The Improvent Of Principal Component Analysis In Evalution Methods

Evaluation is the premise of decision-making. The level of evaluation has a direct impact on decision-making. Evaluation is so important that a large number of scholars at home and abroad make research and exploration continuously, and a lot of evaluation methods and theory exist today. We only make a study on the principal component analysis(PCA).PCA is a powerful tool for dealing with high-dimensional data. Its purpose is to reduce dimension, and to construct principal components to make sure that each principal component is the linear combination of original variables and the number of principal components is less than the number of original variables, in the case of not losing much significant original information, so that we can simplify the process of analyzing the problem.With extensive application, PCA has increasingly shown some shortcomings. Currently the aspects of improvement have two: one is the robust principal component analysis, PCA starts from eigenvalue and eigenvector's calculation of covariance matrix, but covariance is not robust which can make an effect on solving the problem, so RPCA is put forward because covariance matrix has the defect of non-robust; the other is the nonlinear PCA, which is put forward because PCA has the shortcoming of dealing with data in linear relationship only.This research work includes the following:1.Introduce specifically many methods about PCA's improvement: RPCA and nonlinear PCA, and describe their theory and mathematical models.2.In this paper, we propose a robust kernel principal component analysis based on the fuzzy membership, and make a theoretical proof, In KPCA, the input data space X is mapped byΦ: R p→Hto a new high-dimensional feature space H, while this can achieve nonlinear feature extraction, but there are still outliers. We can give each data point in the feature space a membership, that is to say, we give the data set {Φ( x1 ),Φ( x2 ), ,Φ( xn)}the membership {μ1 ,μ2, ,μn}, making that the one who is far away from the center has less membership, corresponding the fuzzy set is {μ1Φ( x1 ),μ2Φ( x2 ), ,μnΦ( xn)}. Making RKPCA would reduce the impact of outliers, and also avoid the bad effect of the PCA.3.In this paper, we propose a combination principal component analysis used in ability evaluation of urban technological innovation. PCA is an objective weight method, and comprehensive index is a subjective weight method, composing them can get the advantages both. Meanwhile, in practical applications, it is possible that evaluation objects' rank is different, but their scores are very close, in order to reflect this proximity, we propose the concept of class rank.