• Journal of Computing Science and Engineering
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• v.4 no.2
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• pp.97-109
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• 2010

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, which is to decompose a data matrix into a product of two factor matrices with all entries restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering), but in some cases NMF produces the results inappropriate to the clustering problems. In this paper, we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. The result of orthogonal NMF can be clearly interpreted for the clustering problems, and also the performance of clustering is usually better than that of the NMF. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.8
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• pp.89-96
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• 2015

Human visual system has chromatic adaptation to determine the color of an object regardless of illumination, whereas digital camera records illumination and reflectance together, giving the color appearance of the scene varied under different illumination. NMFsc(nonnegative matrix factorization with sparseness constraint) was recently introduced to estimate original object color by using sparseness constraint. In NMFsc, low sparseness constraint is used to estimate illumination and high sparseness constraint is used to estimate reflectance. However, NMFsc has an illumination estimation error for images with large uniform area, which is considered as dominant chromaticity. To overcome the defects of NMFsc, illumination estimation via nonnegative matrix factorization with dominant chromaticity image is proposed. First, image is converted to chromaticity color space and analyzed by chromaticity histogram. Chromaticity histogram segments the original image into similar chromaticity images. A segmented region with the lowest standard deviation is determined as dominant chromaticity region. Next, dominant chromaticity is removed in the original image. Then, illumination estimation using nonnegative matrix factorization is performed on the image without dominant chromaticity. To evaluate the proposed method, experimental results are analyzed by average angular error in the real world dataset and it has shown that the proposed method with 5.5 average angular error achieve better illuminant estimation over the previous method with 5.7 average angular error.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.6
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• pp.2098-2114
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• 2021

Light intensity variation is one of the key factors which affect the accuracy of vehicle face re-identification, so in order to improve the robustness of vehicle face features to light intensity variation, a Nonnegative Matrix Factorization model with the constraint of image acquisition time difference is proposed. First, the original features vectors of all pairs of positive samples which are used for training are placed in two original feature matrices respectively, where the same columns of the two matrices represent the same vehicle; Then, the new features obtained after decomposition are divided into stable and variable features proportionally, where the constraints of intra-class similarity and inter-class difference are imposed on the stable feature, and the constraint of image acquisition time difference is imposed on the variable feature; At last, vehicle face matching is achieved through calculating the cosine distance of stable features. Experimental results show that the average False Reject Rate and the average False Accept Rate of the proposed algorithm can be reduced to 0.14 and 0.11 respectively on five different datasets, and even sometimes under the large difference of light intensities, the vehicle face image can be still recognized accurately, which verifies that the extracted features have good robustness to light variation.

• Journal of KIISE:Software and Applications
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• v.36 no.5
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• pp.347-352
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• 2009

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering). In this paper we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.

• ETRI Journal
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• v.35 no.2
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• pp.193-199
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• 2013

This paper addresses nonnegative independent component analysis (NICA), with the aim to realize the blind separation of nonnegative well-grounded independent source signals, which arises in many practical applications but is hardly ever explored. Recently, Bertrand and Moonen presented a multiplicative NICA (M-NICA) algorithm using multiplicative update and subspace projection. Based on the principle of the mutual correlation minimization, we propose another novel cost function to evaluate the diagonalization level of the correlation matrix, and apply the multiplicative exponentiated gradient (EG) descent update to it to maintain nonnegativity. An efficient approach referred to as the EG-NICA algorithm is derived and its validity is confirmed by numerous simulations conducted on different types of source signals. Results show that the separation performance of the proposed EG-NICA algorithm is superior to that of the previous M-NICA algorithm, with a better unmixing accuracy. In addition, its convergence speed is adjustable by an appropriate user-defined learning rate.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.273-281
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• 2003

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.12
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• pp.6028-6042
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• 2019

Since Sparse Nonnegative Matrix Factorization (SNMF) method can control the sparsity of the decomposed matrix, and then it can be adopted to control the sparsity of facial feature extraction and recognition. In order to improve the accuracy of SNMF method for facial feature recognition, new additive iterative rules based on the improved iterative step sizes are proposed to improve the SNMF method, and then the traditional multiplicative iterative rules of SNMF are transformed to additive iterative rules. Meanwhile, to further increase the sparsity of the basis matrix decomposed by the improved SNMF method, a threshold-sparse constraint is adopted to make the basis matrix to a zero-one matrix, which can further improve the accuracy of facial feature recognition. The improved SNMF method based on the additive iterative rules and threshold-sparse constraint is abbreviated as ASNMF, which is adopted to recognize the ORL and CK+ facial datasets, and achieved recognition rate of 96% and 100%, respectively. Meanwhile, from the results of the contrast experiments, it can be found that the recognition rate achieved by the ASNMF method is obviously higher than the basic NMF, traditional SNMF, convex nonnegative matrix factorization (CNMF) and Deep NMF.

• Proceedings of the Korean Information Science Society Conference
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• 2002.10d
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• pp.301-303
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• 2002

Subspace analysis is a popular method for multivariate data analysis and is closely related to factor analysis and principal component analysis (PCA). In the context of image processing (especially positron emission tomography), all data points are nonnegative and it is expected that both basis images and factors are nonnegative in order to obtain reasonable result. In this paper We present a sequential EM algorithm for rectified subspace analysis (subspace in nonnegativity constraint) and apply it to dynamic PET image analysis. Experimental results show that our proposed method is useful in dynamic PET image analysis.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.2
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• pp.3-13
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• 1993

In this study, we develop a B & B type algorithm for the concave minimization problem with 0-1 knapsack constraint. Our algorithm reformulates the original problem into the singly linearly constrained concave minimization problem by relaxing 0-1 integer constraint in order to get a lower bound. But this relaxed problem is the concave minimization problem known as NP-hard. Thus the linear function that underestimates the concave objective function over the given domain set is introduced. The introduction of this function bears the following important meanings. Firstly, we can efficiently calculate the lower bound of the optimal object value using the conventional convex optimization methods. Secondly, the above linear function like the concave objective function generates the vertices of the relaxed solution set of the subproblem, which is used to update the upper bound. The fact that the linear underestimating function is uniquely determined over a given simplex enables us to fix underestimating function by considering the simplex containing the relaxed solution set. The initial containing simplex that is the intersection of the linear constraint and the nonnegative orthant is sequentially partitioned into the subsimplices which are related to subproblems.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.545-558
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• 2013

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.