arXiv Machine Learning June 19, 2026 By Atharva Awari, Nicolas Gillis, Arnaud Vandaele

Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositions

Read the original on arXiv Machine Learning →

arXiv:2512. 17473v3 Announce Type: replace-cross Abstract: We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD).

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arXiv Machine Learning

Aug 11

Understanding Alternating Minimization for Matrix Completion

arXiv:1312. 0925v4 Announce Type: replace Abstract: Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems.

By Moritz Hardt

arXiv Machine Learning

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Maximum-Volume Nonnegative Matrix Factorization

arXiv:2602. 04795v3 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) is a popular data embedding technique.

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arXiv Machine Learning

Jul 16

An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence

arXiv:2607. 13919v1 Announce Type: new Abstract: Nonnegative Matrix Factorization (NMF) is a fundamental tool in unsupervised learning, which approximates a nonnegative matrix by the product of two low-rank nonnegative factors.

By Damien Lesens, J\'er\'emy E. Cohen, Bora U\c{c}ar

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arXiv Machine Learning

Sep 21

Nonnegative Matrix Factorization in the Component-Wise L1 Norm for Sparse Data

arXiv:2603.29715v2 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, X, by the product of two nonnegative factors, WH, where W has r columns a...

By Giovanni Seraghiti, K\'evin Dubrulle, Arnaud Vandaele, Nicolas Gillis

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arXiv Machine Learning

Sep 1

Separable Nonnegative Matrix Factorization Using Powered Ratio-of-Norms Regularization

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By Matthew McCarver, Jing Qin

efficiency

arXiv Machine Learning

Jul 14

Demixing Sparse Signals from Nonlinear Observations using Generalized Non-convex Regularization

arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.

By Raziyeh Takbiri

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