Detecting null patterns in tensor data

TL;DR

This paper introduces a unified framework for efficiently detecting various null patterns in tensor data, including known and novel patterns, using a parameterized algorithm that ensures pattern uniqueness.

Contribution

It presents a general algorithm for detecting a broad class of null tensor patterns, including new patterns that previous methods cannot identify.

Findings

Algorithm effectively detects known tensor patterns.

Introduces new null patterns approximating curves and surfaces.

Ensures the uniqueness of detected patterns.

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.