Clustering Functional Data using Wavelet

Anestis Antoniadis 1 Xavier Brossat 2 Jairo Cugliari 3 Jean-Michel Poggi 4
1 SAM - Statistique Apprentissage Machine
LJK - Laboratoire Jean Kuntzmann
3 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We present two strategies for detecting patterns and clusters in high-dimensional time-dependent functional data. The use on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first strategy uses the distribution of energy across scales to generate a representation that can be sufficient to make the signals well distinguishable. Our new similarity measure combined with an efficient feature selection technique in the wavelet domain is then used within more or less classical clustering algorithms to effectively differentiate among high-dimensional populations. The second strategy uses a similarity measure between the whole time-scale representations that is based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these similarities. Practical performance is illustrated through simulations as well as daily profiles of the French electricity power demand.
Type de document :
Article dans une revue
International Journal of Wavelets, Multiresolution and Information Processing, World Scientific Publishing, 2013, 11 (1), pp.1350003:1-30. 〈10.1142/S0219691313500033〉
Liste complète des métadonnées

https://hal.inria.fr/hal-00942684
Contributeur : Erwan Le Pennec <>
Soumis le : jeudi 6 février 2014 - 11:31:44
Dernière modification le : lundi 9 avril 2018 - 12:22:48

Identifiants

Collections

Citation

Anestis Antoniadis, Xavier Brossat, Jairo Cugliari, Jean-Michel Poggi. Clustering Functional Data using Wavelet. International Journal of Wavelets, Multiresolution and Information Processing, World Scientific Publishing, 2013, 11 (1), pp.1350003:1-30. 〈10.1142/S0219691313500033〉. 〈hal-00942684〉

Partager

Métriques

Consultations de la notice

634