nonnegative matrix factorization (NMF), which decomposes a target matrix into the product of two matrices with nonnegative elements, has been widely used in various fields of signal processing. In visual signal proces...
详细信息
nonnegative matrix factorization (NMF), which decomposes a target matrix into the product of two matrices with nonnegative elements, has been widely used in various fields of signal processing. In visual signal processing, the spatially nonuniformed distribution of perceptually meaningful information in image and video frames calls for a kind of Spatially-Weighted NMF (swNMF) that applies location dependent weights into the decomposition problem. In this paper we introduce swNMF solution based on the hierarchical alternating least squares (HALS) approach. Then we exemplify its application to a new information display diagram named temporal psychovisual modulation (TPVM) with comparison with traditional HALS method and baseline algorithm of multiplicative update (MU). (C) 2017 Elsevier Inc. All rights reserved.
Hyperspectral unmixing is one of the most important techniques in the remote sensing image analysis tasks. In recent decades, nonnegative matrix factorization (NMF) has been shown to be effective for hyperspectral unm...
详细信息
Hyperspectral unmixing is one of the most important techniques in the remote sensing image analysis tasks. In recent decades, nonnegative matrix factorization (NMF) has been shown to be effective for hyperspectral unmixing due to the strong discovery of the latent structure. Most NMFs put emphasize on the spectral information, but ignore the spatial information, which is very crucial for analyzing hyperspectral data. In this paper, we propose an improved NMF method, namely NMF with region sparsity learning (RSLNMF), to simultaneously consider both spectral and spatial information. RSLNMF defines a new sparsity learning model based on a small homogeneous region that is obtained via the graph cut algorithm. Thus RSLNMF is able to explore the relationship of spatial neighbor pixels within each region. An efficient optimization scheme is developed for the proposed RSLNMF, and its convergence is theoretically guaranteed. Experiments on both synthetic and real hyperspectral data validate the superiority of the proposed method over several state-of-the-art unmixing approaches.
Hyperspectral unmixing aims to estimate a set of endmembers and corresponding abundances in pixels. nonnegative matrix factorization (NMF) and its extensions with various constraints have been widely applied to hypers...
详细信息
Hyperspectral unmixing aims to estimate a set of endmembers and corresponding abundances in pixels. nonnegative matrix factorization (NMF) and its extensions with various constraints have been widely applied to hyperspectral unmixing. L-1/2 and L-2 regularizers can be added to NMF to enforce sparseness and evenness, respectively. In practice, a region in a hyperspectral image may possess different sparsity levels across locations. The problem remains as to how to impose constraints accordingly when the level of sparsity varies. We propose a novel nonnegative matrix factorization with data-guided constraints (DGC-NMF). The DGC-NMF imposes on the unknown abundance vector of each pixel with either an L-1/2 constraint or an L-2 constraint according to its estimated mixture level. Experiments on the synthetic data and real hyperspectral data validate the proposed algorithm.
In this paper, a novel regularized nonnegative matrix factorization (NMF) method, called neighbors isometric embedding nonnegative matrix factorization (NINMF), is proposed. The key idea of the NINMF method is to inco...
详细信息
In this paper, a novel regularized nonnegative matrix factorization (NMF) method, called neighbors isometric embedding nonnegative matrix factorization (NINMF), is proposed. The key idea of the NINMF method is to incorporate neighbors isometric regularized constraint in the optimization of the NMF. Hence, the NINMF is able to extract the representation space that preserves neighbor isometric geometry structure. Like most of the graph regularized NMFs, the NINMF method also finds a similarity weights matrix. However, the difference of our proposed method is that the NINMF simultaneously builds similarity weight matrix and performs data representation. The proposed method was applied to solve the problem of image representation using the well-known ORL, Yale and extended YaleB image data sets. The experimental results demonstrate the effectiveness of the proposed NINMF method for image representation.
nonnegative matrix factorization (NMF) has been attracting many scholars in the fields of pattern recognition and data mining to study it since its inception. To date, a large number of variant methods have been propo...
详细信息
nonnegative matrix factorization (NMF) has been attracting many scholars in the fields of pattern recognition and data mining to study it since its inception. To date, a large number of variant methods have been proposed and applied in image retrieval and image Single-Label Annotation (SLA) successfully. However, the effectiveness of NMF for Multi-Label Annotation (MLA) encounters difficulties and is still an open. topic. To meet this goal, this paper proposes a supervised NMF with new matching measurement to enhance MLA accuracy. In contrast with other NMF algorithms with sparse or discriminant constraints, the proposed NMF algorithm implements a supervised training method while integrates feature dimension reduction. What's more, we improve a novel matching measurement function by considering positive and negative samples respectively, which is proved to be more suitable for MLA. In addition, the proposed NMF object function is solved by using the projected gradient method, and image annotation can be achieved. Experiments results on NUSWIDE dataset showed that the proposed algorithm can achieve strong performance compared with existing algorithms in terms of False Rejection Rate (FRR) and False Acceptance Rate (FAR).
We propose a unified and systematic framework for performing online nonnegative matrix factorization in the presence of outliers. Our framework is particularly suited to large-scale data. We propose two solvers based ...
详细信息
We propose a unified and systematic framework for performing online nonnegative matrix factorization in the presence of outliers. Our framework is particularly suited to large-scale data. We propose two solvers based on projected gradient descent and the alternating direction method of multipliers. We prove that the sequence of objective values converges almost surely by appealing to the quasi-martingale convergence theorem. We also show the sequence of learned dictionaries converges to the set of stationary points of the expected loss function almost surely. In addition, we extend our basic problem formulation to various settings with different constraints and regularizers. We also adapt the solvers and analyses to each setting. We perform extensive experiments on both synthetic and real datasets. These experiments demonstrate the computational efficiency and efficacy of our algorithms on tasks such as (parts-based) basis learning, image denoising, shadow removal, and foreground-background separation.
Clustering is one of the basic tasks in data mining and machine learning which aims at discovering hidden structure in the data. For many real-world applications, there often exist many different yet meaningful cluste...
详细信息
Clustering is one of the basic tasks in data mining and machine learning which aims at discovering hidden structure in the data. For many real-world applications, there often exist many different yet meaningful clusterings while most of existing clustering methods only produce a single clustering. To address this limitation, multiple clustering, which tries to generate clusterings that are high quality and different from each other, has emerged recently. In this paper, we propose a novel alternative clustering method that generates non-redundant multiple clusterings sequentially. The algorithm is built upon nonnegative matrix factorization, and we take advantage of the nonnegative property to enforce the non-redundancy. Specifically, we design a quadratic term to measure the redundancy between the reference clustering and the new clustering, and incorporate it into the objective. The optimization problem takes on a very simple form, and can be solved efficiently by multiplicative updating rules. Experimental results demonstrate that the proposed algorithm is comparable to or outperforms existing multiple clustering methods.
Microbiome datasets are often comprised of different representations or views which provide complementary information to understand microbial communities, such as metabolic pathways, taxonomic assignments, and gene fa...
详细信息
Microbiome datasets are often comprised of different representations or views which provide complementary information to understand microbial communities, such as metabolic pathways, taxonomic assignments, and gene families. Data integration methods including approaches based on nonnegative matrix factorization (NMF) combine multi-view data to create a comprehensive view of a given microbiome study by integrating multi-view information. In this paper, we proposed a novel variant of NMF which called Laplacian regularized joint non-negative matrixfactorization (LJ-NMF) for integrating functional and phylogenetic profiles from HMP. We compare the performance of this method to other variants of NMF. The experimental results indicate that the proposed method offers an efficient framework for microbiome data analysis.
nonnegative matrix factorization (NMF) has been attracting intensive attention due to its wide applications. However due to the non-convexity of the NMF models, most of the existing methods are easily stuck into a bad...
详细信息
nonnegative matrix factorization (NMF) has been attracting intensive attention due to its wide applications. However due to the non-convexity of the NMF models, most of the existing methods are easily stuck into a bad local minima, especially in presence of noise or outliers. To alleviate this deficiency, in this paper we propose a novel NMF method by incorporating self-paced learning (SPL) methodology with traditional NMF model, to sequentially include matrix elements into NMF training from easy to complex, which draws the merits of SPL that have been demonstrated to be beneficial in avoiding bad local minima. To make the SPL methodology play a more stable and efficient role in NMF, we suggest to base on multicriteria to select training elements. The effectiveness of the proposed multicriteria self-paced NMF (MSPNMF) method is demonstrated by a series of numerical experiments on synthetic and real face image data. We also discuss the effects of different initializations on MSPNMF. Experimental results show that MSPNMF is sensitive to the starting values and different initializations should be adopted for MSPNMF based on different situations. (C) 2017 Elsevier B.V. All rights reserved.
A pseudo-marginal Markov chain Monte Carlo (PMCMC) method is proposed for nonnegative matrix factorization (NMF). The sampler jointly simulates the joint posterior distribution for the nonnegative matrices and the mat...
详细信息
A pseudo-marginal Markov chain Monte Carlo (PMCMC) method is proposed for nonnegative matrix factorization (NMF). The sampler jointly simulates the joint posterior distribution for the nonnegative matrices and the matrix dimensions which indicate the number of the nonnegative components in the NMF model. We show that the PMCMC sampler is a generalization of a version of the reversible jump Markov chain Monte Carlo. An illustrative synthetic data was used to demonstrate the ability of the proposed PMCMC sampler in inferring the nonnegative matrices and as well as the matrix dimensions. The proposed sampler was also applied to a nuclear magnetic resonance spectroscopy data to infer the number of nonnegative components.
暂无评论