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Lecture 13-14 Face Recognition – Subspace/Manifold Learning

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## Lecture 13-14 Face Recognition – Subspace/Manifold Learning

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**EE4-62 MLCV**Lecture 13-14Face Recognition – Subspace/Manifold Learning Tae-Kyun Kim**EE4-62 MLCV**Face Recognition Applications • Applications include • Automatic face tagging at commercial weblogs • Face image retrieval in MPEG7 (our solution is MPEG7 standard) • Automatic passport control • Feature length film character summarisation • A key issue is in Efficient representation of face images.**Face Recognition vs Object Categorisation**Class 2 Class 1 Intra-class variation Face image data sets Inter-class variation Object categorisation data sets Class 2 Class 1 Intra-class variation Inter-class variation**Both problems are hard, cause we need to minimise**intra-class variations while maximising inter-class variations. Face image variations are subtle, compared to those of generic object categories. Subspace/manifold techniques, over Bag of Words, are primary-arts for face analysis.**Principal Component Analysis (PCA)- Maximum Variance**Formulation of PCA- Minimum-error formulation of PCA- Probabilistic PCA**Minimum-error formulation of PCA**0, otherwise**EE4-62 MLCV**(Recap) Geometrical interpretation of PCA • Principal components are the vectors in the direction of the maximum variance of the projection samples. • For given 2D data points, u1 and u2 are found as PCs • 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.**Eigenfaces (how to train)**• Collect a set of face images • Normalize for scale, orientation (using eye locations) • Construct the covariance matrix and obtain eigenvectors D=wh w h M: number of eigenvectors**EE4-62 MLCV**Eigenfaces (how to use) • Project data onto the subspace • Reconstruction is obtained as • Use the distance to the subspace for face recognition**Eigenfaces (how to use)**x c1 c2 Method 1 : reconstruction by c-th class subspace c3 | assign Method 2 x : mean projection of c-th class data | assign**Matlab Demos – Face Recognition by PCA**Face Images Eigen-vectors and Eigen-value plot Face image reconstruction Projection coefficients (visualisation of high-dimensional data) Face recognition**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.**EE4-62 MLCV**Probabilistic PCA**Unsupervised learning**PCA finds the direction for maximum variance of all data, while LDA (Linear Discriminant Analysis) finds the direction that is optimal in terms of the inter-class/intra-class data variations. PCA vs LDA Refer to the textbook, C. M. Bishop, Pattern Recognition and Machine Learning, Springer**EE4-62 MLCV**Linear model PCA is a linear projection method. It is okay when data is well constrained to a hyperplane. When data lies in a nonlinear manifold, PCA is extended to Kernel PCA by the kernel trick (Lectures 9-10) . Linear Manifold = Subspace Nonlinear Manifold PCA vs Kernel PCA Refer to the textbook, C. M. Bishop, Pattern Recognition and Machine Learning, Springer**Gaussian assumption**PCA models data as Gaussian distributions (2nd order statistics), whereas ICA (Independent Component Analysis) captures higher-order statistics. IC1 PC2 ICA PCA IC2 PC1 PCA vsICA Refer to, A. Hyvarinen, J. Karhunen, E. Oja, Independent Component Analysis, John Wiley & Sons, Inc.**EE4-62 MLCV**PCA bases look holistic and less intuitive. ICA or NMF (Non-negative Matrix Factorisation) yields bases, which capture local facial components. (also by ICA) Daniel D. Lee and H. Sebastian Seung (1999). "Learning the parts of objects by non-negative matrix factorization". Nature401 (6755): 788–791.