K-means clustering is a fundamental unsupervised machine learning algorithm used to partition data into k distinct clusters. The algorithm works by iteratively assigning data points to the nearest cluster centroid and then updating the centroids based on the mean of assigned points. Let's explore how this powerful clustering technique works step by step.
The first step in k-means is initializing the centroids. We can use random selection, where we pick k random data points as initial centroids. A better approach is k-means plus plus initialization, which spreads out the initial centroids to improve convergence. The algorithm then uses the Euclidean distance formula to measure how far each point is from each centroid.
In the assignment step, we calculate the distance from each data point to every centroid using the Euclidean distance formula. Each point is then assigned to the cluster with the nearest centroid. For example, a point at coordinates three comma two would be much closer to the red centroid than the blue one, so it gets assigned to the red cluster. This process ensures every point belongs to exactly one cluster.
After assigning all points to clusters, we update each centroid by calculating the mean position of all points in that cluster. The new centroid coordinates are the average of the x coordinates and the average of the y coordinates of all assigned points. For example, the red cluster with points at two comma two, two point five comma two point five, three comma two, and two comma three would have its centroid moved to two point three seven five comma two point three seven five. This process continues iteratively until the centroids stop moving significantly.
To summarize, k-means clustering is a powerful unsupervised learning algorithm that partitions data into k distinct clusters. The process involves initializing centroids, assigning points to the nearest centroid, updating centroids to cluster means, and repeating until convergence. This algorithm is widely used in customer segmentation, market research, and data analysis across many industries.