Learning Topographic Sparse Coding through Similarity Function

In this paper, we present a novel method to learn the topographic and sparse representation from the natural images. By using two kinds of similarity functions onto the sparse coding bases learned from natural images respectively, we find that these Gabor-like bases inherently contain the topographic information. This method makes those similar bases be close to each other and a topographic organization emerged in the 2-D space. These two kinds of similarity functions are: basis functions similarity in classical sparse model [7] and analysis vectors similarity in encoder/decoder model [2]. Traditional topographic ICA [3] and topographic sparse coding [6] that contain two layer network, however, our proposed model can generate the topographic visualization by using one layer network. The simulation results demonstrate that these two kinds of similarity functions can produce distinct topographic organization of bases, and the analysis vectors similarity provides better results.