As the field of Topological Data Analysis continues to show success in theory and in applications, there has been increasing interest in using tools from this field with methods for machine learning. Using persistent homology, specifically persistence diagrams, as inputs to machine learning techniques requires some mathematical creativity. The space of persistence diagrams does not have the desirable properties for machine learning, thus methods such as kernel methods and vectorization methods have been developed. One such featurization of persistence diagrams by Perea, Munch and Khasawneh uses continuous, compactly supported functions, referred to as "template functions," which results in a stable vector representation of the persistence diagram. In this paper, we provide a method of adaptively partitioning persistence diagrams to improve these featurizations based on localized information in the diagrams. Additionally, we provide a framework to adaptively select parameters required for the template functions in order to best utilize the partitioning method. We present results for application to example data sets comparing classification results between template function featurizations with and without partitioning, in addition to other methods from the literature.
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A Comparative Study of Machine Learning Methods for Persistence Diagrams
Many and varied methods currently exist for featurization, which is the process of mapping persistence diagrams to Euclidean space, with the goal of maximally preserving structure. However, and to our knowledge, there are presently no methodical comparisons of existing approaches, nor a standardized collection of test data sets. This paper provides a comparative study of several such methods. In particular, we review, evaluate, and compare the stable multi-scale kernel, persistence landscapes, persistence images, the ring of algebraic functions, template functions, and adaptive template systems. Using these approaches for feature extraction, we apply and compare popular machine learning methods on five data sets: MNIST, Shape retrieval of non-rigid 3D Human Models (SHREC14), extracts from the Protein Classification Benchmark Collection (Protein), MPEG7 shape matching, and HAM10000 skin lesion data set. These data sets are commonly used in the above methods for featurization, and we use them to evaluate predictive utility in real-world applications.
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- NSF-PAR ID:
- 10327579
- Date Published:
- Journal Name:
- Frontiers in Artificial Intelligence
- Volume:
- 4
- ISSN:
- 2624-8212
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/frai.2021.681174
