• Journal of applied mathematics & informatics
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• v.30 no.1_2
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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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• 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 KIISE:Computing Practices and Letters
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• v.14 no.3
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• pp.296-300
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• 2008

Nonnegative tensor factorization(NTF) is a recent multiway(multilineal) extension of nonnegative matrix factorization(NMF), where nonnegativity constraints are imposed on the CANDECOMP/PARAFAC model. In this paper we consider the Tucker model with nonnegativity constraints and develop a new tensor factorization method, referred to as nonnegative Tucker decomposition (NTD). We derive multiplicative updating algorithms for various discrepancy measures: least square error function, I-divergence, and $\alpha$-divergence.

• ETRI Journal
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• v.39 no.1
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.11
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• pp.965-972
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• 2016

This paper presents results of flight experiments on a navigation algorithm including multiplicative extended Kalman filter for estimating attitude of the guided munition. The filter describes orientation of aircraft by data fusion with low-cost sensors where measurement update is done by multiplication, rather than addition, which is suitable for quaternion representation. In determining attitude from vector observations, the existing approach utilizes a 3-axis accelerometer as a 2-axis inclinometer by measuring gravity to estimate pitch and roll angles, while GNSS velocity is used to derive heading of the vehicle. However, during accelerated maneuvers such as coordinated flight, the accelerometer provides inadequate inclinometer measurements. In this paper, the measurement update process is newly defined to complement the vulnerability by using different vector observations. The acceleration measurement is considered as a result of a centrifugal force and gravity during turning maneuvers and used to estimate roll angle. The effectiveness of the proposed method is verified through flight experiments.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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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.