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IEEE SIGNAL PROCESSING LETTERS,VOL.9,NO.2,FEBRUARY 2002
Face Recognition Using Kernel
Principal Component Analysis
Kwang In Kim,Keechul Jung,and Hang Joon Kim
Abstract—A kernel principal component analysis (PCA)was re-cently propod as a nonlinear extension of a PCA.The basic idea is
to first map the input space into a feature space via nonlinear map-ping and then compute the principal components in that feature space.This letter adopts the kernel PCA as a mechanism for ex-tracting facial features.Through adopting a polynomial kernel,the principal components can be computed within the space spanned by high-order correlations of input pixels making up a facial image,thereby producing a good performance.
Index Terms—Eigenface,face recognition,kernel principal com-ponent analysis,machine learning.
I.I NTRODUCTION
A
PRINCIPAL component analysis (PCA)is a powerful technique for extracting a structure from potentially high-dimensional data ts,which corresponds to extracting
the
eigenvalues
from the input distribution.This eigenvector analysis has already been widely ud in face processing [1],[2].A kernel PCA,recently propod as a nonlinear extension of a PCA [3]–[5]computes the principal components in a high-dimen-sional feature
space
can be formulated in terms of the dot products
in
)without explicitly working
in
Departme
Publish
KIM et al.:FACE RECOGNITION USING KERNEL PRINCIPAL COMPONENT ANALYSIS
41
Fig.1.Face feature extraction architecture with kernel PCA.
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the eigenvectors are sorted in a descending order of their eigen-value size)constitute
the
,various
mappings,
-order correlations between the
entries,,of
the inputtoughest
vector
reprents a face pattern
with as a pixel value,a PCA
in
of
the
is not small
question是什么意思(-dimen-sional input patterns,the dimensionality of the feature
space
that first parates that
class from all the other class and then us an
expert
one-per-
class SVMs,the max-lector picks
class ,
which then
maximizes
However,a max-lector suffers from a scaling problem,be-cau it assumes that all
the
1,the scale is not robust as it only de-pends on a few data,often including outliers [9].In a max--lect
or,the output class is determined by choosing the maximum of all the SVM outputs.However,the outputs of the remaining SVMs,other than the winner,also carry certain information.Moreover,the mean
of
.While this technique shows significant improvements over the bare one-per-class decomposition,preliminary experiments have indicated that a linear normalization is often insufficient for face recognition as the relation
among
by applying a tangent hy-perbolic
function
,a nonlinear
mapping A two-layer neural network,compod of a hidden layer
of size three with a tangent hyperbolic activation function,is adopted for
mapping
112with a
初一英语练习题256-level gray scale.The gray scale was linearly normalized to lie within
[
42IEEE SIGNAL PROCESSING LETTERS,VOL.9,NO.2,FEBRUARY
2002
Fig.2.Experimental results with different polynomial degrees d and number of eigenvectors q :(a)average error rates and (b)standard deviation.
The tuned parameters included the polynomial
degree
as
follows:
.Fig.2shows the results:
(a)average error rates and (b)standard deviation of error rates.
mortal什么意思
A tendency of smaller error rates for the
higher
was obrved,while a saturation point was reached
when (marked with a white bar),which
clearly outperformed the linear PCA (equivalent to a first-degree polynomial kernel PCA:4.1%error rate).Table I shows a sum-mary of the performance of various systems for which results using the ORL databa are available [6],[10]–[12].The pro-pod method produced better results and a significant reduc-tion in the error rate (16.7%)compared with the performances of the best existing system-linear SVMs [6].The 2.5%error rate reported for the propod method was an average of 20simula-
TABLE I
P ERFORMANCES OF V ARIOUS S
can u speak english >tonguesYSTEMS
tions,however,the individual simulations had given error rates as low as 1.5%.
V .C ONCLUSION
A kernel PCA-bad face feature extraction method was pre-nted,whereby the u of a polynomial kernel enables the prin-cipal components to be computed within the product space of the input pixels making up a facial pattern.Using SVMs as the recognizer,experimental results with the ORL databa confirm the effectiveness of the propod method.
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