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Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilises the Bayesian non-negative matrix factorisation (NMF) model to produce a probabilistic…

Machine Learning · Statistics 2010-09-28 Ioannis Psorakis , Stephen Roberts , Ben Sheldon

Hypergraphs provide a powerful framework for modeling complex systems and networks with higher-order interactions beyond simple pairwise relationships. However, graph-based clustering approaches, which focus primarily on pairwise relations,…

Social and Information Networks · Computer Science 2025-07-16 Giuseppe F. Italiano , Athanasios L. Konstantinidis , Anna Mpanti , Fariba Ranjbar

Nonnegative matrix factorization (NMF), which is the approximation of a data matrix as the product of two nonnegative matrices, is a key issue in machine learning and data analysis. One approach to NMF is to formulate the problem as a…

Optimization and Control · Mathematics 2016-11-02 Hideaki Iiduka , Shizuka Nishino

The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found a promising clustering model and can outperform the classical…

Machine Learning · Computer Science 2021-07-29 Shuai Wang , Tsung-Hui Chang , Ying Cui , Jong-Shi Pang

Nonnegative Matrix Factorization (NMF) is a data analysis technique which allows compression and interpretation of nonnegative data. NMF became widely studied after the publication of the seminal paper by Lee and Seung (Learning the Parts…

Numerical Analysis · Mathematics 2008-10-24 Nicolas Gillis , François Glineur

Nonnegative matrix factorization (NMF) has been widely used to learn low-dimensional representations of data. However, NMF pays the same attention to all attributes of a data point, which inevitably leads to inaccurate representation. For…

Machine Learning · Computer Science 2021-11-30 Jiao Wei , Can Tong , Bingxue Wu , Qiang He , Shouliang Qi , Yudong Yao , Yueyang Teng

Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. We interpret the factorization in a new way and use it to generate missing attributes from test data. We provide a joint…

Numerical Analysis · Computer Science 2010-07-05 Mithun Das Gupta

Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular…

Machine Learning · Computer Science 2024-05-07 Farid Saberi-Movahed , Kamal Berahman , Razieh Sheikhpour , Yuefeng Li , Shirui Pan

In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…

Combinatorics · Mathematics 2016-08-15 Peter Diao , Dominique Guillot , Apoorva Khare , Bala Rajaratnam

Nonnegative Matrix Factorization (NMF) is a fundamental tool in unsupervised learning, widely used for tasks such as dimensionality reduction, feature extraction, representation learning, and topic modeling. Many algorithms have been…

Optimization and Control · Mathematics 2025-06-19 Mai-Quyen Pham , Jérémy Cohen , Thierry Chonavel

The Correlation Clustering problem is one of the most extensively studied clustering formulations due to its wide applications in machine learning, data mining, computational biology and other areas. We consider the Correlation Clustering…

Data Structures and Algorithms · Computer Science 2025-03-04 Jianqi Zhou , Zhongyi Zhang , Jiong Guo

Flat minima are strongly associated with improved generalisation in deep neural networks. However, this connection has proven nuanced in recent studies, with both theoretical counterexamples and empirical exceptions emerging in the…

Machine Learning · Computer Science 2026-04-16 Israel Mason-Williams , Gabryel Mason-Williams , Helen Yannakoudakis

Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…

Computational Complexity · Computer Science 2007-05-23 Jiri Sima , Satu Elisa Schaeffer

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise)…

Machine Learning · Computer Science 2021-02-10 Nicolas Gillis , Le Thi Khanh Hien , Valentin Leplat , Vincent Y. F. Tan

Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to…

Machine Learning · Computer Science 2021-09-07 Junjun Pan , Michael K. Ng

Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…

Machine Learning · Statistics 2016-11-18 Cem Aksoylar , Jing Qian , Venkatesh Saligrama

Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…

Numerical Analysis · Mathematics 2019-10-14 Pramod Kaushik Mudrakarta , Shubhendu Trivedi , Risi Kondor

We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…

Machine Learning · Statistics 2026-05-26 Sam Rosen , Jason Xu

This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean…

Machine Learning · Computer Science 2011-03-09 Cédric Févotte , Jérôme Idier

Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to "refine" or "improve" a given…

Machine Learning · Computer Science 2022-02-03 K. Fountoulakis , M. Liu , D. F. Gleich , M. W. Mahoney