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high-dimension
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  高维
    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.
    在统计学习理论的基础上 ,研究了小样本、非线性高维模式识别 ; 研究了有监督学习支持向量网络的非线性分类设计 ;
短句来源
    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。
短句来源
  高维数
    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.
    2.针对支持向量机在参数(包括核函数及其参数)确定方面的问题,提出了进化支持向量机方法,该方法既利用了遗传算法的全局优化能力,又利用了支持向量机在处理小样本、高维数、非线性等问题方面的优良特性;
短句来源
    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.
    由于具有较完备的理论基础和较好的学习性能,能很好地解决小样本、非线性、高维数和局部极小点等实际问题,使它成为继神经网络之后新的研究热点。
短句来源
    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.
    支持向量机(SVM)基于统计学习理论,可以处理高度非线性分类和回归等问题,不但较好地解决了小样本、过学习、高维数、局部最小等实际难题,而且具有很强的泛化(预测)能力。
短句来源
    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.
    人工神经网络方法可对复杂的高维数据进行非线性映射,在模式识别领域得到越来越广泛的应用。
短句来源
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  high-dimension
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.
      
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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.

Kruskal法就是将N个多维(P维)对象点,在近似的意义下,从P维约简到一个较低维数的空间内,寻求一个最佳的空间维数和空间标度,而近似地保存各对象点数据的原始关系。这种方法通常称为多维标度法。

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.

设(N×P)矩阵W是地质数据矩阵(N是样品数,P是变量数),这一矩阵结构特征是N大大于P.以前Q式因子分析必须形成一个通常是高维的N×N矩阵.由于这一高维矩阵,Q式因于分析的应用受到限制.然而R-Q式因子分析只需形成一个(P×P)矩阵W'W(通常P<50).根据W'W,我们用Eckart-young理论同时提取R式和Q式因子,这使得Q式因子分析的实际应用成为可能.R一Q式因子分析的另一优点是R式因子解和Q式因子解可以同时表示在一张平面图上,然后我们就可以在这张图上考察变量之间、样品之间,变量和因子之间以及变量和样品之间的关系.

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.

本文根据非线性动力学观点,从地震活动特征和岩石模拟实验两个方面研究了大地震孕育和发生的动力学过程。初步结果得到:地震活动特征具有统计自相似性,且其时、空分布特征比较复杂,具有非整分维,分别类似于康托尔集合或一维连续统⊕康托尔集合。而且我们发现在主震前,地震活动在相空间呈现一种低维浑沌状态。它们都有一个维数比较低的奇怪吸引子,表现为一种浑沌序。主震后,其地震活动表现为一种维数很高且无饱和值的类随机噪声。岩石失稳破裂前,其声发射活动频度的分布也表现为一种浑沌态,其关联维数值为3.1,高于地震。在信息维研究中,首次发现在大地震发生前和岩石失稳破裂前,均有一个明显的降维过程,表现为一种有序态。随后不确定性增大,其维数值增高,直至大震发生和岩石失稳。同时发现标度性发生变化。首次得到大震前或岩石失稳前无标度区急剧变窄,表现出强烈的临界不稳定性。其它期间包括主震后均不存在上述现象。显然这对探索短期预报具有重要意义。

 
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