Motivated by orthogonal dictionary learning problems, we propose a novel method for matrix factorization, where the data matrix is a product of a Householder matrix and a binary matrix . First, we show that the exact recovery of the factors and from is guaranteed with columns in . Next, we show approximate recovery (in the sense) can be done in polynomial time() with columns in . We hope the techniques in this work help in developing alternate algorithms for orthogonal dictionary learning.
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