A METHOD TO DECIDE THE DIMENSION OF DATA BY THE MDL CRITERION(Multidimensional Data Analysis)

In a noisy condition, we apply the shrinkage method in order to remove some characteristic roots of the sample covariance matrix which are smaller than the optimal threshold level, and we also apply the Approximate-Minimum-Description-Length (AMDL) criterion to decide this optimal threshold level. Since the characteristic roots which are smaller than the optimal threshold level are regarded as the noise components of the data, one obtains the significant characteristic roots by removing them. In other words, one determines the intrinsic and true dimension of data. In this paper we assume the sample covariance matrix has the Wishart distribution so that the limiting joint distribution of the characteristic roots of the sample covariance matrix can be simply obtained. Moreover, we show some numerical examples which compare this method with the conventional methods.