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arXiv · 2408.17425

Detecting null patterns in tensor data

Peter A. Brooksbank·Martin D. Kassabov·James B. Wilson
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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.

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Peter A. Brooksbank, Martin D. Kassabov, James B. Wilson. 2024-08-30. Detecting null patterns in tensor data. https://arxiv.org/abs/2408.17425

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