Discussion On Selecting The Number Of Principal Components

As a data dimensionality reduction technology, the principal component analysis has been combined with comprehensive evaluation,regression analysis and data mining methods. It was widely used in economics, sociology, biology, medical science and other fields. In practical application of principal component, it inevitably involves the problem of the reasonable selection of the number of principal component.Firstly, with the data generated by SAS software, this paper analyses the size of effect of the direction bias and the variance bias of the principal components in different proportion and discrete degree of outlier. Then the article shows that to explore the number of principal components is significant only with the premise of ensuring the robustness of the principal components, and introduces the common standard of choosing the principal components.Then, this paper analyses the problem how to choose the rational number of the principal component when using a combination of analysis in comprehensive evaluation to principal component analysis. By two examples, this paper respectively from two aspects to show the two kinds of reverse problem of comprehensive evaluation of principal component.The two aspects are the different symbol of weight coefficient of variableand sample structure. It also validates the fact that the existing method of selecting principal component cannot solve the reverse problem of comprehensive evaluation of principal component. Put forward to can solve reverse issue of comprehensive evaluation of principal component as criterion to choose a reasonable principal component.Finally, this article analyses the problem how to choose the rational number of principal component when using a combination of principal component analysis and regression analysis. Through an example, this paper shows that the goodness of fit of the final regression is not good with using the Cp criterion and the criterion of the minimum residual mean square, and puts forward the criterion of choosing principal component to make the goodness of fit of the final regression to largest.