A Bilinear Model for Sparse Coding

Recent algorithms for sparse coding and independent component analysis (ICA)have demonstrated how localized features can be learned from natural images. However, these approaches do not take image transformations intoaccount. 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 image featuresand their transformations, the bilinear approach helps reduce redundancy in the image code and provides a basis for transformationinvariant vision.We present results demonstrating bilinear sparse coding of natural images. We also explore an extension of the model that can capture spatial relationships between the independent features of an object, therebyproviding a new framework for parts-based object recognition.