{"paper":{"title":"Persistence Codebooks for Topological Data Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AT"],"primary_cat":"stat.ML","authors_text":"Bartosz Zielinski, Mateusz Juda, Matthias Zeppelzauer, Michal Lipinski, Pawel Dlotko","submitted_at":"2018-02-13T20:49:01Z","abstract_excerpt":"Persistent homology (PH) 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. To this end, we adapt bag-of-words (BoW), vectors of locally aggregated descriptors (VLAD) and Fischer vectors (FV) for the quantization of PDs. Persistence codebooks represent PDs in a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04852","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}