多元时间序列特征降维方法研究

Research on Feature Dimension Reduction Method for Multivariate Time Series

针对常见的降维方法难以有效地保留多元时间序列主要特征的问题,分析了传统PCA方法在多元时间序列降维中的局限性;提出一种基于共同主成分分析的线性降维方法;把共同主成分与核技巧相结合,通过数学推导,将其拓展为基于共同核主成分分析的非线性降维方法;最后分析两种方法的降维有效性.与传统PCA方法相比,基于共同核主成分分析的降维方法可以表达变量间的非线性关系、能够选取合适的核函数和形状参数,因此降维手段更为灵活、对数据的适应性更强.实验结果表明,本文提出的降维方法能够更有效地对多元时间序列进行降维.

Existing dimension reduction methods for multivariate time series can＇t preserve its feature effectively. Firstly, it analyses the drawback of PCA method when it is used in MTS dimension reduction ; Secondly, based on common principal component analy- sis, it proposes a linear dimension reduction method for multivariate time series; Then, based on common kernel principal component analysis which is deduced from common principal component analysis and kernel trick, a nonlinear dimension reduction method is proposed; At last, validity of dimension reduction are compared between different methods. Compared with PCA method, the pro- posed nonlinear method can reflect nonlinear relation between different variables, and is robust to different kinds of data by choosing kernel function and parameters. The results of experiments show that the proposed methods can reduce dimension effectively, and at the same time preserve most feature of multivariate time series.