Supervised learning often requires that data lies on some low dimensional manifolds, which is not valid for very high dimensional signals such as images or sounds. The physics of the signal world induce high degree of variability due to finite group transformations such as translations,
rotations, scaling... and infinite dimensional groups of deformations. Signals can be mapped to lower dimensional manifold while preserving discriminating information,
by building representations which are invariant to finite group actions and Lipschitz continuous to deformations.
Scattering operators build such representations with convolution neural network architectures, which iteratively apply wavelet transforms and modulus operators. It also provides representations of stationary processes, including high order moments which discriminate different processes having same Fourier spectrum. Classification results are shown on structured image patterns, textures
and audio classification.
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