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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Persistent homology for time series and spatial data clustering

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Pereira, Cassio M. M. [1] ; de Mello, Rodrigo F. [1]
Total Authors: 2
[1] Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: EXPERT SYSTEMS WITH APPLICATIONS; v. 42, n. 15-16, p. 6026-6038, SEP 2015.
Web of Science Citations: 11

Topology is the branch of mathematics that studies how objects relate to one another for their qualitative structural properties, such as connectivity and shape. In this paper, we present an approach for data clustering based on topological features computed over the persistence diagram, estimated using the theory of persistent homology. The features indicate topological properties such as Betti numbers, i.e., the number of n-dimensional holes in the discretized data space. The main contribution of our approach is enabling the clustering of time series that have similar recurrent behavior characterized by their attractors in phase space and spatial data that have similar scale-invariant spatial distributions, as traditional clustering techniques ignore that information as they rely on point-to-point dissimilarity measures such as Euclidean distance or elastic measures. We present experiments that confirm the usefulness of our approach with time series and spatial data applications in the fields of biology, medicine and ecology. (C) 2015 Elsevier Ltd. All rights reserved. (AU)

FAPESP's process: 14/13323-5 - An approach based on the stability of clustering algorithms to ensure concept drift detection on data streams
Grantee:Rodrigo Fernandes de Mello
Support Opportunities: Regular Research Grants
FAPESP's process: 13/04453-0 - High dimensional data streams clustering
Grantee:Cássio Martini Martins Pereira
Support Opportunities: Scholarships in Brazil - Post-Doctoral