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What is k-Means Clustering?

The k-Means clustering is a method for forming groups within a large data set. The algorithm tries to assign each data point to exactly one group in several steps so that the data within a cluster are as close to each other as possible and the clusters are as far apart as possible.

What is Clustering?

Clustering refers to finding subgroups within a data set so that data points within a group are as similar as possible and data points between different groups are as different as possible. Clustering takes place on the basis of properties, so-called features. That is, the groups are formed based on the fact that the data points within a cluster have similar feature characteristics.

Since there are no predefined groups to which the algorithm could orient itself during learning, clustering counts as Unsupervised (Machine) Learning. The assignment to groups happens solely on the structures within the data set, which the model has to learn on its own.

When working with large data sets, clustering helps to get a first impression about the features and the distribution of the data points. There are also many other applications for clustering:

  • Market segmentation: An attempt is made to find similar customer groups with comparable purchasing behavior or other characteristics. This information can then be used for marketing activities or new product innovations.
  • Image segmentation: An attempt is made to find the locations within an image that belong to a specific object, e.g. all pixels that are part of a car or the road. This can also be used as a pre-processing step for machine learning models.
  • Document clustering: Within a document, an attempt is made to find passages with similar content focus.

How does the k-Means Algorithm work?

The k-Means algorithm is a special clustering method that iteratively tries to find a total of k clusters in the data set so that each data point belongs to exactly one group. Roughly speaking, there are a total of five steps, which we will look at in detail:

  1. We need to determine the number of clusters k.
  2. Random k data points are determined as cluster centers, the so-called centroids. There are different, so-called initialization methods for choosing the initial cluster centers. The performance of the algorithm can strongly depend on the initial centroids depending on the use case, so different initial scenarios should be tried.
  3. All other data points are assigned to the cluster whose cluster center has the smallest distance to the data point.
  4. Now a new cluster center is calculated for each group. It corresponds to the point in the cluster that has the smallest distance to all other data points in the group.
  5. If the cluster center has not changed at all (or very little), the algorithm stops here. If not, it goes back to step 3 and reassigns the data points to the next cluster.
Das Bild zeigt den Ablauf beim k-Means Clustering.
k-Means Clustering Process

What are the applications of k-Means clustering?

K-means clustering is a popular unsupervised machine learning algorithm that has a wide range of applications in various fields. Some common applications of k-means clustering include:

  1. Image segmentation: K-means clustering can be used to segment an image into different regions based on its color or texture features. This is useful in fields like computer vision and medical imaging.
  2. Customer segmentation: K-means clustering can be used to group customers based on their behavior or demographics. This is useful for businesses to better understand their customers and tailor their marketing strategies accordingly.
  3. Anomaly detection: K-means clustering can be used to detect anomalies or outliers in a dataset, which can be useful in fraud detection or detecting faulty equipment.
  4. Genomic clustering: K-means clustering can be used to cluster genes or proteins based on their expression or functional similarities, which can be useful in biological research.
  5. Social network analysis: K-means clustering can be used to group users in a social network based on their interests or behavior, which can be useful for targeted advertising or recommendation systems.
  6. Document clustering: K-means clustering can be used to cluster documents based on their content, which can be useful for organizing and retrieving large document collections.

These are just a few examples of the many applications of k-means clustering. The versatility and simplicity of the algorithm make it a popular choice for many clustering tasks in various fields.

How to find the right Number of Clusters?

A major drawback of the k-Means clustering method is that one must determine the number of final groups before training the model. Of course, this is actually impossible without knowledge of the data set.

The so-called elbow method supports finding the right number of clusters. For different k values, the sum of all squared distances from the cluster center to the data points is calculated. For a single cluster, this sum is maximum and it becomes zero if we have as many clusters as data points, because then each data point is simply a cluster and the distance between cluster center and data point is correspondingly 0. In between, we try to find the optimum, i.e. the point at which the distances within a cluster are as small as possible and the number of clusters is also as small as possible.

Das Bild zeigt die Ellbogenmethode beim k-Means Clustering.
Elbow Method | Photo: O’Reilly Media

From this graph, we then try to find the so-called knee or elbow, i.e. the point in the graph that has the prominent kink. From this point on, the distance of the points in the cluster does not decrease as much as before. Thus, new clusters do not improve the overall result as much as before. So in this case we should choose k = 3 to get an optimal result.

How do you evaluate the performance of a k-Means cluster?

There are several ways to evaluate the performance of a k-means clustering algorithm. Here are some common evaluation metrics:

  1. The within-cluster sum of squares (WSS): This measures the total sum of distances between each point in a cluster and the centroid of that cluster. The lower the WSS, the more compact the clusters are. However, a low WSS does not necessarily indicate a good clustering solution since it only measures the distance within each cluster.
  2. Silhouette score: This measures how well a data point fits its assigned cluster compared to other clusters. The silhouette score ranges from -1 to 1, with values closer to 1 indicating a well-clustered point and values closer to -1 indicating a poorly-clustered point.
  3. Davies-Bouldin index (DBI): This measures the average similarity between each cluster and its most similar cluster. A lower DBI indicates a better clustering solution.
  4. Calinski-Harabasz index (CHI): This measures the ratio of the between-cluster variance to the within-cluster variance. A higher CHI indicates a better clustering solution.
  5. External validation measures: These measures compare the clustering results to known ground truth, such as manually assigned labels. Common external validation measures include the adjusted Rand index and the F-measure.

It’s important to note that there is no one “best” evaluation metric for k-means clustering, as each metric has its own strengths and weaknesses. Therefore, it’s recommended to use multiple evaluation metrics to get a more comprehensive understanding of the clustering results.

What are the limitations of k-Means Clustering?

K-means clustering is a widely used algorithm for unsupervised Machine Learning, but it has several limitations that should be taken into consideration when using it in practice.

One of the main limitations of the k-means clustering is that it requires the number of clusters to be specified in advance. This can be difficult in situations where the optimal number of clusters is not known beforehand, and selecting the wrong number of clusters can lead to poor results.

Another limitation is its sensitivity to initialization. The algorithm is sensitive to the initial positions of the cluster centroids, which can lead to different results depending on the initialization method used. This means that multiple runs of the algorithm with different initializations may be necessary to obtain a stable clustering solution.

K-means clustering also assumes that clusters are spherical and have equal variance. This may not be appropriate in situations where the data has a more complex structure or where clusters have different shapes and sizes. In such cases, alternative clustering algorithms may be more appropriate.

Finally, k-means clustering can be sensitive to outliers, as they can pull the centroids away from the main cluster. This can result in suboptimal cluster assignments and may require pre-processing steps like outlier removal to improve the results.

Overall, while k-means clustering is a powerful algorithm for unsupervised machine learning, it has several limitations that should be considered when applying it in practice. It is important to carefully choose the number of clusters and initialization method, as well as to evaluate the results using appropriate metrics and visualizations. Additionally, it may be necessary to consider alternative clustering algorithms in situations where the assumptions of k-means clustering are not met.

This is what you should take with you

  • K-Means Clustering is a method for forming groups of large data sets and belongs to the Unsupervised Learning methods.
  • If possible, points within a group/cluster are relatively similar, while data points from different clusters are as different as possible.
  • The k-Means clustering method is used, for example, to determine customer segments or to find areas in images that show the same thing.
  • Using the so-called Elbow method, we can find the optimal number of cluster centers in advance.
  • On this page, you can observe a k-Means clustering model step by step as it is trained.
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