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

• URL: http://arxiv.org/abs/2608.28799v1
• Date: Fri, 28 Aug 2026 19:06:31 GMT
• Title: Separable Nonnegative Matrix Factorization Using Powered Ratio-of-Norms Regularization
• Abstract summary: Separable nonnegative matrix factorization (SNMF) has been widely used for low-rank representation and clustering of nonnegative data.<n>We propose a $ellp/ell$-regularized SNMF model based on a powered ratio of--of---norms regularizer.<n>The proposed approach achieves competitive or improved performance in anchor identification and classification accuracy compared with existing SNMF methods.
• Score: 9.066517501323423
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Separable nonnegative matrix factorization (SNMF) has been widely used for low-rank representation and clustering of nonnegative data, owing to its ability to produce part-based and interpretable decompositions. In particular, SNMF is closely related to graph clustering and community detection. To enhance sparsity and identifiability of the learned factors, we propose an $\ell_1^p/\ell_2$-regularized SNMF model based on a powered ratio-of-norms regularizer. The resulting formulation is nonconvex and nonsmooth, which poses significant challenges for optimization. To address this, we develop efficient algorithms based on the difference-of-convex function algorithm (DCA) and the alternating direction method of multipliers (ADMM). The proposed methods decompose the original problem into tractable subproblems, leveraging closed-form proximal operators associated with the powered norm terms. We establish descent and limiting criticality properties for the DCA scheme and convergence under standard assumptions for the ADMM scheme. Extensive numerical experiments on synthetic datasets and hand gesture classification tasks demonstrate that the proposed approach achieves competitive or improved performance in anchor identification and classification accuracy compared with existing SNMF methods, while maintaining competitive computational efficiency.

Related papers

• Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization [5.524295668575852]
  We propose persistent nonnegative matrix factorization (pNMF) that produces a sequence of persistence-aligned embeddings rather than a single one.<n>We analyze the structural properties of the embeddings along the scale parameter and establish bounds on their increments between consecutive scales.<n>The resulting model defines a nontrivial solution path across scales, rather than a single factorization, which poses new computational challenges.
  arXiv  Detail & Related papers  (2026-02-26T02:23:50Z)
• Principled Algorithms for Optimizing Generalized Metrics in Binary Classification [53.604375124674796]
  We introduce principled algorithms for optimizing generalized metrics, supported by $H$-consistency and finite-sample generalization bounds.<n>Our approach reformulates metric optimization as a generalized cost-sensitive learning problem.<n>We develop new algorithms, METRO, with strong theoretical performance guarantees.
  arXiv  Detail & Related papers  (2025-12-29T01:33:42Z)
• Matrix Factorization for Inferring Associations and Missing Links [5.700773330654261]
  Missing link prediction identifies unseen but potentially existing connections in a network.<n>In proliferation detection, this supports efforts to identify and characterize attempts by state and non-state actors to acquire nuclear weapons.<n>We introduce novel weighted (WNMFk), Boolean (BNMFk), and Recommender (RNMFk) matrix factorization methods, along with ensemble variants incorporating logistic factorization, for link prediction.
  arXiv  Detail & Related papers  (2025-03-06T18:22:46Z)
• A Fresh Look at Generalized Category Discovery through Non-negative Matrix Factorization [83.12938977698988]
  Generalized Category Discovery (GCD) aims to classify both base and novel images using labeled base data. Current approaches inadequately address the intrinsic optimization of the co-occurrence matrix $barA$ based on cosine similarity. We propose a Non-Negative Generalized Category Discovery (NN-GCD) framework to address these deficiencies.
  arXiv  Detail & Related papers  (2024-10-29T07:24:11Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)
• Supervised Class-pairwise NMF for Data Representation and Classification [2.7320863258816512]
  Non-negative Matrix factorization (NMF) based methods add new terms to the cost function to adapt the model to specific tasks. NMF method adopts unsupervised approaches to estimate the factorizing matrices.
  arXiv  Detail & Related papers  (2022-09-28T04:33:03Z)
• Log-based Sparse Nonnegative Matrix Factorization for Data Representation [55.72494900138061]
  Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness in representing nonnegative data with parts-based representations. We propose a new NMF method with log-norm imposed on the factor matrices to enhance the sparseness. A novel column-wisely sparse norm, named $ell_2,log$-(pseudo) norm, is proposed to enhance the robustness of the proposed method.
  arXiv  Detail & Related papers  (2022-04-22T11:38:10Z)
• Jointly Modeling and Clustering Tensors in High Dimensions [6.072664839782975]
  We consider the problem of jointly benchmarking and clustering of tensors. We propose an efficient high-maximization algorithm that converges geometrically to a neighborhood that is within statistical precision.
  arXiv  Detail & Related papers  (2021-04-15T21:06:16Z)
• Self-supervised Symmetric Nonnegative Matrix Factorization [82.59905231819685]
  Symmetric nonnegative factor matrix (SNMF) has demonstrated to be a powerful method for data clustering. Inspired by ensemble clustering that aims to seek better clustering results, we propose self-supervised SNMF (S$3$NMF) We take advantage of the sensitivity to code characteristic of SNMF, without relying on any additional information.
  arXiv  Detail & Related papers  (2021-03-02T12:47:40Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• Augmentation of the Reconstruction Performance of Fuzzy C-Means with an Optimized Fuzzification Factor Vector [99.19847674810079]
  Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information granules. In this paper, we augment the FCM-based degranulation mechanism by introducing a vector of fuzzification factors. Experiments completed for both synthetic and publicly available datasets show that the proposed approach outperforms the generic data reconstruction approach.
  arXiv  Detail & Related papers  (2020-04-13T04:17:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.