Time Dependent Principal Component Analysis
Principal Component Analysis (PCA) is one of the useful descriptive methods for multivariate data. One aim of the methods is to construct new variables by a linear combination from original variables and illustrate the structure of variables and individuals on a new space based on new variables. In this method principal components have some meanings to summarize variables. Suppose that we obtained principal components at two time points. Then principal components obtained from data at different times will have different meanings if linear combinations of variables are different. For example, the first principal component at time 1 and that at time 2 do not always have the same meanings, as seen in the following example. The first principal component at time 1 may appear as the second or the third principal component at time 2, thus changing the meanings of the first principal components from two time points. Therefore care must be exercised for the interpretation of results from different time points.
In this paper we will propose a method to connect smoothly principal components or loadings from different time points.
KeywordsPrincipal Component Analysis Data Matrix Multivariate Data American Statistical Association Descriptive Method
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