Research on large margin classifiers from the “local” and “global” view has become an active topic in machine learning and pattern recognition. Inspired from the typical local and global learning machine Maxi–Min Margin Machine () and the idea of the Locality Preserving Projections (LPP), we propose a novel large margin classifier, the Generalized Locality Preserving Maxi–Min Margin Machine (), where the within-class matrices are constructed using the labeled training points in a supervised way, and then used to build the classifier. The within-class matrices of preserve the intra-class manifold in the training sets, as well as the covariance matrices which indicate the global projection direction in the model. Moreover, the connections among , and LFDA are theoretically analyzed, and we show that can be considered as a generalized machine. The is also more robust since it requires no assumption on data distribution while Gaussian data distribution is assumed in the machine. Experiments on data sets from the machine learning repository demonstrate its advantage over in both local and global learning performance.