Persistent homology for time series and spatial data clustering

Autor(es)

Pereira, Cassio M. M. ^[1] ; de Mello, Rodrigo F. ^[1]

Afiliação do(s) autor(es)

^[1] Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: EXPERT SYSTEMS WITH APPLICATIONS; v. 42, n. 15-16, p. 6026-6038, SEP 2015.
• Citações Web of Science: 11

Resumo

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)

• Processo FAPESP: 14/13323-5 - Abordagem baseada na estabilidade de algoritmos de agrupamento de dados para garantir a detecção de mudanças de conceito em fluxos de dados
• Beneficiário: Rodrigo Fernandes de Mello
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/04453-0 - Agrupamento de fluxos contínuos de dados de alta dimensionalidade
• Beneficiário: Cássio Martini Martins Pereira
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado