Subspace Learning for Face Recognition on PIE database

Algorithms | Data
A random subset with p (=5,10,...,130) 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 50 Train 70 Train 90 Train 110 Train 130 Train
Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim Error Dim
Baseline NC 81.1±0.7 1024 77.8±0.9 1024 73.9±1.1 1024 71.3±1.4 1024 67.7±1.8 1024 65.7±1.7 1024 63.9±1.5 1024 62.8±1.5 1024 61.3±1.2 1024
NN 69.9±0.8 1024 55.6±0.9 1024 38.2±0.7 1024 28±0.6 1024 16.3±0.5 1024 10.6±0.4 1024 7.2±0.4 1024 5.1±0.4 1024 3.9±0.3 1024
PCA NC
NN
LDA
options.Fisherface=1		 NC 30.1±1.4 67 21.8±0.9 67 15.3±0.7 67 8±0.4 67 5.2±0.2 67 4.3±0.2 67 3.9±0.2 67 3.6±0.2 67 3.4±0.3 67
NN 31±1.5 67 22.1±0.9 67 15.5±0.7 67 7.9±0.3 67 4.8±0.2 67 4±0.2 67 3.4±0.2 67 3.2±0.2 67 2.9±0.3 66
LDA
options.PCARatio=1		 NC 31.8±1.2 67 25.7±0.7 67 15.3±0.7 67 8±0.4 67 5.2±0.2 67 4.3±0.2 67 3.9±0.2 67 3.6±0.2 67 3.4±0.3 67
NN 31.8±1.2 67 25.7±0.7 67 15.5±0.7 67 7.9±0.3 67 4.8±0.2 67 4±0.2 67 3.4±0.2 67 3.2±0.2 67 2.9±0.3 66
R-LDA
options.ReguAlpha=0.01		 NC 23.3±1.5 67 12.1±0.7 67 6.6±0.4 67 5±0.3 67 3.9±0.2 67 3.5±0.2 67 3.2±0.2 67 3.1±0.2 67 3±0.2 67
NN 22.1±1.5 67 11.1±0.7 67 5.9±0.3 67 4.3±0.2 67 3.2±0.2 67 2.8±0.2 67 2.5±0.2 66 2.4±0.2 67 2.3±0.2 65
S-LDA
options.ReguAlpha=0.01
 NC 23.5±1.3 67 12±0.7 67 6.4±0.4 67 4.8±0.3 67 3.6±0.2 67 3.2±0.2 67 2.9±0.1 67 2.8±0.2 67 2.6±0.3 67
NN
22.1±1.2
 67
10.6±0.6
 67
5.2±0.3
 67
3.6±0.2
 67
2.5±0.2
 66
2.1±0.2
 65
1.8±0.1
 60
1.7±0.2
 65
1.6±0.2
 44
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 50 Train 70 Train 90 Train 110 Train 130 Train
Error Dim Error Dim Error Dim 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 ...