模糊主成分分析方法的研究与分析

主成分分析(PCA)是一种广泛应用于数据压缩的多元统计分析方法.然而,经典主成分分析它对极端值及缺失值非常的敏感,而极端值与缺失数据会带来残缺或错误的分析结果.针对经典主成分分析的缺点本文提出了模糊数学期望、模糊离差、模糊方差、模糊协方差及模糊相关系数的概念,从而提出了一种有效方法来改进经典主成分分析,即模糊主成分分析(Fuzzy PCA).把模糊数学的知识应用到主成分分析中,使模糊集参与决策分析,使人为因素带来的不确定性达到最小,从而大大提高了分析结果的准确性和可信度.同时,本文以模糊主成分分析为出发点,建立了一个数据分析平台,平台具有可移植性,为其它使用提供了通用接口,为解决类似问题提供极大方便.

Research and Analysis of Fuzzy Principal Component Analysis

Principal component analysis(PCA) is a favorite multivariate statistical method for data compression and information extraction.However,it is well known that PCA is sensitive to outliers and missing data,but it maybe get deformity and error result.As to this problem,this paper puts forward the concepts of fuzzy expectation,fuzzy deviation,fuzzy variance,fuzzy covariance and fuzzy correlation,then introduces a powerful approach to improve the PCA(fuzzy PCA).It can be explained that if fuzzy math is applied into PCA by making fuzzy sets to participate in decision-making,it can raise accuracy and reliability of the decision results.At the same time,this paper establishes a data analysis platform that has transplant ability and offers general interfaces to other uses;it has offered maximum convenience to solve similar problems.