In this work, we apply topic modeling using non-negative matrix factorization (NMF) on the COVID-19 Open Research Dataset (CORD-19) to uncover the underlying thematic structure and its evolution within the extensive b...
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Lee and Seung (2000) introduced numerical solutions for non-negative matrix factorization (NMF) using iterative multiplicative update algorithms. These algorithms have been actively utilized as dimensionality reductio...
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Multi-label learning is more complicated than single-label learning since the semantics of the instances are usually overlapped and not *** effectiveness of many algorithms often fails when the correlations in the fea...
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Multi-label learning is more complicated than single-label learning since the semantics of the instances are usually overlapped and not *** effectiveness of many algorithms often fails when the correlations in the feature and label space are not fully *** this end,we propose a novel non-negative matrix factorization(NMF)based modeling and training algorithm that learns from both the adjacencies of the instances and the labels of the training *** the modeling process,a set of generators are constructed,and the associations among generators,instances,and labels are set up,with which the label prediction is *** the training process,the parameters involved in the process of modeling are ***,an NMF based algorithm is proposed to determine the associations between generators and instances,and a non-negative least square optimization algorithm is applied to determine the associations between generators and *** proposed algorithm fully takes the advantage of smoothness assumption,so that the labels are properly *** experiments were carried out on six set of *** results demonstrate the effectiveness of the proposed algorithms.
Coclustering heterogeneous data has attracted extensive attention recently due to its high impact on various important applications, such us text mining, image retrieval, and bioinformatics. However, data coclustering...
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Coclustering heterogeneous data has attracted extensive attention recently due to its high impact on various important applications, such us text mining, image retrieval, and bioinformatics. However, data coclustering without any prior knowledge or background information is still a challenging problem. In this paper, we propose a Semisupervised non-negative matrix factorization (SS-NMF) framework for data coclustering. Specifically, our method computes new relational matrices by incorporating user provided constraints through simultaneous distance metric learning and modality selection. Using an iterative algorithm, we then perform trifactorizations of the new matrices to infer the clusters of different data types and their correspondence. Theoretically, we prove the convergence and correctness of SS-NMF coclustering and show the relationship between SS-NMF with other well-known coclustering models. Through extensive experiments conducted on publicly available text, gene expression, and image data sets, we demonstrate the superior performance of SS-NMF for heterogeneous data coclustering.
In this short note, we focus on the use of the generalized Kullback-Leibler (KL) divergence in the problem of non-negative matrix factorization (NM[F). We will show that when using the generalized KL divergence as cos...
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In this short note, we focus on the use of the generalized Kullback-Leibler (KL) divergence in the problem of non-negative matrix factorization (NM[F). We will show that when using the generalized KL divergence as cost function for NIVIF, the row sums and the column sums of the original matrix are preserved in the approximation. We will use this special characteristic in several approximation problems. (c) 2007 Elsevier Inc. All rights reserved.
As the atmospheric system is characterized by highly complex interactions between a large number of physical variables, it is a challenging task for researchers to break up the complicated structures into a few signif...
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As the atmospheric system is characterized by highly complex interactions between a large number of physical variables, it is a challenging task for researchers to break up the complicated structures into a few significant modes of variability. An innovative technique, called non-negative matrix factorization (NMF), developed to provide a reduced-dimensional representation of large-scale non-negative data and to extract underlying features, is introduced as a tool for meteorological applications. The method is used to decompose space-time meteorological fields into spatial patterns and associated time indices in order to advance our knowledge of dominant atmospheric processes. For the Northern Hemisphere the 500 hPa geopotential field together with sea level pressure (SLP) are analysed using an up-to-date NMF algorithm as well as a helpful method of NMF initialization based on Singular Value Decomposition (SVD). Several NMF patterns correspond to the variations identified by traditional EOF analysis, such as the East Atlantic and the Pacific/North American Pattern. For the North Atlantic Oscillation the NMF identifies sub-patterns: The positive phase is associated with systems of pressure variation over the Pacific Ocean and the Arctic, respectively, the negative phase resembles the EOF pattern. As the NMF patterns not only represent variability, like EOF patterns, but also are fractions of the total observed values, we demonstrate for a location near Nikolski, Alaska, the temporal development of the geopotential as a superposition of NMF-factors. Copyright (C) 2009 Royal Meteorological Society
non-negative matrix factorization (NMF) is a powerful tool for data science researchers, and it has been successfully applied to data mining and machine learning community, due to its advantages such as simple form, g...
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non-negative matrix factorization (NMF) is a powerful tool for data science researchers, and it has been successfully applied to data mining and machine learning community, due to its advantages such as simple form, good interpretability and less storage space. In this paper, we give a detailed survey on existing NMF methods, including a comprehensive analysis of their design principles, characteristics and drawbacks. In addition, we also discuss various variants of NMF methods and analyse properties and applications of these variants. Finally, we evaluate the performance of nine NMF methods through numerical experiments, and the results show that NMF methods perform well in clustering tasks.
non-negative matrix factorization (NMF) is a popular technique for pattern recognition, data analysis, and dimensionality reduction, the goal of which is to decompose non-negative data matrix X into a product of basis...
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non-negative matrix factorization (NMF) is a popular technique for pattern recognition, data analysis, and dimensionality reduction, the goal of which is to decompose non-negative data matrix X into a product of basis matrix A and encoding variable matrix S with both A and S allowed to have only non-negative elements. In this paper, we consider Amari's alpha-divergence as a discrepancy measure and rigorously derive a multiplicative updating algorithm (proposed in our recent work) which iteratively minimizes the alpha-divergence between X and AS. We analyze and prove the monotonic convergence of the algorithm using auxiliary functions. In addition, we show that the same algorithm can be also derived using Karush-Kuhn-Tucker (KKT) conditions as well as the projected gradient. We provide two empirical study for image denoising and EEG classification, showing the interesting and useful behavior of the algorithm in cases where different values of alpha (alpha = 0.5,1,2) are used. (C) 2008 Elsevier B.V. All rights reserved.
non-negative matrix factorization (NMF) has recently attracted much attention due to its good interpretation in perception science and widely applications in various fields. In this paper, a novel graph regularized NM...
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non-negative matrix factorization (NMF) has recently attracted much attention due to its good interpretation in perception science and widely applications in various fields. In this paper, a novel graph regularized NMF algorithm called NMF with locality constrained adaptive graph (NMF-LCAG) is proposed. Compared with other NMF based algorithms, the proposed NMF-LCAG algorithm has the following advantages: 1) Unlike the traditional NMF method which neglects the geometric information of original data, the proposed algorithm introduces a locality constrained graph to discover the latent manifold structure of the data and 2) Different from most graph regularized NMF algorithms in which the graphs are predefined and kept unchanged during the NMF procedure, two locality constraint terms are employed in our NMF-LCAG to adaptively optimize the graph. Thus, the weight matrix of graph and low dimensional features of data can be simultaneously learned by our algorithm, which makes NMF-LCAG more flexible than other approaches. Moreover, an iterative updating strategy is developed to optimize the objective function of our algorithm and the convergence analysis is also given. Extensive experiments are conducted on four face image databases and three UCI datasets to demonstrate the effectiveness of the proposed NMF-LCAG algorithm. Compared with some other related algorithms, the proposed NMF-LCAG algorithm can achieve at least 1% similar to 3% accuracy improvement in most cases.
matrixfactorization is useful to extract the essential low-rank structure from a given matrix and has been paid increasing attention. A typical example is non-negative matrix factorization (NMF), which is one type of...
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matrixfactorization is useful to extract the essential low-rank structure from a given matrix and has been paid increasing attention. A typical example is non-negative matrix factorization (NMF), which is one type of unsupervised learning, having been successfully applied to a variety of data including documents, images and gene expression, where their values are usually non-negative. We propose a new model of NMF which is trained by using auxiliary information of overlapping groups. This setting is very reasonable in many applications, a typical example being gene function estimation where functional gene groups are heavily overlapped with each other. To estimate true groups from given overlapping groups efficiently, our model incorporates latent matrices with the regularization term using a mixed norm. This regularization term allows group-wise sparsity on the optimized low-rank structure. The latent matrices and other parameters are efficiently estimated by a block coordinate gradient descent method. We empirically evaluated the performance of our proposed model and algorithm from a variety of viewpoints, comparing with four methods including MMF for auxiliary graph information, by using both synthetic and real world document and gene expression data sets.
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