Simultaneous Diagonalization Algorithms with Applications in Multivariate Statistics
The matrix B which minimizes Ф is said to transform S to almost parallel-diagonal form. We give an algorithm for minimizing Ф over B in (i) the group of orthogonal p × p matrices, and (ii) the set of nonsingular p × p matrices such that diag(B′B) = I p , and study its convergence. Statistical applications of the algorithm occur in maximum likelihood estimation of (i) common principal components for dependent random vectors (Neuenschwander 1994), and (ii) common canonical variates (Neuenschwander and Flury 1994). This work generalizes and extends the FG diagonalization algorithm of Flury and Gautschi (1986).
KeywordsCanonical Correlation Analysis Orthogonal Matrix Input Matrix Multivariate Statistical Model Positive Definite Symmetric Matrice
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