Persistence codebooks for topological data analysis

被引:8
作者
Zielinski, Bartosz [1 ]
Lipinski, Michal [1 ]
Juda, Mateusz [1 ]
Zeppelzauer, Matthias [2 ]
Dlotko, Pawel [3 ]
机构
[1] Jagiellonian Univ, Inst Comp Sci & Comp Math, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland
[2] St Polten Univ Appl Sci, Media Comp Grp, Inst Creat Media Technol, Matthias Corvinus Str 15, A-3100 St Polten, Austria
[3] Polish Acad Sci, Dioscuri Ctr Topol Data Anal, Inst Math, Jana & Jedrzeja Sniadeckich 8, PL-00656 Warsaw, Poland
关键词
Persistent homology; Machine learning; Persistence diagrams; Bag of words; VLAD; Fisher vectors; HOMOLOGY;
D O I
10.1007/s10462-020-09897-4
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
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.
引用
收藏
页码:1969 / 2009
页数:41
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