{ "source_file": "0930", "source_platform": "Medium", "author": "Ivo Bernardo", "title_listed": "Unsupervised Learning Series: Exploring the Mean-Shift Algorithm", "keywords": "", "domain": "机器学习", "content_type": "深度技术解析", "is_paid_flag": "否", "url": "https://towardsdatascience.com/unsupervised-learning-series-exploring-mean-shift-algorithm-2be0adc6354c/", "publish_date": "2024-08-20", "corpus_stage": "", "notes": "", "id": "5799ee4c0c88", "collected_at": "2026-10-02T05:52:46", "title": "Unsupervised Learning Series: Exploring the Mean-Shift Algorithm | Towards Data Science", "body_markdown": "![Revisit consent button](../images/body-df29beacd7496220cc94.svg)\nWe value your privacy\nWe use cookies to enhance your browsing experience, serve personalised ads or content, and analyse our traffic. 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It also helps in adverstising on the website.\n\n\n * Cookie\nedgebucket\n * Duration\nsession\n * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n * Cookie\ndid\n * Duration\n1 year\n * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Artificial Intelligence](https://towardsdatascience.com/category/artificial-intelligence/)\n# Unsupervised Learning Series: Exploring the Mean-Shift Algorithm\nLet's learn one of the most famous density-based clustering algorithms, Mean-Shift.\n[Ivo Bernardo](https://towardsdatascience.com/author/ivopbernardo/)\nAugust 19, 202410 min read\n![](../images/000.jpg)\n_K-Means, Hierarchical Clustering, Expectation-Maximization,_ and _DBScan_ are probably the most famous clustering algorithms you may know in the context of Machine Learning.\nHowever, there is another density-based algorithm that has been solving a variety of problems, ranging from satellite image segmentation to object tracking, and its name is mean-shift. This algorithm is renowned for finding the modes of a specific dataset by building clusters around areas with higher data point densities.\nVisualizing mean-shift is easy. Normally, I use the skyscraper skyline analogy. If you consider a skyscraper skyline:\nLearn this step by step with the interactive [AI Engineer](https://roadmap.sh/ai-engineer) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps.\n![Two Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer](../images/001.jpeg)\nTwo Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer\nWe can clearly see two different clusters of density if we consider the skyscrapers as our datapoints:\n![Two Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer](../images/002.png)\nTwo Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer\nBut let's expand the image below, to see more skyscraper areas. As we expeand the image, we can see other clusters of density, with different \"peak\" size:\n![Four Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer](../images/003.png)\nFour Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer\nThe goal of the mean-shift algorithm is to find these different clusters (of varying peak) within a dataset. It achieves this by shifting the cluster means until they reaches a \"peak\", similarly to _dbscan._\nIt's a powerful technique to leverage, particularly when our data contains non-spherical clusters.\nIn this blog post, we will:\n * See a step-by-step implementation of the mean-shift algorithm.\n * Check the `sklearn` implementation of the algorithm.\n * Go through a practical use case of the algorithm using real-data.\n\n\nIf you would like, you can also check the other blog posts of this unsupervised learning series, using the links below:\n * [K-means](https://towardsdatascience.com/unsupervised-learning-method-series-exploring-k-means-clustering-d129fff3ab6a?sk=0618fadb196a71ce4b9f378f9ee83107)\n * [Hierarchical Clustering](https://towardsdatascience.com/unsupervised-learning-series-exploring-hierarchical-clustering-15d992467aa8?sk=87714b0d7aa252330dd7a8d3b1c620f4)\n * [Self-Organizing Maps](https://towardsdatascience.com/unsupervised-learning-series-exploring-self-organizing-maps-fe2efde9f7a1?sk=0a2649f9b411c236c2682729a5e616b4)\n * [DBScan](https://towardsdatascience.com/unsupervised-learning-series-exploring-dbscan-624c820290ce?sk=b12738fd430804b400cabc7910329555)\n\n\nCompared to the latter (_DBScan_ , another density based algorithm), mean-shift only requires the tuning of one hyperparameter. This comes with a cost, as it doesn't provide the robustness to outliers that _DBScan_ can offer.\nHope you're ready, and let's start!\n* * *\n## Why K-Means doesn't work for Non-Spherical Shapes\nFor our introduction of the mean-shift algorithm, we'll start by understanding why traditional clustering methods fail on some datasets. Take the following dataset with generated customer data. Our two variables are _annual income (in k euros)_ and _average spending_ for a group of customers:\n![Customer Dataset - Image by Author](../images/004.png)\nCustomer Dataset - Image by Author\nVisually, it's hard to understand the number of different clusters we have on this dataset. We can consider three, four or five. For example, if we consider 5 different clusters, we'll probably outline the following:\n![Customer Dataset Visual Clusters— Image by Author](../images/005.png)\nCustomer Dataset Visual Clusters— Image by Author\nThe image above is tricking us a bit, though. As with most clustering algorithms that deal with distances, it's important to standardize our data - let's do that:\n![Customer Standardized Dataset— Image by Author](../images/006.png)\nCustomer Standardized Dataset— Image by Author\nNow, our densities are a bit different:\n![Customer Standardized Dataset Visual Clusters - Image by Author](../images/007.png)\nCustomer Standardized Dataset Visual Clusters - Image by Author\nAnother hypothesis is to combine some these data points into 3 or 4 clusters. Of course, doing this visually is a bit tricky, so how does K-Means behave in this dataset - first let's see the 5 cluster example:\n![K-Means solution on Dataset - Image by Author](../images/008.png)\nK-Means solution on Dataset - Image by Author\nAs you can see, K-Means clustering has some trouble to define these clusters. Mostly, this happens due to the _non-spherical_ nature of the data. Let's see what happens if I fit a k-means solution with 4 clusters:\n![4 Clusters K-Means solution on Dataset - Image by Author](../images/009.png)\n4 Clusters K-Means solution on Dataset - Image by Author\nIt's an interesting solution, but becoming too influenced by outliers. Notice how these 3 data points impact one of the clusters in a major way:\n![Outliers influencing - Image by Author](../images/010.png)\nOutliers influencing - Image by Author\nNow let's see what happens with _mean-shift_ :\n![Mean-Shift Solution - Image by Author](../images/011.png)\nMean-Shift Solution - Image by Author\nWe see clusters that are more aligned with the density we've seen before. Although the solution is not perfect, it's an interesting pattern discovered by the algorithm.\nBut why is mean-shift so different from K-Means? As usual, no question is left unanswered - let's see!\n* * *\n## Mean-Shift Walkthrough, step-by-step\nFirst, we'll start with a clean version of our dataset (without any clusters assigned). Mean-shift starts with a random data point (highlighted in orange below):\n![Random Data Point Selected - Image by Author](../images/012.png)\nRandom Data Point Selected - Image by Author\nNext step is to draw a circle around this data point with a radius (hyperparameter of the algorithm). I'll define 0.1 as the value of the radius of our circle:\n![Radius Definition - Image by Author](../images/013.png)\nRadius Definition - Image by Author\n _Note: From now on, I'll show squared plots so that we can correctly see the circles generated by the radius. Default matplotlib definitions shows an elipsis as the plot is stretched on the x-axis._\nWe now need to perform a crucial step of the mean-shift algorithm: **the shifting operation!**\nThis is actually very simple. Depending on the kernel, we will drag this orange point to its center of density. The most famous _kernels_ to use within mean-shift are:\n * Gaussian kernel\n * Mexican-hat\n * Uniform kernel\n\n\nThe gaussian and mexican-hat kernels consider the points that are farther from the center should have less influence in the shifting operation. The uniform kernel is a bit less flexible and states that any data point within the radius should have equal influence in the shifting operation.\nWe'll use uniform kernel as an example, due to its simplicity, although gaussian kernel is also used often.\nFirst, we need to assess which data points are within our radius:\n![Highlighted points within the radius - Image by Author](../images/014.png)\nHighlighted points within the radius - Image by Author\nI'll consider that every data point that touches some part of the radius is part of the cirle. Subsetting these data points (and the point itself):\n![Subset of Customers within the Radius - Image by Author](../images/015.png)\nSubset of Customers within the Radius - Image by Author\nNow, we can use the averages both _age_ and _annual _income_ of this subset of customers to drag the \"centroid\".\n * _age_ average is approximately 0.0679\n * _annual _income_ average is approximately 0.324\n\n\nThese are the two values that contain the coordinates where we are going to shift our mean inside the radius:\n![Mean shift operation - Image by Author](../images/016.png)\nMean shift operation - Image by Author\nOur centroid gets shifted northwest. Let's reposition it:\n![Shifted Centroid - Image by Author](../images/017.png)\nShifted Centroid - Image by Author\nIn this case, our new radius touches the same data points. Our centroid converged to this region and it will stay there.\nNext iteration is doing exactly the same for every data point. Let's visualize what would happen with another data point in a different region:\n![Second Random Data Point Example - Image by Author](../images/018.png)\nSecond Random Data Point Example - Image by Author\nIn this case, the mean would shift southeast. If we start in an isolated data point:\n![Third Random Data Point Example - Image by Author](../images/019.png)\nThird Random Data Point Example - Image by Author\nIn this case, the mean that started on this data point won't change. This data point will form a cluster by itself.\nDuring the algorithm run, different data points will land in a same \"center of mass\". Tthese peaks will be combined to become a cluster (different implementations of _mean-shift_ may do this last step in different ways). The key is that all implementations respect the principle: \"same density peak, same cluster\".\nDepending on the implementation, the algorithm will finish when one of the conditions is met:\n * Reaches a certain number of iterations given by the user. One iteration is equal to one pass through all the data points.\n * The centroids no longer move after a few iterations.\n * Some implementations define that when all cluster peaks are within a radius boundary, the algorithm should finish.\n\n\nIn `sklearn` 's implementation, the choice is route number 1 - after 300 iterations the algorithm stops, by default.\nMean-shift has only one important hyperparameter - the radius. Compare the following two solutions:\n![Radius = 0.1 - Image by Author](../images/013.png)\nRadius = 0.1 - Image by Author\nWe are revisiting our first example - in this case, our radius is 0.1. What happens we we raise this value?\n![Radius = 0.5— Image by Author](../images/body-439d616bb9616876746a.png)\nRadius = 0.5— Image by Author\nWith a radius of 0.5, we can see that more points will tend to navigate to the same density peak. The downside of the radius hyperparameter (user defined) is that it's the same for every data point. Due to that, mean-shift may not be able to lead very well with datasets that contain clusters of different densities.\nWith no surprise, shifting is the most important operation of the algorithm! It's time to see it in action, using the `sklearn` implementation!\n* * *\n### Mean-shift in Action\nAs customer segmentantion is one of the oldest (and most relevant) usages of clustering algorithms, we'll play around with the Wholesale Customer Dataset, available on [UCI's Machine Learning Repository](https://archive.ics.uci.edu/dataset/292/wholesale+customers).\nWe'll start with the usual load operation of the dataset:\npython\n\n```\nimport pandas as pd\nwholesale_customers = pd.read_csv('data/Wholesale customers data.csv')\n```\n\nHere's a preview of it:\n![Preview of Wholesale Customer Dataset - Image by Author](../images/body-b3376062ed6f744ecbc4.png)\nPreview of Wholesale Customer Dataset - Image by Author\nAccording to the metadata available at the UCI repository, the description of the columns is the following:\n * FRESH: annual spending (m.u.) on fresh products (Continuous);\n * MILK: annual spending (m.u.) on milk products (Continuous);\n * GROCERY: annual spending (m.u.)on grocery products (Continuous);\n * FROZEN: annual spending (m.u.)on frozen products (Continuous)\n * DETERGENTS_PAPER: annual spending (m.u.) on detergents and paper products (Continuous)\n * DELICATESSEN: annual spending (m.u.)on and delicatessen products (Continuous);\n * CHANNEL: Customer's Channel - Horeca (Hotel/Restaurant/Cafe) or Retail channel (Nominal)\n * REGION: Customers's Region: \" Lisbon, Oporto or Other (Nominal)\n\n\nFor this example, we'll only use the monetary values.\nThe first step in our mean-shift solution is to determine the `bandwith` of the algorithm. The `bandwith` represents the radius we've seen in the step-by-step example.\nEstimating bandwith manually is very hard. One cool function we have in `sklearn` is `estimate_bandwith` that uses nearest neighbors average distance to find a good baseline value.\nBut before checking the bandwidth, do you think there is something missing? We are dealing with an algorithm that relates to distances, so... we need standardization!\npython\n\n```\nfrom sklearn.preprocessing import MinMaxScaler\n\nmmc = MinMaxScaler()\nscaled_dataset = mmc.fit_transform(\n wholesale_customers[['Fresh','Milk','Grocery','Frozen','Detergents_Paper','Delicassen']]\n)\n```\n\nWith the scaled dataset, we can run `estimate_bandwith` :\npython\n\n```\nfrom sklearn.cluster import MeanShift, estimate_bandwidth\n\nbandwith_estimation = estimate_bandwidth(scaled_dataset)\n```\n\nThe estimated bandwith was approximately 0.183. We can now fit the algorithm to the scaled dataset:\npython\n\n```\nmeanshiftmodel = MeanShift(bandwidth=bandwith_estimation)\nwholesale_customers['meanshift_clustering'] = meanshiftmodel.fit_predict(\n scaled_dataset\n)\n```\n\nLet's see how many data points we have per cluster:\nscss\n\n```\nwholesale_customers['meanshift_clustering'].value_counts()\n```\n\n![Clusters' data points count - Image by Author](../images/body-c816166eb1662e2aaa88.png)\nClusters' data points count - Image by Author\nWe have some clusters that only contain one data point. These are probably outliers isolated by our radius. There's three alternatives we can use:\n * We can remove uni-variate outliers manually before fitting the algorithm.\n * We can remove these clusters from our dataset.\n * We can raise the bandwith we are using and re-run the clustering solution again.\n\n\nLet's go through the latter!\nmakefile\n\n```\nmeanshiftmodel = MeanShift(bandwidth=bandwith_estimation+0.1)\nwholesale_customers['meanshift_clustering_extra_band'] = meanshiftmodel.fit_predict(\n scaled_dataset\n)\n```\n\nChecking the clusters again:\n![Clusters' data points count - Image by Author](../images/body-ed513f0eee20e3874746.png)\nClusters' data points count - Image by Author\nOh no! Too high. Tweaking the `bandwidth` parameter is difficult. Let's settle with the first solution we have and remove outlier clusters manually:\njava\n\n```\noutlier_clusters = (\n wholesale_customers['meanshift_clustering'].value_counts().loc[\n wholesale_customers['meanshift_clustering'].value_counts() <= 3\n ]\n).index\n\nclustering_solution = wholesale_customers.loc[~wholesale_customers.meanshift_clustering.isin(outlier_clusters)]\n```\n\nAnd checking the profiling of our clusters:\ncss\n\n```\nclustering_solution.groupby(['meanshift_clustering']).mean().iloc[:,2:]\n```\n\n![Cluster Profilling - Image by Author](../images/body-ffea1e717bf4f4a3ca1f.png)\nCluster Profilling - Image by Author\nCool! So our first cluster (Cluster 0) is characterized by moderate fresh buyers with low values on the other categories.\nCluster 1 is characterized by high grocery and detergent shoppers.\nFinally, cluster 4 is characterized by high grocery and frozen shoppers.\nA word of cautioning about this type of profilling - using simple _mean profiling_ on density clusters is a biased solution (particularly in mean-shift, where clusters may not be spherical). An alternative to profile and check the quality of the clustering is to plot the clustering solution with [T-SNE](https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding) or UMAP embeddings.\nAlso, by the distribution of the data points in the clusters, this is not a good dataset to apply a density based clustering method. When you see a high concentration of data points in a single cluster, other methods should be tested (but don't forget to play around with the bandwidth parameter first).\n* * *\nHope you've enjoyed this blog post on mean-shift clustering! As mentioned, this is an interesting density based algorithm that can find out interesting patterns in your data.\nOn the upside, mean-shift can find out non-spherical clusters on the data, while uncovering the different distribution peaks. On the downside, it tends to isolate outliers as clusters. Also, the bandwith hyperparameter is relatively difficult to tweak.\nIf you are curious about other unsupervised learning algorithms, feel free to check the other blog posts of this series:\n * [K-means](https://towardsdatascience.com/unsupervised-learning-method-series-exploring-k-means-clustering-d129fff3ab6a?sk=0618fadb196a71ce4b9f378f9ee83107)\n * [Hierarchical Clustering](https://towardsdatascience.com/unsupervised-learning-series-exploring-hierarchical-clustering-15d992467aa8?sk=87714b0d7aa252330dd7a8d3b1c620f4)\n * [Self-Organizing Maps](https://towardsdatascience.com/unsupervised-learning-series-exploring-self-organizing-maps-fe2efde9f7a1?sk=0a2649f9b411c236c2682729a5e616b4)\n * [DBScan](https://towardsdatascience.com/unsupervised-learning-series-exploring-dbscan-624c820290ce?sk=b12738fd430804b400cabc7910329555)\n\n\nIf you want to read / see more content related to AI and DS, subscribe my youtube Channel \"_The Data Journey_ \":\n![https://www.youtube.com/@TheDataJourney42](../images/body-e04dbadcee26f5165210.png)\n\n_The dataset used in this blog post is Wholesale Customer Dataset with license Creative Commons Attribution 4.0 (_)\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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It also helps in adverstising on the website.\n\n\n * Cookie\nedgebucket\n * Duration\nsession\n * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n * Cookie\ndid\n * Duration\n1 year\n * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Artificial Intelligence](https://towardsdatascience.com/category/artificial-intelligence/)\n# Unsupervised Learning Series: Exploring the Mean-Shift Algorithm\nLet's learn one of the most famous density-based clustering algorithms, Mean-Shift.\n[Ivo Bernardo](https://towardsdatascience.com/author/ivopbernardo/)\nAugust 19, 202410 min read\n![](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/0h3Zt9LVvd5u_4yQz-scaled.jpg)\n_K-Means, Hierarchical Clustering, Expectation-Maximization,_ and _DBScan_ are probably the most famous clustering algorithms you may know in the context of Machine Learning.\nHowever, there is another density-based algorithm that has been solving a variety of problems, ranging from satellite image segmentation to object tracking, and its name is mean-shift. This algorithm is renowned for finding the modes of a specific dataset by building clusters around areas with higher data point densities.\nVisualizing mean-shift is easy. Normally, I use the skyscraper skyline analogy. If you consider a skyscraper skyline:\nLearn this step by step with the interactive [AI Engineer](https://roadmap.sh/ai-engineer) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps.\n![Two Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1aIGiyzyAsH1zqIEKP0B2tg.jpeg)\nTwo Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer\nWe can clearly see two different clusters of density if we consider the skyscrapers as our datapoints:\n![Two Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1m_MwkZajucMwNIxEvtHmVA.png)\nTwo Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer\nBut let's expand the image below, to see more skyscraper areas. As we expeand the image, we can see other clusters of density, with different \"peak\" size:\n![Four Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1w65ooBG03ORXBpt094g9Rg.png)\nFour Clusters of Density using Skyscrapers - Image generated by AI in Microsoft Image Designer\nThe goal of the mean-shift algorithm is to find these different clusters (of varying peak) within a dataset. It achieves this by shifting the cluster means until they reaches a \"peak\", similarly to _dbscan._\nIt's a powerful technique to leverage, particularly when our data contains non-spherical clusters.\nIn this blog post, we will:\n * See a step-by-step implementation of the mean-shift algorithm.\n * Check the `sklearn` implementation of the algorithm.\n * Go through a practical use case of the algorithm using real-data.\n\n\nIf you would like, you can also check the other blog posts of this unsupervised learning series, using the links below:\n * [K-means](https://towardsdatascience.com/unsupervised-learning-method-series-exploring-k-means-clustering-d129fff3ab6a?sk=0618fadb196a71ce4b9f378f9ee83107)\n * [Hierarchical Clustering](https://towardsdatascience.com/unsupervised-learning-series-exploring-hierarchical-clustering-15d992467aa8?sk=87714b0d7aa252330dd7a8d3b1c620f4)\n * [Self-Organizing Maps](https://towardsdatascience.com/unsupervised-learning-series-exploring-self-organizing-maps-fe2efde9f7a1?sk=0a2649f9b411c236c2682729a5e616b4)\n * [DBScan](https://towardsdatascience.com/unsupervised-learning-series-exploring-dbscan-624c820290ce?sk=b12738fd430804b400cabc7910329555)\n\n\nCompared to the latter (_DBScan_ , another density based algorithm), mean-shift only requires the tuning of one hyperparameter. This comes with a cost, as it doesn't provide the robustness to outliers that _DBScan_ can offer.\nHope you're ready, and let's start!\n* * *\n## Why K-Means doesn't work for Non-Spherical Shapes\nFor our introduction of the mean-shift algorithm, we'll start by understanding why traditional clustering methods fail on some datasets. Take the following dataset with generated customer data. Our two variables are _annual income (in k euros)_ and _average spending_ for a group of customers:\n![Customer Dataset - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1EumgQ-VZeB-4pUWr9sYRvQ.png)\nCustomer Dataset - Image by Author\nVisually, it's hard to understand the number of different clusters we have on this dataset. We can consider three, four or five. For example, if we consider 5 different clusters, we'll probably outline the following:\n![Customer Dataset Visual Clusters— Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1ksdkf3MXfAY7F10u4O1fNA.png)\nCustomer Dataset Visual Clusters— Image by Author\nThe image above is tricking us a bit, though. As with most clustering algorithms that deal with distances, it's important to standardize our data - let's do that:\n![Customer Standardized Dataset— Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1mWtBBFfm1HPvbuT12vLTFw.png)\nCustomer Standardized Dataset— Image by Author\nNow, our densities are a bit different:\n![Customer Standardized Dataset Visual Clusters - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1I1vh8lqH5HHwSc7A43qLlA.png)\nCustomer Standardized Dataset Visual Clusters - Image by Author\nAnother hypothesis is to combine some these data points into 3 or 4 clusters. Of course, doing this visually is a bit tricky, so how does K-Means behave in this dataset - first let's see the 5 cluster example:\n![K-Means solution on Dataset - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1MTpmYrflNXxGcMv2sVdWKQ.png)\nK-Means solution on Dataset - Image by Author\nAs you can see, K-Means clustering has some trouble to define these clusters. Mostly, this happens due to the _non-spherical_ nature of the data. Let's see what happens if I fit a k-means solution with 4 clusters:\n![4 Clusters K-Means solution on Dataset - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1yX85XEpkBVKpg3ji0yiYsg.png)\n4 Clusters K-Means solution on Dataset - Image by Author\nIt's an interesting solution, but becoming too influenced by outliers. Notice how these 3 data points impact one of the clusters in a major way:\n![Outliers influencing - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1kEyV-CufAfHr6zycf0aNNw.png)\nOutliers influencing - Image by Author\nNow let's see what happens with _mean-shift_ :\n![Mean-Shift Solution - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1ju3hOR7CZ6HDQGCEg5qF0A.png)\nMean-Shift Solution - Image by Author\nWe see clusters that are more aligned with the density we've seen before. Although the solution is not perfect, it's an interesting pattern discovered by the algorithm.\nBut why is mean-shift so different from K-Means? As usual, no question is left unanswered - let's see!\n* * *\n## Mean-Shift Walkthrough, step-by-step\nFirst, we'll start with a clean version of our dataset (without any clusters assigned). Mean-shift starts with a random data point (highlighted in orange below):\n![Random Data Point Selected - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1FDk7a_8sli_95A0-EfeYVg.png)\nRandom Data Point Selected - Image by Author\nNext step is to draw a circle around this data point with a radius (hyperparameter of the algorithm). I'll define 0.1 as the value of the radius of our circle:\n![Radius Definition - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1fYkzgzHv-qnsZHCX6x9BjQ.png)\nRadius Definition - Image by Author\n _Note: From now on, I'll show squared plots so that we can correctly see the circles generated by the radius. Default matplotlib definitions shows an elipsis as the plot is stretched on the x-axis._\nWe now need to perform a crucial step of the mean-shift algorithm: **the shifting operation!**\nThis is actually very simple. Depending on the kernel, we will drag this orange point to its center of density. The most famous _kernels_ to use within mean-shift are:\n * Gaussian kernel\n * Mexican-hat\n * Uniform kernel\n\n\nThe gaussian and mexican-hat kernels consider the points that are farther from the center should have less influence in the shifting operation. The uniform kernel is a bit less flexible and states that any data point within the radius should have equal influence in the shifting operation.\nWe'll use uniform kernel as an example, due to its simplicity, although gaussian kernel is also used often.\nFirst, we need to assess which data points are within our radius:\n![Highlighted points within the radius - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/17s2QOu0Fo0WmonAL9dbORA.png)\nHighlighted points within the radius - Image by Author\nI'll consider that every data point that touches some part of the radius is part of the cirle. Subsetting these data points (and the point itself):\n![Subset of Customers within the Radius - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/17RVNFIYSZ8-QtTtqOpPXDA.png)\nSubset of Customers within the Radius - Image by Author\nNow, we can use the averages both _age_ and _annual _income_ of this subset of customers to drag the \"centroid\".\n * _age_ average is approximately 0.0679\n * _annual _income_ average is approximately 0.324\n\n\nThese are the two values that contain the coordinates where we are going to shift our mean inside the radius:\n![Mean shift operation - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1TMwnJRlhKt7ii-gPm9T1xg.png)\nMean shift operation - Image by Author\nOur centroid gets shifted northwest. Let's reposition it:\n![Shifted Centroid - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1y64ZjqWWBc7SYCCo24XJMA.png)\nShifted Centroid - Image by Author\nIn this case, our new radius touches the same data points. Our centroid converged to this region and it will stay there.\nNext iteration is doing exactly the same for every data point. Let's visualize what would happen with another data point in a different region:\n![Second Random Data Point Example - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1Wmf8iXFt8bzljy8ffHeGDQ.png)\nSecond Random Data Point Example - Image by Author\nIn this case, the mean would shift southeast. If we start in an isolated data point:\n![Third Random Data Point Example - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1Cyy_Mdubh5vm8BEXNttm7A.png)\nThird Random Data Point Example - Image by Author\nIn this case, the mean that started on this data point won't change. This data point will form a cluster by itself.\nDuring the algorithm run, different data points will land in a same \"center of mass\". Tthese peaks will be combined to become a cluster (different implementations of _mean-shift_ may do this last step in different ways). The key is that all implementations respect the principle: \"same density peak, same cluster\".\nDepending on the implementation, the algorithm will finish when one of the conditions is met:\n * Reaches a certain number of iterations given by the user. One iteration is equal to one pass through all the data points.\n * The centroids no longer move after a few iterations.\n * Some implementations define that when all cluster peaks are within a radius boundary, the algorithm should finish.\n\n\nIn `sklearn` 's implementation, the choice is route number 1 - after 300 iterations the algorithm stops, by default.\nMean-shift has only one important hyperparameter - the radius. Compare the following two solutions:\n![Radius = 0.1 - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1fYkzgzHv-qnsZHCX6x9BjQ.png)\nRadius = 0.1 - Image by Author\nWe are revisiting our first example - in this case, our radius is 0.1. What happens we we raise this value?\n![Radius = 0.5— Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1FOrhkw4CAF9ZlkgBWlubxg.png)\nRadius = 0.5— Image by Author\nWith a radius of 0.5, we can see that more points will tend to navigate to the same density peak. The downside of the radius hyperparameter (user defined) is that it's the same for every data point. Due to that, mean-shift may not be able to lead very well with datasets that contain clusters of different densities.\nWith no surprise, shifting is the most important operation of the algorithm! It's time to see it in action, using the `sklearn` implementation!\n* * *\n### Mean-shift in Action\nAs customer segmentantion is one of the oldest (and most relevant) usages of clustering algorithms, we'll play around with the Wholesale Customer Dataset, available on [UCI's Machine Learning Repository](https://archive.ics.uci.edu/dataset/292/wholesale+customers).\nWe'll start with the usual load operation of the dataset:\npython\n\n```\nimport pandas as pd\nwholesale_customers = pd.read_csv('data/Wholesale customers data.csv')\n```\n\nHere's a preview of it:\n![Preview of Wholesale Customer Dataset - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1i1u6AWLl7WyEIivMovoYiQ.png)\nPreview of Wholesale Customer Dataset - Image by Author\nAccording to the metadata available at the UCI repository, the description of the columns is the following:\n * FRESH: annual spending (m.u.) on fresh products (Continuous);\n * MILK: annual spending (m.u.) on milk products (Continuous);\n * GROCERY: annual spending (m.u.)on grocery products (Continuous);\n * FROZEN: annual spending (m.u.)on frozen products (Continuous)\n * DETERGENTS_PAPER: annual spending (m.u.) on detergents and paper products (Continuous)\n * DELICATESSEN: annual spending (m.u.)on and delicatessen products (Continuous);\n * CHANNEL: Customer's Channel - Horeca (Hotel/Restaurant/Cafe) or Retail channel (Nominal)\n * REGION: Customers's Region: \" Lisbon, Oporto or Other (Nominal)\n\n\nFor this example, we'll only use the monetary values.\nThe first step in our mean-shift solution is to determine the `bandwith` of the algorithm. The `bandwith` represents the radius we've seen in the step-by-step example.\nEstimating bandwith manually is very hard. One cool function we have in `sklearn` is `estimate_bandwith` that uses nearest neighbors average distance to find a good baseline value.\nBut before checking the bandwidth, do you think there is something missing? We are dealing with an algorithm that relates to distances, so... we need standardization!\npython\n\n```\nfrom sklearn.preprocessing import MinMaxScaler\n\nmmc = MinMaxScaler()\nscaled_dataset = mmc.fit_transform(\n wholesale_customers[['Fresh','Milk','Grocery','Frozen','Detergents_Paper','Delicassen']]\n)\n```\n\nWith the scaled dataset, we can run `estimate_bandwith` :\npython\n\n```\nfrom sklearn.cluster import MeanShift, estimate_bandwidth\n\nbandwith_estimation = estimate_bandwidth(scaled_dataset)\n```\n\nThe estimated bandwith was approximately 0.183. We can now fit the algorithm to the scaled dataset:\npython\n\n```\nmeanshiftmodel = MeanShift(bandwidth=bandwith_estimation)\nwholesale_customers['meanshift_clustering'] = meanshiftmodel.fit_predict(\n scaled_dataset\n)\n```\n\nLet's see how many data points we have per cluster:\nscss\n\n```\nwholesale_customers['meanshift_clustering'].value_counts()\n```\n\n![Clusters' data points count - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1Ez35VygiUC_VOGC-S3_Z_Q.png)\nClusters' data points count - Image by Author\nWe have some clusters that only contain one data point. These are probably outliers isolated by our radius. There's three alternatives we can use:\n * We can remove uni-variate outliers manually before fitting the algorithm.\n * We can remove these clusters from our dataset.\n * We can raise the bandwith we are using and re-run the clustering solution again.\n\n\nLet's go through the latter!\nmakefile\n\n```\nmeanshiftmodel = MeanShift(bandwidth=bandwith_estimation+0.1)\nwholesale_customers['meanshift_clustering_extra_band'] = meanshiftmodel.fit_predict(\n scaled_dataset\n)\n```\n\nChecking the clusters again:\n![Clusters' data points count - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1MdqkdomiX3-y_loIR6nUg.png)\nClusters' data points count - Image by Author\nOh no! Too high. Tweaking the `bandwidth` parameter is difficult. Let's settle with the first solution we have and remove outlier clusters manually:\njava\n\n```\noutlier_clusters = (\n wholesale_customers['meanshift_clustering'].value_counts().loc[\n wholesale_customers['meanshift_clustering'].value_counts() <= 3\n ]\n).index\n\nclustering_solution = wholesale_customers.loc[~wholesale_customers.meanshift_clustering.isin(outlier_clusters)]\n```\n\nAnd checking the profiling of our clusters:\ncss\n\n```\nclustering_solution.groupby(['meanshift_clustering']).mean().iloc[:,2:]\n```\n\n![Cluster Profilling - Image by Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/1nGuB1wNb9pNXqOV53WzUZA.png)\nCluster Profilling - Image by Author\nCool! So our first cluster (Cluster 0) is characterized by moderate fresh buyers with low values on the other categories.\nCluster 1 is characterized by high grocery and detergent shoppers.\nFinally, cluster 4 is characterized by high grocery and frozen shoppers.\nA word of cautioning about this type of profilling - using simple _mean profiling_ on density clusters is a biased solution (particularly in mean-shift, where clusters may not be spherical). An alternative to profile and check the quality of the clustering is to plot the clustering solution with [T-SNE](https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding) or UMAP embeddings.\nAlso, by the distribution of the data points in the clusters, this is not a good dataset to apply a density based clustering method. When you see a high concentration of data points in a single cluster, other methods should be tested (but don't forget to play around with the bandwidth parameter first).\n* * *\nHope you've enjoyed this blog post on mean-shift clustering! As mentioned, this is an interesting density based algorithm that can find out interesting patterns in your data.\nOn the upside, mean-shift can find out non-spherical clusters on the data, while uncovering the different distribution peaks. On the downside, it tends to isolate outliers as clusters. Also, the bandwith hyperparameter is relatively difficult to tweak.\nIf you are curious about other unsupervised learning algorithms, feel free to check the other blog posts of this series:\n * [K-means](https://towardsdatascience.com/unsupervised-learning-method-series-exploring-k-means-clustering-d129fff3ab6a?sk=0618fadb196a71ce4b9f378f9ee83107)\n * [Hierarchical Clustering](https://towardsdatascience.com/unsupervised-learning-series-exploring-hierarchical-clustering-15d992467aa8?sk=87714b0d7aa252330dd7a8d3b1c620f4)\n * [Self-Organizing Maps](https://towardsdatascience.com/unsupervised-learning-series-exploring-self-organizing-maps-fe2efde9f7a1?sk=0a2649f9b411c236c2682729a5e616b4)\n * [DBScan](https://towardsdatascience.com/unsupervised-learning-series-exploring-dbscan-624c820290ce?sk=b12738fd430804b400cabc7910329555)\n\n\nIf you want to read / see more content related to AI and DS, subscribe my youtube Channel \"_The Data Journey_ \":\n![https://www.youtube.com/@TheDataJourney42](https://assets.insightmediagroup.io/media/wp-content/uploads/2024/08/0vtKZ-2w694nStZ4B.png)\n\n_The dataset used in this blog post is Wholesale Customer Dataset with license Creative Commons Attribution 4.0 (_)\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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