o:4470 Persistence codebooks for topological data analysis en 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. Fachhochschule St. Pölten St. Pölten University of Applied Sciences Persistent homology Machine learning Persistence diagrams Bag of words VLAD Fisher vectors 1552099 https://doi.org/10.1007/s10462-020-09897-4 1552102 https://link.springer.com/article/10.1007%2Fs10462-020-09897-4 1552101 1573-7462 2021-07-15T12:31:43.096Z 44 yes 46 Matthias Zeppelzauer Media Computing Group, Institute of Creative Media Technologies, St. Pölten University of Applied Sciences Paweł Dłotko Dioscuri Centre in Topological Data Analysis, Institute of Mathematics, Polish Academy of Sciences person Bartosz Zieliński Institute of Computer Science and Computer Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University person Michał Lipiński Institute of Computer Science and Computer Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University person Mateusz Institute of Computer Science and Computer Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University person 1556250 application/pdf 3305321 https://phaidra.fhstp.ac.at/o:4470 no yes 16 Copyright © 2020, The Author(s) 70 1552253 4 Artificial Intelligence Review 54 3 1969 2009 Springer Nature 2020-09-01