MahNMF: Manhattan Non-negative Matrix Factorization

Understand

Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$.

• NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between $X$ and $W^T H$ to model the Poisson noise or the Gaussian noise.
• In practice, when the noise distribution is heavy tailed, they cannot perform well.
• This paper presents Manhattan NMF (MahNMF) which minimizes the Manhattan distance between $X$ and $W^T H$ for modeling the heavy tailed Laplacian noise.