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In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an…

Machine Learning · Computer Science 2019-11-15 Anthony Degleris , Nicolas Gillis

This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density…

Numerical Analysis · Mathematics 2025-07-30 Xun Tang , Rajat Dwaraknath , Lexing Ying

Semi-Nonnegative Matrix Factorization (semi-NMF) extends classical Nonnegative Matrix Factorization (NMF) by allowing the basis matrix to contain both positive and negative entries, making it suitable for decomposing data with mixed signs.…

Machine Learning · Computer Science 2025-08-12 Lu Chenggang

We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a…

Machine Learning · Computer Science 2018-01-08 Olivier Gouvert , Thomas Oberlin , Cédric Févotte

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…

Numerical Analysis · Mathematics 2025-11-11 Junjun Pan , Valentin Leplat , Michael Ng , Nicolas Gillis

Deriving health indicators of rotating machines is crucial for their maintenance. However, this process is challenging for the prevalent adopted intelligent methods since they may take the whole data distributions, not only introducing…

Machine Learning · Computer Science 2024-09-04 Wenyang Hu , Gaetan Frusque , Tianyang Wang , Fulei Chu , Olga Fink

This paper addresses the problem of noise reduction with simultaneous components extrac- tion in vibration signals for faults diagnosis of bearing. The observed vibration signal is modeled as a summation of two components contaminated by…

Sound · Computer Science 2016-08-09 Wangpeng He , Yin Ding , Yanyang Zi , Ivan W. Selesnick

Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive…

Machine Learning · Computer Science 2020-03-20 Ioannis Panageas , Stratis Skoulakis , Antonios Varvitsiotis , Xiao Wang

Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF…

Machine Learning · Statistics 2023-09-26 Duc Toan Nguyen , Eric C. Chi

Non-Negative Matrix Factorization (NMF) is an unsupervised learning method offering low-rank representations across various domains such as audio processing, biomedical signal analysis, and image recognition. The incorporation of…

Machine Learning · Computer Science 2025-10-09 Yasaman Torabi , Shahram Shirani , James P. Reilly

The problem of local damage diagnosis (based on the detection of impulsive and periodic signals) is discussed. Both features should be checked, as fault frequency must be linked to the true value calculated for a given machine and speed.…

Signal Processing · Electrical Eng. & Systems 2024-09-26 Daniel Kuzio , Radosław Zimroz , Agnieszka Wyłomańska

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

Fault diagnosis and failure prognosis are essential techniques in improving the safety of many manufacturing systems. Therefore, on-line fault detection and isolation is one of the most important tasks in safety-critical and intelligent…

Artificial Intelligence · Computer Science 2011-07-19 Rafik Mahdaoui , Leila Hayet Mouss , Mohamed Djamel Mouss , Ouahiba Chouhal

In this work, we study the problem of common and unique feature extraction from noisy data. When we have N observation matrices from N different and associated sources corrupted by sparse and potentially gross noise, can we recover the…

Machine Learning · Computer Science 2025-08-25 Naichen Shi , Salar Fattahi , Raed Al Kontar

We augment the nonnegative matrix factorization method for audio source separation with cues about directionality of sound propagation. This improves separation quality greatly and removes the need for training data, with only a twofold…

Machine Learning · Statistics 2017-05-30 Noah D. Stein

The pull test is a destructive detection method, and it can t measure the actual length of the bolt. As such, ultrasonic echo is one of the most important non-destructive testing methods for bolt quality detection. In this paper, the…

Signal Processing · Electrical Eng. & Systems 2017-11-15 Juncai Xu , Qingwen Ren

Fault detection at rotating machinery with the help of vibration sensors offers the possibility to detect damage to machines at an early stage and to prevent production downtimes by taking appropriate measures. The analysis of the vibration…

Signal Processing · Electrical Eng. & Systems 2020-08-03 Oliver Mey , Willi Neudeck , André Schneider , Olaf Enge-Rosenblatt

Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…

Machine Learning · Computer Science 2025-02-04 Matej Mihelčić , Pauli Miettinen

The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…

The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system.…

Physics and Society · Physics 2014-02-04 Laetitia Gauvin , André Panisson , Ciro Cattuto