Skip to Main content Skip to Navigation
Reports

Clustering functional data using wavelets

Anestis Antoniadis 1 Xavier Brossat 2 Jairo Cugliari 2, 3, 4, * Jean-Michel Poggi 4, 3
* Corresponding author
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK [2007-2015] - Laboratoire Jean Kuntzmann [2007-2015], Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019]
4 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
Abstract : We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based 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 method uses the distribution of energy across scales generate a handy number of features that can be sufficient to still 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 method uses dissimilarity measures between the whole time-scale representations and are based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these dissimilarities. Practical performance of these methods that jointly designs both the feature selection in the wavelet domain and the classification distance is demonstrated through simulations as well as daily profiles of the French electricity power demand.
Complete list of metadatas

https://hal.inria.fr/inria-00559115
Contributor : Jairo Cugliari <>
Submitted on : Wednesday, May 18, 2011 - 12:50:45 PM
Last modification on : Wednesday, October 14, 2020 - 3:59:18 AM
Long-term archiving on: : Friday, August 19, 2011 - 2:20:15 AM

Files

RR-7515.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00559115, version 2

Collections

Citation

Anestis Antoniadis, Xavier Brossat, Jairo Cugliari, Jean-Michel Poggi. Clustering functional data using wavelets. [Research Report] RR-7515, INRIA Grenoble - Rhone-Alpes. 2011, pp.30. ⟨inria-00559115v2⟩

Share

Metrics

Record views

771

Files downloads

2371