K-Means clustering is one of the most widely used unsupervised machine learning algorithms for grouping similar data objects into distinct clusters. It partitions a dataset into K clusters, where each data point belongs to the cluster with the nearest centroid. The algorithm minimizes the within-cluster sum of squared distances (WCSS), thereby ensuring that objects within the same cluster are highly similar while those in different clusters are as distinct as possible. The implementation of the K-Means algorithm involves the following steps: 1. Select the desired number of clusters (K). 2. Randomly initialize K centroids from the dataset. 3. Compute the Euclidean distance between each data point and every centroid. 4. Assign each data point to the nearest centroid, thereby forming clusters. 5. Recalculate the centroid of each cluster by taking the mean of all points assigned to it. 6. Repeat the assignment and centroid update steps until cluster memberships no longer change or the improvement becomes negligible. For example, consider a two-dimensional dataset with observations representing customer purchasing behavior. Suppose K = 3 is selected. After initialization, the algorithm groups nearby customers into three clusters. During successive iterations, the centroids gradually move toward the center of their respective groups. Eventually, stable clusters emerge where intra-cluster similarity is maximized and inter-cluster similarity is minimized. The generated clusters can be analyzed using several characteristics. Cluster size indicates how many observations belong to each group. Cluster centroid represents the average feature values of the members. Cluster compactness is evaluated through WCSS, where lower values indicate tighter clusters. Separation between clusters is measured by