Simultaneous tensor subspace selection and clustering: the equivalence of high order svd and k-means clustering

Singular Value Decomposition (SVD)/Principal Component Analysis (PCA) have played a vital role in finding patterns from many datasets. Recently tensor factorization has been used for data mining and pattern recognition in high index/order data. High Order SVD (HOSVD) is a commonly used tensor factorization method and has recently been used in numerous applications like graphs, videos, social networks, etc. In this paper we prove that HOSVD does simultaneous subspace selection (data compression) and K-means clustering widely used for unsupervised learning tasks. We show how to utilize this new feature of HOSVD for clustering. We demonstrate these new results using three real and large datasets, two on face images datasets and one on hand-written digits dataset. Using this new HOSVD clustering feature we provide a dataset quality assessment on many frequently used experimental datasets with expected noise levels.