原始的非线性维数约减算法是无监督的，不能直接用于模式识别。
The original nonlinear dimensionality reduction algorithms are non-supervised, which can't directly be applied in pattern recognition.
最后通过线性参变控制，获得了用有限维数线性矩阵不等式描述的充分条件。
A sufficient condition is obtained using finite dimension linear matrix inequalities (LMI) describing by linear (parameter-variety) control.
在线性规划支撑矢量机中，对其VC维数界作了适当的放宽。
In linear programming linear SVMs, the bound of the VC dimension is loosened properly.
经过分析得出了孔隙度、渗透率与分形维数之间有良好的线性关系这一结论。
After analyzing we conclude that there are linear relationships between porosity, permeability and fractal dimension.
从分形原理出发，提出了非线性机械设备系统信号的分形计算维数的概念。
In the paper, fractal calculating dimension, which is based on fractal theory, is put forwards.
关联维数的全程变化趋势可以反映液压缸运行过程中非线性弹簧的变化特征；
The varying trend of whole process can be used to reflect the varying characteristics of nonlinear spring of moving hydraulic cylinder.
分形维数与钢渣微粉的比表面积间满足良好的线性关系，并与钢渣基水泥材料的胶凝性能良性相关。
A good linear relationship meet between fractal dimension and specific surface area of slag powder, and positive correlation with the cementitious properties of steel slag-based cement material.
对于这样一个高维数、非线性的小样本问题，许多传统的模式识别方法都容易出现过学习或欠学习现象。
When solving this small sample problem with high dimension and nonlinear, many traditional pattern recognition methods will tend to occur overfitting phenomenon.
支持向量机(SVM)作为一种新型的非线性建模方法，适合于处理小样本和高维数的建模问题。
Support vector machines (SVM) is a new nonlinear modeling method which is suitable for solving small samples and high dimension modeling problems.
用极大代数意义下的线性系统理论提出了一种与系统矩阵维数无关的，模块网络迭代法。
By the linear theory in the max-algebra, it presents the block network iterative method which is independent of the dimension of system matrix.
在软测量建模过程中，基于支持向量机的算法能较好地解决小样本、非线性、高维数、局部极小点等问题。
In model establishment of soft-sensing, the problems of small sample, non-linearity, high dimensions and local minimal value can be well solved by support vector machine algorithm.
结合孔隙结构分形维数计算原理，通过线性回归计算了各类孔隙的分形维数。
Combined the calculation principle of fractal dimension of porous structure, the fractal dimensions of three types of pore were obtained by linear regression.
相关维数是定量描述非线性时间序列的一个重要参数，在脑电、心电等生物医学信号的特征描述方面得到了广泛地应用。
Correlation dimension is an important parameter to measure a nonlinear time sequence quantitatively, and it is widely used to analyze biomedical signal, such as EEG and ECG.
通过演化曲线可以看出，分形维数与损伤变量随应力的递增均呈非线性增加，但分维的变化较平缓；
The evolution curve show known that fractal dimension and damage variable present nonlinear increase with the increment of stress, and the change of fractal dimension is relatively smooth.
分形维数是描述自然界和非线性系统中不光滑和不规则几何体的有效工具，是所有分形对象的主要特征之一。
Fractal dimension is usually an effective way that used to describe the non-smooth and non-regular geometry objects in the nature and non-liner systems.
边界单元法降低了求解空间的维数，减少了离散线性方程组的阶数，输入数据比较少，而工作效率高。
This method reduces the number of space dimension, makes the equation system lower order, less data input and higher efficiency .
同时针对神经网络易于陷入局部极值、结构难以确定和泛化能力较差的缺点，引入了能很好解决小样本、非线性和高维数问题的支持向量回归机来进行油气田开发指标的预测；
The method of support vector regression which can well resolve the problem with the insufficient swatch, nonlinear and high dimension is introduction to predict the development index of gas-field.
于是，这些传统方法常常被模型选择与过学习问题、非线性和维数灾难问题、局部极小点问题等困扰。
Therefore, the traditional methods are inclined to bring many problems like model-choosing, over-fitting, non-linear, disaster of dimensionality, local minimum.
电源优化问题具有高维数、非线性、随机性等特点，常规的优化算法难以求解到最优解。
The generation expansion optimization is high dimension, nun-linear, randomness problems. The convention algorithm hardly finds the best solution.
支持向量机是一种新的机器学习方法，它具有推广能力强、非线性和高维数等一系列优点。
Support Vector machine (SVM) is a new method of machine learning. It has some advantages such as generalization ability, nonlinear and high dimensions.
同时给出了输入输出维数相等时的解耦并完全线性化的充要条件。
When the output vector dimensions equal to the input vector dimensions, the necessary and sufficient conditions for decoupling and complete linearization to nonlinear system are given.
作为一种新的机器学习方法，SV M能较好地解决小样本、非线性、高维数和局部极小点等实际问题。
As a new machine learning method, SVM can solve the small sample, nonlinear, high dimension and local minima, the actual problem.
为克服数据库因果关系条件概率矩阵维数灾，将因果关系转化为线性多项式，可使计算简便。
To overcome dimension curse of conditional probability matrix, casual rules in databases is converted to linear polynomial, which makes calculation simple.
本文以抽水蓄能电站及有压引水式水电站为典型对象对水力系统各建筑物建立了整体参数优化数学模型，其后又针对该模型的目标函数不可求导、计算量大、维数多、非线性的特点。
This paper take pumped storage station and diversion type power station as typical objects of study and gives out a global optimal model of the parameters of the water way structures.
它在解决小样本、非线性及高维数等问题中表现出许多特有的优势。
It has many particular advantages on resolving such problems as small sample, nonlinearity and high dimension.
结果表明，支持向量机比BP神经网络有较高的预测精度，并且具有小样本、高维数及非线性等优点。
The result indicates, that the accuracy of predictions by SVMs is better then the predictions of BP neural networks, and with some merits of small samples, multi-dimensions and non-linear.
结果表明，岩体强度强相关于岩体中节理分布的分形维数，分维增大导致岩体强度非线性降低。
It shows the strength of jointed rocks strongly depends on the fractal dimension of joints in rocks. The small increase of fractal...
结果表明，岩体强度与岩体中节理分布的分形维数密切相关，分形维数增大导致岩体强度非线性降低。
The result shows that the strength of jointed rocks strongly depends on the fractal dimension of rock joints. The small increase of fractal dimension will lead to rapid decrease of rock strength.
结果表明，岩体强度与岩体中节理分布的分形维数密切相关，分形维数增大导致岩体强度非线性降低。
The result shows that the strength of jointed rocks strongly depends on the fractal dimension of rock joints. The small increase of fractal dimension will lead to rapid decrease of rock strength.
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