Exogenous Forces in the Development of Our Banking System

Abstract

A new method to optimize with orthonormal constraints is described, where a particular composition of plane (Givens) rotations is used to parameterize decision variables in terms of angles. It is showed that this parameterization is complete and that any orthonormal k-by-nmatrix can be derived to a set of no more than kn-k(k+1) angles. The technique is applied to the emph {feature extraction problem} where a linear subspace is optimized with respect to non-linear objective functions. The Optimal Discriminative Projection (ODP) algorithm is described. ODP is a data compression or feature extraction algorithm that combines powerful model optimization with regularization to avoid over training. The ODP is used primarily for classification problems