Nonnegative Matrix Factorization in the Component-Wise L1 Norm for Sparse Data
Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, X, by the product of two nonnegative factors, WH, where W has r columns and H has r rows. In this paper, we consider NMF using the component-wise L1 norm as the error measure (L1-NMF), which is suited for data corrupted by heavy-tailed noise, such as Laplace noise or salt and pepper noise, or in the presence of outliers. Our first contribution is an NP-hardness proof for L1-NMF, even when r=1, in contrast to the standard NMF that uses least squares. Our second contribution is to analyze, under simplified probabilistic assumptions, how the sparsity in the data enforces zero solution in the optimal scalar update in th...
| Authors | Giovanni Seraghiti, Kévin Dubrulle, Arnaud Vandaele et al. |
|---|---|
| Primary category | cs.LG |
| Published | 31 March 2026 |
| Last updated at source | 18 September 2026 |
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