1. Face Recognition & Biometric Systems Support Vector Machines (part 2)

2. Face Recognition & Biometric Systems Plan of the lecture SVM – main issues repeated Soft margin Multi-class problems Applications to face recognition Training set optimization

3. Face Recognition & Biometric Systems SVM – main issues Aim: data classification Two stages: learning (training) classification

4. Face Recognition & Biometric Systems SVM – main issues Solves linearly separable problems Input data are transformed mapping into higher dimensions Training: find optimal hyperplane margin maximisation

5. Face Recognition & Biometric Systems SVM – main issues A function: Data mapping: x  (x) Dot product used in all calculations Dot product -> kernel of convolution No need to know the function 

6. Face Recognition & Biometric Systems Convolution kernels Linear Polynomial RBF (radial basis functions)

7. Face Recognition & Biometric Systems SVM – main issues Optimal hyperplane: w 0 x + b 0 = 0 for 2D data it is a line Optimal margin width:

8. Face Recognition & Biometric Systems SVM – main issues Optimal hyperplane: y i – class label  i – Lagrange multipliers (obtained during optimisation)

9. Face Recognition & Biometric Systems SVM – main issues Lagrange coefficients (  ): calculated for every vector from the training set non-zero for support vectors equal zero for the majority of vectors Training set after the optimisation: support vectors  coefficients for every vector number of vectors reduced

10. Face Recognition & Biometric Systems Training 11... nn

11. Face Recognition & Biometric Systems SVM – main issues Classification of a vector: x r, x s – support vectors from opposite classes

12. Face Recognition & Biometric Systems Soft margin Error allowed during the training: Number of errors minimised Optimised function must be modified

13. Face Recognition & Biometric Systems Soft margin Margin maximisation Minimisation of functional (F – monotonic, convex function): C – penalty parameter presentation Constraints:

14. Face Recognition & Biometric Systems Soft margin Optimisation without the soft margin:

15. Face Recognition & Biometric Systems Soft margin Optimisation with the soft margin (for F(u) = u 2 ):

16. Face Recognition & Biometric Systems Multi-class problem Example

17. Face Recognition & Biometric Systems Multi-class problem Based on two-class problem solved by the SVM N classes in the training set Possible solutions: base-class approach 1 – N comparisons 1 – 1 comparisons

18. Face Recognition & Biometric Systems The base-class approach one class selected as a base class each class compared with the base class the strongest response decides Classification of a single vector: (N – 1) two-class classifications

19. Face Recognition & Biometric Systems The base-class approach

20. Face Recognition & Biometric Systems The base-class approach

21. Face Recognition & Biometric Systems The base-class approach

22. Face Recognition & Biometric Systems The base-class approach

23. Face Recognition & Biometric Systems The base-class approach

24. Face Recognition & Biometric Systems The base-class approach Advantages: high speed effective when non-base classes are easily separable Disadvantages: problems with separating non-base classes

25. Face Recognition & Biometric Systems 1 – N comparisons Each class compared with the rest The strongest response decides Classification of a single vector: N two-class classifications Compared to the base-class approach: more universal (symmetry) comparable speed

26. Face Recognition & Biometric Systems 1 – N comparisons

27. Face Recognition & Biometric Systems 1 – 1 comparisons Each class compared with each other The highest precision Classification of a single vector: N(N – 1)/2 two-class classifications Very slow method

28. Face Recognition & Biometric Systems SVM for face recognition Detection and verification Feature vectors comparison Multi-method fusion Other applications

29. Face Recognition & Biometric Systems Face detection Ellipse detection Generalised Hough Transform a set of face candidates Normalisation of the candidates Verification image (as a vector) classified by the SVM multi-class approach

30. Face Recognition & Biometric Systems Feature vectors comparison Aim: measure similarity between feature vectors Distance-based similarity: Euclidean distance Mahalanobis distance Similarity measured by the SVM: two vectors subtracted from each other create a difference vector difference vector classified K1 1 K1 2 K1 n... K2 1 K2 2 K2 n...

31. Face Recognition & Biometric Systems SVM The same class Different classes K1 1 - K2 1... K1 2 - K2 2 K1 n - K2 n Feature vectors comparison

32. Face Recognition & Biometric Systems Feature vectors comparison Good improvement for EBGM Eigenfaces not improved similar results to other metrics

33. Face Recognition & Biometric Systems Multi-method fusion Many feature extraction methods S1S1 S2S2 SnSn... S K1K1 K2K2 KnKn Two imagesFeature vectorsSimilarities K1K1 K2K2 KnKn...

34. Face Recognition & Biometric Systems Multi-method fusion Vector of similarities classified linear kernel polynomial kernel time-consuming classification SVM applied only for the training linear kernel – weights for the methods (dimensions stand for methods) average mean based on the weights

35. Face Recognition & Biometric Systems Other applications Assessment of recognition accuracy vector of sorted similarities to the elements in the gallery can be used for many images of the same person Image quality estimation e.g. elimination of blurred images

36. Face Recognition & Biometric Systems SVM – limitations Constant and small number of classes too much time-consuming for many classes Training set: must be representative optimal number of elements The parameters must be tuned Relevance Vector Machines

37. Face Recognition & Biometric Systems Training set optimization Representative training set: similarity to the classified data universal classification rules difficult to acquire Real training sets: data acquired automatically low quality, faulty data large number of data

38. Face Recognition & Biometric Systems Training set optimization Selection of available data subset drawn randomly genetic algorithms Genetic algorithms heuristic optimization technique evolutional strategy population of individuals fitness genetic operators:  selection  mutation  crossover

39. Face Recognition & Biometric Systems Training set optimization Population drawn Effectiveness test Population of training sets Evolutional operations Class +Class – N elements Individual + – Individual SVM training Effectiveness test Fittness

40. Face Recognition & Biometric Systems SVM compared to ANN Support Vector Machines: more transparent calculations more controllable than neural networks implements various types of ANN useful for image processing Artificial Neural Networks: more applications (e.g. compression) dedicated hardware solutions

41. Face Recognition & Biometric Systems Summary Soft margin – automatic selection Multi-class problems: can be solved basing on two-class problems various approaches Many possible applications in the area of face recognition Training set optimization

42. Face Recognition & Biometric Systems Thank you for your attention! Next time: Elastic Bunch Graph Matching