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Title: Learning metrics for persistence-based summaries and applications for graph classification
Recently a new feature representation framework based on a topological tool called persistent homology (and its persistence diagram summary) has gained much momentum. A series of methods have been developed to map a persistence diagram to a vector representation so as to facilitate the downstream use of machine learning tools. In these approaches, the importance (weight) of different persistence features are usually pre-set. However often in practice, the choice of the weight-functions hould depend on the nature of the specific data at hand. It is thus highly desirable to learn a best weight-function (and thus metric for persistence diagrams) from labelled data. We study this problem and develop a new weighted kernel, called WKPI, for persistence summaries, as well as an optimization framework to learn the weight (and thus kernel). We apply the learned kernel to the challenging task of graph classification, and show that our WKPI-based classification framework obtains similar or (sometimes significantly) better results than the best results from a range of previous graph classification frameworks on benchmark datasets.  more » « less
Award ID(s):
1740761
NSF-PAR ID:
10180702
Author(s) / Creator(s):
;
Date Published:
Journal Name:
33rd Conf. Neural Information Processing Systems (NeuRIPS)
Page Range / eLocation ID:
9855-9866
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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