A Bilinear Model for Sparse Coding

Recent algorithms for sparse coding and independent component analy- sis (ICA) have demonstrated how localized features can be learned from natural images. However, these approaches do not take image transfor- mations into account. As a result, they produce image codes that are redundant because the same feature is learned at multiple locations. We describe an algorithm for sparse coding based on a bilinear generative model of images. By explicitly modeling the interaction between im- age features and their transformations, the bilinear approach helps reduce redundancy in the image code and provides a basis for transformation- invariant vision. We also explore an extension of the model that can capture spatial relationships between the independent features of an ob- ject, thereby providing a new framework for parts-based object recogni- tion.