SIMPLIFICATION OF HIGH-DIMENSIONAL CHAOSBY PRINCIPAL COMPONENT ANALYSIS BASED ON PROJECTION PURSUIT
高维混沌降维的投影追踪主分量分析法

Since some physiological signals, such as EEG are generated from high dimensional chaotic system, low-dimensional chaos theories and algorithms are not suitable for them. To make feasible application of such theories and algorithms to high-dimensional system, a nonlinear technique called Principal Component Analysis based on Projection Pursuit (PP PCA) is introduced, which decomposes any signal into an orthogonal linear expansion of waveforms. These waveforms are selected to best match the signal structure. First, an application of PP PCA to linearly and nonlinearly mixed noisy periodical signals is described. Next, multiple Lorenz attractor is formed. PP PCA is performed to simplify this high-dimensional system. Estimation of correlation dimension(D2) shows its effectiveness in reducing dimension, to make a simpler system. The important original information is also retained discussed. This simulation proves that it is possible to further apply PP PCA to high-dimensional chaos in EEG.