TitlePersistence Codebooks for Topological Data Analysis
Publication TypeJournal Article
Year of Publication2018
AuthorsZielinski, B., M. Juda, and M. Zeppelzauer
JournalarXiv preprint arXiv:1802.04852
KeywordsBag of Words, Computational Topology, Machine learning, pattern recognition, Persistence diagram, Persistence Homology, Topological Data Analysis
AbstractTopological 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.