Learnable Group Transform For Time-Series

We propose a novel approach to filter bank learning for time-series by considering spectral decompositions of signals defined as a Group Transform. This framework allows us to generalize classical time-frequency transformations such as the Wavelet Transform, and to efficiently learn the representation of signals. While the creation of the wavelet transform filter-bank relies on affine transformations of a mother filter, our approach allows for non-linear transformations. The transformations induced by such maps enable us to span a larger class of signal representations, from wavelet to chirplet-like filters. We propose a parameterization of such a non-linear map such that its sampling can be optimized for a specific task and signal. The Learnable Group Transform can be cast into a Deep Neural Network. The experiments on diverse time-series datasets demonstrate the expressivity of this framework, which competes with state-of-the-art performances.