基于类别信息的监督局部保持投影方法

摘要

局部保持投影算法(LPP)是拉普拉斯映射(LE)的线性近似,但LPP作为一种无监督方法,并没有有效利用已有的类别信息提高分类效率.为此提出一种基于类别信息的监督局部保持投影方法(SLPP-LI).在学习投影矩阵时,SLPP-LI综合利用了流形的几何结构和已有训练点的类别信息,通过调整控制参数的取值,有效地利用已知的低维信息,并且直接求解线性方程获得高维数据的低维模型.通过在多个人脸数据库和手写数字库上的对比实验,表明了SLPP-LI对于高维数据的初始维数以及训练数据的数目并不敏感,与主分量分析法(PCA)、LPP、正交LPP( OLPP)、有监督的LPP(SLPP)相比,均具有较高的识别率,充分说明SLPP-LI算法能够有效处理分类问题.%Locality Preserving Projection ( LPP) is an approximation of Laplacian Eigenmap (LE), but it is an unsupervised method, and does not take advantage of the existing classification information to improve the classification efficiency. Therefore, a supervised locality preserving projection named SLPP-LI method was proposed based on class information. In the study of projection matrix, SLPP-LI took advantage of the comprehensive utilization of the geometrical structure of the manifold and the class information of the existing train set, SLPP-LI can effectively take advantage of the known low dimensional information by adjusting the control parameters and obtain the low-dimensional models of high dimensional data by directly solving the linear equation. The comparative experiments with several face databases and handwritten digital databases show, SLPP-LI is neither sensitive to the original dimension of high dimension data, nor the number of the training data. For the same kind of problems, SLPP-LI has higher recognition rate compared with PCA, LPP, OLPP and SLPP, and it can effectively deal with the classification issues.