The k-Means algorithm is one of the most widely used unsupervised learning methods for partitioning data into homogeneous groups. This study explores the efficacy of k-Means clustering on three real-world datasets: a synthetic 2D blob dataset, a customer segmentation dataset based on spending behavior, and a global cities dataset based on geographic coordinates. We analyze the influence of data scaling, initial centroid selection (random vs k-means++), and the number of clusters (k) using silhouette score, elbow method, and PCA visualizations. The study also highlights the limitations of k-Means such as sensitivity to outliers and non-convex cluster shapes, offering guidelines for practical implementation.

k-Means, unsupervised learning, clustering, silhouette score, elbow method, k-means++, PCA visualization, customer segmentation, geospatial clustering.

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