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Clustering Noisy Signals with Structured Sparsity Using Time-Frequency Representation

We propose a simple and efficient time-series clustering framework particularly suited for low Signal-to-Noise Ratio (SNR), by simultaneous smoothing and dimensionality reduction aimed at preserving clustering information. We extend the sparse K-means algorithm by incorporating structured sparsity, and use it to exploit the multi-scale property of wavelets and group structure in multivariate signals. Finally, we extract features invariant to translation and scaling with the scattering transform, which corresponds to a convolutional network with filters given by a wavelet operator, and use the network's structure in sparse clustering. By promoting sparsity, this transform can yield a low-dimensional representation of signals that gives improved clustering results on several real datasets.