Homology, Homotopy and Applications
Volume 14 (2012)
A fast algorithm for constructing topological structure in large data
Pages: 221 – 238
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.
data analysis, topological structure, complex network, clustering, Betti number
2010 Mathematics Subject Classification
11F23, 62H30, 68U05