Document Type
Article
Publication Date
2022
Publisher
Journal of Machine Learning Research (JMLR)
Source Publication
Journal of Machine Learning Research (JMLR)
Source ISSN
1532-4435
Abstract
In Topological Data Analysis, a common way of quantifying the shape of data is to use a persistence diagram (PD). PDs are multisets of points in R2 computed using tools of algebraic topology. However, this multi-set structure limits the utility of PDs in applications. Therefore, in recent years efforts have been directed towards extracting informative and efficient summaries from PDs to broaden the scope of their use for machine learning tasks. We propose a computationally efficient framework to convert a PD into a vector in Rn, called a vectorized persistence block (VPB). We show that our representation possesses many of the desired properties of vector-based summaries such as stability with respect to input noise, low computational cost and flexibility. Through simulation studies, we demonstrate the effectiveness of VPBs in terms of performance and computational cost for various learning tasks, namely clustering, classification and change point detection.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Chan, Kit C.; Islambekov, Umar; Luchinsky, Alexey; and Sanders, Rebecca, "A Computationally Efficient Framework for Vector Representation of Persistence Diagrams" (2022). Mathematical and Statistical Science Faculty Research and Publications. 131.
https://epublications.marquette.edu/math_fac/131
Comments
Published version. Journal of Machine Learning Research (JMLR), Vol. 23 (2022). Publisher link. © 2022 Journal of Machine Learning Research (JMLR). Used with permission.
CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/.