Subspace Learning for Face Recognition on Yale database

Algorithms | Data

A random subset with p (=2,3,...,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 57.2±5.5 1024 48.9±4.2 1024 43.4±4.2 1024 39.8±4.4 1024 37.8±5.4 1024 34.7±4.8 1024 31.7±6.1 1024
NN 56.6±3.9 1024 50.6±4.2 1024 47.4±3.9 1024 43.8±4.1 1024 41.3±4.7 1024 39.8±4.8 1024 36.4±5 1024
PCA NC 57.2±5.5 29 48.9±4.2 44 43.4±4.1 57 39.8±4.4 73 37.8±5.4 89 34.7±4.8 99 31.6±6.2 74
NN 56.6±3.9 29 50.6±4.2 44 47.4±3.9 58 43.8±4.1 74 40.8±4.6 32 39.5±5.5 30 35.9±5.5 30
LDA
options.Fisherface=1
NC 52.4±4.6 10 34.3±4.1 14 25.9±4.4 14 20.4±3.7 14 17.9±3.6 14 16.1±4.7 14 14.3±3.8 14
NN 52.8±4.5 10 35.1±4.7 14 27.1±4.5 14 21.2±3.4 14 18.7±3.9 14 17.6±4.9 14 14.9±4.2 14
LDA
options.PCARatio=1
NC 42.5±4.7 14 31.3±3.7 14 25.5±4.6 14 21.6±3.4 14 18.5±3.8 14 17.2±4 14 16±3.7 14
NN 42.5±4.7 14 31.3±3.7 14 25.5±4.6 14 21.6±3.4 14 18.5±3.8 14 17.2±4 14 16±3.7 14
R-LDA
options.ReguAlpha=0.001
NC 42.1±4.8 14 28.6±3.5 14 21.6±4 14 17.4±3.2 14 15.1±4.1 14 13.2±3.4 14 10.2±3.4 14
NN 42.1±4.8 14 28.6±3.6 14 21.6±4 14 17.4±3.3 14 15.1±4.1 14 13.4±3.4 14 10.3±3.4 14
S-LDA
options.ReguAlpha=0.01
NC
37.5±4.9
14
25.5±4.7
14
19.3±3.1
14
14.7±3.1
14
12.3±3.7
14
10.3±3.4
14
8.7±3.6
14
NN
37.5±4.9
14 25.6±4.6 14 19.7±3.3 14 14.9±3.2 14
12.3±3.7
14 10.5±3.5 14
8.7±3.5
14
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).

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
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 ...