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Nonnegative matrix factorization (NMF) is a popular method in machine learning and signal processing to decompose a given nonnegative matrix into two nonnegative matrices. In this paper, we propose new algorithms, called…

Optimization and Control · Mathematics 2025-09-29 Shota Takahashi , Mirai Tanaka , Shiro Ikeda

Upon the discovery of adversarial attacks, robust models have become obligatory for deep learning-based systems. Adversarial training with first-order attacks has been one of the most effective defenses against adversarial perturbations to…

Computer Vision and Pattern Recognition · Computer Science 2021-08-24 Inci M. Baytas , Debayan Deb

Adversarial learning has emerged as one of the successful techniques to circumvent the susceptibility of existing methods against adversarial perturbations. However, the majority of existing defense methods are tailored to defend against a…

Machine Learning · Computer Science 2021-06-28 Divyam Madaan , Jinwoo Shin , Sung Ju Hwang

Adversarial training based on the maximum classifier discrepancy between two classifier structures has achieved great success in unsupervised domain adaptation tasks for image classification. The approach adopts the structure of two…

Computer Vision and Pattern Recognition · Computer Science 2022-04-19 Yiju Yang , Taejoon Kim , Guanghui Wang

Non-negative blind source separation (non-negative BSS), which is also referred to as non-negative matrix factorization (NMF), is a very active field in domains as different as astrophysics, audio processing or biomedical signal processing.…

Machine Learning · Statistics 2014-10-27 Jérémy Rapin , Jérôme Bobin , Anthony Larue , Jean-Luc Starck

Matrix factorization techniques, especially Nonnegative Matrix Factorization (NMF), have been widely used for dimensionality reduction and interpretable data representation. However, existing NMF-based methods are inherently single-scale…

Machine Learning · Computer Science 2026-02-27 Jichao Zhang , Ran Miao , Limin Li

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

While deep neural networks have achieved remarkable success in various computer vision tasks, they often fail to generalize to new domains and subtle variations of input images. Several defenses have been proposed to improve the robustness…

Computer Vision and Pattern Recognition · Computer Science 2021-09-08 Omid Poursaeed , Tianxing Jiang , Harry Yang , Serge Belongie , SerNam Lim

The vulnerability of neural network classifiers to adversarial attacks is a major obstacle to their deployment in safety-critical applications. Regularization of network parameters during training can be used to improve adversarial…

Machine Learning · Computer Science 2024-05-28 Sheng Yang , Jacob A. Zavatone-Veth , Cengiz Pehlevan

In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions,…

Numerical Analysis · Computer Science 2017-03-03 Nicolas Gillis

Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as…

Statistics Theory · Mathematics 2019-06-10 Naoki Hayashi , Sumio Watanabe

Deep Convolution Neural Networks (CNNs) can easily be fooled by subtle, imperceptible changes to the input images. To address this vulnerability, adversarial training creates perturbation patterns and includes them in the training set to…

Computer Vision and Pattern Recognition · Computer Science 2022-09-19 Muzammal Naseer , Salman Khan , Munawar Hayat , Fahad Shahbaz Khan , Fatih Porikli

Traditional source separation approaches train deep neural network models end-to-end with all the data available at once by minimizing the empirical risk on the whole training set. On the inference side, after training the model, the user…

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…

Machine Learning · Computer Science 2020-02-28 Ankit Raj , Yoram Bresler , Bo Li

Training Generative Adversarial Networks (GANs) remains a challenging problem. The discriminator trains the generator by learning the distribution of real/generated data. However, the distribution of generated data changes throughout the…

Computer Vision and Pattern Recognition · Computer Science 2024-01-05 Wentian Zhang , Haozhe Liu , Bing Li , Jinheng Xie , Yawen Huang , Yuexiang Li , Yefeng Zheng , Bernard Ghanem

Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…

Machine Learning · Statistics 2020-01-28 Kaiyi Ji , Jian Tan , Jinfeng Xu , Yuejie Chi

The vulnerability of Deep Neural Networks to adversarial perturbations presents significant security concerns, as the imperceptible perturbations can contaminate the feature space and lead to incorrect predictions. Recent studies have…

Computer Vision and Pattern Recognition · Computer Science 2024-06-18 Kejia Zhang , Juanjuan Weng , Junwei Wu , Guoqing Yang , Shaozi Li , Zhiming Luo

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

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

Domain generalization (DG) deals with the problem of domain shift where a machine learning model trained on multiple-source domains fail to generalize well on a target domain with different statistics. Multiple approaches have been proposed…

Computer Vision and Pattern Recognition · Computer Science 2020-07-29 Prashant Pandey , Mrigank Raman , Sumanth Varambally , Prathosh AP