The recognition process has three steps. First, we calculate the face subspace from the training samples; then the new face image to be identified is projected into k-dimensional subspace by using (PCA, LDA, LPP and OLPP); finally, the new face image is identified by a nearest neighbor classifier.

In both LPP and OLPP, we need to construct the affinity matrix, we use the following matlab codes to construct the affinity matrix. Please refer the help of 'constructW.m' for detail explanations for these parameters.
%====================================
options = [];
options.Metric = 'Cosine';
options.NeighborMode = 'Supervised';
options.WeightMode = 'Cosine';
options.bSelfConnected = 1;
options.gnd = gnd_Train;

W = constructW(fea_Train,options);
%=================================
You can also try other graph construction methods and select other weighting schems. Particularly, you may want to try heat kernel which is supposed to be superior to 0/1 and cosine weights. However, there is a parameter t which needs to be set. In our experience, LPP is not sensitive to t, so you may empirically set it. When there is a large amount of training data, you may want to try model selection methods, such as cross validation.


Also, we keep all the non-zero eigenvalues in the PCA step of LPP and OLPP, i.e. ====================================
options = [];
options.PCARatio = 1;

[Vec,Val]=LPP(fea_Train,W,options);
%=================================

The data is used without further pre-processing.

The only difference of the experimental results shown on the right from previous one is that we pre-process the data by normalizing each face vector to the unit.

For more detailed explanations of these experiments, please refer our paper: Deng Cai, Xiaofei He, Jiawei Han and Hongjiang Zhang, "Orthogonal Laplacianfaces for Face Recognition", IEEE Transactions on Image Processing, 2006. To Appear