Learning metrics for persistence-based summaries and applications for
graph classification
release_e5l5nh5pbzhodnwwwtvnekwqwq
by
Qi Zhao, Yusu Wang
2019
Abstract
Recently a new feature representation and data analysis methodology based on
a topological tool called persistent homology (and its corresponding
persistence diagram summary) has started to attract 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, and in these approaches, the importance (weight) of different
persistence features are often preset. However often in practice, the choice of
the weight function should depend on the nature of the specific type of data
one considers, and 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 a good metric for
persistence summaries. Both our kernel and optimization problem have nice
properties. We further 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 a
collection of benchmark datasets.
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