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Perturbation Robust Representations of Topological Persistence Diagrams

  • Anirudh SomEmail author
  • Kowshik Thopalli
  • Karthikeyan Natesan Ramamurthy
  • Vinay Venkataraman
  • Ankita Shukla
  • Pavan Turaga
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11211)

Abstract

Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in non-linear dynamical modeling. The increasing success of these methods is attributed to the complementary information that topology provides, as well as availability of tools for computing topological summaries such as persistence diagrams. However, persistence diagrams are multi-sets of points and hence it is not straightforward to fuse them with features used for contemporary machine learning tools like deep-nets. In this paper we present theoretically well-grounded approaches to develop novel perturbation robust topological representations, with the long-term view of making them amenable to fusion with contemporary learning architectures. We term the proposed representation as Perturbed Topological Signatures, which live on a Grassmann manifold and hence can be efficiently used in machine learning pipelines. We explore the use of the proposed descriptor on three applications: 3D shape analysis, view-invariant activity analysis, and non-linear dynamical modeling. We show favorable results in both high-level recognition performance and time-complexity when compared to other baseline methods.

Keywords

Invariance learning Topological data analysis Persistence diagrams Grassmann manifold Perturbed topological signature 

Notes

Acknowledgments

This work was supported in part by ARO grant number W911NF-17-1-0293 and NSF CAREER award 1452163.

Supplementary material

474212_1_En_38_MOESM1_ESM.pdf (1.1 mb)
Supplementary material 1 (pdf 1126 KB)

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Authors and Affiliations

  1. 1.Geometric Media LabArizona State UniversityTempeUSA
  2. 2.IBM Thomas J. Watson Research CenterYorktown HeightsUSA
  3. 3.Indraprastha Institute of Information Technology-DelhiDelhiIndia

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