BKYY dimension reduction and determination

A new theory is proposed for dimension reduction and determination (DRD), called the Bayesian Kullback Ying-Yang (BKYY) learning theory, which is a special case BYY learning system. This theory not only includes the conventional factor analysis, principal component analysis (PCA) type linear mapping, and LMSER based nonlinear PCA as special cases, but also provides a unified general framework with a stochastic implementing procedure for developing various linear and nonlinear DRD techniques together with a new theory for determining the dimension k of the reduced subspace. As examples, we provide: 1) a new batch and adaptive algorithm for factor analysis, 2) criteria for determining the number of factors and the dimension of PCA subspace, 3) a procedure for a specific nonlinear BYY DRD based on Gaussian mixtures, and 4) extensions for auto-association and LMSER nonlinear PCA. Some experimental results are demonstrated.