On the basis of statistical learning theory, we studied high-dimension nonlinear pattern recognition with small specimen and design of nonlinear classification of support vector network with supervised learning.

On that basis,mapping of high-dimension attributes onto low-dimension attributes in attributes space is carried out by K-L transform and eliminated the correlation among the attributes so that can effectively solve the optimized issue of attributes combination.

在此基础上 ,通过 K- L 变换将属性空间的高维属性映射为低维属性 ,且去除了属性之间的相关性 ,从而有效地解决了属性组合的优化问题。

Support vector machine(SVM) is a new machine learning method based on statistical learning theory. It can process the high nonlinear problems with classification and regression. SVM not only can solve some problems,such as small-sample,over-fitting,high-dimension and local minimum,but also has higher generalization(forecasting) ability than that of the artificial neural networks.

Artificial neural network can implement a non-linear mapping for high-dimension complex data and it has been widely used in the field of pattern recognition.

The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space.

The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space.

Low-and high-dimension limits of a phase separation model

The Belinsky-Zakharov inverse scatteringmethod is extended to a double high-dimension form.

Algorithms of determining maximum (in modulus) complex-conjugate eigenvalues are considered as applied to finding eigenvalues of high-dimension matrices according to the Khilenko method.

Today water resource is very important in the world. The variation of annual runoff not only influences economy and people′s living standards, but also restricts the economic development. To solve these problems, accurately predicting the variation of annual runoff is indispensable to scientifically utilize water resources. Being the output of a rainfall runoff system of drainage basin, the annual runoff time series is a very complex dynamic phenomenon varying from region to region and changing with time, which...

Today water resource is very important in the world. The variation of annual runoff not only influences economy and people′s living standards, but also restricts the economic development. To solve these problems, accurately predicting the variation of annual runoff is indispensable to scientifically utilize water resources. Being the output of a rainfall runoff system of drainage basin, the annual runoff time series is a very complex dynamic phenomenon varying from region to region and changing with time, which includes lots of past information of all variations and hides many laws. The evolution treads of annual runoff time series are often time irreversible, nonlinear with weak dependence. Now traditional methods for predicting annual runoff usually use linear technique, but the forecasting precision is not satisfactory, owing to complexity of its intrinsic evolutions, and its close and complicated relationships to climate change and other hydrologic effect factors. In order to predict the high dimension complex dynamic systems of the annual runoff system, a new model-projection pursuit threshold regressive (PPTR) model is presented in this paper. A scheme of PPTR modeling is also given to reduce the computational amount, a new function of projection indexes is constructed, the relation of projection value and predicted object can be described with threshold regressive (TR) model, and it is suggested that both the function of projection indexes and the parameters of TR model can be optimized by using a real coded genetic algorithm developed by the authors. The examples of predicting annual runoff show that PPTR model is both practical and effective. PPTR model is simple and general, which overcomes the shortcomings of large amount of computation and difficulty of computer programming in traditional projection pursuit methods, benefits the more applications of projection pursuit, and gives a new approach to resolving the high dimension, nonlinear complex predictive problems.

Pattern recognition of support vector network with supervising learning is studied in this paper. On the basis of statistical learning theory, we studied high-dimension nonlinear pattern recognition with small specimen and design of nonlinear classification of support vector network with supervised learning. A hybrid algorithm for solving nonlinear optimization problem is constructed. To deal with the classification of oil and gas, we studied deeply into the extraction of feature parameters and selection...

Pattern recognition of support vector network with supervising learning is studied in this paper. On the basis of statistical learning theory, we studied high-dimension nonlinear pattern recognition with small specimen and design of nonlinear classification of support vector network with supervised learning. A hybrid algorithm for solving nonlinear optimization problem is constructed. To deal with the classification of oil and gas, we studied deeply into the extraction of feature parameters and selection of inner product function. The proposed method can satisfactorily overcome the drawbacks of under or over learning problems of neural network. Desired results have been reached by applying the method to MT data.

Projection pursuit (PP) is a new statistic method, which is good at analyzing no n-normal and non-linear high-dimensional data. It searches for the project di rection reflecting on the structure characteristics of high-dimensional dada ob jectively by projecting and reducing dimensions, and solves "dimension curse" and non-normality and non-linearity among high-dimensions data. The article c ombines the PP technique with auto-regression model of time sequence analysis, and builds up the prediction model of...

Projection pursuit (PP) is a new statistic method, which is good at analyzing no n-normal and non-linear high-dimensional data. It searches for the project di rection reflecting on the structure characteristics of high-dimensional dada ob jectively by projecting and reducing dimensions, and solves "dimension curse" and non-normality and non-linearity among high-dimensions data. The article c ombines the PP technique with auto-regression model of time sequence analysis, and builds up the prediction model of projection pursuit auto-regression (PPAR) . PPAR model tries to realize two-dimensional forecast of magnitude and time, i .e. forecasting the magnitude and time of an event in the fixed research region, and creates the projection pursuit auto-regression model of two-dimensional s eismic time sequence. In the study, we choose first the northern Tianshan area a s the test site, and the results of the regression fitting and pretest test are good, so we could realize tow-dimensional forecast. Considering the value of fo recast practice, i.e. moderately strong earthquake, we take the whole Tianshan m ountain area as our research area. Let the magnitude thresholds of time sequence are 5.0 and 5.5 respectively, and build up the models with data of undeleted-a ftershocks and deleted-aftershocks. Comparing the two models, the latter is bet ter than the former, particularly is to forecast time sequence. Their qualified ration of pretest tests are both high, so they are available for forecasting mag nitude and time of an event.