Extracting Discriminant Features of Faces Using Kernel Discriminant Analysis
Yongmin Li ,
Shaogang Gong and
Heather
Liddell
 Representation: PCA, LDA, KPCA, or KDA?
 A Toy Problem
 Extract the Discriminant Features of MultiView Faces
 Relavant Publications
Principal Component Analysis (PCA) has been widely adopted to reduce
dimensionality and extract abstract features of faces. But the
features extracted by PCA are actually ``global'' features for all
face classes, thus they are not necessarily much representative for
discriminating one face class from others. Linear Discriminant
Analysis (LDA), which seeks to find a linear transformation by
maximising the betweenclass variance and minimising the withinclass
variance, proved to be a suitable technique for face recognition.
However, both the PCA and LDA are linear techniques which may be less
efficient when severe nonlinearity is involved. To extract the
nonlinear principal components, the Kernel PCA (KPCA) was developed
for pattern recognition and has been adopted to construct a nonlinear
models aiming at corresponding dynamic appearances of both shape and
texture across views. However, similar to the linear PCA, KPCA
captures the overall variance of all patterns which are not
necessary significant for discriminant purpose. In this work, the
Kernel Discriminant Analysis (KDA), a nonlinear discriminant approach
based on the kernel technique which has been successfully used in KPCA
is developed for extracting the nonlinear discriminant features
We use a toy problem to illustrate the characteristics of KDA as shown
in Figure 1. Two classes of
patterns denoted by circles and crosses respectively have a
significant nonlinear distribution. From left to right are the
discriminant curves and the distribution of the one dimension feature
of PCA, LDA, KPCA and KDA respectively. Among them, the KDA achieves
the best performance: the discriminant curve accurately separates the
two classes of patterns, and the feature intensity correctly reflects
the actual pattern distribution.
Figure 1:
Solving a nonlinear classification problem with PCA, LDA, KPCA and KDA.

Modelling the appearance of faces across multiple views is much more
challenging than that from a fixed view for the following reasons:

the severe nonlinearity caused by rotation in depth, selfocclusion,
selfshading and illumination change;

the appearance of different people from a same view is more similar
than that of one person from different views.
In this work, we apply the KDA to extract the discriminant features
for multiview face recognition. The patterns used for face
recognition is represented by the shapeandposefree texture
patterns, which are extracted by fitting a multiview dynamic face
model on face images and warping them to the model mean shape in
frontal view. Figure 2
shows the original face images, fitted multiview face model overlaid
on the face images, and the warped shapeandposefree
texture patterns.
Figure 2:
Extract the shapeandposefree texture patterns of multiview
face images using a multiview face model.

We first apply the PCA to a set of these shapeandposefree
texture patterns.
Figure 3(a) illustrates the
variation of the first PCA dimension with respect to the pose
change. The patterns belonging to a same face class are linked
together. Figure 3(b)
shows the distribution of the texture patterns in the first two PCA
dimension. It is noted that the variation from different face classes
is not efficiently isolated from that from pose change, or more
precisely, the former is even overwhelmed by the latter.
Figure 3: Multiview face
recognition problem: variation from different face classes
vs. variation from pose change. (a) variation of the 1st PCA dimension
wrt pose change. (b) pattern distribution in the first two
PCA dimensions.

Then we apply the KDA to the face patterns of the same face classes as
shown in Figure 3. The variation and distribution
of the patterns are shown in Figure 4(a) and
Figure 4(b) respectively. Compared to the results of the
PCA patterns in Figure 3, the improvement in terms
of discriminant capability is significant. It is
interesting to note from Figure 4 that the
patterns of different face classes are separable when two KDA
dimensions are used only, while these patterns are mingled together when
the PCA is employed in Figure 3.
Figure 4:
Distribution of the KDA patterns obtained from the same face images
as in Figure 3.

Relavant Publications

Y. Li, S. Gong, and H. Liddell.
Learning to
recognise faces across views and over time using Kernel Discriminant
Analysis.
Technical report, Queen Mary, University of London,
2001.

Y. Li, S. Gong, and H. Liddell.
Modelling
faces dynamically across views and over time.
Technical
report, Queen Mary, University of London, 2001.
Yongmin Li
20010207