Isomap Algorithm And Its Application To The Classification Of EEG Generation Source

Scientists are working with large volumes of high-dimensional data in informational era. Dimensionality reduction is an important technique, finding meaningful low-dimensional structures hidden in their high-dimensional observations.The algorithms of dimensionality reduction can be classified into two categories: linear and nonlinear dimensionality reduction method. PCA, a linear dimensionality reduction method, is simple to implement, and guaranteed to discover the true structure of data lying on or near a linear subspace of the high-dimensional input space. But this algorithm cannot solve nonlinear problem.As a representational algorithm of nonlinear dimensionality reduction methods, Isomap is a global optimal algorithm. It builds on CDMS but seeks to preserve the intrinsic geometry of data, as captured in the geodesic manifold distances between all pairs of data points. In this paper we research the two method, and importantly study and discuss Isomap and its application .The main work of this paper include:1) On the basis of dimensionality reduction theory, we research and analyze the linear dimensionality reduction technique such as Principal Component Analysis (PCA), and nonlinear dimensionality reduction methods, such as Isometric Mapping (Isomap) and S-Isomap . Then, we respectively analyze the instance of PCA and Isomap,Isomap and S-Isomap.2) We importantly study Support Vector Machine method, including the principle, the mathematical model and structure of SVM.3) We do the emulation experiment of EEG generation source by combing Isomap and SVM. In our experimentation, the main work is to test the dimensionality reduction ability of Isomap, the tolerant capability to noise, and the infection to the result, and to analyze the result of the emulation experiment.