Learning Performance Of Kernel Fisher Discriminant Analysis Based On Markov Sampling

Fisher linear discriminant is a classical dimension reduction and classification algorithms in pattern recognition, its basic idea is to make the high dimensional pattern project to best identify vector space, in order to extract classification information and the compress the feature space dimension. After the projection, the data achieve the maxium class separation distance and the minimum inter-class separation distance in the new subspace model, namely, the pattern has the best separability in the space.In this article, we consider Fisher linear discriminant generalization performance under dependent identically distributed data. We first set up the generalization ability of Fisher discriminant analysis based on the Markov chains with uniformly ergodic Markov chain(u.e.M.c.) properties. And we then prove the Fisher discriminant analysis under uniformly ergodic Markov chain samples is consistent. In the inspiration of Markov chain Monte Marlo (MCMC) method, we put forward a Markov sampling algorithm which can produce uniformly ergodic Markov chain (u. e. M.c.) under the given limited sample set. Finally, under the real data, we have the binary classification experiment and multi-classification experiment. We find Fisher discriminant has smaller error rate under the data produced by Markov sampling algorithm, compared with i. i. d. sampling.