Subspace Representation for Face Recognition Presenters: Jian Li and Shaohua Zhou.
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Transcript of Subspace Representation for Face Recognition Presenters: Jian Li and Shaohua Zhou.
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
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
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 …
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) = <f(x) , f(y)> Gaussian kernel: exp(- 0.5 |x –
y|^2/sigma^2)
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
FERET Database Facial expression and illumination
variation 200 classes, 3 images/class, 24 by
21Set1
Set2
Set3
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
Probabilistic PCA (PPCA) -- II Assume e has covariance matrix,
pho*I R = U * D * U’ W = Um * (Dm – pho*I) ^(1/2) Pho = mean of the remaining eigenvalues
Implemented algorithm B. Moghaddam ’01
W = Um * (Dm) ^(1/2) - 2log P(y) = sum (Pci^2/Di) + e^2 / pho + const
Construct inter-person space
Probabilistic KPCA (PKPCA) Replace PCA by KPCA in the PPCA
algorithm Estimating e by computing sum of
all remaining PC’s.
ICA Independent face
PCA pre-whitening: X1 = U’ * X Y = W * X1
Independent facial expression Y = W * X’
Kernel ICA F. Bach and M. I. Jordan ‘01 ‘Kernel trick’ is played when
measuring independence Canonical correlation -- independence
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Comparison of 4 methods
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PCA PPCA FDA ICA*
PoseExpressionIlluminationAverage
Comparison of Kernel/Non-kernel methods
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Non-Kernel Kernel
PoseExpressionIlluminationAverage