1. Mixture of SVMs for Face Class Modeling
J.Meynet, V.Popovici, J.-Ph. Thiran
MLMI 04

2. Outline Introduction Presentation of the Work
Context
The face detection task
Principal Component Analysis
Classification with Support Vector Machines
Mixture of Support Vector Machines
With independent subsets
With k-means clustering
Experiments and Results
Conclusions and Future Work

3. Face Detection Methods
Image-Based Detection
Consider face as a whole object
Eigenfaces
Fisher’s Linear Discriminant
Neural Network, SVM
HMM
SNoW
Geometrical-based methods
Find precise parts of the face
and reassemble them for the final decision
Top-down
Bottom-up …

4. Principle of the detection
Pre-processing with a cascade of boosted Haar-Like Features
=>Real-time face detector
Principal Component Analysis (PCA)
Dimensionality reduction
Classification with a Mixture of SVM
Random sampling or k-means clustering + -
P.Viola, M.Jones, ”Robust real-time object detection.” International Journal of computer Vision, 2002.

5. Eigenfaces Space PCA and Eigenfaces PCA …
Sirovich, Kirby, ”Low-dimensional procedure for the characterization of human faces, 1987

6. Distance From Feature Space
DFFS F
DIFS
DFFS
Construction of the classification vector:

7. Support Vector Machines (SVM)
Find the hyperplane that correctly separates the data while maximising the margin.
Optimisation:
Lagrange multipliers i:
Kernels:
V. Popovici, J.-Ph. Thiran, "Face Detection using SVM Trained in Eigenfaces Space", 4th International Conference on Audio- and Video-Based Biometric Person Authentication, Surrey, UK, 2003

8. Mixture of SVMs (MSVM)
Why? Building a face detection system requires a large amount of examples => make the training easier
Principle
1- Split initial dataset into N+1 subsets
By random sampling
Or by K-means clustering
2- Train N first SVMs
3- Pass the N+1th subset through the SVMs, train the 2nd layer SVM on the margins. X 1 2 N
N+1
SVM-1
SVM-N m
SVM-L2

9. Mixture of SVMs 2 Sampling techniques:
1- Random partitioning
M+1 independent subsets
2- Clustering
- Draw 1 random subset for the SVM-L2
- K-means clustering on the remaining examples
M clusters for training the SVM-L1-i
SVM-L1-i are trained using cross-validation, with RBF kernels:
SVM-L2 trained on the margins:
It learns a function that assembles the confidences of each individual expert.

10. Mixture of SVMs Output of the mixture: Advantages:
Single SVM: problem of complexity
MSVM: problems of complexity
=> clearly advantageous

11. Experiments and Results I
Database
Face images from Banca and XM2VTS
Non faces chosen by bootstrapping on randomly selected images
Estimation of a correct dimensionality for the eigenfaces space
900000
14000
non faces
7822
8256
faces
Validation
Training
20x15 images
Number of eigenfaces needed to keep 85% of total variation

12. Experiments and Results II
Random sampling or clustering
(x5)
SVM-L1-i
(x5)
1000 F
2000 NF
8256 F
14000 NF
SVM-L2
2256 F
4000 NF
Random sampling:
Reduce the importance of outliers or unusual examples
Clustering:
Each SVM-L1-i performs like an expert on its own domain
98.86
99.00
76.47
86.23
SVM-L1-1
K-Means
R.S
Non Faces(%)
Faces(%)
Classifier
97.68
90.00
82.32
84.91
SVM-L1-2
98.77
99.02
81.23
85.13
SVM-L1-3
99.12
99.13
77.12
84.64
SVM-L1-4
74.29
85.66
SVM-L1-5
96.43
98.14
95.37
93.60
SVM-L2

13. Experiments and Results III
Generalisation
Classifier
Faces(%)
Non Faces(%)
Total N° SV
MSVM, RS
MSVM, KM
Single SVM
93.60
95.37
92.8
99.42
96.43
98.14
1673
1420
2504
Better generalisation capabilities than a single SVM;
MSVM improves the training time and the true positive rate;
Less Support Vectors => lower computation complexity.
Results on Banca images pre-processed by boosted Haar-Like features

14. Conclusions - Future Work
Boosted local feature-based classifiers pre-pocessing
real-time processing
Dimensionality reduction by PCA ( + DFFS)
Decrease the complexity of the classification task
Extension to the SVM technique which performs well on large datasets.
Decrease the training and classification time
Improve discrimination capabilities
Try other clustering techniques in eigenfaces space based on more appropriate metrics.