Product Sparse Coding

Sparse coding is a widely involved technique in computer vision. However, the expensive computational cost can hamper its applications, typically when the codebook size must be limited due to concerns on running time. In this paper, we study a special case of sparse coding in which the codebook is a Cartesian product of two subcodebooks. We present algorithms to decompose this sparse coding problem into smaller subproblems, which can be separately solved. Our solution, named as Product Sparse Coding (PSC), reduces the time complexity from O(K) to O(√K) in the codebook size K. In practice, this can be 20-100× faster than standard sparse coding. In experiments we demonstrate the efficiency and quality of this method on the applications of image classification and image retrieval.