Research Of Principal Components Analysis Methods Based On Fuzzy Sets Theory

One of the common features of this kind of problem is that many variable features provide some repeat information in a certain degree. Therefore people hope that, in the course of quantitative analysis of data, people can conduct the dimension reduction of higher dimensional data and/or the feature extraction beforehand so that we use less dimensional data and unrelated new variables to reflect the most information from prior variables. The analysis of main elements is the best ideal device to meet this requirement.However, although the analysis of main elements is a mature way and an ideal effectiveness, its basic idea is to construct a range of linear combinations of original variables by means of linear transformation, and every main element only reflects the linear dependence of different variables existing in original data. For given dataset, if different variables are nonlinear relation, or non-numerical data, the effectiveness of main elements analysis will be lost, even can't be conducted.Fuzzy set theory is a kind of mathematics method to deal with and settle the vague and/or fuzzy phenomenon existing in the real world. From its initial stage to nowadays it also provides some effective ways of settlement. The research paper selects two problems of the data dimension reduction with non-linear relativeness among variables and the data dimension reduction in different regions to make initial research with the help of related thoughts existing in fuzzy set theory.To counter the problem of non-linear feature extraction, the paper raises the main elements analysis algorithm based on fuzzy similarity measure. This algorithm adopts the matrix of fuzzy similarity measure in place of the covariance matrix of the main elements analysis algorithm to extract the main parts of nonlinear correlation so as to make information provided by these new variables more efficient than classical main elements analysis algorithm.To counter the problem of fuzzy figures or regional figure data feature extraction, the paper offers a simple convenient method of main elements analysis of regional data. This algorithm uses the fuzzy clustering analysis approach of mature regional figures data and the main elements analysis of easier center-radius. In this case the research paper uses the median of regional figures data and information provided by radius showing the advantage of easy calculation.In order to verify the feasibility and efficiency of two algorithms provided by the paper, with help of the analysis approach of fuzzy system theory, we compare two real life datasets with the experiment so as to realize the complete research process from thoughts description to algorithms design and to verification of instance.