An approach to build a multi-class classifier is proposed in this paper. This approach consists of a derivation to show under which loss function an optimal classifier can be obtained. It also consists of a method of selection of principal components for multi-class classification through univariate logistic regressions. And it consists of a derivation of certain derivatives to rank the features using two-layered neural network classifier. An experiment of using a two-layered neural network to test the proposed approach was carried out. The performance of the proposed method of dada reduction was found better than those of some other methods in this particular experiment. And the features that have high ranking of influence were found credible.