Geometric metrics for topological representations

Anirudh Som, Karthikeyan Natesan Ramamurthy, Pavan Turaga

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations

Abstract

In this chapter, we present an overview of recent techniques from the emerging area of topological data analysis (TDA), with a focus on machinelearning applications. TDA methods are concerned with measuring shape-related properties of point-clouds and functions, in a manner that is invariant to topological transformations. With a careful design of topological descriptors, these methods can result in a variety of limited, yet practically useful, invariant representations. The generality of this approach results in a flexible design choice for practitioners interested in developing invariant representations from diverse data sources such as image, shapes, and time-series data. We present a survey of topological representations and metrics on those representations, discuss their relative pros and cons, and illustrate their impact on a few application areas of recent interest.

Original languageEnglish (US)
Title of host publicationHandbook of Variational Methods for Nonlinear Geometric Data
PublisherSpringer International Publishing
Pages415-441
Number of pages27
ISBN (Electronic)9783030313517
ISBN (Print)9783030313500
StatePublished - Apr 3 2020

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science(all)

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