Principal Component Analysis - Relation Between PCA and K-means Clustering

Relation Between PCA and K-means Clustering

It has been shown recently (2001,2004) that the relaxed solution of K-means clustering, specified by the cluster indicators, is given by the PCA principal components, and the PCA subspace spanned by the principal directions is identical to the cluster centroid subspace specified by the between-class scatter matrix. Thus PCA automatically projects to the subspace where the global solution of K-means clustering lies, and thus facilitates K-means clustering to find near-optimal solutions.