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Abstract:
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Non-negative Matrix Factorization(NMF) is a popular clustering and dimension reduction method by decomposing a non-negative matrix into the product of two lower dimension matrices composed of basis vectors. In this paper, we propose a Semi-orthogonal NMF method that enforces one of the matrix to be orthogonal, thereby preserving the rank of the factorization and providing an alternative interpretation. Our method guarantees strict orthogonality by implementing the Cayley Transformation to force the solution path to be on the Stiefeld Manifold, as opposed to the approximated orthogonality solutions in existing literature. We apply a line search update scheme along with an SVD-based initialization which results in rapid convergence of the algorithm compared to other popular update schemes. In addition, we present two separate formulations of our method for both continuous and binary design matrices. Through experiments on various simulated data sets, we show that our model has an advantage over other NMF variations regarding the accuracy of the factorization, rate of convergence, and especially the degree of orthogonality, while also being computationally competitive.
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