• Journal of Computing Science and Engineering
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• 제4권2호
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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.

• 전자공학회논문지
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• 제52권8호
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• pp.89-96
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• 2015

인간의 시각은 색순응을 통해서 사물의 색을 광원의 색에 영향 없이 인지 할 수 있다. 반면에, 카메라는 입력 값을 그대로 기록하기 때문에, 광원에 따라 물체의 색이 다르게 나타난다. 최근에 희박성 제약조건의 비음수 행렬 분해(nonnegative matrix factorization with sparseness constraint; NMFsc)를 이용한 광원추정 방법이 제안되었다. 이 방법은 낮은 희박성 제약조건을 사용해서 광원을 추정하고, 높은 희박성 제약조건을 사용해서 반사율을 추정한다. 하지만, 희박성 제약조건의 비음수 행렬분해를 이용한 광원 추정 방법은, 영상의 전역적인 정보를 사용하므로, 영상에서 동일한 색이 넓은 영역에 존재하는 경우, 추정된 광원이 큰 오차를 가진다. 이러한 단점을 보완하기 위해, 영상에서 주색도 분석과 희박성 제약조건의 비음수 행렬 분해를 이용한 광원 추정 방법을 제안하였다. 먼저 주색도를 분석하기 위해 영상을 색도 좌표계로 옮기고 색도 히스토그램을 이용하여 유사한 색도를 가지는 영역들로 영상을 분할한다. 다음으로 영상의 주색도는 분할된 영상들 중 색도의 표준편차가 가장 적은 영상의 색도로 선택한다. 마지막으로 주색도 분석 결과와 희박성 제약조건의 비음수 행렬 분해를 이용해 입력 영상에서 주색도 성분을 제거하고 최종적인 광원을 추정한다. 실제 촬영 영상에 대한 평균 각오차를 사용하여 기존의 방법과의 성능을 비교하였고, 그 결과 제안하는 방법의 평균 각 오차는 5.5를 나타내어 영상의 주 색도를 포함하여 광원을 추정한 기존 방법의 평균 각 오차 5.7 보다 우수한 성능을 나타내었다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권6호
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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.

• 한국정보과학회논문지:소프트웨어및응용
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• 제36권5호
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• pp.347-352
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• 2009

주어진 비음수 데이터를 두 개의 비음수 행렬의 곱의 형태로 표현하는 비음수 행렬 분해(Nonnegative Matrix Factorization)는 비음수 데이터의 다변량 분석에서 폭넓게 사용되고 있는 방법이다. 비음수 행렬 분해는 집단화(Clustering), 특히 문서의 집단화에서 유용하게 쓰일 수 있다. 본 논문에서는 주어진 문서들로부터 구성된 단어-문서 행렬을 두 개의 비음수 행렬의 곱으로 분해할 때, 그 중 하나의 행렬에 직교 제한을 주는 비음수 행렬의 직교 분해(Orthogonal Nonnegative Matrix Factorization) 방법을 다룬다. 현존하는 비음수 행렬의 직교 분해 방법은 직교 제한과 관련된 항을 더해주는 방식을 사용하지만, 여기서는 Stiefel 다양체 위에서의 실제 기울기를 직접 구하여 곱셈의 업데이트 알고리즘을 유도하였다. 다양한 문서 데이터에 대한 실험을 통해 새롭게 유도된 비음수 행렬의 직교 분해 방법이 기존의 비음수 행렬 분해나 기존의 비음수 행렬의 직교 분해보다 문서 집단화에서 우수한 성능을 나타냄을 보였다.

• ETRI Journal
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• 제35권2호
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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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• 제11권1_2호
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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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• 제13권12호
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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.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2002년도 가을 학술발표논문집 Vol.29 No.2 (2)
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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.

• 대한산업공학회지
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• 제19권2호
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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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• 제31권3_4호
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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.