Parsimonious Convolutional Representations -- application to physiological signals and deep learning interpetability.

Summary Convolutional representations extract recurrent patterns that help to understand the local structure in a set of signals. They are suitable for physiological signal analysis, which requires visualizations that highlight relevant information. These representations are also related to deep learning models. In this manuscript, we describe algorithmic and theoretical advances around these models. We first show that Singular Spectrum Analysis can efficiently compute a convolutional representation. This representation is dense and we describe an automated procedure to make it more interpretable. We then propose an asynchronous algorithm to accelerate convolutional parsimonious coding. Our algorithm presents a super-linear acceleration. In a second part, we analyze the links between representations and neural networks. We propose an additional learning step, called post-training, which improves the performance of the trained network by ensuring that the last layer is optimal. Then we study the mechanisms that make it possible to accelerate parsimonious coding with neural networks. We show that this is related to a factorization of the Gram matrix of the dictionary. Finally, we illustrate the interest of using convolutional representations for physiological signals. Convolutional dictionary learning is used to summarize walking signals and gaze motion is subtracted from oculometric signals with Singular Spectrum Analysis.