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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

As the amount of text data continues to grow, topic modeling is serving an important role in understanding the content hidden by the overwhelming quantity of documents. One popular topic modeling approach is non-negative matrix…

Information Retrieval · Computer Science 2022-08-23 Maksim E. Eren , Nick Solovyev , Manish Bhattarai , Kim Rasmussen , Charles Nicholas , Boian S. Alexandrov

Audio DNNs have demonstrated impressive performance on various machine listening tasks; however, most of their representations are computationally costly and uninterpretable, leaving room for optimization. Here, we propose a novel approach…

Sound · Computer Science 2025-08-20 Andrew Chang , Yike Li , Iran R. Roman , David Poeppel

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

Medical image segmentation is vital for modern healthcare and is a key element of computer-aided diagnosis. While recent advancements in computer vision have explored unsupervised segmentation using pre-trained models, these methods have…

Computer Vision and Pattern Recognition · Computer Science 2025-08-07 Mosong Ma , Tania Stathaki , Michalis Lazarou

Collaborative filtering is one of the most popular techniques in designing recommendation systems, and its most representative model, matrix factorization, has been wildly used by researchers and the industry. However, this model suffers…

Information Retrieval · Computer Science 2019-12-17 Yixin Su , Sarah Monazam Erfani , Rui Zhang

Nonnegative matrix factorization (NMF) is now a common tool for audio source separation. When learning NMF on large audio databases, one major drawback is that the complexity in time is O(FKN) when updating the dictionary (where (F;N) is…

Machine Learning · Statistics 2011-06-22 Augustin Lefèvre , Francis Bach , Cédric Févotte

Speech representation and modelling in high-dimensional spaces of acoustic waveforms, or a linear transformation thereof, is investigated with the aim of improving the robustness of automatic speech recognition to additive noise. The…

Computation and Language · Computer Science 2015-03-31 Matthew Ager , Zoran Cvetkovic , Peter Sollich

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the…

Artificial Intelligence · Computer Science 2009-04-22 Nikolaos Vasiloglou , Alexander G. Gray , David V. Anderson

Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…

Numerical Analysis · Computer Science 2017-12-07 Gabriele Torre , Michael Graber

Convolutional Neural Networks (CNNs) with U-shaped architectures have dominated medical image segmentation, which is crucial for various clinical purposes. However, the inherent locality of convolution makes CNNs fail to fully exploit…

Image and Video Processing · Electrical Eng. & Systems 2022-12-14 Pooya Ashtari , Diana M. Sima , Lieven De Lathauwer , Dominique Sappey-Marinier , Frederik Maes , Sabine Van Huffel

While models in audio and speech processing are becoming deeper and more end-to-end, they as a consequence need expensive training on large data, and are often brittle. We build on a classical model of human hearing and make it…

Sound · Computer Science 2024-09-16 Ruolan Leslie Famularo , Dmitry N. Zotkin , Shihab A. Shamma , Ramani Duraiswami

Speech foundation models (SFMs) are increasingly hailed as powerful computational models of human speech perception. However, since their representations are inherently black-box, it remains unclear what drives their alignment with brain…

Neurons and Cognition · Quantitative Biology 2025-09-26 Riki Shimizu , Richard J. Antonello , Chandan Singh , Nima Mesgarani

We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity…

Machine Learning · Computer Science 2020-06-16 Nicolas Nadisic , Arnaud Vandaele , Jeremy E. Cohen , Nicolas Gillis

We introduce a novel way to incorporate prior information into (semi-) supervised non-negative matrix factorization, which we call differentiable dictionary search. It enables general, highly flexible and principled modelling of mixtures…

Audio and Speech Processing · Electrical Eng. & Systems 2022-11-29 Lukáš Samuel Marták , Rainer Kelz , Gerhard Widmer

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

In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…

Optimization and Control · Mathematics 2015-04-24 Yat Tin Chow , Kazufumi Ito , Jun Zou

Nonnegative matrix factorization (NMF) has been shown recently to be tractable under the separability assumption, under which all the columns of the input data matrix belong to the convex cone generated by only a few of these columns.…

Machine Learning · Statistics 2014-05-27 Nicolas Gillis , Robert Luce

Nonsmooth Nonnegative Matrix Factorization (nsNMF) is capable of producing more localized, less overlapped feature representations than other variants of NMF while keeping satisfactory fit to data. However, nsNMF as well as other existing…

Computer Vision and Pattern Recognition · Computer Science 2018-03-21 Jinshi Yu , Guoxu Zhou , Andrzej Cichocki , Shengli Xie

Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this paper we propose…