Geometric metrics for topological representations

Anirudh Som, Karthikeyan Natesan Ramamurthy, Pavan Turaga

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations


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
Number of pages27
ISBN (Electronic)9783030313517
ISBN (Print)9783030313500
StatePublished - Apr 3 2020

ASJC Scopus subject areas

  • General Mathematics
  • General Computer Science


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