Minimum Synthesis and Learning Algorithm for A Hybrid Nonlinear Predictor

现在有一天，我们有很多问题，环境问题，环境流行病，经济危机，人口问题，自然破坏，自然保护，and so on. In order to solve these problems，这是非常重要的分析进程，这些phenomena可以regarded as timeseries. Mainly they are nonlinear time series. So，nonlinear prediction becomes very important.(1) A nonlinear PredictorIn this research project，我们已经开发了一个hybrid nonlinear predictorwhich a neural network and a feed-forward linear predictor.自neural network haslinear output unit，非linear part和部分非linear part可以预测神经网络。part is predicted by the linear predictor.(2) Learning AlgorithmsAn improved Learning algorithm hasbeen proposed,这是一个增强的神经网络和线性预测。learning algorithm has been proposed for noisy nonlinear time series prediction.(3) NonlinearityAnalysis of Time SeriesPrediction is the mapping from the past samplex(n-1)=[x(n-1),x(n-2),..,x(n- n)] to the next sample x(n). When the past samples x(n)x(n D22 D2-1) are similar, however，the next samples x(n - D21 - D2) and x(n - D22 - D2) are far from to each other, then，nonlinearity of this time series is high. A measure，(4) Prediction of Real Nonlinear Time SeriesThe这一属性之前介绍。proposed method applied to many the real nonlinear time series，包含Chaos，water levels of some lake, fog generation，因此on The proposed hybrid nonlinear predictor demonstrated good performance compared with Theconventional methods。

Now a day, we have a lot of problems, environmental disruption, environmental pollution, economic crisis, population problem, natural disaster, nature conservation, and so on. In order to solve these problems, it is very important to analyze progress of these phenomena. These phenomena can be regarded as time series. Mainly they are nonlinear time series. So, nonlinear prediction becomes very important.(1) A Nonlinear PredictorIn this research project, we have developed a hybrid nonlinear predictor, which combines a neural network and a feed-forward linear predictor. Since the neural network has linear output unit, most of nonlinear part and some linear part can be predicted by the neural network. The remaining part is predicted by the linear predictor.(2) Learning AlgorithmsAn improved learning algorithm has been proposed, which separately optimize the neural network and the linear predictor in this order. An enhanced learning algorithm has been proposed for noisy nonlinear time series prediction.(3) Nonlinearity Analysis of Time SeriesPrediction is the mapping from the past sample x(n-1)=[x(n-1),x(n-2),..,x(n-N)] to the next sample x(n). When the past samples x(nィイD21ィエD2-1) and x(nィイD22ィエD2-1) are similar, however, the next samples x(nィイD21ィエD2) and x(nィイD22ィエD2) are far from to each other, then, nonlinearity of this time series is high. A measure, which can evaluate this property has been introduced.(4) Prediction of Real Nonlinear Time SeriesThe proposed method was applied to many the real nonlinear time series, including Chaos, water levels of some lake, fog generation, and so on. The proposed hybrid nonlinear predictor demonstrated good performance compared with the conventional methods.