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Non-negative matrix factorization (NMF) is a prob- lem with many applications, ranging from facial recognition to document clustering. However, due to the variety of algorithms that solve NMF, the randomness involved in these algorithms,…

Numerical Analysis · Mathematics 2018-12-17 Connor Sell , Jeremy Kepner

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in…

Machine Learning · Computer Science 2007-05-23 Patrik O. Hoyer

This paper proposes two linear projection methods for supervised dimension reduction using only the first and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model…

Information Theory · Computer Science 2024-08-13 Biao Chen , Joshua Kortje

Community structures detection is one of the fundamental problems in complex network analysis towards understanding the topology structures of the network and the functions of it. Nonnegative matrix factorization (NMF) is a widely used…

Social and Information Networks · Computer Science 2018-01-22 Zhenhai Chang , Hui-Min Cheng , Chao Yan , Xianjun Yin , Zhong-Yuan Zhang

We study a general factor analysis framework where the $n$-by-$p$ data matrix is assumed to follow a general exponential family distribution entry-wise. While this model framework has been proposed before, we here further relax its…

Methodology · Statistics 2025-12-02 Liang Wang , Luis Carvalho

This article introduces new multiplicative updates for nonnegative matrix factorization with the $\beta$-divergence and sparse regularization of one of the two factors (say, the activation matrix). It is well known that the norm of the…

Machine Learning · Computer Science 2024-03-13 Arthur Marmin , José Henrique de Morais Goulart , Cédric Févotte

Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…

Computer Vision and Pattern Recognition · Computer Science 2017-07-31 Zhenxing Guo , Shihua Zhang

This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…

Optimization and Control · Mathematics 2013-02-05 Victor Bittorf , Benjamin Recht , Christopher Re , Joel A. Tropp

This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still…

Machine Learning · Computer Science 2010-06-15 Andri Mirzal , Masashi Furukawa

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a…

Machine Learning · Statistics 2015-01-26 Paul Honeine , Fei Zhu

Nonnegative matrix factorization (NMF) has been successfully applied to many areas for classification and clustering. Commonly-used NMF algorithms mainly target on minimizing the $l_2$ distance or Kullback-Leibler (KL) divergence, which may…

Information Retrieval · Computer Science 2014-10-07 Le Li , Jianjun Yang , Yang Xu , Zhen Qin , Honggang Zhang

Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…

Machine Learning · Computer Science 2023-11-07 Mengyuan Zhang , Kai Liu

We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and…

Machine Learning · Computer Science 2016-10-28 Thomas Brouwer , Jes Frellsen , Pietro Lio'

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

Computation · Statistics 2014-07-29 Tim Salimans , David A. Knowles

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…

Machine Learning · Statistics 2020-10-13 Viet Anh Nguyen , Xuhui Zhang , Jose Blanchet , Angelos Georghiou

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Machine Learning · Statistics 2014-01-10 Jason Gejie Liu , Shuchin Aeron

The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data…

Statistics Theory · Mathematics 2015-04-21 Jean Lafond

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

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are…

Information Theory · Computer Science 2015-11-23 Yangyang Xu , Wotao Yin , Zaiwen Wen , Yin Zhang

In this paper, we develop a new elegant framework relying on the Kullback-Leibler Information Criterion to address the design of one-stage adaptive detection architectures for multiple hypothesis testing problems. Specifically, at the…

Signal Processing · Electrical Eng. & Systems 2021-03-23 Pia Addabbo , Sudan Han , Fillippo Biondi , Gaetano Giunta , Danilo Orlando