Discriminative high order SVD: Adaptive tensor subspace selection for image classification, clustering, and retrieval

Tensor based dimensionality reduction has recently attracted attention from computer vision and pattern recognition communities for both feature extraction and data compression. As an unsupervised method, High-Order Singular Value Decomposition (HOSVD) searches for low-rank subspaces such that the low-rank approximation error is minimized. In this paper, we propose a new unsupervised high-order tensor decomposition approach which employs the strength of discriminative analysis and K-means clustering to adaptively select subspaces that improve the clustering, classification, and retrieval capabilities of HOSVD. We provide both theoretical analysis to guarantee that our new method generates more discriminative subspaces and empirical studies on several public computer vision data sets to show the consistent improvement of our method over existing methods.