CLUSTERING FUNCTIONAL DATA USING WAVELETS

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.