phaidra.ustp.at o:4470 DOI https://doi.org/10.1007/s10462-020-09897-4 Persistence codebooks for topological data analysis Fachhochschule St. Pölten 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 eng Persistent homology Machine learning Persistence diagrams Bag of words VLAD Fisher vectors 2021-07-20T13:29:21.358Z LOMv1.0 Author BEGIN:VCARD VERSION:3.0 N:Zeppelzauer;Matthias; FN:Matthias Zeppelzauer END:VCARD BEGIN:VCARD VERSION:3.0 N:Dłotko;Paweł; FN:Paweł Dłotko END:VCARD BEGIN:VCARD VERSION:3.0 N:Zieliński;Bartosz; FN:Bartosz Zieliński END:VCARD BEGIN:VCARD VERSION:3.0 N:Lipiński;Michał; FN:Michał Lipiński END:VCARD BEGIN:VCARD VERSION:3.0 N:;Mateusz; FN:Mateusz END:VCARD https://w3id.org/kim/hcrt/scheme https://w3id.org/kim/hcrt/text Textdokument Text LOMv1.0 yes https://creativecommons.org/licenses/by/4.0 application/pdf 3305321 https://phaidra.ustp.at/o:4470 https://phaidra.ustp.at/api/object/o:4470/thumbnail LOMv1.0 discipline