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.
non-negative matrix factorization (NMF) is becoming an important tool for information retrieval and pattern recognition. However, in the applications of image decomposition, it is not enough to discover the intrinsic ...
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non-negative matrix factorization (NMF) is becoming an important tool for information retrieval and pattern recognition. However, in the applications of image decomposition, it is not enough to discover the intrinsic geometrical structure of the observation samples by only considering the similarity of different images. In this paper, symmetric manifold regularized objective functions are proposed to develop NMF based learning algorithms (called SMNMF), which explore both the global and local features of the manifold structures for image clustering and at the same time improve the convergence of the graph regularized NMF algorithms. For different initializations, simulations are utilized to confirm the theoretical results obtained in the convergence analysis of the new algorithms. Experimental results on COIL20, ORL, and JAFFE data sets demonstrate the clustering effectiveness of the proposed algorithms by comparing with the state-of-the-art algorithms.
non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it doe...
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non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in parts-based representations. In this paper, we show how explicitly incorporating the notion of 'sparseness' improves the found decompositions. Additionally, we provide complete MATLAB code both for standard NMF and for our extension. Our hope is that this will further the application of these methods to solving novel data-analysis problems.
This work is devoted to the factorization of an observation matrix into additive factors, respectively a contribution matrix G and a profile matrix F which enable to identify many pollution sources. The search for G a...
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This work is devoted to the factorization of an observation matrix into additive factors, respectively a contribution matrix G and a profile matrix F which enable to identify many pollution sources. The search for G and F is achieved through non-negative matrix factorization techniques which alternatively look for the best updates on G and F. These methods are sensitive to noise and initialization, and as for any blind source separation method give results up to a scaling factor and a permutation. A Weighted non-negative matrix factorization extension has also been proposed in the literature, so that different standard deviations of the data matrix components are taken into account. However, some estimated profile components may be inconsistent with practical experience. To prevent this issue, we propose an informed non-negative matrix factorization, where some components of the profile matrix are set to zero or to a constant positive value. A special parametrization of the profile matrix is developed in order to freeze some profile components and to let free the other ones. The problem amounts to solve a family of quadratic sub-problems. A Maximization Minimization strategy leads to some global analytical expressions of both factors. These techniques are used to estimate source contributions of airborne particles from both industrial and natural influences. The relevance of the proposed approach is shown on a real dataset. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
Sentiment analysis, also named opinion mining, is an important task in e-commerce. Recent years, many researchers have been focused on fine-grained sentiment analysis. Aspect level opinion mining detects the detailed ...
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Sentiment analysis, also named opinion mining, is an important task in e-commerce. Recent years, many researchers have been focused on fine-grained sentiment analysis. Aspect level opinion mining detects the detailed sentiments about features of products. However, current aspect identification methods mainly focus on extracting explicit appeared aspects. The task of implicit aspect identification is still a big challenge in sentiment analysis. In this paper, we propose a novel implicit aspect identification approach based on non-negative matrix factorization. The approach first clusters product aspects by combining the co-occurrence information with intra-relations of aspect and opinion words, which can enhance the performance of aspect clustering substantially. In the next step, the approach collects context information of aspects, and represents review sentences by word vectors. Finally, a classifier is constructed to identify and predict the target implicit aspects. We also prove the convergence of our approach. Experimental results demonstrate that our approach outperforms baseline methods in most cases.
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.
Traditional clustering algorithms are inapplicable to many real-world problems where limited knowledge from domain experts is available. Incorporating the domain knowledge can guide a clustering algorithm, consequentl...
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Traditional clustering algorithms are inapplicable to many real-world problems where limited knowledge from domain experts is available. Incorporating the domain knowledge can guide a clustering algorithm, consequently improving the quality of clustering. In this paper, we propose SS-NMF: a semi-supervised non-negative matrix factorization framework for data clustering. In SS-NMF, users are able to provide supervision for clustering in terms of pairwise constraints on a few data objects specifying whether they "must" or "cannot" be clustered together. Through an iterative algorithm, we perform symmetric tri-factorization of the data similarity matrix to infer the clusters. Theoretically, we show the correctness and convergence of SS-NMF. Moveover, we show that SS-NMF provides a general framework for semi-supervised clustering. Existing approaches can be considered as special cases of it. Through extensive experiments conducted on publicly available datasets, we demonstrate the superior performance of SS-NMF for clustering.
We analyzed muscle excitation estimation systematically by non-negative matrix factorization (NMF) from surface electromyograms (EMG) during dynamic contractions of biceps brachii (BB) muscles. We used motor unit acti...
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We analyzed muscle excitation estimation systematically by non-negative matrix factorization (NMF) from surface electromyograms (EMG) during dynamic contractions of biceps brachii (BB) muscles. We used motor unit action potentials (MUAPs) estimated experimentally from surface EMGs during slow dynamic contractions of BB muscles in healthy young males, and convolved them by simulated motor unit firing patterns. Different uncorrelated muscle excitation and muscle shortening profiles were combined when generating the EMG signals from left and right BBs (64 channels per muscle). EMG signals were rectified, low-passed filtered and decomposed by NMF into 2, 3, 4 or 6 components. The identified NMF components demonstrated good separation of left and right BB activity, but relatively large sensitivity of NMF components to muscle shortening, especially at high levels of muscle excitation. When averaged across different numbers of identified NMF components at excitation levels ranging from 40 to 80%, the average correlation coefficient between the NMF components and muscle shortening profiles was 0.45 +/- 0.15. At excitation levels between 0 and 40 % these correlations decreased to 0.15 +/- 0.09. Therefore, NMF components reflect both muscle excitation and muscle shortening profiles.
In through-wall radar imaging (TWRI), the presence of the wall greatly reduces the performance of target detection algorithms. The signal reflected from the wall is stronger than the signal reflected from the target a...
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In through-wall radar imaging (TWRI), the presence of the wall greatly reduces the performance of target detection algorithms. The signal reflected from the wall is stronger than the signal reflected from the target and masks the target. The physical properties of the wall or the reflections from the back and side walls in the environment where the target is located make the problem even more difficult. Within the scope of this study, the non-negative matrix factorization (NMF)-based approaches that we proposed for clutter removal in ground penetrating radar systems were adapted to the TWR problem. Moreover, a new NMF-based method which provides a better modelling of the wall component using sparsity constraint is introduced. Comparison with traditional subspace-based methods such as principal component analysis, singular value decomposition and low rank and sparse method robust principal component analysis for an experimental dataset validates that sparsity-guided NMF-based methods provide the best results.
non-negative matrix factorization (NMF) is a very effective method for high dimensional data analysis, which has been widely used in information retrieval, computer vision, and pattern recognition. NMF aims to find tw...
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non-negative matrix factorization (NMF) is a very effective method for high dimensional data analysis, which has been widely used in information retrieval, computer vision, and pattern recognition. NMF aims to find two non-negative matrices whose product approximates the original matrix well. It can capture the underlying structure of data in the low dimensional data space using its parts-based representations. However, NMF is actually an unsupervised method without making use of prior information of data. In this paper, we propose a novel pairwise constrained non-negative matrix factorization with graph Laplacian method, which not only utilizes the local structure of the data by graph Laplacian, but also incorporates pairwise constraints generated among all labeled data into NMF framework. More specifically, we expect that data points which have the same class label will have very similar representations in the low dimensional space as much as possible, while data points with different class labels will have dissimilar representations as much as possible. Consequently, all data points are represented with more discriminating power in the lower dimensional space. We compare our approach with other typical methods and experimental results for image clustering show that this novel algorithm achieves the state-of-the-art performance.
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