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 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'; |
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 ... |
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 ... |