93 research outputs found
Sparse Matrix Factorization
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 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 . We further discuss the
relation among sparse matrix factorization, deep learning, sparse recovery and
dictionary learning.Comment: 20 page
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