Subspace Learning for Face Recognition on Yale-B database

Algorithms | Data
A random subset with p (=5,10,...,50) images per individual was taken with labels to form the training set, and the rest of the database was considered to be the testing set. For each given p, we average the results over 50 random splits and report the mean as well as the standard deviation.

The training samples are used to learn the projective functions. Both the training and the testing images are then mapped into lower dimensional subspace where recognition is carried out by using nearest neighbor classifier (NN) and nearest centroid classifier (NC). For the baseline method, the recognition is simply performed in the original 1024-dimensional image space without any dimensionality reduction.

NC: nearest centroid classifier, which classifies a test example according to the label of its nearest centroid (centroid of each class in the training set).
NN: nearest neighbor classifier

The algorithms R-xxx are the regularized version. we use the following options:
options.Reg = 1;
options.ReguType='Ridge'

The algorithms S-xxx are the spatially smooth version. we use the following options:
options.Reg = 1;
options.ReguType = 'Custom';
load('TensorR_32x32.mat');
options.regularizerR = regularizerR;
Please see details in D. Cai, X. He, Y. Hu, J. Han, and T. Huang, "Learning a Spatially Smooth Subspace for Face Recognition", in CVPR'07, 2007. ( pdf )

Parameters (related to the graph construction) for different algorithms
LPP family NPE family IsoProjection family LSDA family MFA family
options.Metric = 'Cosine';
options.NeighborMode = 'Supervised';
options.WeightMode = 'Cosine';

Pre-process the data by normalizing each face image vector to unit.

5 Train 10 Train 20 Train 30 Train 40 Train 50 Train
Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim
Baseline NC 87.9±1.1 1024 85.5±1.3 1024 82.2±1.8 1024 78.9±2.7 1024 75.7±2.4 1024 71.2±2.9 1024
NN 63.6±1.6 1024 46.4±1.1 1024 30.4±1.1 1024 22.6±1.2 1024 18.1±1 1024 15.7±1.5 1024
PCA NC 87.9±1.1 183 85.5±1.3 326 82.2±1.8 521 78.9±2.7 691 75.7±2.4 682 71.2±2.9 694
NN 63.6±1.6 188 46.4±1.1 378 30.4±1.1 736 22.5±1.2 799 18.1±1 911 15.7±1.5 989
LDA
options.Fisherface=1		 NC 24.4±1.7 37 12.5±1.1 37 8.7±0.9 37 13.3±1.2 37 4.4±0.7 37 2.2±0.6 37
NN 24.5±1.8 37 12.5±1.1 37 8.7±0.9 37 13.3±1.2 37 4.4±0.7 37 2.2±0.6 37
LDA
options.PCARatio=1		 NC 23.7±1.6 37 13±1 37 10.3±0.8 37 13.3±1.2 37 4.4±0.7 37 2.2±0.6 37
NN 23.7±1.6 37 13±1 37 10.3±0.8 37 13.3±1.2 37 4.4±0.7 37 2.2±0.6 37
R-LDA
options.ReguAlpha=0.01
 NC 23.3±2 37 10.4±1.1 37 3.8±0.7 37 1.8±0.5 37 1.1±0.4 37
0.6±0.4
 37
NN
22.8±2
 37
10±1.1
 37
3.6±0.7
 37
1.7±0.4
 37
1±0.3
 37
0.6±0.3
 37
S-LDA
options.ReguAlpha=0.01		 NC
NN
LPP
options.PCARatio=1		 NC
NN
R-LPP
options.ReguAlpha=0.01		 NC
NN
S-LPP
options.ReguAlpha=0.01		 NC
NN
OLPP
options.PCARatio=1		 NC
NN
TensorLPP
options.nRepeat=10		 NC
NN
More will be added ...

Pre-process the face image by scaling features (pixel values) to [0,1] (divided by 256).

5 Train 10 Train 20 Train 30 Train 40 Train 50 Train
Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim
Baseline NC
NN
PCA NC
NN
LDA
options.Fisherface=1		 NC
NN
LDA
options.PCARatio=1		 NC
NN
R-LDA
options.ReguAlpha=0.01		 NC
NN
S-LDA
options.ReguAlpha=0.01		 NC
NN
LPP
options.PCARatio=1		 NC
NN
R-LPP
options.ReguAlpha=0.01		 NC
NN
S-LPP
options.ReguAlpha=0.01		 NC
NN
OLPP
options.PCARatio=1		 NC
NN
TensorLPP
options.nRepeat=10		 NC
NN
More will be added ...