Non-negative reduced biquaternion matrix factorization (NRBMF) uses the product of reduced biquaternion (RB) matrices to incorporate the non-negativity constraints of color image pixels into the factorization process. However, NRBMF mainly focuses on reconstruction accuracy and does not exploit the local geometric structure of image data, which may limit the discriminative ability of the learned low-dimensional features.
arXiv:2606. 08291v1 Announce Type: new Abstract: We study the symmetric multi-type orthogonal non-negative matrix tri-factorization problem, where several symmetric non-negative matrices are simultaneously approximated by factors of the form $GS_{i}G^{\top}$, with a shared non-negative and orthogonal factor $G$.
arXiv:2608.28799v1 Announce Type: cross Abstract: Separable nonnegative matrix factorization (SNMF) has been widely used for low-rank representation and clustering of nonnegative data, owing to its a...
arXiv:2606. 02887v1 Announce Type: new Abstract: Symmetric nonnegative matrix factorization (Symmetric NMF) approximates a matrix as $WW^T$ with nonnegative rectangular factor $W$.
arXiv:2607. 20084v1 Announce Type: cross Abstract: Non--negative matrix factorization (NMF) has become an established dimensionality reduction technique for extracting latent structures from non--negative data and has found widespread applications in fields such as bioinformatics, text mining, image analysis, and recommender systems.
arXiv:2407. 21740v3 Announce Type: replace-cross Abstract: Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness.
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...
arXiv:2602. 04795v3 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) is a popular data embedding technique.
arXiv:2608. 12757v1 Announce Type: cross Abstract: Laplacian-regularized minimization is fundamental in signal processing and machine learning, but is limited by the dense and ill-conditioned nature of the graph Laplacian pseudoinverse.
The paper introduces an efficient method for learning balanced signed graph Laplacians directly from data. By extending the CLIME sparse inverse covariance estimation framework, it formulates a linear programming problem for each Laplacian column with sign constraints that enforce positive edges between nodes of the same polarity and negative edges otherwise. The authors develop a tailored ADMM-based sparse LP solver, prove convergence properties, and demonstrate through experiments that the learned balanced graphs outperform existing methods and allow the reuse of spectral filtering tools, wavelets, and graph neural networks designed for positive graphs.
arXiv:2412. 07041v4 Announce Type: replace-cross Abstract: Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications.
arXiv:2511. 07109v2 Announce Type: replace-cross Abstract: Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling.
arXiv:2609.14307v1 Announce Type: new Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, u...