Structured multi-classification is a typical supervised learning problem, where each training instance is equipped with a set of candidate labels among which only one is the true label. This problem is often plagued by the slow training speed and the low classification accuracy. The goal of this paper is to propose a novel framework called normalizing quadratic Mapping and principal component Dimensionality Reduction analysis (MDR) Neural Network. Thorough experiments demonstrate it sets the new state of the art, accelerating the convergence of neural network and improving the accuracy of classification recognition with a few number of training rounds.