Kernelization of Tensor-Based Models for Multiway Data Analysis: Processing of Multidimensional Structured Data

Abstract

Tensors (also called multiway arrays) are a generalization of vectors and matrices to higher dimensions based on multilinear algebra. The development of theory and algorithms for tensor decompositions (factorizations) has been an active area of study within the past decade, e.g., [1] and [2]. These methods have been successfully applied to many problems in unsupervised learning and exploratory data analysis. Multiway analysis enables one to effectively capture the multilinear structure of the data, which is usually available as a priori information about the data. Hence, it might provide advantages over matrix factorizations by enabling one to more effectively use the underlying structure of the data. Besides unsupervised tensor decompositions, supervised tensor subspace regression and classification formulations have been also successfully applied to a variety of fields including chemometrics, signal processing, computer vision, and neuroscience.