Detecting null patterns in tensor data

Abstract

This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in statistics and signal processing, low-rank tensor decompositions, and Tucker decompositions. It also includes a new family of null patterns -- not known to be detectable by current methods -- that can be thought of as continuous decompositions approximating curves and surfaces. We present a general algorithm to detect null patterns in each class using a parameter we call a \textit{chisel} that tunes the search to patterns of a prescribed shape. We also show that the patterns output by the algorithm are essentially unique.