Homology, Homotopy and Applications

A fast algorithm for constructing topological structure in large data

Xu Liu, Zheng Xie, and Dongyun Yi

Full-text: Open access

Abstract

Discovering and constructing the topological structure in data has attracted the attention within the community of data analysis. However, most methods developed so far are unsuitable for very large sets of data because of their computational difficulties. This paper presents a fast algorithm for constructing the inherent topological structure in large sets of data that might be noisy in order to enhance the MAPPER algorithm introduced by Singh, Mémoli and Carlsson. The limitation of our method, as shown by our experiments, lies with the storage in the main memory rather than the computing time.

Article information

Source
Homology Homotopy Appl., Volume 14, Number 1 (2012), 221-238.

Dates
First available in Project Euclid: 12 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.hha/1355321072

Mathematical Reviews number (MathSciNet)
MR2954674

Zentralblatt MATH identifier
1243.68162

Subjects
Primary: 11F23: Relations with algebraic geometry and topology 68U05: Computer graphics; computational geometry [See also 65D18] 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Keywords
Data analysis topological structure complex network clustering Betti number

Citation

Liu, Xu; Xie, Zheng; Yi, Dongyun. A fast algorithm for constructing topological structure in large data. Homology Homotopy Appl. 14 (2012), no. 1, 221--238. https://projecteuclid.org/euclid.hha/1355321072


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