mlsanityData to 7 Oct 2026

The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification

arXiv 2106.02146 ↗First posted 3 Jun 2021cs.IT cs.LG math.FAcited by 9

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Abstract (arXiv)

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 [ACHA 45 (2018), no. 3, 616-641] to arbitrary (signed) signals on overlineℝ. 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.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 13 of its 49 references that are in the map. First posted on arXiv 3 Jun 2021.

Builds on

13 of 49 references.

References · 13

  1. 2015Optimal Transport for Domain Adaptationcited by 457
  2. 2019Generalized Sliced Wasserstein Distancescited by 205
  3. 2015Sliced Wasserstein Kernels for Probability Distributionscited by 64
  4. 2015The Radon cumulative distribution transform and its application to image classificationcited by 28
  5. 2015The Cumulative Distribution Transform and Linear Pattern Classificationcited by 19
  6. 2020Linearized Optimal Transport for Collider Eventscited by 16
  7. 2019Unnormalized Optimal Transportcited by 15
  8. 2020Partitioning signal classes using transport transforms for data analysis and machine learningcited by 15
  9. 2020Radon cumulative distribution transform subspace modeling for image classificationcited by 14
  10. 2016A Transportation Lp Distance for Signal Analysiscited by 11
  11. 2021The Linearized Hellinger--Kantorovich Distancecited by 11
  12. 2015Unbalanced Optimal Transport: Dynamic and Kantorovich Formulationcited by 6
1 more
  1. 2017Discovery and visualization of structural biomarkers from MRI using transport-based morphometrycited by 6

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Cited by year

Citing papers per year: 2022: 3; 2023: 2; 2024: 0; 2025: 4.

9 papers.

  1. 2022End-to-End Signal Classification in Signed Cumulative Distribution Transform Spacecited by 7
  2. 2023LCOT: Linear circular optimal transportcited by 4
  3. 2025Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classificationcited by 3
  4. 2022Signed Cumulative Distribution Transform for Parameter Estimation of 1-D Signalscited by 1
  5. 2023The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Imagescited by 1
  6. 2022Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysiscited by 0
  7. 2025An Efficient Transport-Based Dissimilarity Measure for Time Series Classification under Warping Distortionscited by 0
  8. 2025Improved Hyperspectral Anomaly Detection via Unsupervised Subspace Modeling in the Signed Cumulative Distribution Transform Domaincited by 0
  9. 2025Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognitioncited by 0