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 language | English (US) |
---|---|
Title of host publication | Handbook of Variational Methods for Nonlinear Geometric Data |
Publisher | Springer International Publishing |
Pages | 415-441 |
Number of pages | 27 |
ISBN (Electronic) | 9783030313517 |
ISBN (Print) | 9783030313500 |
State | Published - Apr 3 2020 |
ASJC Scopus subject areas
- General Mathematics
- General Computer Science