Title: Persistence Codebooks for Topological Data Analysis,
Abstract: Topological data analysis, such as persistent homology has shown beneficial
properties for machine learning in many tasks. Topological representations,
such as the persistence diagram (PD), however, have a complex structure
(multiset of intervals) which makes it difficult to combine with typical
machine learning workflows. We present novel compact fixed-size vectorial
representations of PDs based on clustering and bag of words encodings that cope
well with the inherent sparsity of PDs. Our novel representations outperform
state-of-the-art approaches from topological data analysis and are
computationally more efficient.