Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

equilibrium point Related Publications

3 Convergence Analysis of an Alternative Gradient Algorithm for Non-Negative Matrix Factorization

Authors: Mao Ye, Tao Li, Zijian Liu, Chenxue Yang, Jiao Bao

Abstract:

Non-negative matrix factorization (NMF) is a useful computational method to find basis information of multivariate nonnegative data. A popular approach to solve the NMF problem is the multiplicative update (MU) algorithm. But, it has some defects. So the columnwisely alternating gradient (cAG) algorithm was proposed. In this paper, we analyze convergence of the cAG algorithm and show advantages over the MU algorithm. The stability of the equilibrium point is used to prove the convergence of the cAG algorithm. A classic model is used to obtain the equilibrium point and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the cAG algorithm are obtained, which help reducing the evaluation time and is confirmed in the experiments. By using the same method, the MU algorithm has zero divisor and is convergent at zero has been verified. In addition, the convergence conditions of the MU algorithm at zero are similar to that of the cAG algorithm at non-zero. However, it is meaningless to discuss the convergence at zero, which is not always the result that we want for NMF. Thus, we theoretically illustrate the advantages of the cAG algorithm.

Keywords: Stability, Convergence, equilibrium point, Non-negative matrix factorizations, cAG algorithm

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2 Existence and Stability Analysis of Discrete-time Fuzzy BAM Neural Networks with Delays and Impulses

Authors: Chao WANG, Yongkun Li

Abstract:

In this paper, the discrete-time fuzzy BAM neural network with delays and impulses is studied. Sufficient conditions are obtained for the existence and global stability of a unique equilibrium of this class of fuzzy BAM neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Some numerical examples are given to demonstrate the effectiveness of the obtained results.

Keywords: equilibrium point, Global exponential stability, Discrete-time fuzzy BAM neural networks, ─▒mpulses, global asymptotical stability

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1 On the Fuzzy Difference Equation xn+1 = A +

Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

Abstract:

In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: persistence, boundedness, Fuzzy difference equation, equilibrium point, asymptotic behaviour

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