On Shift-Invariant Sparse Coding

The goals of this paper are: 1) the introduction of a shiftinvariant sparse coding model together with learning rules for this model; 2) the comparison of this model to the traditional sparse coding model; and 3) the analysis of some limitations of the newly proposed approach. To evaluate the model we will show that it can learn features from a toy problem as well as note-like features from a polyphonic piano recording. We further show that the shift-invariant model can help in overcoming some of the limitations of the traditional model which occur when learning less functions than are present in the true generative model. We finally show a limitation of the proposed model for problems in which mixtures of continuously shifted functions are used.