Tensor Similarity in Two Modes

Abstract

Multiway datasets are widespread in signal processing and play an important role in blind signal separation, array processing, and biomedical signal processing, among others. One key strength of tensors is that their decompositions are unique under mild conditions, which allows the recovery of features or source signals. In several applications, such as classification, we wish to compare factor matrices of the decompositions. Though this is possible by first computing the tensor decompositions and subsequently comparing the factors, these decompositions are often computationally expensive. In this paper, we present a similarity method that indicates whether the factors in two modes are essentially equal without explicitly computing them. Essential equality conditions, which ensure the theoretical validity of our approach, are provided for various underlying tensor decompositions. The developed algorithm provides a computationally efficient way to compare factors. The method is illustrated in a context of emitter movement detection and fluorescence data analysis.