Subspace Learning for Face Recognition on ORL database

Algorithms | Data
A random subset with p (=2,3,4,5,6,7,8) 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.

2 Train 3 Train 4 Train 5 Train 6 Train 7 Train 8 Train
Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim
Baseline NC 32.6±3.4 1024 25.9±2.9 1024 22.1±2.6 1024 19.3±2.6 1024 17.8±3.1 1024 16.4±3.4 1024 15.2±3.9 1024
NN 33.1±3.4 1024 23.4±2.3 1024 17.9±2.2 1024 13.7±2.4 1024 11.4±2.2 1024 8.7±2.4 1024 7.5±2.4 1024
PCA NC 32.6±3.4 79 25.9±2.9 113 22.1±2.6 151 19.3±2.6 185 17.8±3.1 228 16.4±3.4 240 15.1±3.9 224
NN 33.1±3.4 79 23.4±2.3 119 17.9±2.2 159 13.7±2.4 199 11.4±2.2 238 8.7±2.4 278 7.5±2.4 319
LDA
options.Fisherface=1		 NC 28.4±3.7 37 15.9±2.2 39 10.3±2 39 6.9±1.5 39 5.6±2 39 4.6±2 39 3.6±1.8 39
NN 28.5±3.8 24 16±2.2 39 10.6±2 39 7.2±1.7 39 6±2.3 39 4.7±2.1 39 3.7±1.8 39
LDA
options.PCARatio=1		 NC 22.3±3 39 13.9±2.4 39 10±1.8 39 7.3±1.4 39 6±2.1 39 5±1.9 39 3.8±2 39
NN 22.3±3 39 13.9±2.4 39 10±1.8 39 7.3±1.4 39 6±2.1 39 5±1.9 39 3.8±2 39
R-LDA
options.ReguAlpha=0.01		 NC 20.9±3.3 39 11.6±2 39 7.3±1.7 39 4.3±1.4 39 3.3±1.9 39 2.3±1.4 38 1.6±1.4 39
NN 20.9±3.4 39 11±2 39 6.3±1.6 39 3.6±1.2 39 2.7±1.6 39 1.9±1.3 33 1.5±1.3 39
S-LDA
options.ReguAlpha=0.01
 NC
17.1±2.8
 39 8.6±1.8 39 4.9±1.6 29 3±1 31 2.2±1.1 24 1.7±1.1 30 1.2±1 22
NN
17.1±2.7
 39
8.1±1.8
 39
4.1±1.6
 28
2.3±1
 39
1.6±1
 39
1.2±0.9
 33
0.8±0.9
 28
LPP
options.PCARatio=1		 NC 22±3.2 39 13.8±2.3 43 9.7±1.6 46 6.8±1.6 164 5.9±1.9 55 4.8±1.7 38 3.5±1.9 38
NN 22±3.2 39 13.8±2.3 39 9.7±1.7 39 6.8±1.6 39 5.9±1.9 39 4.8±1.7 38 3.5±1.9 38
R-LPP
options.ReguAlpha=0.01		 NC 20.9±3.3 40 11.7±2 39 7.3±1.7 45 4.4±1.5 39 3.3±2 46 2.3±1.4 38 1.6±1.4 39
NN 20.9±3.4 39 10.9±2 39 6.4±1.6 39 3.6±1.2 39 2.7±1.6 40 1.9±1.3 33 1.6±1.3 39
S-LPP
options.ReguAlpha=0.01
 NC
17.1±2.8
 42 8.6±1.8 41 4.9±1.6 29 3.1±1.1 31 2.2±1.1 24 1.7±1.1 30 1.2±1.1 17
NN
17.1±2.9
 38
8.1±1.8
 39
4.1±1.5
 28
2.3±1
 39
1.6±1
 39
1.2±1
 41
0.6±0.8
 41
OLPP
options.PCARatio=1		 NC 20.5±3.5 39 11±2 43 6.7±1.7 40 4±1.3 40 3±1.7 43 2.3±1.6 49 1.7±1.2 41
NN 20.5±3.5 39 10.8±2 48 6.4±1.6 58 3.8±1.3 58 2.9±1.6 53 2.2±1.3 58 1.5±1.4 53
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).

2 Train 3 Train 4 Train 5 Train 6 Train 7 Train 8 Train
Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim
Baseline NC 29.4±3.1 1024 23.8±2.7 1024 20±2.4 1024 18.2±2.9 1024 16.5±2.9 1024 14.8±3.1 1024 13.7±3.2 1024
NN 29.6±3.1 1024 21.1±2.5 1024 15.5±2.1 1024 11.9±2.1 1024 9.7±2.2 1024 7.6±2.6 1024 6±2.7 1024
PCA NC 29.4±3.1 78 23.7±2.8 116 20±2.4 154 18.2±2.9 191 16.5±2.9 177 14.8±3.1 228 13.7±3.2 297
NN 29.6±3.1 79 21.1±2.5 119 15.5±2.1 158 11.9±2.2 189 9.6±2.2 202 7.5±2.7 202 5.9±2.6 213
LDA
options.Fisherface=1		 NC 24.3±3.1 36 13.8±2.2 39 8.8±1.9 39 6±1.3 39 4.6±2 39 4.2±2.1 39 3±1.5 39
NN 24.5±3.3 28 13.7±2.4 39 8.8±2 39 6.1±1.5 39 4.8±1.8 39 4.5±2 39 3.2±1.7 38
LDA
options.PCARatio=1		 NC 20.3±2.8 39 12.8±2 39 8.9±1.8 39 6.6±1.6 39 5.4±2.2 39 4.4±1.7 39 3.4±1.8 39
NN 20.3±2.8 39 12.8±2 39 8.9±1.8 39 6.6±1.6 39 5.4±2.2 39 4.4±1.7 39 3.4±1.8 39
R-LDA
options.ReguAlpha=1		 NC
NN
S-LDA
options.ReguAlpha=1
 NC 14.9±2.4 38 7.6±1.5 39 4.3±1.7 39 2.6±1.2 39 1.9±1.2 22 1.5±1 23 1.1±1.2 16
NN
14.9±2.4
 38
7.3±1.5
 39
4±1.6
 39
2.3±1.1
 39
1.8±1
 24
1.3±1.1
 30
1±1.1
 16
LPP
options.PCARatio=1		 NC 20.1±2.9 39 12.7±2.3 39 8.6±2 44 6.4±1.6 39 5.2±2 39 4.1±1.6 207 3.1±1.7 39
NN 20.1±2.9 39 12.7±2.3 39 8.6±2 39 6.4±1.6 39 5.2±2 39 4.2±1.6 39 3±1.8 45
R-LPP
options.ReguAlpha=1		 NC
NN
S-LPP
options.ReguAlpha=1
 NC 14.9±2.4 39 7.6±1.5 50 4.3±1.6 26 2.6±1.2 39 1.9±1.1 24 1.5±1 23 1.1±1.2 16
NN
14.9±2.4
 39
7.3±1.5
 39
4±1.6
 39
2.3±1.1
 39
1.7±1
 24
1.3±1.1
 30
0.9±1
 42
OLPP
options.PCARatio=1		 NC 17.2±3.1 39 9.2±2 39 5.6±1.5 41 3.5±1.2 41 2.8±1.5 41 2.2±1.4 46 1.5±1.4 43
NN 17.2±3.1 39 9.2±2 39 5.6±1.5 39 3.4±1.3 41 2.7±1.4 42 2.1±1.4 54 1.6±1.4 41
TensorLPP
options.nRepeat=10		 NC
NN
More will be added ...