Group Invariant Dictionary Learning

The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection basic building blocks. In application domains where such techniques are deployed, we frequently encounter datasets some form symmetry or invariance is present. Motivated by this observation, develop framework for dictionaries under constraint that blocks remains invariant symmetries. Our procedure relies on action matrix group acting data, and subsequently introducing convex penalty function so to induce sparsity with respect elements. specializes convolutional when consider integer shifts. Using properties positive semidefinite Hermitian Toeplitz matrices, an extension learns continuous numerical experiments synthetic ECG show incorporation symmetries priors most valuable dataset has few data-points, full range inadequately expressed in dataset.