Abstract
Nonnegative matrix factorization (NMF) was a classic model for dimensional reduction. Manhattan NMF is a variant version of NMF that uses a L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm cost function as the objective function instead of the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -norm cost function. Manhattan NMF can be formulated as a nonconvex nonsmooth optimization problem. An algorithm framework for solving the Manhattan NMF problem based on the alternating direction method of multiplication is presented to us. Compared with the existed algorithm, our proposed algorithm is more effective by experiments on synthetic and real data sets.
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