OPTIMALITY CRITERIA FOR PRINCIPAL COMPONENT ANALYSIS AND GENERALIZATIONS

Principal components analysis can be derived from various criteria. Be cause these give essentially the same results, the question of which c riterion should be used has not received much attention. Nevertheless, it can be argued that the approach of Pearson and Eckart & Young, bas ed on variance explained by components, is more elegant and flexible t han the (more popular) approach of Hotelling, which is concerned with variance that components have rather than explain. When two or more co rrelation or covariance matrices, based on the same variables, are to be analyzed in generalized component analysis, the question of which c riterion is used becomes of utmost importance. A taxonomy of generaliz ed principal component methods is given. It appears that generalized c omponent analysis based on the Hotelling criterion coincides with one particular generalization based on the criterion of Pearson and Eckart & Young.