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null (Ed.)Abstract In many dimension reduction problems in statistics and machine learning, such as principal component analysis, canonical correlation analysis, independent component analysis, and sufficient dimension reduction, it is important to determine the dimension of the reduced predictor, which often amounts to estimating the rank of a matrix. This problem is called order determination. In this paper, we propose a novel and highly effective order-determination method based on the idea of predictor augmentation. We show that, if we augment the predictor by an artificially generated random vector, then the part of the eigenvectors of the matrix induced by the augmentation display a pattern that reveals information about the order to be determined. This information, when combined with the information provided by the eigenvalues of the matrix, greatly enhances the accuracy of order determination.more » « less
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