Sparse Matrix Factorization

11/13/2013

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by   Behnam Neyshabur, et al.

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We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and values of hidden units. We prove that under certain assumptions for a sparse linear deep network with n nodes in each layer, our algorithm is able to recover the structure of the network and values of top layer hidden units for depths up to Õ(n^1/6). We further discuss the relation among sparse matrix factorization, deep learning, sparse recovery and dictionary learning.