Multilinear Principal Component Analysis for Tensor Data: A Survey

Abstract

With the advances in data collection and storage capabilities, massive multidimensional data are being generated. These massive multidimensional data are usually very high-dimensional, with a large amount of redundancy, and only occupying a subspace of the input space. A tensor, a generalization of vectors and matrices, is a potential tool to govern these high dimension data. Normally, linear subspace learning (LSL) algorithms are traditional dimensionality reduction techniques. Unfortunately, they often become inadequate when dealing with tensor data. Recently, interests have grown in multilinear subspace learning (MSL), a novel approach to dimensionality reduction of multidimensional tensor data. This article provides an overview of methodological and theoretical developments of the multilinear PCA (MPCA).