Degenerate Solution To Support Vector Machine And Weighed LSSVM Local Method For Predicting Chaotic Time Series

The determination of an underlying structure from a limited number of observation is the core objective of statistical learning theory. Many important learning problems fall within this framework. These include supervised and unsupervised learning. In the supervised learning framework, the support vector machine (SVM), proposed recently by Vapnik and co-workers, has developed a kind of new general learning algorithm. As results of aiming at minimizing structure risk, the support vector machine can pay attention to the empirical training error and the generalization ability. It has been proved a powerful tool in dealing with learning problem.As for current research about SVM, these contain fundamental research and applied research. The solution to SVM is a fundamental research important aspect. The reason is that it has relation with the existence of the optimal separating hyperplane in sample space or reproduce kernel Hilbert space. If the optimal separating hyperplan does not exist, carrying out learning task by SVM is invalid. This dissertation points out that when the solution to SVM degenerates, the optimal separating hyperplan does not exist, whether it exists or not is decided by the distribution of sample. Through the optimized theory, we give necessary and sufficient conditions for degeneration of the support vector solution. We also give the significance of the corresponding geometry. In order to avoid occurrence of this phenomenon, some methods are proposed. As regards the applied research about SVM, modelling of the non-linear time series and prediction for them based on SVM is an important branch. Recently, some kinds of SVM such as LSSVM, LSSVD, SVD, are used for forcasting chaotic time series and gain satisfied effect. However, the basic fact is neglected that since chaotic time series come from a complex system, by finite samples, obtaining the model that can accurately reflect the complex system is a difficult thing. With the purpose of overcoming the difficulty, a new chaotic time series forecast method is proposed that choose partial samples to predict based on weighted Least squares support vector. The method is based on the fact that obtaining complex system partial model is less difficult than obtaining complex system overall model, and prediction for chaotic time series is decided by the partial model for the complex system. The simulation results show that this method is valuable and feasible.