K-Means Clustering is a fundamental unsupervised machine learning algorithm. It partitions a dataset into K distinct clusters, where each data point belongs to the cluster with the nearest centroid. The algorithm is widely used for data analysis, customer segmentation, and pattern recognition.
The first step in K-Means clustering is initialization. We must choose the number of clusters K, which is typically determined by domain knowledge or techniques like the elbow method. Then we randomly place K centroids in the data space. These centroids will serve as the initial cluster centers.
In the assignment step, we calculate the Euclidean distance from each data point to all centroids. Each point is then assigned to the cluster with the nearest centroid. This creates our initial clusters, where points are colored according to their assigned cluster.
In the update step, we recalculate the centroids by finding the mean position of all points assigned to each cluster. The centroids move to these new positions, which better represent the center of their respective clusters. This process continues iteratively until convergence.
The algorithm repeats the assignment and update steps until convergence. Convergence occurs when centroids no longer move significantly between iterations. At this point, we have our final clusters with stable boundaries. K-Means has successfully partitioned the data into distinct groups based on similarity.