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|
|Number of pages||27|
|State||Published - Apr 3 2020|
ASJC Scopus subject areas
- Computer Science(all)