主曲线成分分析

Principal Curve Component Analysis

广泛应用的第一主成分是对数据集的一维线性最优描述,主曲线是第一主成分的非线性推广。线性主成分分析是一种线性分析方法,而数据通常是非线性的。用线性方法分析非线性数据在分析能力上常常是受限的。为此在对线性主成分分析非线性数据研究的基础上,提出了一种新的非线性成分分析方法,即主曲线成分分析。该方法从数据本身出发进行非线性分析,强调非参数特性,能有效地建模非线性数据。实现主曲线成分分析时,采用了改进的神经网络建模方法,该建模方法以其较强的近似性能很好地表达了非线性关系。仿真实验结果表明,主曲线成分分析能很好地解决非线性主成分问题,应用前景广阔。

The first linear principal component is the optimal linear 1-d summarization of the data. Principal curves are nonlinear generalizations of the first linear principal component. Principal component analysis is a linear method, but the most data are nonlinear. Sometimes the linear principal component analysis works inadequately when the data are nonlinear. In this paper, a new nonlinear analytic method, principal curve component analysis (PC^2A) is proposed. This method can model nonlinear data effectively, which analyzes the data from its inherence and emphasizes the non-parametric characteristic. And the method uses the advanced neural network to model data. This is an excellent approach for expressing the nonlinear relationship because of its universal approximation property. Experimental results show that principal curve component analysis is excellent for solving nonlinear principal component problem, and it has great applications potentials.