The Convergence Analysis Of Interval Normalizing Oja-Xu MCA Algorithm

Minor component analysis (MCA) is a very important statistical method to find the direction in which input signals have the smallest covariance. And it has a wide application in the fields of data analysis and signal processing. The artificial neural network has high self-adaptability, error tolerance and the parallel processing capabilities, and is ideal for high dimensional signal minor component extraction. Recently, many MCA neural networks learning algorithms are used for minor component analysis, including the deterministic discrete time (DDT) method. DDT method can maintain the discrete behaviors, and the learning rate can be a positive constant. The Oja-Xu MCA algorithm is one of this kind of methods. Unfortunately this algorithm is not convergent. Based on this, a modified MCA learning algorithm is proposed by adding a normalization step, and the convergence is proved. To improve the convergence speed and reduce the computational complexity, two modified methods are proposed:fixed interval normalizing method and adaptive interval normalizing method. In this paper, the two modified methods are studied, and some convergence results are obtained.The structure of this paper is organized as follows:In Chapter 1, a brief introduction of ANN and the knowledge of MCA learning algorithm are given. In Chapter 2, the convergence of the fixed interval normalizing method is analyzed, and a necessary and sufficient condition for convergence is obtained. And then we give the numerical experiments to compare the convergence speed with the algorithm normalizing each step, In Chapter 3, the convergence of adaptive interval normalizing method is discussed, and some numerical experiments are given to show the theoretical results.