SELECTING KERNEL EIGENFACES FOR FACE RECOGNITION WITH ONE TRAINING
SAMPLE PER SUBJECT
Jie Wang, K.N.Plataniotis and A.N.Venetsanopolous
The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto
10 King’s College Road, Toronto, M5A 3G4, ONTARIO, CANADA
{jwang,kostas,anv}@dsp.utoronto.ca
ABSTRACT
It is well-known that supervised learning techniques such as linear
discriminant analysis (LDA) often suffer from the so called small
sample size problem when apply to solve face recognition problems.
This is due to the fact that in most cases, the number of training sam-
ples is much smaller than the dimensionality of the sample space.
The problem becomes even more severe if only one training sample
is available for each subject. In this paper, followed by the well-
known unsupervised technique, kernel principal component analy-
sis(KPCA), a novel feature selection scheme is proposed to estab-
lish a discriminant feature subspace in which the class separabil-
ity is maximized. Extensive experiments performed on the FERET
database indicate that the proposed scheme significantly boosts the
recognition performance of the traditional KPCA solution.
1. INTRODUCTION
Face recognition(FR) has received more and more attentions with a
wide range of applications such as access control, forensic identifi-
cation and human computer interface. Although numerous FR algo-
rithms have been proposed in the past two decades with the state-of-
the-art reported in the survey of [1],it still remains as a difficult prob-
lem far from well solved. This is due to the fact that faces exhibit
significant variations in appearance due to illumination, expression,
pose and aging factors. At the same time, examples available for
training a FR machine are usually limited. To the extreme case, when
each subject only has one image sample, the recognition problem
becomes even more challenging. In such a case, some well-known
supervised learning techniques such as linear discriminant analysis
(LDA)[2] even fail to apply since the intrapersonal information can
not be obtained from one image sample per subject.
One training sample problem is a realistic problem existing in
many applications such as surveillance photo identification. One
possible solution to this problem is to apply an unsupervised learn-
ing technique on the given samples such as the so-called projection
combined principal component analysis ((PC)
2
A)[3] and SVD per-
turbation method (SVD)[4] which are extensions of the well-known
principal component analysis (PCA) solution [5]. The proposals in-
troduced pre-processing schemes followed by a standard PCA. An-
other possible solution is to artificially generate extra samples for
each subject under consideration such as moving the original image
in four directions[6]. However, as stated in [7], the generated sam-
This work is partially supported by a Bell University Lab research grant
and the CITO Student Internship Program. The authors would like to thank
the FERET Technical Agent, the U.S. National Institute of Standards and
Technology for providing the FERET database.
ples are usually highly correlated and should not be considered as
truly independent training samples.
Different from the above mentioned solutions which only use the
given samples to train FR machines, in [8], based on the traditional
eigenface (PCA) solution, we proposed a feature selection scheme
in a generic learning (GL) framework. Within the GL framework,
a PCA machine is built by using a generic database which contains
the subjects other than those to be recognized in real operations. This
is based on the assumption that human faces exhibit similar intrap-
ersonal variations so that the discriminant information among the
specific subjects could be learnt from other subjects. Since PCA is
an unsupervised learning technique without considering the class la-
bel, inter- and intra- personal variations are coupled together in the
extracted PCA space. Therefore, a feature selection scheme was pro-
posed to apply on the extracted eigenfaces. The selected eigenfaces
span a feature subspace in which the class separability is maximized.
In this paper, we extend the proposed method [8] into a non-linear
space by using the so-called kernel machine techniques. By combin-
ing the strength of the proposed feature selection scheme in [8] and
the kernel techniques[9], a novel kernel eigenface selection scheme
is proposed which allows for a non-linear solution to the problem. A
KPCA machine[10] is firstly trained on the generic database, and a
feature selection procedure is applied on the extracted kernel eigen-
faces thereafter. It will be further observed that the method proposed
in [8] is a special case of the proposed here algorithm when a linear
kernel function is used.
The rest of the paper is organized as follows. We start by briefly
reviewing the eigenface selection scheme in section 2. Following
that, the kernel eigenface selection procedure is discussed in section
3 with the selection criterion and procedure described in details. Ex-
perimentations on the FERET [11] database are presented in section
4 followed by a conclusion drawn in section 5.
2. REVIEW OF EIGENFACE SELECTION
In this section, the idea of selecting eigenfaces will be briefly re-
viewed. Let G be the gallery set containing G subjects to be recog-
nized. Each subject is represented by a face image g
i
,i=1, 2, ..., G.
Let Z = {Z
i
}
C
i=1
be the generic data database, containing C sub-
jects with each subject Z
i
= {z
ij
}
C
i
j=1
, consisting of C
i
samples z
ij
with a total of N =
P
C
i=1
C
i
samples, where z
ij
∈R
S
. Please
note, there is no overlapping between G and Z. PCA is then ap-
plied on the generic training set obtaining at most N − 1 meaningful
eigenvectors with non zero eigenvalues when the number of training
samples is smaller than the dimensionality of the sample space.
PCA is an unsupervised linear technique which produces the
most expressive subspace for face representation but not necessary
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