# Lecture 13-14 Face Recognition Subspace/Manifold Learning

Τεχνίτη Νοημοσύνη και Ρομποτική

17 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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Lecture 13
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14

Face
Recognition

Subspace/Manifold
Learning

Tae
-
Kyun Kim

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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

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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

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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

N
D
R
X

,...
,
1
1
x
x
X
X
X
N
S
T

M
D
R
U
U
SU

,
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Eigenfaces

Project data onto the
subspace

Reconstruction is
obtained as

Use the distance to the
subspace for face
recognition

D
M
R
Z
X
U
Z
N
M
T


,
,
UZ
X
Uz
u
z
x
M
i
i
i

~
,
~
1
x
~
||
~
||
x
x

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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 PCA

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Maximum likelihood PCA

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Limitations of PCA

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Unsupervised
learning

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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

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IC1

IC2

PC1

PC2

PCA
vs

ICA (Independent Component
Analysis)

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(also by ICA)