doi:https://doi.org/10.1007/s10462-020-09897-4 HTTP/WWW: https://link.springer.com/article/10.1007%2Fs10462-020-09897-4 ISSN: 1573-7462 https://phaidra.ustp.at/o:4470 application/pdf Springer Nature Copyright © 2020, The Author(s) Persistence codebooks for topological data analysis 2020-09-01 article eng ISSN:1573-7462 Artificial Intelligence Review 54(3), 1969-2009 (2020-09-01) Fachhochschule St. Pölten Persistent homology Machine learning Persistence diagrams Bag of words VLAD Fisher vectors CC BY 4.0 International http://creativecommons.org/licenses/by/4.0/ Zeppelzauer, Matthias (Media Computing Group, Institute of Creative Media Technologies, St. Pölten University of Applied Sciences) Dłotko, Paweł (Dioscuri Centre in Topological Data Analysis, Institute of Mathematics, Polish Academy of Sciences) Zieliński, Bartosz (Institute of Computer Science and Computer Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University) Lipiński, Michał (Institute of Computer Science and Computer Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University) Mateusz (Institute of Computer Science and Computer Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University) Persistent homology is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine with typical machine learning workflows. In this paper we introduce persistence codebooks, a novel expressive and discriminative fixed-size vectorized representation of PDs that adapts to the inherent sparsity of persistence diagrams. To this end, we adapt bag-of-words, vectors of locally aggregated descriptors and Fischer vectors for the quantization of PDs. Persistence codebooks represent PDs in a convenient way for machine learning and statistical analysis and have a number of favorable practical and theoretical properties including 1-Wasserstein stability. We evaluate the presented representations on several heterogeneous datasets and show their (high) discriminative power. Our approach yields comparable—and partly even higher—performance in much less time than alternative approaches. St. Pölten University of Applied Sciences