scholarly journals On Nonnegative Matrix Factorization Algorithms for Signal-Dependent Noise with Application to Electromyography Data

2014 ◽  
Vol 26 (6) ◽  
pp. 1128-1168 ◽  
Author(s):  
Karthik Devarajan ◽  
Vincent C. K. Cheung
Keyword(s):  
Language Processing ◽  
Matrix Factorization ◽  
Large Scale ◽  
Goodness Of Fit ◽  
Nonnegative Matrix Factorization ◽  
Gaussian Model ◽  
Nonnegative Matrix ◽  
Theoretic Approach ◽  
Multiplicative Updates ◽  
Nonnegativity Constraints

Nonnegative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two nonnegative matrices, W and H, where [Formula: see text]. It has been successfully applied in the analysis and interpretation of large-scale data arising in neuroscience, computational biology, and natural language processing, among other areas. A distinctive feature of NMF is its nonnegativity constraints that allow only additive linear combinations of the data, thus enabling it to learn parts that have distinct physical representations in reality. In this letter, we describe an information-theoretic approach to NMF for signal-dependent noise based on the generalized inverse gaussian model. Specifically, we propose three novel algorithms in this setting, each based on multiplicative updates, and prove monotonicity of updates using the EM algorithm. In addition, we develop algorithm-specific measures to evaluate their goodness of fit on data. Our methods are demonstrated using experimental data from electromyography studies, as well as simulated data in the extraction of muscle synergies, and compared with existing algorithms for signal-dependent noise.

scholarly journals Local Topic Discovery via Boosted Ensemble of Nonnegative Matrix Factorization

2017 ◽  
Author(s):  
Sangho Suh ◽  
Jaegul Choo ◽  
Joonseok Lee ◽  
Chandan K. Reddy
Keyword(s):  
Matrix Factorization ◽  
Topic Modeling ◽  
Large Scale ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Gradient Boosting ◽  
Ensemble Model ◽  
High Quality ◽  
Residual Matrix ◽  
The Given

Nonnegative matrix factorization (NMF) has been increasingly popular for topic modeling of large-scale documents. However, the resulting topics often represent only general, thus redundant information about the data rather than minor, but potentially meaningful information to users. To tackle this problem, we propose a novel ensemble model of nonnegative matrix factorization for discovering high-quality local topics. Our method leverages the idea of an ensemble model to successively perform NMF given a residual matrix obtained from previous stages and generates a sequence of topic sets. The novelty of our method lies in the fact that it utilizes the residual matrix inspired by a state-of-the-art gradient boosting model and applies a sophisticated local weighting scheme on the given matrix to enhance the locality of topics, which in turn delivers high-quality, focused topics of interest to users.

Constructing large-scale cortical brain networks from scalp EEG with Bayesian nonnegative matrix factorization

2020 ◽  
Vol 125 ◽  
pp. 338-348 ◽  
Author(s):  
Chanlin Yi ◽  
Chunli Chen ◽  
Yajing Si ◽  
Fali Li ◽  
Tao Zhang ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Large Scale ◽  
Nonnegative Matrix Factorization ◽  
Brain Networks ◽  
Nonnegative Matrix ◽  
Scalp Eeg

A Novel Image Retrieval System Based on Histogram Factorization and Contextual Similarity Learning

2013 ◽  
Vol 380-384 ◽  
pp. 4148-4151 ◽  
Author(s):  
Sivakolundu Jayasekara ◽  
Hithanadura Dassanayake ◽  
Anil Fernando
Keyword(s):  
Image Retrieval ◽  
Matrix Factorization ◽  
Large Scale ◽  
Nonnegative Matrix Factorization ◽  
Retrieval System ◽  
Nonnegative Matrix ◽  
Bag Of Words ◽  
Similarity Learning ◽  
Query Image ◽  
Image Retrieval System

Image retrieval has been a top topic in the field of both computer vision and machine learning for a long time. Content based image retrieval, which tries to retrieve images from a database visually similar to a query image, has attracted much attention. Two most important issues of image retrieval are the representation and ranking of the images. Recently, bag-of-words based method has shown its power as a representation method. Moreover, nonnegative matrix factorization is also a popular way to represent the data samples. In addition, contextual similarity learning has also been studied and proven to be an effective method for the ranking problem. However, these technologies have never been used together. In this paper, we developed an effective image retrieval system by representing each image using the bag-of-words method as histograms, and then apply the nonnegative matrix factorization to factorize the histograms, and finally learn the ranking score using the contextual similarity learning method. The proposed novel system is evaluated on a large scale image database and the effectiveness is shown.

scholarly journals An Overlapping Community Detection Approach in Ego-Splitting Networks Using Symmetric Nonnegative Matrix Factorization

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 869
Author(s):  
Mingqing Huang ◽  
Qingshan Jiang ◽  
Qiang Qu ◽  
Abdur Rasool
Keyword(s):  
Community Detection ◽  
Matrix Factorization ◽  
Large Scale ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Overlapping Community Detection ◽  
Detection Approach ◽  
Overlapping Community ◽  
Large Scale Networks ◽  
Symmetric Nonnegative Matrix Factorization

Overlapping clustering is a fundamental and widely studied subject that identifies all densely connected groups of vertices and separates them from other vertices in complex networks. However, most conventional algorithms extract modules directly from the whole large-scale graph using various heuristics, resulting in either high time consumption or low accuracy. To address this issue, we develop an overlapping community detection approach in Ego-Splitting networks using symmetric Nonnegative Matrix Factorization (ESNMF). It primarily divides the whole network into many sub-graphs under the premise of preserving the clustering property, then extracts the well-connected sub-sub-graph round each community seed as prior information to supplement symmetric adjacent matrix, and finally identifies precise communities via nonnegative matrix factorization in each sub-network. Experiments on both synthetic and real-world networks of publicly available datasets demonstrate that the proposed approach outperforms the state-of-the-art methods for community detection in large-scale networks.

scholarly journals Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization

2012 ◽  
Vol 24 (4) ◽  
pp. 1085-1105 ◽  
Author(s):  
Nicolas Gillis ◽  
François Glineur
Keyword(s):  
Data Analysis ◽  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Computational Cost ◽  
Nonnegative Matrix ◽  
Careful Analysis ◽  
Hyperspectral Data ◽  
Projected Gradient Method ◽  
Multiplicative Updates

Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this letter, we consider two well-known algorithms designed to solve NMF problems: the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Cichocki et al. We propose a simple way to significantly accelerate these schemes, based on a careful analysis of the computational cost needed at each iteration, while preserving their convergence properties. This acceleration technique can also be applied to other algorithms, which we illustrate on the projected gradient method of Lin. The efficiency of the accelerated algorithms is empirically demonstrated on image and text data sets and compares favorably with a state-of-the-art alternating nonnegative least squares algorithm.

scholarly journals A Quasi-Likelihood Approach to Nonnegative Matrix Factorization

2016 ◽  
Vol 28 (8) ◽  
pp. 1663-1693 ◽  
Author(s):  
Karthik Devarajan ◽  
Vincent C. K. Cheung
Keyword(s):  
Matrix Factorization ◽  
Goodness Of Fit ◽  
Nonnegative Matrix Factorization ◽  
Linear Models ◽  
Expectation Maximization Algorithm ◽  
Nonnegative Matrix ◽  
Nonlinear Effects ◽  
Biomedical Signal Processing ◽  
Link Functions ◽  
Unified View

A unified approach to nonnegative matrix factorization based on the theory of generalized linear models is proposed. This approach embeds a variety of statistical models, including the exponential family, within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi-likelihood. Using this framework, a family of algorithms for handling signal-dependent noise is developed and its convergence proved using the expectation-maximization algorithm. In addition, a measure to evaluate the goodness of fit of the resulting factorization is described. The proposed methods allow modeling of nonlinear effects using appropriate link functions and are illustrated using an application in biomedical signal processing.

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