Subspace Representation for Face Recognition

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Subspace Representation for Face Recognition
Presenters Jian Li and Shaohua Zhou
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Overview

• 4 different subspace representations
• PCA, PPCA, LDA, and ICA
• 2 options
• Kernel v.s. Non-Kernel
• 2 databases with 3 different variations
• Pose, Facial expression, and Illumination

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Subspace representations

• Training data X (d,n)
• X x1, x2, , xn
• Subspace decomposition matrix W (d,m)
• W w1, w2, , wm
• Representation Y (m,n)
• Y W X

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PCA, PPCA, LDA and ICA

• PCA, in an unsupervised manner, minimizes the
  representation error X Y.
• LDA, in a supervised manner, minimizes the
  within-class distance while maximizing the
  between-class distance.
• ICA, in an unsupervised manner, maximizes the
  independence between Y s.
• Probabilistic PCA, coming late

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Kernel or Non-Kernel

• Often somewhere reduces to some forms related to
  dot product
• Kernel trick
• Replacing dot product by kernel function
• Mapping the original data space into a
  high-dimensional feature space
• K(x,y) ltf(x) , f(y)gt
• Gaussian kernel exp(- 0.5 x y2/sigma2)

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Gallery, Probe, Pre-processing

• Training dataset
• Testing dataset
• Gallery Reference images in testing
• Probe Probe images in testing
• Pre-processing
• Down-sampling
• Zero-mean-unit-variance
• x x - mean(x) / var(x)
• Crop face region only

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ATT Database

• Pose variation
• 40 classes, 10 images/class, 28 by 23

Set1
Set2 (Mirror of Set1)
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FERET Database

• Facial expression and illumination variation
• 200 classes, 3 images/class, 24 by 21

Set1
Set2
Set3
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Probabilistic PCA (PPCA) -- I

• PCA only extracts PCs thereby losing
  probabilistic flavor
• PPCA add this by interpreting the reconstruction
  error as confidence level
• y u W x e
• Different choices of e
• Factor analysis,
• PPCA (Tipping and Bishop 99)
• PCA

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Probabilistic PCA (PPCA) -- II

• Assume e has covariance matrix, phoI
• R U D U
• W Um (Dm phoI) (1/2)
• Pho mean of the remaining eigenvalues
• Implemented algorithm
• B. Moghaddam 01
• W Um (Dm) (1/2)
• - 2log P(y) sum (Pci2/Di) e2 / pho
  const
• Construct inter-person space

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Probabilistic KPCA (PKPCA)

• Replace PCA by KPCA in the PPCA algorithm
• Estimating e by computing sum of all remaining
  PCs.

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ICA

• Independent face
• PCA pre-whitening X1 U X
• Y W X1
• Independent facial expression
• Y W X

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Kernel ICA

• F. Bach and M. I. Jordan 01
• Kernel trick is played when measuring
  independence
• Canonical correlation -- independence

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Experimental Setup

• Training
• Ranking the gallery based on the distance or
  probability
• CMS curve

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Distance Metric

• SAD, SQD, Correlation (mean removed)

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Tweaking Gaussian kernel width
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Eigenfaces Fisherfaces
Eigenfaces
Fisherfaces
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Independent Basis Faces Facial Features
Ind. Faces
Ind. Facial Features
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Performance on pose variation
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Performance on facial expression variation
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Performance on illumination variation
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Comparison of 4 methods
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Comparison of Kernel/Non-kernel methods
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Computational load

• Training time
• PCA lt LDA lt PPCA lt ICA
• KPCA lt KLDA lt PKPCA ltlt KICA
• Testing time
• PCA LDA ICA lt PPCA
• KPCA KLDA KICA lt PKPCA