中文摘要：

提出了一种新的有监督降维方法：拉普拉斯最大最小判别分析（Laplacian MinMax Discriminant Analysis,LMMDA）.LMMDA通过样本空间中成对点之间的距离定义类内和类间散度矩阵,并通过最小化类内散度、最大化类间散度以求得最优投影矩阵.在LMMDA最优子空间中,类内样本更为紧致,类间样本更为松弛.样本集的结构信息包含在类内、类间的Laplacian矩阵,并可以对最优投影子空间加以控制.在多个数据集上的实验证明了该算法的有效性.

英文摘要：

A new algorithm,Laplacian MinMax Discriminant Analysis（LMMDA）,is proposed in this paper for supervised dimensionality reduction.LMMDA aims at learning a linear transformation which is an extension of Linear Discriminant Analysis（LDA）. Specifically,we define the within-class scatter and the between-class scatter using similarities which are based on pairwise distances in sample space.After the transformation,the considered pairwise samples within the same class are as close as possible,while those between classes are as far as possible.The structural information of classes is contained in the within-class and the between-class Laplacian matrices.Thus the discriminant projection subspace can be derived by controlling the structural evolution of Laplacian matrices.The performance on several data sets demonstrates the competence of the proposed algorithm.