1. EE4-62 MLCV Lecture 13-14 Face Recognition – Subspace/Manifold Learning Tae-Kyun Kim 1 EE4-62 MLCV

2. Face Image Tagging and Retrieval Face tagging at commercial weblogs Key issues – User interaction for face tags – Representation of a long- time accumulated data – Online and efficient learning 2 Active research area in Face Recognition Test and MPEG-7 for face image retrieval and automatic passport control Our proposal promoted to MPEG7 ISO/IEC standard

3. EE4-62 MLCV Principal Component Analysis (PCA) - Maximum Variance Formulation of PCA - Minimum-error formulation of PCA - Probabilistic PCA 3

4. EE4-62 MLCV Maximum Variance Formulation of PCA 4

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9. Minimum-error formulation of PCA 9

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15. EE4-62 MLCV Applications of PCA to Face Recognition 15

16. EE4-62 MLCV (Recap) Geometrical interpretation of PCA Principal components are the vectors in the direction of the maximum variance of the projection samples. Each two-dimensional data point is transformed to a single variable z1 representing the projection of the data point onto the eigenvector u1. The data points projected onto u1 has the max variance. Infer the inherent structure of high dimensional data. The intrinsic dimensionality of data is much smaller. For given 2D data points, u1 and u2 are found as PCs 16

17. EE4-62 MLCV Eigenfaces Collect a set of face images Normalize for scale, orientation (using eye locations) Construct the covariance matrix and obtain eigenvectors w h D=wh 17

18. EE4-62 MLCV Eigenfaces Project data onto the subspace Reconstruction is obtained as Use the distance to the subspace for face recognition 18 EE4-62 MLCV

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20. EE4-62 MLCV Matlab Demos – Face Recognition by PCA 20

21. EE4-62 MLCV Face Images Eigen-vectors and Eigen-value plot Face image reconstruction Projection coefficients (visualisation of high- dimensional data) Face recognition 21

22. EE4-62 MLCV Probabilistic PCA A subspace is spanned by the orthonormal basis (eigenvectors computed from covariance matrix) Can interpret each observation with a generative model Estimate (approximately) the probability of generating each observation with Gaussian distribution, PCA: uniform prior on the subspace PPCA: Gaussian dist. 22 EE4-62 MLCV

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26. EE4-62 MLCV Probabilistic PCA 26 EE4-62 MLCV

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31. EE4-62 MLCV Maximum likelihood PCA 31

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36. EE4-62 MLCV Limitations of PCA 36

37. EE4-62 MLCV Unsupervised learning 37 PCA vs LDA (Linear Discriminant Analysis)

38. EE4-62 MLCV Linear model Linear Manifold = Subspace Nonlinear Manifold 38 EE4-62 MLCV PCA vs Kernel PCA

39. EE4-62 MLCV Gaussian Distribution Assumption 39 IC1 IC2 PC1 PC2 PCA vs ICA (Independent Component Analysis)

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