisions.</p>



<p class="wp-block-paragraph">To use this technique effectively, it&#8217;s important to understand essential concepts such as covariance, lasso regression, and affinity propagation. Once you understand these concepts, you can apply them to analyze price time series data and identify hidden patterns.</p>



<p class="wp-block-paragraph">Finally, visualizing the results in two and three dimensions can better understand the relationships between coins and their respective clusters. The resulting crypto market map can be a powerful tool for investors to gain insight into the market&#8217;s structure and make informed investment decisions.</p>



<div class="wp-block-group"><div class="wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained">
<div class="wp-block-kadence-infobox kt-info-box_317393-a1"><span class="kt-blocks-info-box-link-wrap info-box-link kt-blocks-info-box-media-align-top kt-info-halign-left"><div class="kt-infobox-textcontent"><h2 class="kt-blocks-info-box-title">Disclaimer</h2><p class="kt-blocks-info-box-text">This article does not constitute financial advice. Stock markets can be very volatile and are generally difficult to predict. Predictive models and other forms of analytics applied in this article only serve the purpose of illustrating machine learning use cases.</p></div></span></div>
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<h2 class="wp-block-heading">What is Stock Market Clustering?</h2>



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<p class="wp-block-paragraph">Clustering stock markets refers to grouping stocks based on their similarities or common characteristics. This can be done using various clustering algorithms, which analyze the data and assign each stock market to a cluster based on its similarity to other stock markets in the same cluster. In this article, we will run a cluster analysis on historical time series data. This approach involves grouping stocks into clusters based on their historical performance over a certain period of time. </p>



<p class="wp-block-paragraph">Clustering stock market data can be useful for a variety of purposes, such as identifying patterns or trends in the data, comparing the performance of different stocks or sectors, or generating investment recommendations. However, it&#8217;s important to keep in mind that clustering is just one tool among many for analyzing stock market data, and it&#8217;s important to consider a range of factors when making investment decisions. It can also be used to compare the performance of different stock markets and identify potential risks or correlations between them.</p>



<p class="wp-block-paragraph">Also: <a href="https://www.relataly.com/cryptocurrency-price-charts-with-color-overlay-python/2820/" target="_blank" rel="noreferrer noopener">Color-Coded Cryptocurrency Price Charts in Python</a></p>
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<figure class="wp-block-image size-full"><img fetchpriority="high" decoding="async" width="509" height="506" data-attachment-id="12694" data-permalink="https://www.relataly.com/neural-network-machine-learning-python-affinity-propagation-midjourney-relataly-crypto-min/" data-orig-file="https://www.relataly.com/wp-content/uploads/2023/03/neural-network-machine-learning-python-affinity-propagation-midjourney-relataly-crypto-min.png" data-orig-size="509,506" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="neural network machine learning python affinity propagation midjourney relataly crypto-min" data-image-description="&lt;p&gt;neural network machine learning python affinity propagation midjourney relataly crypto-min&lt;/p&gt;
" data-image-caption="&lt;p&gt;neural network machine learning python affinity propagation midjourney relataly crypto-min&lt;/p&gt;
" data-large-file="https://www.relataly.com/wp-content/uploads/2023/03/neural-network-machine-learning-python-affinity-propagation-midjourney-relataly-crypto-min.png" src="https://www.relataly.com/wp-content/uploads/2023/03/neural-network-machine-learning-python-affinity-propagation-midjourney-relataly-crypto-min.png" alt="neural network machine learning python midjourney relataly crypto market map" class="wp-image-12694" srcset="https://www.relataly.com/wp-content/uploads/2023/03/neural-network-machine-learning-python-affinity-propagation-midjourney-relataly-crypto-min.png 509w, https://www.relataly.com/wp-content/uploads/2023/03/neural-network-machine-learning-python-affinity-propagation-midjourney-relataly-crypto-min.png 300w, https://www.relataly.com/wp-content/uploads/2023/03/neural-network-machine-learning-python-affinity-propagation-midjourney-relataly-crypto-min.png 140w" sizes="(max-width: 509px) 100vw, 509px" /><figcaption class="wp-element-caption">We can use a crypto market map to illustrate the price correlation between cryptocurrencies.</figcaption></figure>
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<h2 class="wp-block-heading">What&#8217;s the Problem with Prototype-based Clustering?</h2>



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<p class="wp-block-paragraph">Clustering is an unsupervised learning technique that groups similar objects into clusters and separates them from different ones. One of the most popular clustering techniques is <a href="https://www.relataly.com/category/machine-learning-algorithms/k-means/" target="_blank" rel="noreferrer noopener">k-means</a>. K-means belongs to the so-called prototype-based clustering techniques, which divide data points into a predefined number of groups (in the case of k-means, the groups are of equal variance). </p>



<p class="wp-block-paragraph">The prototype-based clustering approach works great if the number of clusters in a dataset is known and the clusters have similar despair. However, when we deal with real-world problems, we often encounter more complex data for which the optimal number of clusters is unknown and difficult or even impossible to guess. In such a case, affinity propagation has a significant advantage because it can automatically estimate the number of clusters. </p>
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<h2 class="wp-block-heading">Affinity Propagation: What it is and How it Works </h2>



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<p class="wp-block-paragraph">The idea of affinity propagation is to identify clusters by measuring the similarity of data points relative to one another. The algorithm chooses data points as cluster centers that best represent other data points near them. </p>



<p class="wp-block-paragraph">We can imagine the process of identifying these representative data points as an election. Each data point (i) is a voter who casts votes and a candidate (k) who can receive votes from other voters. Votes are a measure of the similarity of data points. A voter who gives many votes to a candidate expresses that this data point is similar to him and therefore is suitable for representing him as a cluster center. The voting process continues until the algorithm reaches a consensus and selects a set number of cluster candidates.</p>
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<figure class="wp-block-image size-large"><img decoding="async" width="1024" height="383" data-attachment-id="8208" data-permalink="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/image-5/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2022/05/image-5.png" data-orig-size="1584,592" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-5" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2022/05/image-5.png" src="https://www.relataly.com/wp-content/uploads/2022/05/image-5-1024x383.png" alt="Affinity Propagation: Data points cast votes for candidates and receive votes from other data points " class="wp-image-8208" srcset="https://www.relataly.com/wp-content/uploads/2022/05/image-5.png 1024w, https://www.relataly.com/wp-content/uploads/2022/05/image-5.png 300w, https://www.relataly.com/wp-content/uploads/2022/05/image-5.png 768w, https://www.relataly.com/wp-content/uploads/2022/05/image-5.png 1536w, https://www.relataly.com/wp-content/uploads/2022/05/image-5.png 1584w" sizes="(max-width: 1024px) 100vw, 1024px" /><figcaption class="wp-element-caption">Affinity Propagation: Data points cast votes for candidates and receive votes from other data points </figcaption></figure>
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<p class="wp-block-paragraph">The clustering process involves many separate steps (<a href="https://towardsdatascience.com/unsupervised-machine-learning-affinity-propagation-algorithm-explained-d1fef85f22c8" target="_blank" rel="noreferrer noopener">This article</a> provides a detailed description of the steps involved) and works with several matrices: </p>



<ul class="wp-block-list">
<li>The similarity matrix assesses the suitability of data points (candidates) to act as cluster centers.</li>



<li>The availability matrix (or responsibility matrix) collects the support of the data points for the candidates (potential cluster centers) and their suitability to represent them.</li>



<li>The criterion matrix sums up the results and defines the clusters. Data points with equal scores in the criterion matrix are considered part of the same cluster.</li>
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<figure class="wp-block-image size-full"><img decoding="async" width="691" height="334" data-attachment-id="8274" data-permalink="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/image-9/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2022/05/image-9.png" data-orig-size="691,334" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-9" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2022/05/image-9.png" src="https://www.relataly.com/wp-content/uploads/2022/05/image-9.png" alt="Criterion Matrix: Data Points (Cryptos) with equal numbers are part of the same cluster" class="wp-image-8274" srcset="https://www.relataly.com/wp-content/uploads/2022/05/image-9.png 691w, https://www.relataly.com/wp-content/uploads/2022/05/image-9.png 300w" sizes="(max-width: 691px) 100vw, 691px" /><figcaption class="wp-element-caption">Criterion Matrix: Data Points (Cryptos) with equal numbers are part of the same cluster</figcaption></figure>
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<h2 class="wp-block-heading" id="h-time-series-clustering-using-affinity-propagation-visualizing-cryptocurrency-market-structures-in-python">Time Series Clustering using Affinity Propagation &#8211; Visualizing Cryptocurrency Market Structures in Python</h2>



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<p class="wp-block-paragraph">Ready to implement affinity propagation in Python to analyze the crypto market structure and create a visual representation of price similarity? Let&#8217;s dive in!</p>



<p class="wp-block-paragraph">First, we define a portfolio of cryptocurrencies and download their historical price quotes from coinmarketcap. We then visualize the time series on separate line charts to ensure that the data has been loaded successfully. After preparing and cleaning the data, we can move on to clustering the cryptocurrencies into groups with similar price movements using Affinity Propagation.</p>



<p class="wp-block-paragraph">Unlike other clustering algorithms, we don&#8217;t set the number of clusters in advance. Instead, we let affinity propagation determine the optimal number of clusters for our portfolio. Finally, we calculate the covariance matrix between clusters and arrange the cryptocurrencies on a 2D map into clusters. We create a network overlay based on covariance to better understand the relationships between different clusters.</p>



<p class="wp-block-paragraph">With affinity propagation, we can identify hidden patterns in the crypto market and group coins into clusters based on their past price fluctuations. This process allows us to identify promising entry and exit points, ultimately helping us make smarter investment decisions. Plus, the 2D map and network overlay help us visualize the relationships between different clusters and coins.</p>
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<figure class="wp-block-image size-full"><img decoding="async" width="456" height="509" data-attachment-id="10401" data-permalink="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/image-33-2/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2022/12/image-33.png" data-orig-size="456,509" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-33" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2022/12/image-33.png" src="https://www.relataly.com/wp-content/uploads/2022/12/image-33.png" alt="exemplary price correlation map created with the help of the affinity propagation clustering algorithm, python scikit-learn" class="wp-image-10401" srcset="https://www.relataly.com/wp-content/uploads/2022/12/image-33.png 456w, https://www.relataly.com/wp-content/uploads/2022/12/image-33.png 269w" sizes="(max-width: 456px) 100vw, 456px" /><figcaption class="wp-element-caption">We can use affinity propagation to cluster financial assets and visualize them on a map.</figcaption></figure>
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<p class="wp-block-paragraph">The Python code for this tutorial is available in the relataly repository on GitHub.</p>



<div class="wp-block-kadence-advancedbtn kb-buttons-wrap kb-btns_03b447-31"><a class="kb-button kt-button button kb-btn_03610b-ed kt-btn-size-standard kt-btn-width-type-full kb-btn-global-inherit kt-btn-has-text-true kt-btn-has-svg-true wp-block-button__link wp-block-kadence-singlebtn" href="https://github.com/flo7up/relataly-public-python-tutorials/blob/master/00%20Data%20Visualization/042%20Vizualizing%20Stock%20Market%20Structures%20using%20Cluster%20Analysis%20in%20Python.ipynb" target="_blank" rel="noreferrer noopener"><span class="kb-svg-icon-wrap kb-svg-icon-fe_eye kt-btn-icon-side-left"><svg viewBox="0 0 24 24"  fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"  aria-hidden="true"><path d="M1 12s4-8 11-8 11 8 11 8-4 8-11 8-11-8-11-8z"/><circle cx="12" cy="12" r="3"/></svg></span><span class="kt-btn-inner-text">View on GitHub </span></a>

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<h3 class="wp-block-heading" id="h-prerequisites">Prerequisites</h3>



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<p class="wp-block-paragraph">Before beginning the coding part, ensure that you have set up your Python 3 environment and required packages. Consider <a href="https://www.anaconda.com/products/individual" target="_blank" rel="noreferrer noopener">Anaconda </a>if you don&#8217;t have a Python environment set up yet. To set it up, you can follow the steps in&nbsp;<a href="https://www.relataly.com/category/data-science/setup-anaconda-environment/" target="_blank" rel="noreferrer noopener">this tutorial</a>. Also, make sure you install all required packages. In this tutorial, we will be working with the following standard packages:&nbsp;</p>



<ul class="wp-block-list">
<li><a href="https://pandas.pydata.org/" target="_blank" rel="noreferrer noopener">pandas</a></li>



<li><a href="https://numpy.org/" target="_blank" rel="noreferrer noopener">NumPy</a></li>



<li><a href="https://matplotlib.org/" target="_blank" rel="noreferrer noopener">matplotlib</a></li>



<li><a href="https://seaborn.pydata.org/api.html" target="_blank" rel="noreferrer noopener">Seaborn</a></li>
</ul>



<p class="wp-block-paragraph">Please also make sure you have the <a href="https://pypi.org/project/cryptocmd/" target="_blank" rel="noreferrer noopener">Cmcscaper</a> package installed. We will be using it to download past crypto prices from coinmarketcap.</p>



<p class="wp-block-paragraph">You can install these packages using console commands:</p>



<ul class="wp-block-list">
<li><em>pip install &lt;package name&gt;</em></li>



<li><em>conda install &lt;package name&gt;</em>&nbsp;(if you are using the anaconda packet manager)</li>
</ul>
</div>



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<h3 class="wp-block-heading" id="h-step-1-load-the-stock-market-data">Step #1: Load the Stock Market Data</h3>



<p class="wp-block-paragraph">We start by loading historical crypto price data from Coinmarketcap. To download the data, we use Cmcscraper, a Python library that allows us to collect Coinmarketcap data without signing up for the official API.</p>



<p class="wp-block-paragraph">The download returns a dataframe with daily price quotes (Close, Open, Avg) for cryptocurrencies between 2016 and today. You can use the dictionary (&#8220;symbol_dict&#8221;) to control which cryptos you want to include in the data. We limit the data we use in our cluster analysis to the last 50 days. In this way, we let the correlation consider earlier price developments. But it&#8217;s up to you to specify a different period. In addition, instead of using absolute price values, we will use daily percentage fluctuations.</p>



<p class="wp-block-paragraph">Also: <a href="https://www.relataly.com/streaming-crypto-prices-via-the-gate-io-api-with-python/3982/" target="_blank" rel="noreferrer noopener">Requesting Crypto Price Data from the Gate.io REST API in Python</a></p>



<p class="wp-block-paragraph">Loading the data can take several minutes, depending on how many cryptocurrencies we include in the request. So it makes sense not to load the data every time you run the code. Therefore, the code below stores the historical prices in a CSV file. </p>



<p class="wp-block-paragraph">The script will check if the data already exists if you run the code below. If it does, it will use the data from the CSV file. Otherwise, it will load a fresh copy of the data from coinmarketcap.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># A tutorial for this file is available at www.relataly.com
# Tested with Python 3.8.8, Matplotlib 3.5, Scikit-learn 0.24.1, Seaborn 0.11.1, numpy 1.19.5

from cryptocmd import CmcScraper
import pandas as pd 
import matplotlib.pyplot as plt 
import numpy as np 
import seaborn as sns
from sklearn import cluster, covariance, manifold
import requests
import json


#get a dictionary of the top 100 coin symbols and names from an API
def get_symbol_dict():
    url = 'https://api.coinmarketcap.com/data-api/v3/cryptocurrency/listing?start=1&amp;limit=50&amp;sortBy=market_cap&amp;sortType=desc&amp;convert=USD&amp;cryptoType=all&amp;tagType=all&amp;audited=false'
    response = requests.get(url)
    data = json.loads(response.text)
    df = pd.DataFrame(data['data']['cryptoCurrencyList'])

    # exclude stable coins
    df = df[~df['symbol'].isin(['USDT', 'USDC', 'BUSD', 'DAI', 'TUSD', 'PAX', 'GUSD', 'HUSD', 'USDK', 'USDS', 'USDP', 'USDN', 'USDSB', 'USDX', 'USD++', 'BIDR', 'IDRT', 'VAI', 'BGBP'])]
    df = df[['symbol', 'name']]
    df = df.set_index('symbol')
    df = df.to_dict()
    df = df['name']
    return df

symbol_dict = get_symbol_dict()


# Download historic crypto prices via CmcScraper
def load_fresh_data_and_save_to_disc(symbol_dict, save_path):
    # Extract symbols and names from the symbol_dict
    symbols, names = np.array(sorted(symbol_dict.items())).T
    
    # Initialize an empty DataFrame for storing the prices
    df_crypto = pd.DataFrame()

    # Download and process the price data for each symbol
    for symbol in symbols:
        print(f&quot;Fetching prices for {symbol}...&quot;)
        
        # Download the price data using CmcScraper
        scraper = CmcScraper(symbol)
        df_coin_prices = scraper.get_dataframe()

        # Process the price data and add it to df_crypto
        df = pd.DataFrame({
            f&quot;{symbol}_Open&quot;: df_coin_prices[&quot;Open&quot;],
            f&quot;{symbol}_Close&quot;: df_coin_prices[&quot;Close&quot;],
            f&quot;{symbol}_Avg&quot;: (df_coin_prices[&quot;Close&quot;] + df_coin_prices[&quot;Open&quot;]) / 2,
            f&quot;{symbol}_p&quot;: (df_coin_prices[&quot;Open&quot;] - df_coin_prices[&quot;Close&quot;]) / df_coin_prices[&quot;Open&quot;]
        })
        df_crypto = pd.concat([df_crypto, df], axis=1)

    # Save the price data to a CSV file
    X_df_filtered = df_crypto.filter(like=&quot;_p&quot;)
    X_df_filtered.to_csv(save_path + &quot;historical_crypto_prices.csv&quot;)

    return names, symbols, X_df_filtered
        

# If set to False the data will only be downloaded when you execute the code
# Set to True, if you want a fresh copy of the data.  
fetch_new_data = True 
save_path = '' # path where the price data will be stored in a csv file

# Fetch fresh data via the scraping package, or use data from the csv file on disk
if fetch_new_data == False:
    try:
        print('loading from disk')
        X_df_filtered = pd.read_csv(save_path + 'historical_crypto_prices.csv')
        if 'Unnamed: 0' in X_df_filtered.columns: 
            X_df_filtered = X_df_filtered.drop(['Unnamed: 0'], axis=1)
            symbols, names = np.array(sorted(symbol_dict.items())).T
        print(list(X_df_filtered.columns))
    except:
        print('no existing price data found - loading fresh data from coinmarketcap and saving them to disk')
        names, symbols, X_df_filtered = load_fresh_data_and_save_to_disc(symbol_dict, save_path)
        print(list(symbols))
else:
       print('loading fresh data from coinmarketcap and saving them to disk')
       names, symbols, X_df_filtered = load_fresh_data_and_save_to_disc(symbol_dict, save_path)
       print(list(symbols))

# Limit the price data to the last t days
t= 14 # in days
X_df_filtered = X_df_filtered[:t]
X_df_filtered.head()</pre></div>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:false,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;null&quot;,&quot;mime&quot;:&quot;text/plain&quot;,&quot;theme&quot;:&quot;3024-day&quot;,&quot;lineNumbers&quot;:false,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:false,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Plain Text&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;text&quot;}">	ACM_p		ADA_p		ARK_p		ATM_p		ATOM_p		AVAX_p		BAT_p		BCH_p		BLZ_p		BNB_p		...	THETA_p		UNI_p		USDT_p		VET_p		WAVES_p		XLM_p		XMR_p		XRP_p		ZIL_p		ZRX_p
0	0.031987	-0.037645	-0.005702	0.030928	-0.005897	-0.012404	-0.012262	-0.022529	0.008072	-0.007111	...	-0.021994	-0.023758	-0.000103	-0.021024	-0.015416	-0.004096	-0.022988	-0.027397	-0.016659	-0.012255
1	0.028192	0.065034	0.122306	0.010310	0.093558	0.106811	0.082863	0.075567	0.062105	0.054733	...	0.067264	0.081040	0.000136	0.077203	0.092987	0.078562	0.111519	0.071696	0.076484	0.085094
2	0.040771	0.016097	-0.133345	0.018963	0.011304	-0.033328	-0.007616	0.011458	-0.019993	0.005134	...	-0.005104	-0.024190	0.000077	0.002218	0.008920	0.004139	-0.031822	-0.012107	-0.003906	-0.021170
3	-0.027698	0.005129	-0.031516	-0.002639	0.022235	-0.008117	0.003969	0.019119	0.015403	0.005920	...	0.007992	0.027203	0.000003	0.000701	0.010739	0.005324	-0.007914	0.007168	0.004556	-0.003786
4	-0.021129	-0.019053	0.003273	-0.008121	0.002883	-0.004927	0.002548	-0.000599	0.028492	-0.012181	...	0.000198	-0.025817	-0.000047	-0.002800	-0.051515	-0.004861	0.015134	-0.000596	-0.010343	0.004530</pre></div>



<p class="wp-block-paragraph">The data looks good, so let&#8217;s continue.</p>



<h3 class="wp-block-heading">Step #2 Plotting Crypto Price Charts</h3>



<p class="wp-block-paragraph">Now that the data is available, we can visualize it in various line graphs. The visualization helps us better understand what kind of data we are dealing with and check if the download was successful.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Create Prices Charts for all Cryptocurrencies
list_length = X_df_filtered.shape[1]
ncols = 10
nrows = int(round(list_length / ncols, 0))
height = list_length/3 if list_length &gt; 30 else 4
fig, axs = plt.subplots(nrows=nrows, ncols=ncols, sharex=True, sharey=True, figsize=(20, height))
for i, ax in enumerate(fig.axes):
        if i &lt; list_length:
            sns.lineplot(data=X_df_filtered, x=X_df_filtered.index, y=X_df_filtered.iloc[:, i], ax=ax)
            ax.set_title(X_df_filtered.columns[i])
plt.show()</pre></div>



<figure class="wp-block-image size-large is-resized"><img decoding="async" data-attachment-id="8232" data-permalink="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/price-charts-stock-price-prediction/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2022/05/price-charts-stock-price-prediction.png" data-orig-size="1176,790" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="price-charts-stock-price-prediction" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2022/05/price-charts-stock-price-prediction.png" src="https://www.relataly.com/wp-content/uploads/2022/05/price-charts-stock-price-prediction-1024x688.png" alt="Clustering Crypto Market Structures with Affinity Propagation: Daily Price Quotes for different Cryptocurrencies" class="wp-image-8232" width="937" height="629" srcset="https://www.relataly.com/wp-content/uploads/2022/05/price-charts-stock-price-prediction.png 1024w, https://www.relataly.com/wp-content/uploads/2022/05/price-charts-stock-price-prediction.png 300w, https://www.relataly.com/wp-content/uploads/2022/05/price-charts-stock-price-prediction.png 768w, https://www.relataly.com/wp-content/uploads/2022/05/price-charts-stock-price-prediction.png 1176w" sizes="(max-width: 937px) 100vw, 937px" /></figure>



<p class="wp-block-paragraph">We can see the lineplots for all cryptocurrencies and everything looks as expected.</p>



<h3 class="wp-block-heading" id="h-step-3-clustering-cryptocurrencies-using-affinity-propagation">Step #3 Clustering Cryptocurrencies using Affinity Propagation</h3>



<p class="wp-block-paragraph">Next, we must prepare the data and run the affinity propagation algorithm. For some cryptocurrencies, we may encounter data that contains NaN values. Because clustering is sensitive to missing values, we must ensure good data quality. In addition, the Python code below will convert the DataFrame into a NumPy array and transpose it into a form where we have crypto assets as records and the days as columns.</p>



<p class="wp-block-paragraph">Running the code below returns a dictionary of clusters with the cryptocurrencies assigned to them by the affinity propagation algorithm.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Drop NaN values
X_df = pd.DataFrame(np.array(X_df_filtered)).dropna()
# Transpose the data to structure prices along columns
X = X_df.copy()
X /= X.std(axis=0)
X = np.array(X)
# Define an edge model based on covariance
edge_model = covariance.GraphicalLassoCV()
# Standardize the time series
edge_model.fit(X)
# Group cryptos to clusters using affinity propagation
# The number of clusters will be determined by the algorithm
cluster_centers_indices , labels = cluster.affinity_propagation(edge_model.covariance_, random_state=1)
cluster_dict = {}
n_labels = labels.max()
print(f&quot;{n_labels} Clusters&quot;)
for i in range(n_labels + 1):
    clusters = ', '.join(names[labels == i])
    print('Cluster %i: %s' % ((i + 1), clusters))
    cluster_dict[i] = (clusters)</pre></div>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:false,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;null&quot;,&quot;mime&quot;:&quot;text/plain&quot;,&quot;theme&quot;:&quot;3024-day&quot;,&quot;lineNumbers&quot;:false,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:false,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Plain Text&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;text&quot;}">9 Clusters
Cluster 1: Binance Coin, Cake Defi
Cluster 2: Bitcoin Cash, Bitcoin, BitTorrent, Decred, EOS, Ethereum Classic, Ethereum, Ampleforth, Komodo, Solana, Sys Coin, DOT
Cluster 3: Celsius
Cluster 4: Doge Coin
Cluster 5: Cardano, ATOM, Avalance, Enjin, Internet Computer, Link, Loopring, Polygon, IOTA, NEO, Synthetix, Theta, Vechain
Cluster 6: Litecoin
Cluster 7: ACM Token, Atletico Madrid Token, Chilliz, Juventus Turin Token, PSG Token
Cluster 8: LRC
Cluster 9: Tether
Cluster 10: ARK, Battoken, BLZ, Digibyte, AS Rom Token, WAVES, Stellar Lumen, Monero, Ripple, Zilliqa, Zer0</pre></div>



<p class="wp-block-paragraph">We can see that the algorithm has identified 13 different clusters in the data and a couple of clusters with only a single member. You will most likely encounter different results depending on when you run it. </p>



<h3 class="wp-block-heading">Step #4 Create a 2D Positioning Model based on the Graph Structure</h3>



<p class="wp-block-paragraph">In addition to clusters, we want to show the covariance between cryptocurrencies in our Crypto Market map. We need a graph-like structure that contains the covariance and position data of the cryptocurrencies for each crypto pair.</p>



<p class="wp-block-paragraph">In addition, we use a node position model that calculates their relative position on a 2D plane from the covariance of the cryptocurrencies. However, the positions are only relative, so the absolute axes have no meaning.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Create a node_position_model that find the best position of the cryptos on a 2D plane
# The number of components defines the dimensions in which the nodes will be positioned
node_position_model = manifold.LocallyLinearEmbedding(n_components=2, eigen_solver='dense', n_neighbors=20)
embedding = node_position_model.fit_transform(X.T).T
# The result are x and y coordindates for all cryptocurrencies
pd.DataFrame(embedding)
# Create an edge_model that represents the partial correlations between the nodes
partial_correlations = edge_model.precision_.copy()
d = 1 / np.sqrt(np.diag(partial_correlations))
partial_correlations *= d
partial_correlations *= d[:, np.newaxis]
# Only consider partial correlations above a specific threshold (0.02)
non_zero = (np.abs(np.triu(partial_correlations, k=1)) &gt; 0.02)
# Convert the Positioning Model into a DataFrame
data = pd.DataFrame.from_dict({&quot;embedding_x&quot;:embedding[0],&quot;embedding_y&quot;:embedding[1]})
# Add the labels to the 2D positioning model
data[&quot;labels&quot;] = labels
print(data.shape)
data.head()</pre></div>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:false,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;null&quot;,&quot;mime&quot;:&quot;text/plain&quot;,&quot;theme&quot;:&quot;3024-day&quot;,&quot;lineNumbers&quot;:false,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:false,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Plain Text&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;text&quot;}">(48, 3)
	embedding_x	embedding_y	labels
0	0.400590	-0.136473	6
1	-0.081908	-0.086039	4
2	-0.033982	-0.038526	9
3	0.416745	0.076849	6
4	-0.041938	0.031966	4</pre></div>



<p class="wp-block-paragraph">The next step is to create a graph of the partial correlations. </p>



<h3 class="wp-block-heading">Step #5 Visualize the Crypto Market Structure</h3>



<p class="wp-block-paragraph">Our goal is to visualize differences in the covariance between crypto pairs by varying the connection strengths. We calculate the line strength by normalizing the covariance of the crypto pairs. In addition, we visualize the distribution of the covariance. </p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Create an array with the segments for connecting the data points
start_idx, end_idx = np.where(non_zero) 
segments = [[np.array([embedding[:, start], embedding[:, stop]]).T, start, stop] for start, stop in zip(start_idx, end_idx)]
# Create a normalized representation of partial correlation between crypto currencies
# We can later use covariance to vizualize the strength of the connections
pc = np.abs(partial_correlations[non_zero])
normalized = (pc-min(pc))/(max(pc)-min(pc))
# plot the distribution of covariance between the cryptocurrencies
sns.histplot(pc)</pre></div>



<figure class="wp-block-image size-full is-resized"><img decoding="async" data-attachment-id="8251" data-permalink="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/covariance-histogram/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2022/05/covariance-histogram.png" data-orig-size="382,248" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="covariance-histogram" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2022/05/covariance-histogram.png" src="https://www.relataly.com/wp-content/uploads/2022/05/covariance-histogram.png" alt="cryptocurrency market structure visualization with affinity propagation, histogram of covariance between historical crypto prices" class="wp-image-8251" width="540" height="351" srcset="https://www.relataly.com/wp-content/uploads/2022/05/covariance-histogram.png 382w, https://www.relataly.com/wp-content/uploads/2022/05/covariance-histogram.png 300w" sizes="(max-width: 540px) 100vw, 540px" /></figure>



<p class="wp-block-paragraph">The hist plot shows that the covariance between the crypto pairs is mostly below 0.005.</p>



<p class="wp-block-paragraph">Finally, it is time to map cryptocurrencies on a 2D plane. To do this, we first define the cryptocurrencies using their relative position data with a scatterplot. We set the color of the points based on their clusters so that points in the same cluster are colored the same. Subsequently, we connect the points to the data from the edge model. The covariance between the crypto pairs determines the strength of their connections.</p>



<p class="wp-block-paragraph">We also define the color of the connections as follows. </p>



<ul class="wp-block-list">
<li>The map only shows connections with a covariance greater than 0.002.</li>



<li>Connections with a covariance greater than 0.05 are colored red. </li>



<li>Otherwise, connections between points within a cluster are shown in the cluster&#8217;s color. </li>



<li>We color connections in grey that are between points of different clusters.</li>
</ul>



<p class="wp-block-paragraph">Last but not least, we add the labels of the cryptocurrencies.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Visualization
plt.figure(1, facecolor='w', figsize=(20, 8))
plt.clf()
ax = plt.axes([0., 0., 1., 1.])

# Plot the nodes using the coordinates of our embedding
sc = sns.scatterplot(
    data=data,
    x=&quot;embedding_x&quot;,
    y=&quot;embedding_y&quot;,
    zorder=1,
    s=350 * d ** 2,
    c=labels,
    cmap=plt.cm.nipy_spectral,
    alpha=.9,
    #palette=&quot;muted&quot;,
)

# Plot the covariance edges between the nodes (scatter points)
line_strength = 3.2
    
for index, ((x, y), start, stop) in enumerate(segments):     
    norm_partial_correlation = normalized[index]
    if list(data.iloc[[start]]['labels'])[0] == list(data.iloc[[stop]]['labels'])[0]:
        if norm_partial_correlation &gt; 0.5:
            color = 'red'; linestyle='solid'
        else:
            color = plt.cm.nipy_spectral(list(data.iloc[[start]]['labels'])[0] / float(n_labels)); linestyle='solid'
    else:
        if norm_partial_correlation &gt; 0.5:
            color = 'red'; linestyle='solid'
        else:
            color = 'grey'; linestyle='dashed'
    # Plot the edges
    # if x and y larger than 0
    if x[0] &gt; 0 and y[0] &gt; 0:
        plt.plot(x, y, alpha=.4, zorder=0, linewidth=normalized[index]*line_strength, color=color, linestyle=linestyle)

    
# Labels the nodes and position the labels to avoid overlap with other labels
for name, label, (x, y) in zip(names, labels, embedding.T):
    color = plt.cm.nipy_spectral(label / float(n_labels))
    ax.annotate(
        name,
        xy=(x, y),
        xytext=(5, 2),
        textcoords='offset points',
        ha='right',
        va='bottom',
        fontsize=10,
        color='black',
        bbox=dict(facecolor='w', edgecolor=&quot;w&quot;, alpha=.0),
     )</pre></div>



<figure class="wp-block-image size-large is-resized"><img decoding="async" data-attachment-id="8229" data-permalink="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/cryptocurrency-map/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2022/05/cryptocurrency-map.png" data-orig-size="1473,590" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="cryptocurrency-map" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2022/05/cryptocurrency-map.png" src="https://www.relataly.com/wp-content/uploads/2022/05/cryptocurrency-map-1024x410.png" alt="Visualizing the Crypto Market Structure - Clusters of Cryptocurrencies determined by Affinity Propagation, Connections between cryptocurrencies defined by partial covariance in daily price fluctuations" class="wp-image-8229" width="1177" height="471" srcset="https://www.relataly.com/wp-content/uploads/2022/05/cryptocurrency-map.png 1024w, https://www.relataly.com/wp-content/uploads/2022/05/cryptocurrency-map.png 300w, https://www.relataly.com/wp-content/uploads/2022/05/cryptocurrency-map.png 768w, https://www.relataly.com/wp-content/uploads/2022/05/cryptocurrency-map.png 1473w" sizes="(max-width: 1177px) 100vw, 1177px" /></figure>



<p class="wp-block-paragraph">Note that you will likely see a different map when you run the code on your machine. Differences result from changes in market prices and covariance that lead to other graph structures. </p>



<p class="wp-block-paragraph">Let&#8217;s see what the crypto market map tells us.</p>



<h4 class="wp-block-heading">Interpreting the Cryptomarket Map</h4>



<p class="wp-block-paragraph">The 2D crypto market map tells us several things:</p>



<ul class="wp-block-list">
<li>Most cryptos fall into the light green and dark green clusters corresponding to different types of crypto (Decentralized Finance Coins, NFT/Metaverse Coins).</li>



<li>There is a significant covariance between large-cap players in the crypto space, such as Cardano and Loopring and Ethereum and Bitcoin, which is plausible considering recent price movements. Some results are surprising, for example, the partial correlation between NEO and Ethereum Classic. </li>



<li>Some clusters are isolated and contain only a single member, for example, Tether, Komodo, AC Milan token, Wave token, and Dogecoin). The reason is that the prices of these coins/tokens have developed independently of the market.<ul><li> Tether is a stablecoin that does not change in price. It, therefore, strongly differs from the other cryptocurrencies on our map. </li></ul>
<ul class="wp-block-list">
<li>Komodo has been trading sideways without following the general market trend. </li>



<li>And the MCM token is a soccer token that has recently outperformed the market.</li>
</ul>
</li>



<li>Soccer tokens are colored in dark blue. These tokens&#8217; prices correlate with how the soccer clubs performed during the current season. It, therefore, makes perfect sense that these tokens are grouped into a cluster. An exception is the AC Milan token, which recently performed better than the other soccer tokens.</li>
</ul>



<h3 class="wp-block-heading">Step #6 Creating a 3D Representation</h3>



<p class="wp-block-paragraph">Instead of a 2D representation of the data points, we can also use a 3D node positioning model. For this purpose, the node positioning model distributes the affinity values over three dimensions.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Find the best position of the cryptos on a 3D plane
node_position_model = manifold.LocallyLinearEmbedding(n_components=3, eigen_solver='dense', n_neighbors=20)
embedding = node_position_model.fit_transform(X.T).T
# The result are x and y coordindates for all cryptocurrencies
pd.DataFrame(embedding)
# Display a graph of the partial correlations
partial_correlations = edge_model.precision_.copy()
d = 1 / np.sqrt(np.diag(partial_correlations))
partial_correlations *= d
partial_correlations *= d[:, np.newaxis]
non_zero = (np.abs(np.triu(partial_correlations, k=1)) &gt; 0.02)
data = pd.DataFrame.from_dict({&quot;embedding_x&quot;:embedding[0],&quot;embedding_y&quot;:embedding[1],&quot;embedding_z&quot;:embedding[1]})
data[&quot;labels&quot;] = labels
data[&quot;names&quot;] = names
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure(figsize=(20,20))
ax = fig.add_subplot(projection='3d')
xs = data[&quot;embedding_x&quot;]
ys = data[&quot;embedding_y&quot;]
zs = data[&quot;embedding_z&quot;]
sc = ax.scatter(xs, ys, zs, c=labels, s=100)
    
for i in range(len(data)):
    x = xs[i]
    y = ys[i]
    z = zs[i]
    label = data[&quot;names&quot;][i]
    ax.text(x, y, z, label)
    
plt.legend(*sc.legend_elements(), bbox_to_anchor=(1.05, 1), loc=2)
plt.show()</pre></div>



<figure class="wp-block-image size-large is-resized"><img decoding="async" data-attachment-id="8243" data-permalink="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/3d-cluster-representation-affinity-propagation/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2022/05/3d-cluster-representation-affinity-propagation.png" data-orig-size="1210,1101" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="3d-cluster-representation-affinity-propagation" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2022/05/3d-cluster-representation-affinity-propagation.png" src="https://www.relataly.com/wp-content/uploads/2022/05/3d-cluster-representation-affinity-propagation-1024x932.png" alt="3d representation of the cryptocurrency market structure, affinity propagation relataly" class="wp-image-8243" width="891" height="811" srcset="https://www.relataly.com/wp-content/uploads/2022/05/3d-cluster-representation-affinity-propagation.png 1024w, https://www.relataly.com/wp-content/uploads/2022/05/3d-cluster-representation-affinity-propagation.png 300w, https://www.relataly.com/wp-content/uploads/2022/05/3d-cluster-representation-affinity-propagation.png 768w, https://www.relataly.com/wp-content/uploads/2022/05/3d-cluster-representation-affinity-propagation.png 1210w" sizes="(max-width: 891px) 100vw, 891px" /></figure>



<h2 class="wp-block-heading" id="h-summary">Summary</h2>



<div class="wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex">
<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow" style="flex-basis:66.66%">
<p class="wp-block-paragraph">Affinity propagation is a powerful technique for clustering items when the optimal number of clusters is unknown. In this article, we&#8217;ve demonstrated how to apply affinity propagation to analyze the cryptocurrency market and identify groups of assets based on similar price fluctuations.</p>



<p class="wp-block-paragraph">In our example, we identified 13 groups of cryptocurrencies without specifying the number of clusters in advance. We also visualized the market structure on a 2D and 3D map using a node distribution technique. This approach can be extended to analyze and cluster stock markets, highlighting complex price patterns among multiple financial assets.</p>



<p class="wp-block-paragraph">Once you&#8217;ve identified clusters, you can dive deeper into individual groups. Sometimes, outliers that temporarily break out of their usual pattern indicate interesting investment opportunities. These outliers can eventually return to the price pattern of their group, or they may represent forerunners of their group, indicating broader market movements.</p>



<p class="wp-block-paragraph">By using affinity propagation, we can visualize financial assets in a new and exciting way. If you have any questions or comments about this approach, please let me know.</p>
</div>



<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow" style="flex-basis:33.33%"></div>
</div>



<h2 class="wp-block-heading" id="h-sources-and-further-reading">Sources and Further Reading</h2>



<p class="wp-block-paragraph">This article modifies some of the code from <a href="https://scikit-learn.org/stable/auto_examples/applications/plot_stock_market.html#sphx-glr-auto-examples-applications-plot-stock-market-py" target="_blank" rel="noreferrer noopener">Scikit-learn and adapts it from the stock market</a> to cryptocurrencies.</p>



<ol class="wp-block-list">
<li><a href="https://amzn.to/3yIQdWi" target="_blank" rel="noreferrer noopener">Jansen (2020) Machine Learning for Algorithmic Trading: Predictive models to extract signals from market and alternative data for systematic trading strategies with Python</a></li>



<li><a href="https://amzn.to/3S9Nfkl" target="_blank" rel="noreferrer noopener">Aurélien Géron (2019) Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems </a></li>



<li><a href="https://amzn.to/3EKidwE" target="_blank" rel="noreferrer noopener">David Forsyth (2019) Applied Machine Learning Springer</a></li>



<li><a href="https://amzn.to/3MAy8j5" target="_blank" rel="noreferrer noopener">Andriy Burkov (2020) Machine Learning Engineering</a></li>



<li>Images are created using Midjourney, an AI that creates images from text.</li>
</ol>



<p class="has-contrast-2-color has-base-3-background-color has-text-color has-background wp-block-paragraph"><em>The links above to Amazon are affiliate links. By buying through these links, you support the Relataly.com blog and help to cover the hosting costs. Using the links does not affect the price.</em></p>
<p>The post <a href="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/">Unveiling Hidden Patterns in the Cryptocurrency Market with Affinity Propagation and Python</a> appeared first on <a href="https://www.relataly.com">relataly.com</a>.</p>
]]></content:encoded>
					
					<wfw:commentRss>https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/feed/</wfw:commentRss>
			<slash:comments>1</slash:comments>
		
		
		<post-id xmlns="com-wordpress:feed-additions:1">8114</post-id>	</item>
		<item>
		<title>Cluster Analysis with k-Means in Python</title>
		<link>https://www.relataly.com/simple-cluster-analysis-with-k-means-with-python/5070/</link>
					<comments>https://www.relataly.com/simple-cluster-analysis-with-k-means-with-python/5070/#respond</comments>
		
		<dc:creator><![CDATA[Florian Follonier]]></dc:creator>
		<pubDate>Sun, 27 Jun 2021 18:21:01 +0000</pubDate>
				<category><![CDATA[Algorithms]]></category>
		<category><![CDATA[Clustering]]></category>
		<category><![CDATA[Correlation]]></category>
		<category><![CDATA[Covariance]]></category>
		<category><![CDATA[K-Means]]></category>
		<category><![CDATA[Python]]></category>
		<category><![CDATA[Scikit-Learn]]></category>
		<category><![CDATA[Seaborn]]></category>
		<category><![CDATA[Synthetic Data]]></category>
		<category><![CDATA[Use Cases]]></category>
		<category><![CDATA[Beginner Tutorials]]></category>
		<category><![CDATA[Unsupervised Learning]]></category>
		<guid isPermaLink="false">https://www.relataly.com/?p=5070</guid>

					<description><![CDATA[<p>Embark on a journey into the world of unsupervised machine learning with this beginner-friendly Python tutorial focusing on K-Means clustering, a powerful technique used to group similar data points into distinct clusters. This invaluable tool helps us make sense of complex datasets, finding hidden patterns and associations without the need for a predetermined target variable. ... <a title="Cluster Analysis with k-Means in Python" class="read-more" href="https://www.relataly.com/simple-cluster-analysis-with-k-means-with-python/5070/" aria-label="Read more about Cluster Analysis with k-Means in Python">Read more</a></p>
<p>The post <a href="https://www.relataly.com/simple-cluster-analysis-with-k-means-with-python/5070/">Cluster Analysis with k-Means in Python</a> appeared first on <a href="https://www.relataly.com">relataly.com</a>.</p>
]]></description>
										<content:encoded><![CDATA[
<div class="wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex">
<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow">
<div class="wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex">
<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow" style="flex-basis:66.66%">
<p class="wp-block-paragraph">Embark on a journey into the world of unsupervised machine learning with this beginner-friendly Python tutorial focusing on K-Means clustering, a powerful technique used to group similar data points into distinct clusters. This invaluable tool helps us make sense of complex datasets, finding hidden patterns and associations without the need for a predetermined target variable. This comes in handy, especially when dealing with data whose similarities and differences aren&#8217;t immediately apparent.</p>



<p class="wp-block-paragraph">Divided into two insightful sections, this blog post first delves into the theoretical foundation of the K-Means clustering algorithm. We&#8217;ll explore its real-world applications, its strengths, and its weaknesses, providing a comprehensive overview of what makes K-Means an essential tool in any data scientist&#8217;s toolkit.</p>



<p class="wp-block-paragraph">In the second part of the blog, we switch gears and dive into a hands-on Python tutorial. Here, we&#8217;ll walk you through a practical example of K-Means clustering, using it to uncover three distinct spherical clusters within a synthetic dataset. To round up, we&#8217;ll put our model to the test, using it to predict clusters within a test dataset, and then we&#8217;ll visualize the results for easy understanding.</p>



<p class="wp-block-paragraph">Whether you&#8217;re a seasoned data scientist or a beginner looking to dip your toes into the field, this blog post offers a simple and accessible introduction to cluster engineering with K-Means in Python. Follow along, and uncover the hidden potential of your data today!</p>
</div>



<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow" style="flex-basis:33.33%">
<figure class="wp-block-image size-full"><img decoding="async" width="508" height="512" data-attachment-id="12672" data-permalink="https://www.relataly.com/rubber-ducks-machine-learning-python-tutorial-relataly-midjourney-min/" data-orig-file="https://www.relataly.com/wp-content/uploads/2023/03/rubber-ducks-machine-learning-python-tutorial-relataly-midjourney-min.png" data-orig-size="508,512" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="rubber ducks machine learning python tutorial relataly midjourney-min" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2023/03/rubber-ducks-machine-learning-python-tutorial-relataly-midjourney-min.png" src="https://www.relataly.com/wp-content/uploads/2023/03/rubber-ducks-machine-learning-python-tutorial-relataly-midjourney-min.png" alt="Patterns are everywhere, and machine learning can help to expose and understand them better. Image created with Midjourney. " class="wp-image-12672" srcset="https://www.relataly.com/wp-content/uploads/2023/03/rubber-ducks-machine-learning-python-tutorial-relataly-midjourney-min.png 508w, https://www.relataly.com/wp-content/uploads/2023/03/rubber-ducks-machine-learning-python-tutorial-relataly-midjourney-min.png 298w, https://www.relataly.com/wp-content/uploads/2023/03/rubber-ducks-machine-learning-python-tutorial-relataly-midjourney-min.png 140w" sizes="(max-width: 508px) 100vw, 508px" /><figcaption class="wp-element-caption">Patterns are everywhere, and machine learning can help to expose and understand them better. Image created with <a href="http://www.midjourney.com" target="_blank" rel="noreferrer noopener">Midjourney</a>. </figcaption></figure>
</div>
</div>
</div>
</div>



<h2 class="wp-block-heading" id="h-findings-clusters-in-multivariate-data-with-k-means">Findings Clusters in Multivariate Data with k-Means</h2>



<div class="wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex">
<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow" style="flex-basis:66.66%">
<p class="wp-block-paragraph">K-Means clustering is a prominent unsupervised machine learning algorithm utilized to partition datasets into a predefined number (&#8216;k&#8217;) of distinct clusters, each brimming with similar data points. To begin, the algorithm identifies &#8216;k&#8217; random data points which serve as the initial centroids &#8211; the central points representing each cluster. It then proceeds in an iterative fashion, continuously reassigning each data point to the centroid nearest to it, followed by updating each centroid to the average of the data points assigned to its cluster. This process repeats until the centroids no longer change positions or until a set maximum number of iterations is reached.</p>



<p class="wp-block-paragraph">The underlying objective of the K-Means algorithm is to minimize the within-cluster sum of squares (WCSS), a metric indicating the cumulative distance between each data point within a cluster and its corresponding centroid. By reducing the WCSS, K-Means aims to form the most compact and clearly separable clusters.</p>



<p class="wp-block-paragraph">The K-Means algorithm has garnered substantial popularity in the field of data science for its speed and simplicity in implementation. However, it isn&#8217;t without its limitations. It requires the number of clusters to be specified beforehand and operates under the assumption that all clusters are spherical and uniformly sized. In the following sections, we&#8217;ll delve into the intricacies of this powerful yet straightforward algorithm and discuss its use in real-world applications.</p>
</div>



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<figure class="wp-block-image size-large is-resized"><img decoding="async" data-attachment-id="5079" data-permalink="https://www.relataly.com/simple-cluster-analysis-with-k-means-with-python/5070/image-83-2/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2021/06/image-83.png" data-orig-size="567,452" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-83" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2021/06/image-83.png" src="https://www.relataly.com/wp-content/uploads/2021/06/image-83.png" alt="Three clusters in a dataset that were separated by the k-Means algorithms" class="wp-image-5079" width="355" height="283" srcset="https://www.relataly.com/wp-content/uploads/2021/06/image-83.png 567w, https://www.relataly.com/wp-content/uploads/2021/06/image-83.png 300w" sizes="(max-width: 355px) 100vw, 355px" /><figcaption class="wp-element-caption">Three clusters in a dataset that were separated by the k-Means algorithms</figcaption></figure>
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</div>



<p class="wp-block-paragraph"></p>



<h3 class="wp-block-heading" id="h-understanding-the-mechanics-of-k-means-clustering-algorithm">Understanding the Mechanics of K-Means Clustering Algorithm</h3>



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<p class="wp-block-paragraph">At its core, K-Means clustering is a dynamic algorithm designed to simplify complex data patterns. This machine learning model is a champion of unsupervised learning, adept at grouping similar data points into a predetermined number (&#8216;k&#8217;) of unique clusters.</p>



<p class="wp-block-paragraph">Starting the process, the K-Means algorithm selects &#8216;k&#8217; random data points, which act as the initial centroids or the central figures of the clusters. The algorithm then goes through a series of iterative steps, continually allocating each data point to its closest centroid, and recalibrating the centroid to be the mean of all data points that are assigned to its cluster. This cycle repeats until we achieve stable centroids, i.e., they stop moving, or until a pre-set maximum number of iterations is completed.</p>



<p class="wp-block-paragraph">The fundamental goal of K-Means lies in minimizing the within-cluster sum of squares (WCSS). This term refers to the sum of the distances of each data point in a cluster to its centroid. By lowering WCSS, K-Means strives to construct compact clusters that are distinctly separate from each other.</p>



<p class="wp-block-paragraph">In the illustration below, we assume a cluster with three cluster centers. K-Means carries out several steps to partition the data.</p>



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<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow">
<ol class="wp-block-list">
<li>Initially, the algorithm k chooses random starting positions for the centroids. Alternatively, we can also position the centroids manually.</li>



<li>Then the algorithm calculates the distance between the data points and the three centroids. The data points are assigned to the closest centroid/cluster where the cluster variance increases the least.</li>



<li>Next, the algorithm calculates the Euclidean distance between the centroids and their assigned data points. The result is linear decision boundaries that separate the clusters but are not yet optimal.</li>



<li>From then on, the algorithm optimizes the centroids&#8217; positions to lower the resulting clusters&#8217; variance. Then, the previous steps are repeated: averaging, assigning the data points to clusters, and shifting the centroids.</li>
</ol>



<p class="wp-block-paragraph">The process ends when the positions of the centroids do not change anymore.</p>



<figure class="wp-block-image size-large is-resized"><img decoding="async" data-attachment-id="5099" data-permalink="https://www.relataly.com/simple-cluster-analysis-with-k-means-with-python/5070/image-88-2/#main" data-orig-file="https://www.relataly.com/wp-content/uploads/2021/06/image-88.png" data-orig-size="1183,1093" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-88" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2021/06/image-88.png" src="https://www.relataly.com/wp-content/uploads/2021/06/image-88-1024x946.png" alt="K-means partitions a set of data by iteratively optimizing the centroids and the decision boundaries that result from them. " class="wp-image-5099" width="787" height="726" srcset="https://www.relataly.com/wp-content/uploads/2021/06/image-88.png 1024w, https://www.relataly.com/wp-content/uploads/2021/06/image-88.png 300w, https://www.relataly.com/wp-content/uploads/2021/06/image-88.png 1183w" sizes="(max-width: 787px) 100vw, 787px" /><figcaption class="wp-element-caption">k-Means iteratively optimizes the decision boundaries between clusters</figcaption></figure>
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</div>
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<h3 class="wp-block-heading" id="h-how-many-clusters">How many Clusters?</h3>



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<p class="wp-block-paragraph">A particular challenge is that k-means requires estimating the number of clusters k. When tackling new clustering problems, we usually don&#8217;t know the optimal number of clusters. Unless the data is not too complex, we can often estimate the number of centers by looking at one or more scatter plots. However, this approach only works when the data has a few dimensions. For complex data with many dimensions, it is common to experiment with varying numbers of k to find an appropriate size for the problem. We can automate this process using hyperparameter tuning techniques such as <a href="https://www.relataly.com/hyperparameter-tuning-with-grid-search/2261/" target="_blank" rel="noreferrer noopener">grid search</a> or <a href="https://www.relataly.com/using-random-search-to-tune-the-hyperparameters-of-a-random-decision-forest-with-python/6875/" target="_blank" rel="noreferrer noopener">random search</a>. The idea is to try out different cluster sizes and identify the size that best differentiates between clusters.</p>



<h3 class="wp-block-heading" id="h-pros-and-cons-of-k-means-clustering">Pros and Cons of k-Means Clustering</h3>



<p class="wp-block-paragraph">Although K-Means is esteemed for its swift operation and uncomplicated implementation, it comes with a set of constraints. We need to know the strengths and weaknesses of clustering techniques such as k-Means. In general, clustering can reveal structures and relationships in data supervised machine learning methods like classification likely would not uncover. In particular, when we suspect different subgroups in the data that differ in their behavior, clustering can help discover what makes these groups unique.</p>



<p class="wp-block-paragraph">K-Means, in particular, possesses a unique ability to detect and segregate spherical-shaped clusters efficiently. However, its performance may falter when faced with clusters embodying more intricate structures like half-moons or circles, often struggling to differentiate them accurately.</p>



<p class="wp-block-paragraph">Another potential limitation of K-Means lies in its prerequisite of specifying the number of clusters in advance. This requirement can prove challenging when the true number of clusters within a dataset is unknown or ambiguous. In such scenarios, alternative clustering techniques, such as <a href="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/" target="_blank" rel="noreferrer noopener">affinity propagation</a> or <a href="https://wp.me/pbUnJO-2WP">hi</a><a href="https://wp.me/pbUnJO-2WP" target="_blank" rel="noreferrer noopener">erarchical clustering</a>, might be more suitable, as they possess the ability to automatically determine the optimal number of clusters.</p>



<h3 class="wp-block-heading" id="h-applications-of-clustering">Applications of Clustering</h3>



<p class="wp-block-paragraph">The k-means algorithm is used in a variety of applications, including the following:</p>



<ul class="wp-block-list">
<li>A typical use case for clustering is in <strong>marketing and market segmentation</strong>. Here clustering is used to identify meaningful segments of similar customers. The similarity can be based on demographic data (age, gender, etc.) or customer behavior (for example, the time and amount of a purchase).</li>



<li><strong>Medical research</strong> uses clustering to divide patient groups into different subgroups, for example, to assess stroke risk. After clustering, the next step is to develop separate prediction models for the subgroups to estimate the risk more accurately.</li>



<li>An application in the financial sector is outlier detection in <strong>fraud detection</strong>. Banks and credit card companies use clustering to detect unusual transactions and flag them for verification. </li>



<li><strong>Spam filtering</strong>: The input data are attributes of emails (text length, words contained, etc.) and help separate spam from non-spam emails.</li>
</ul>



<h2 class="wp-block-heading" id="h-implementing-a-k-means-clustering-model-in-python">Implementing a K-Means Clustering Model in Python</h2>



<p class="wp-block-paragraph">In the following, we run a cluster analysis on <a href="https://www.relataly.com/category/apis/synthetic-data/" target="_blank" rel="noreferrer noopener">synthetic data</a> using Python and scikit-learn. We aim to train a K-Means cluster model in Python that distinguishes three clusters in the data. Given that the data is synthetic, we&#8217;re already privy to which cluster each data point pertains to. This foreknowledge enables us to evaluate the performance of our model post-training, gauging how effectively it can differentiate between the three predefined clusters.</p>



<p class="wp-block-paragraph">The code is available on the GitHub repository.</p>



<div class="wp-block-kadence-advancedbtn kb-buttons-wrap kb-btns_3c55f5-f1"><a class="kb-button kt-button button kb-btn_79ce02-f1 kt-btn-size-standard kt-btn-width-type-full kb-btn-global-inherit kt-btn-has-text-true kt-btn-has-svg-true wp-block-button__link wp-block-kadence-singlebtn" href="https://github.com/flo7up/relataly-public-python-tutorials/blob/master/03%20Clustering/041%20Simple%20Clustering%20using%20K-means%20with%20Python.ipynb" target="_blank" rel="noreferrer noopener"><span class="kb-svg-icon-wrap kb-svg-icon-fe_eye kt-btn-icon-side-left"><svg viewBox="0 0 24 24"  fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"  aria-hidden="true"><path d="M1 12s4-8 11-8 11 8 11 8-4 8-11 8-11-8-11-8z"/><circle cx="12" cy="12" r="3"/></svg></span><span class="kt-btn-inner-text">View on GitHub </span></a>

<a class="kb-button kt-button button kb-btn_172639-a2 kt-btn-size-standard kt-btn-width-type-full kb-btn-global-inherit kt-btn-has-text-true kt-btn-has-svg-true wp-block-button__link wp-block-kadence-singlebtn" href="https://github.com/flo7up/relataly-public-python-API-tutorials" target="_blank" rel="noreferrer noopener"><span class="kb-svg-icon-wrap kb-svg-icon-fa_github kt-btn-icon-side-left"><svg viewBox="0 0 496 512"  fill="currentColor" xmlns="http://www.w3.org/2000/svg"  aria-hidden="true"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg></span><span class="kt-btn-inner-text">Relataly GitHub Repo </span></a></div>
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<h3 class="wp-block-heading" id="h-prerequisites">Prerequisites</h3>



<p class="wp-block-paragraph">Before beginning the coding part, make sure that you have set up your Python 3 environment and required packages. If you don&#8217;t have an environment, consider the&nbsp;<a href="https://www.anaconda.com/products/individual" target="_blank" rel="noreferrer noopener">Anaconda Python environment</a>. To set it up, you can follow the steps in&nbsp;<a href="https://www.relataly.com/category/data-science/setup-anaconda-environment/" target="_blank" rel="noreferrer noopener">this tutorial</a>.</p>



<p class="wp-block-paragraph">Also, make sure you install all required packages. In this tutorial, we will be working with the following standard packages:&nbsp;</p>



<ul class="wp-block-list">
<li><em><a href="https://pandas.pydata.org/" target="_blank" rel="noreferrer noopener">pandas</a></em></li>



<li><em><a href="https://numpy.org/" target="_blank" rel="noreferrer noopener">NumPy</a></em></li>



<li><em><a href="https://matplotlib.org/" target="_blank" rel="noreferrer noopener">matplotlib</a></em></li>
</ul>



<p class="wp-block-paragraph">This article uses the k-means clustering algorithm from the Python library <a rel="noreferrer noopener" href="https://scikit-learn.org/stable/" target="_blank">Scikit-learn</a>. We also use <a data-type="URL" data-id="https://seaborn.pydata.org/" href="https://seaborn.pydata.org/" target="_blank" rel="noreferrer noopener">Seaborn </a>for visualization.</p>



<p class="wp-block-paragraph">You can install these libraries using console commands:</p>



<ul class="wp-block-list">
<li><em>pip install &lt;package name&gt;</em></li>



<li><em>conda install &lt;package name&gt;</em>&nbsp;(if you are using the anaconda packet manager)</li>
</ul>



<h3 class="wp-block-heading" id="h-step-1-generate-synthetic-data">Step #1: Generate Synthetic Data</h3>



<p class="wp-block-paragraph">We start with the generation of synthetic data. For this purpose, we use the make_blobs function from the scikit-learn library. The function generates random clusters in two dimensions spherically arranged around a center. In addition, the data contains the respective cluster to which the data points belong. We use a scatterplot to visualize the data. </p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}">import pandas as pd
import numpy as np
import seaborn as sns
from matplotlib import pyplot as plt
from sklearn.model_selection import train_test_split as train_test_split
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import classification_report, confusion_matrix

# Generate synthetic data
features, labels = make_blobs(
    n_samples=400,
    centers=3,
    cluster_std=2.75,
    random_state=42
)

# Visualize the data in scatterplots
def scatter_plots(df, palette):
    fig, ax = plt.subplots(nrows=1, ncols=2, sharex=True, figsize=(20, 8))
    fig.subplots_adjust(hspace=0.5, wspace=0.2)
    

    ax1 = plt.subplot(1,2,1)
    sns.scatterplot(ax = ax1, data=df, x='x', y='y', hue= 'labels', palette=palette)
    plt.title('Clusters')
    
    ax2 = plt.subplot(1,2,2)
    sns.scatterplot(ax = ax2, data=df, x='x', y='y')
    plt.title('How the model sees the data during training')

palette = {1:&quot;tab:cyan&quot;,0:&quot;tab:orange&quot;, 2:&quot;tab:purple&quot;}
df = pd.DataFrame(features, columns=['x', 'y'])
df['labels'] = labels
scatter_plots(df, palette)</pre></div>



<figure class="wp-block-image size-large"><img decoding="async" width="1024" height="433" data-attachment-id="5061" data-permalink="https://www.relataly.com/image-77-2/" data-orig-file="https://www.relataly.com/wp-content/uploads/2021/06/image-77.png" data-orig-size="1172,496" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-77" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2021/06/image-77.png" src="https://www.relataly.com/wp-content/uploads/2021/06/image-77-1024x433.png" alt="Clusters vs how the model sees the data during training" class="wp-image-5061" srcset="https://www.relataly.com/wp-content/uploads/2021/06/image-77.png 1024w, https://www.relataly.com/wp-content/uploads/2021/06/image-77.png 300w, https://www.relataly.com/wp-content/uploads/2021/06/image-77.png 768w, https://www.relataly.com/wp-content/uploads/2021/06/image-77.png 1172w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<h3 class="wp-block-heading" id="h-step-2-preprocessing">Step #2: Preprocessing</h3>



<p class="wp-block-paragraph">There are some general things to keep in mind when preparing data for use with K-Means clustering:</p>



<ul class="wp-block-list">
<li><strong>Missing data and outliers</strong>: if we have missing entries in our data, we need to handle these, for example, by removing the records or filling the missing values with a mean or median. In addition, K-means is sensitive to outliers. Therefore, make sure that you eliminate outliers from the training data. </li>



<li><strong>Normalization</strong>: K-Means can only deal with integer values. So, either we map the categorical variables to integer values or use one-hot-encoding to create separate binary variables. </li>



<li><strong>Dimensionality reduction</strong>: In general, having too many variables in a dataset can negatively affect the performance of clustering algorithms. A good practice is to keep the number of variables below 30, for example, by using techniques for dimensionality reduction such as Principal-Component-Analysis.</li>



<li><strong>Scaling</strong>: Important to note is also that K-means require scaling the data.</li>
</ul>



<p class="wp-block-paragraph">Our synthetic dataset is free of outliers or missing values. Therefore, we only need to scale the data. In addition, we separate the class labels of the clusters from the training set and split the data into a train- and a test dataset. </p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Scale the data
scaler = StandardScaler()
scaled_features = scaler.fit_transform(features)

X = scaled_features #Training data
y = labels #Prediction label

# Split the data into x_train and y_train data sets
X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.7, random_state=0)</pre></div>



<h3 class="wp-block-heading" id="h-step-3-train-a-k-means-clustering-model">Step #3: Train a k-Means Clustering Model</h3>



<p class="wp-block-paragraph">Once we have prepared the data, we can begin the cluster analysis by training a K-means model. Our model uses the k-means algorithm from Python <a href="https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html?highlight=kmeans#sklearn.cluster.KMeans" target="_blank" rel="noreferrer noopener">scikit-learn library</a>. We have various options to configure the clustering process: </p>



<ul class="wp-block-list">
<li><strong>n_clusters</strong><em>: </em>The number of clusters we expect in the data. </li>



<li><strong>n_init</strong><em>: </em>The number of iterations k-means will run with different initial centroids. The algorithm returns the best model. </li>



<li><strong>max_iter</strong><em>: The max number of iterations for a single run</em></li>
</ul>



<p class="wp-block-paragraph">We expect three clusters and configure the algorithm to run ten iterations.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Create a k-means model with n clusters
kmeans = KMeans(
    init=&quot;random&quot;,
    n_clusters=3,
    n_init=10,
    max_iter=300,
    random_state=42
)

# fit the model
kmeans.fit(X_train)
print(f'Converged after {kmeans.n_iter_} iterations')</pre></div>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:false,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;null&quot;,&quot;mime&quot;:&quot;text/plain&quot;,&quot;theme&quot;:&quot;3024-day&quot;,&quot;lineNumbers&quot;:false,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:false,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Plain Text&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;text&quot;}">Converged after 4 iterations</pre></div>



<p class="wp-block-paragraph">Our model has already converged after four iterations. Next, we will look at the results.</p>



<h3 class="wp-block-heading" id="h-step-4-make-and-visualize-predictions">Step #4: Make and Visualize Predictions</h3>



<p class="wp-block-paragraph">Next, we&#8217;ll be delving into the practical aspect of our Python tutorial by analyzing the performance of our trained K-Means model using synthetic data.</p>



<p class="wp-block-paragraph">In the following Python code, we:</p>



<ul class="wp-block-list">
<li>Extract the cluster centers from the trained K-Means model and unscale them.</li>



<li>Add the predicted and actual labels to our unscaled training data.</li>



<li>Define a function, <code>scatter_plots()</code>, that creates two scatter plots: one for the predicted labels and another for the actual labels.</li>



<li>Call this function, passing the training data, cluster centers, and a color palette as arguments.</li>
</ul>



<p class="wp-block-paragraph">Please note:</p>



<ul class="wp-block-list">
<li>We use a dictionary as a color palette to differentiate between clusters.</li>



<li>The colors between the two plots may not match due to K-Means assigning numbers to clusters without prior knowledge of initial labels.</li>
</ul>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Get the cluster centers from the trained K-means model
cluster_center = scaler.inverse_transform(kmeans.cluster_centers_)
df_cluster_centers = pd.DataFrame(cluster_center, columns=['x', 'y'])

# Unscale the predictions
X_train_unscaled = scaler.inverse_transform(X_train)
df_train = pd.DataFrame(X_train_unscaled, columns=['x', 'y'])
df_train['pred_label'] = kmeans.labels_
df_train['true_label'] = y_train

def scatter_plots(df, cc, palette):
    fig, ax = plt.subplots(nrows=1, ncols=2, sharex=True, figsize=(20, 8))
    fig.subplots_adjust(hspace=0.5, wspace=0.2)
    
    # Print the predictions    
    ax2 = plt.subplot(1,2,1)
    sns.scatterplot(ax = ax2, data=df, x='x', y='y', hue='pred_label', palette=palette)
    sns.scatterplot(ax = ax2, data=cc, x='x', y='y', color='r', marker=&quot;X&quot;)
    plt.title('Predicted Labels')

    # Print the actual values
    ax1 = plt.subplot(1,2,2)
    sns.scatterplot(ax = ax1, data=df, x='x', y='y', hue= 'true_label', palette=palette)
    sns.scatterplot(ax = ax1, data=cc, x='x', y='y', color='r', marker=&quot;X&quot;)
    plt.title('Actual Labels')


# The colors between the two plots may not match.
# This is because K-means does not know the initial labels and assigns numbers to clusters 
palette = {1:&quot;tab:cyan&quot;,0:&quot;tab:orange&quot;, 2:&quot;tab:purple&quot;}
scatter_plots(df_train, df_cluster_centers, palette)</pre></div>



<figure class="wp-block-image size-large is-resized"><img decoding="async" data-attachment-id="5062" data-permalink="https://www.relataly.com/image-78-2/" data-orig-file="https://www.relataly.com/wp-content/uploads/2021/06/image-78.png" data-orig-size="1172,496" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-78" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2021/06/image-78.png" src="https://www.relataly.com/wp-content/uploads/2021/06/image-78-1024x433.png" alt="actual clusters vs predicted cluster of the K-means model" class="wp-image-5062" width="1106" height="468" srcset="https://www.relataly.com/wp-content/uploads/2021/06/image-78.png 1024w, https://www.relataly.com/wp-content/uploads/2021/06/image-78.png 300w, https://www.relataly.com/wp-content/uploads/2021/06/image-78.png 768w, https://www.relataly.com/wp-content/uploads/2021/06/image-78.png 1172w" sizes="(max-width: 1106px) 100vw, 1106px" /></figure>



<p class="wp-block-paragraph">The scatterplot above shows that K-Means found the three clusters. As a side note, the colors between the two plots do not match because K-means does not know the initial labels and assigns numbers to clusters. </p>



<h3 class="wp-block-heading" id="h-step-5-measuring-model-performance">Step #5: Measuring Model Performance</h3>



<p class="wp-block-paragraph">Next, we measure the performance of our clustering model. K-means is an unsupervised machine learning algorithm, which means that it is used to cluster data points into groups based on their similarity, without the use of labeled training data. However, we can compare the cluster assignments to the labels attached to the data and see if the model can predict them correctly. In this way, we can use traditional classification metrics such as accuracy and f1_score to measure the performance of our clustering model.</p>



<p class="wp-block-paragraph">First, we unify the cluster labels as A, B, and C.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># The predictive model has the labels 0 and 1 reversed. We will correct that first. 
#df_train['pred_test'] = df_train['pred_labels'].map({2:2, 1:3, 0:1})
df_eval = df_train.copy()
df_eval['true_label'] = df_eval['true_label'].map({0:'A', 1:'B', 2:'C'})
df_eval['pred_label'] = df_eval['pred_label'].map({0:'B', 1:'A', 2:'C'})
df_eval.head(10)</pre></div>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:false,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;null&quot;,&quot;mime&quot;:&quot;text/plain&quot;,&quot;theme&quot;:&quot;3024-day&quot;,&quot;lineNumbers&quot;:false,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:false,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Plain Text&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;text&quot;}">	x			y			pred_label	true_label
0	-9.007547	-10.302910	C			C
1	1.009238	7.009681	A			B
2	-6.565501	-6.466780	C			C
3	2.389772	7.727235	B			B
4	-5.422666	-2.915796	C			C
5	-12.024305	-7.846772	C			C
6	-4.006250	9.319323	A			A
7	-6.297788	6.435267	A			A
8	2.169238	3.325947	B			B
9	-5.140506	-4.205585	C			C</pre></div>



<p class="wp-block-paragraph">It is a common practice to create scatterplots on the predictions to visually verify the quality of the clusters and their decision boundaries. The following scatter plot shows the correctly assigned values and where our model was wrong.</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Scatterplot on correctly and falsely classified values
df_eval.loc[df_eval['pred_label'] == df_eval['true_label'], 'Correctly classified?'] = 'True' 
df_eval.loc[df_eval['pred_label'] != df_eval['true_label'], 'Correctly classified?'] = 'False' 

plt.rcParams[&quot;figure.figsize&quot;] = (10,8)
sns.scatterplot(data=df_eval, x='x', y='y', color='r', hue='Correctly classified?')</pre></div>



<figure class="wp-block-image size-large is-resized"><img decoding="async" data-attachment-id="5065" data-permalink="https://www.relataly.com/image-81-2/" data-orig-file="https://www.relataly.com/wp-content/uploads/2021/06/image-81.png" data-orig-size="614,480" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-81" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2021/06/image-81.png" src="https://www.relataly.com/wp-content/uploads/2021/06/image-81.png" alt="A 2-d scatterplot that shows the correctly assigned values and where our  K-means model was wrong." class="wp-image-5065" width="711" height="556" srcset="https://www.relataly.com/wp-content/uploads/2021/06/image-81.png 614w, https://www.relataly.com/wp-content/uploads/2021/06/image-81.png 300w" sizes="(max-width: 711px) 100vw, 711px" /></figure>



<p class="wp-block-paragraph">The K-Means model correctly assigned most data points (blue) to their actual cluster. The few misclassified points are located at a decision boundary between two clusters (marked in orange).</p>



<div class="wp-block-codemirror-blocks-code-block code-block"><pre class="CodeMirror" data-setting="{&quot;showPanel&quot;:true,&quot;languageLabel&quot;:false,&quot;fullScreenButton&quot;:true,&quot;copyButton&quot;:true,&quot;mode&quot;:&quot;python&quot;,&quot;mime&quot;:&quot;text/x-python&quot;,&quot;theme&quot;:&quot;monokai&quot;,&quot;lineNumbers&quot;:true,&quot;styleActiveLine&quot;:false,&quot;lineWrapping&quot;:true,&quot;readOnly&quot;:true,&quot;fileName&quot;:&quot;&quot;,&quot;language&quot;:&quot;Python&quot;,&quot;maxHeight&quot;:&quot;400px&quot;,&quot;modeName&quot;:&quot;python&quot;}"># Create a confusion matrix
def evaluate_results(model, y_true, y_pred, class_names):
    tick_marks = [0.5, 1.5, 2.5]
    
    # Print the Confusion Matrix
    fig, ax = plt.subplots(figsize=(10, 6))
    results_log = classification_report(y_true, y_pred, target_names=class_names, output_dict=True)
    results_df_log = pd.DataFrame(results_log).transpose()
    matrix = confusion_matrix(y_true,  y_pred)
    model_score = score(y_pred, y_true, average='macro')
    
    sns.heatmap(pd.DataFrame(matrix), annot=True, fmt=&quot;d&quot;, linewidths=.5, cmap=&quot;YlGnBu&quot;)
    plt.xlabel('Predicted label'); plt.ylabel('Actual label')
    plt.title('Confusion Matrix on the Test Data')
    plt.yticks(tick_marks, class_names); plt.xticks(tick_marks, class_names)
    
    print(results_df_log)


y_true = df_eval['true_label']
y_pred = df_eval['pred_label']
class_names = ['A', 'B', 'C']
evaluate_results(kmeans, y_true, y_pred, class_names)</pre></div>



<figure class="wp-block-image size-large is-resized"><img decoding="async" data-attachment-id="5064" data-permalink="https://www.relataly.com/image-80-2/" data-orig-file="https://www.relataly.com/wp-content/uploads/2021/06/image-80.png" data-orig-size="682,588" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" data-image-title="image-80" data-image-description="" data-image-caption="" data-large-file="https://www.relataly.com/wp-content/uploads/2021/06/image-80.png" src="https://www.relataly.com/wp-content/uploads/2021/06/image-80.png" alt="confusion matrix on the predictions generated by our k-means model" class="wp-image-5064" width="658" height="568" srcset="https://www.relataly.com/wp-content/uploads/2021/06/image-80.png 682w, https://www.relataly.com/wp-content/uploads/2021/06/image-80.png 300w" sizes="(max-width: 658px) 100vw, 658px" /></figure>



<p class="wp-block-paragraph">As we can see, the model has done a good job of grouping the labels into the attached classes.</p>



<h2 class="wp-block-heading" id="h-summary">Summary</h2>



<p class="wp-block-paragraph">algorithm, capable of parsing intricate datasets into discrete, non-overlapping clusters. With this guide, you should have a clear understanding of how this algorithm operates, as well as its unique strengths and potential limitations. Remember, k-Means excels when dealing with spherical clusters but may struggle with clusters of more complex shapes.</p>



<p class="wp-block-paragraph">We walked through how to implement the k-Means algorithm in Python, using it to identify spherical clusters within synthetic data. Moreover, we explored different methods to evaluate and visualize a clustering model&#8217;s performance, providing you with valuable tools to effectively analyze and group your data.</p>



<p class="wp-block-paragraph">Whether it&#8217;s anomaly detection in time-series data or customer segmentation, k-Means can be a powerful tool in your data science arsenal. If you&#8217;re interested in anomaly detection, feel free to explore my recent article on the subject, written with Python enthusiasts in mind. Armed with this knowledge, you&#8217;re ready to embark on your own data exploration journey using k-Means clustering.</p>



<p class="wp-block-paragraph">If you are interested in this topic, check out my recent article on <a href="https://www.relataly.com/multivariate-outlier-detection-using-isolation-forests-in-python-detecting-credit-card-fraud/4233/" target="_blank" rel="noreferrer noopener">anomaly detection with Python</a>. And if you have any questions, please ask them in the comments.</p>



<p class="wp-block-paragraph">Did you know that customer segmentation is an area where real-world data can be prone to bias and unfairness? If you&#8217;re concerned that your models may reflect the same bias, check out our latest article on <a href="https://www.relataly.com/building-fair-machine-machine-learning-models-with-fairlearn/12804/" target="_blank" rel="noreferrer noopener">addressing fairness in machine learning with fairlearn</a>.</p>



<h2 class="wp-block-heading">Sources and Further Reading</h2>



<div class="wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex">
<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow">
<div class="wp-block-group"><div class="wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained">
<h4 class="wp-block-heading"><strong>Books on Clustering</strong></h4>



<ul class="wp-block-list">
<li><a href="https://amzn.to/3Gb5kfj" target="_blank" rel="noreferrer noopener">&#8220;Data Clustering: Algorithms and Applications&#8221; by Charu C. Aggarwal</a>: This book covers a wide range of clustering algorithms, including hierarchical clustering, and discusses their applications in various fields.</li>



<li><a href="https://amzn.to/3WmhGXB" target="_blank" rel="noreferrer noopener">&#8220;Data Mining: Practical Machine Learning Tools and Techniques&#8221; by Ian H. Witten and Eibe Frank</a>: This book is a comprehensive introduction to data mining and machine learning, including a chapter on hierarchical clustering.</li>
</ul>



<div style="display: inline-block;">
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</div>
</div></div>
</div>



<div class="wp-block-column is-layout-flow wp-block-column-is-layout-flow">
<div class="wp-block-group"><div class="wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained">
<h4 class="wp-block-heading"><strong>Books on Machine Learning</strong></h4>



<ul class="wp-block-list">
<li><a href="https://amzn.to/3S9Nfkl" target="_blank" rel="noreferrer noopener">Aurélien Géron (2019) Hands-On Machine Learning</a></li>



<li><a href="https://amzn.to/3EKidwE" target="_blank" rel="noreferrer noopener">David Forsyth (2019) Applied Machine Learning Springer</a></li>
</ul>



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<p class="has-contrast-2-color has-base-3-background-color has-text-color has-background wp-block-paragraph"><em>The links above to Amazon are affiliate links. By buying through these links, you support the Relataly.com blog and help to cover the hosting costs. Using the links does not affect the price.</em></p>



<h4 class="wp-block-heading">Related Articles on Clustering</h4>



<ol class="wp-block-list">
<li><a href="https://wp.me/pbUnJO-2WP" target="_blank" rel="noreferrer noopener">Hierarchical clustering for customer segmentation in Python</a>: We present an alternative approach to k-means that can determine the number of the clusters themselves and works well if the distributions of the groups in the data is more complex.</li>



<li><a href="https://www.relataly.com/crypto-market-cluster-analysis-using-affinity-propagation-python/8114/" target="_blank" rel="noreferrer noopener">Clustering crypto markets using affinity propagation in Python</a>: This article applies cluster analysis to crypto markets and creates a market map for various cryptocurrencies.</li>
</ol>
<p>The post <a href="https://www.relataly.com/simple-cluster-analysis-with-k-means-with-python/5070/">Cluster Analysis with k-Means in Python</a> appeared first on <a href="https://www.relataly.com">relataly.com</a>.</p>
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