THE SIGNED CUMULATIVE DISTRIBUTION TRANSFORM FOR 1-D SIGNAL ANALYSIS AND CLASSIFICATION

被引：5

作者：

Aldroubi, Akram ^{[1
]}

Martin, Rocio Diaz ^{[1
]}

Medri, Ivan ^{[1
]}

Rohde, Gustavo K. ^{[2
]}

Thareja, Sumati ^{[1
]}

机构：

[1] Vanderbilt Univ, Dept Math, 1326 Stevenson Ctr, Nashville, TN 37240 USA

[2] Univ Virginia, Dept Elect & Comp Engn, Dept Biomed Engn, Charlottesville, VA 22904 USA

来源：

FOUNDATIONS OF DATA SCIENCE | 2022年 / 4卷 / 01期

关键词：

Cumulative Distribution Transform; data analysis; classification; machine learning; OPTIMAL MASS-TRANSPORT;

D O I：

10.3934/fods.2022001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution Transform [29] to arbitrary (signed) signals on (R) over bar. We present both forward (analysis) and inverse (synthesis) formulas for the transform, and describe several of its properties including translation, scaling, convexity, linear separability and others. Finally, we describe a metric in transform space, and demonstrate the application of the transform in classifying (detecting) signals under random displacements.

引用

页码：137 / 163

页数：27

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