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。

2 In view of confirming the SVM parameter(including nucleus funtion and its parameter), the author puts forward evolutionary support vector machine method which combines the global optimization characteristic of genetic algorithms withchoice features which SVM solves the questions such as little sample, high-dimension and nonlinear.

Because it has quite perfect theoretical properties and good learning performance, and can solve some practical problems such as a little sample, non-linear, high-dimension and part minimized value, SVM becomes the new research hotspot after the research of Artificial Nerve Net.

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.

Kruskal method is one of nonmetric multidimensional scaling. Depending on the dissimilarity of the objects in study, it conducts calculation in an order from low to higher dimension, to provide the choosing of an optimum dimensionality and an optimum scaling, but with the maintenance of the original relations among the objects.In this paper, we have chosen two groups of geological data. One is of skarn copper deposit, the other is of the Fusulinids of Permian.Using FORTRAN algorithmic language, we have compiled...

Kruskal method is one of nonmetric multidimensional scaling. Depending on the dissimilarity of the objects in study, it conducts calculation in an order from low to higher dimension, to provide the choosing of an optimum dimensionality and an optimum scaling, but with the maintenance of the original relations among the objects.In this paper, we have chosen two groups of geological data. One is of skarn copper deposit, the other is of the Fusulinids of Permian.Using FORTRAN algorithmic language, we have compiled the source program, and calculated it on EC1040 computer. Finally, a geological explanation was given. It is proved that the Kruskal method is effective in solving geological problems.

If an (N×P) matrix W is the geological data matrix, where N is the number of samples and P the number of variables, then the matrix features an N much greater then P. Previously, an (N×N) matrix, which is usually a high dimension matrix, must be formed in Q-mode factor analysis. Therefore it has only a restricted application owing to the high dimension matrix. The R-Q mode factor analysis, however, only needs to form a ( P × P ) matrix W'W(usually P<50). On the basis of W'W, we can extract both R-mode and Q-mode...

If an (N×P) matrix W is the geological data matrix, where N is the number of samples and P the number of variables, then the matrix features an N much greater then P. Previously, an (N×N) matrix, which is usually a high dimension matrix, must be formed in Q-mode factor analysis. Therefore it has only a restricted application owing to the high dimension matrix. The R-Q mode factor analysis, however, only needs to form a ( P × P ) matrix W'W(usually P<50). On the basis of W'W, we can extract both R-mode and Q-mode factors simultaneously by invoking the Eckart - young theorem, which makes the actual application of Q-mode factor possible. Another advantage of the R-Q mode factor analysis is that Q-mode factor and R- mode factor can be shown simultaneously on a plan. Then we can observe the relationship between the variables, between the samples, between the variables and factors and between the samples and variables on the plan.

This paper,based on the point of view of nonlinear dynamics,studies the dynamic processes of seismogeny and occurrence of large earthquakes from the two aspects of seismicity characteristics and rock experiment.Primary results got are that seismicity chara- cteristics possesses self-similarity in statistics,is more complex in features of temporal -spatial distribution,has non-integral fractal dimension and is respectively simular to Cantor set or one-dimensional continuum⊕Cantor set.But we have found that seismic...

This paper,based on the point of view of nonlinear dynamics,studies the dynamic processes of seismogeny and occurrence of large earthquakes from the two aspects of seismicity characteristics and rock experiment.Primary results got are that seismicity chara- cteristics possesses self-similarity in statistics,is more complex in features of temporal -spatial distribution,has non-integral fractal dimension and is respectively simular to Cantor set or one-dimensional continuum⊕Cantor set.But we have found that seismic activities show a low dimensional chaotic state in phase space before the mainshock;and these seismic activities all have a strange attractor of lower dimension and appear as a chaotic order. after the mainshock the seismicity displays a kind of random noise with very high dimension and no saturation value. Before rock failure fracture,the frequency distribution of acoustic emission activity also appears in a chaotic state and its correlation dimension value is 3.1,which is above that of the earthquake.In studies of information dimension,it has been found for the first time that there always exists an evident process of decreasing dimension,with an orderly state,before the occurrence of a large earthquake and rock failure fracture.And then,indeterminacy increases and so does the dimension value until the occurrence of the large earthquake or rock failure fracture.At the same time the scaling changes,and it has been found for the first time that before the occurrence of a large earthquake or rock failure,the non-scaling area abruptly narrows,showing extremely critical instability.The phenomena mentioned above do not appear at other periods,including the post-mainshock period.Obviously this is significant in the exploration of the laws for short-period earthqua- ke prediction.