• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.201-210
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• 2012

A modified multiplicative update algorithms is presented for computing the nearest correlation matrix. The convergence property is analyzed in details and a sufficient condition is given to guarantee that the proposed approach will not breakdown. A number of numerical experiments show that the modified multiplicative updating algorithm is efficient, and comparable with the existing algorithms.

• 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.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
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• 제14권3호
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• pp.296-300
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• 2008

최근에 개발된 Nonnegative tensor factorization(NTF)는 비음수 행렬 분해(NMF)의 multiway(multilinear) 확장형이다. NTF는 CANDECOMP/PARAFAC 모델에 비음수 제약을 가한 모델이다. 본 논문에서는 Tucker 모델에 비음수 제약을 가한 nonnegative Tucker decomposition(NTD)라는 새로운 텐서 분해 모델을 제안한다. 제안된 NTD 모델을 least squares, I-divergence, $\alpha$-divergence를 이용한 여러 목적함수에 대하여 fitting하는 multiplicative update rule을 유도하였다.

• ETRI Journal
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• 제39권1호
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• pp.21-29
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• 2017

This paper addresses the problem of unsupervised speech separation based on robust non-negative matrix factorization (RNMF) with ${\beta}$-divergence, when neither speech nor noise training data is available beforehand. We propose a robust version of non-negative matrix factorization, inspired by the recently developed sparse and low-rank decomposition, in which the data matrix is decomposed into the sum of a low-rank matrix and a sparse matrix. Efficient multiplicative update rules to minimize the ${\beta}$-divergence-based cost function are derived. A convolutional extension of the proposed algorithm is also proposed, which considers the time dependency of the non-negative noise bases. Experimental speech separation results show that the proposed convolutional RNMF successfully separates the repeating time-varying spectral structures from the magnitude spectrum of the mixture, and does so without any prior training.

• 한국항공우주학회지
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• 제44권11호
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• pp.965-972
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• 2016

유도형 탄약은 비행속도 증가를 이용한 기존의 사거리 증가 방식과 다르게 정밀 유도제어를 사거리 연장 및 정밀 타격하는 기술을 기반으로 한다. 고회전으로 상승하는 탄은 탄도 정점에서 후미 날개를 전개하여 회전을 감소하고, 최종적으로 회전을 제거한 후 비행하게 된다. 주 날개 전개 전 탄체 뒤집힘 감지를 위하여 자세 추정이 요구되는데, 회전 감속 중에서는 일정한 회전을 가정한 기존의 유도무기 자세 추정 기법을 사용할 수 없다. 또한, 비행 시에는 횡축 가속도를 제어하기 때문에 중력 가속도 성분을 기반으로 하는 일반적인 무인기의 자세 추정 기법은 큰 오차를 발생한다. 이러한 문제를 해결하기 위해 본 논문에서는 저속 회전 및 비행 중 자세추정기법을 제시하고, 무인기에 탑재하여 비행 실험을 통해 검증하였다. 저속 회전 중 자세 추정 기법은 롤 각을 상태변수로 갖는 칼만 필터 형태로 구성하였다. 비행 시 자세 추정 기법은 사원수를 이용한 곱연산 확장형 칼만 필터를 기반으로 하며, 가속도 측정치가 중력 가속도뿐만 아니라 선회에 의한 구심력을 포함하도록 측정 모델을 개선하였다.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.365-380
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• 2012

Non-negative matrix factorization (NMF) is a very efficient method to explain the relationship between functions for finding basis information of multivariate nonnegative data. The multiplicative update (MU) algorithm is a popular approach to solve the NMF problem, but it fails to approach a stationary point and has inner iteration and zero divisor. So the elementwisely alternating projected gradient (eAPG) algorithm was proposed to overcome the defects. In this paper, we use the fact that the equilibrium point is stable to prove the convergence of the eAPG algorithm. By using a classic model, the equilibrium point is obtained and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the eAPG algorithm are obtained, which can accelerate the convergence. In addition, the conditions, which satisfy that the non-zero equilibrium point exists and is stable, can cause that the algorithm converges to different values. Both of them are confirmed in the experiments. And we give the mathematical proof that the eAPG algorithm can reach the appointed precision at the least iterations compared to the MU algorithm. Thus, we theoretically illustrate the advantages of the eAPG algorithm.