Research Of Method And Application On Dimensionality Reduction Of High Dimensional Data Based On Multivariate Chart

After analyzing the challenge and difficulty when facing at multi-class high dimensional data, the method of multi-layer and hierarchical dimensionality reduction based on multivariate chart representation has been proposed in this paper.Firstly, the important and impendence in dimensionality reduction are analyzed by the investigation of relational literatures. It is the vital and mutual problem that how reduces dimensionality of high dimensional data and find the method to understand and solve the problem easily in many science fields. The geometrical distribution, statistical distribution, presentation of high dimensional data type in mathematics, the definition of dimensionality reduction and intrinsic dimensionality have been discussed in detail.Secondly, the dimensionality reduction methods of high dimensional data are classified into two categories with different projection. The linear methods which usually are involved with Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), etc. is introduced briefly. The nonlinear methods whose generally include Multi-Dimensional Scale (MDS), Self-Organize Map networks (SOM), Locally Linear Embedding (LLE) and Isometric Map (Isomap) is also indicated. The advantages and disadvantages of linear and nonlinear methods in dimensionality reduction are discussed subsequently.Thirdly, the pixels presentation method has been put forward to present high dimensional data vividly. The principles of graphical features and features fusion have been illustrated in manner of the graphic. The method of the multi-layer and hierarchical dimensionality reduction based on multivariate chart representation has been expatiated with emphasis. In addition, radar chart representation, which has already been put to use very earlier and widely in all of the multivariate chart representation, has beenemployed to explain this idea of the multi-layer and hierarchical dimensionality reduction.Finally, the partial datasets of machine learning dataset (or benchmark dataset), which has been usually used to evaluating the validity of new method for dimensionality reduction and classifier, and some classical datasets whose appear in many science fields, have been adopted to validate the validity of this method in this papers. The objective comment on the performance and existent problem of this method are briefly given in the end.