Group Invariant Scattering

Pattern classification often requires using translation invariant representations, which are stable and hence Lipschitz continuous to deformations. A Fourier transform does not provide such Lipschitz stability. Scattering operators are obtained by iterating on wavelet transforms and modulus operators. The resulting representation is proved to be translation invariant and Lipschitz continuous to deformations, up to a log term. It is computed with a non-linear convolution network, which scatters functions along an infinite set of paths. Invariance to the action of any compact Lie subgroup of the general linear group is obtained with a combined scattering, which iterates over wavelet transforms defined on this group. Scattering representations yield new metrics on stationary processes, which are stable to random deformations.