K-means Clustering Algorithm Implementation

The K-means clustering algorithm begins by randomly initializing cluster centers according to the predefined number of clusters. The implementation typically involves selecting k random data points as initial centroids using functions like numpy.random.choice(). Data similarity is measured by computing Euclidean distances between each data point and all cluster centers, which can be efficiently implemented using vectorized operations with numpy.linalg.norm(). Through iterative reassignment of points to the nearest centroid and recalculation of centroid positions, the algorithm converges to final clustering results. The selection of initial cluster count (k-value) is critical and often determined through domain knowledge or experimental methods like the elbow method using within-cluster sum of squares (WCSS) analysis. Random centroid initialization helps avoid local optima, though advanced techniques like k-means++ provide better starting points. The resulting clusters reveal inherent data structures and patterns, serving as foundation for subsequent data analysis and decision-making processes. The algorithm typically terminates when centroid movements fall below a threshold or maximum iterations are reached, ensuring computational efficiency.