A Local Discriminant Projection Method Based on Objective Space

In the existing local discriminant analysis methods, weight matrices in objective functions are determined by neighborhood relationship (in original space) of samples before they are projected, without consideration of changes of the neighborhood after the projection. In order to depict the optimization goal of classification more accurately, a local discriminant projection method based on objective space is proposed, in which weight matrices in objective function are determined by the neighborhood of projected samples, namely, neighborhood in objective space. The objective function is optimized by an iterative procedure. The underlying idea of the new method is that the desired projection should make neighbors, in objective space, of the same class close and neighbors of different class apart. Experiment results show that the method overcomes effectively the problems of local discriminant analysis in original space and achieves good performance on both synthetic data and standard data set of handwriting digital.