ee4-62 mlcv lecture 13-14 face recognition – subspace/manifold learning tae-kyun kim 1 ee4-62 mlcv
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Lecture 13-14Face Recognition – Subspace/Manifold Learning
Tae-Kyun Kim
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EE4-62 MLCVFace 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
• 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
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Principal Component Analysis (PCA)- Maximum Variance Formulation of PCA- Minimum-error formulation of PCA
- Probabilistic PCA
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Maximum Variance Formulation of PCA
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Minimum-error formulation of PCA
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Applications of PCA to Face Recognition
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(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
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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
NDRX
,...,1
1 xxXXXN
S T
MDRUUSU ,
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Eigenfaces• Project data onto the
subspace
• Reconstruction is obtained as
• Use the distance to the subspace for face recognition
DMRZXUZ NMT ,,
UZXUzuzxM
iii
~,~
1
x~||~|| xx
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x
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Matlab Demos – Face Recognition by PCA
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• Face Images• Eigen-vectors and Eigen-value plot• Face image reconstruction• Projection coefficients (visualisation of high-
dimensional data)• Face recognition
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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.
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Continuous Latent Variables
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Probabilistic PCAEE4-62 MLCV
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Maximum likelihood PCA
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Limitations of PCA
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Unsupervised learning
PCA vs LDA (Linear Discriminant Analysis)
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Linear model
Linear Manifold = Subspace Nonlinear
Manifold
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PCA vs Kernel PCA
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Gaussian Distribution Assumption
IC1
IC2
PC1
PC2
PCA vs ICA (Independent Component Analysis)
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(also by ICA)