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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\u2014and partly even higher\u2014performance in much less time than alternative approaches.<\/jats:p>","DOI":"10.1007\/s10462-020-09897-4","type":"journal-article","created":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T18:35:06Z","timestamp":1598985306000},"page":"1969-2009","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Persistence codebooks for topological data analysis"],"prefix":"10.1007","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3063-3621","authenticated-orcid":false,"given":"Bartosz","family":"Zieli\u0144ski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Micha\u0142","family":"Lipi\u0144ski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mateusz","family":"Juda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthias","family":"Zeppelzauer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pawe\u0142","family":"D\u0142otko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,9,1]]},"reference":[{"key":"9897_CR1","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.cviu.2013.10.014","volume":"121","author":"ADRGC Aadcock","year":"2014","unstructured":"Aadcock ADRGC (2014) Classification of hepatic lesions using the matching metric. 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