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recognition algorithms [ 6 - 10 ] have been proposed to be used in this case. Principal compon-
ent analysis (PCA) [ 11 , 7 , 6 ] is one of the common and known methods of pattern recognition
and face recognition [ 12 , 13 ] that has been used a lot in biometrics. PCA, however, is a lin-
ear method which makes it unable to properly deal with nonlinear patterns which might be
in data. To overcome the mentioned drawback of PCA, kernel principal component analys-
is (KPCA) [ 14 , 8 ] was proposed, which is known to be more appropriate than PCA in many
cases, such as pattern recognition and face recognition. It is because of the fact that using ker-
nel function in the system makes it nonlinear. Kernel entropy component analysis (KECA) is
also an extension on KPCA that has been introduced in finger vein area [ 15 , 16 ] as well as some
extensions of two-dimensional PCA [ 17 ] . The mentioned reasons motivated us to conduct a
comparative analysis between two known and mostly used methods called PCA and KPCA
[ 9 , 18 - 20 ] in finger vein recognition. The main difference between PCA and KPCA is the fact
that PCA is a linear method, whereas KPCA is the nonlinear version of PCA in which ker-
nel transforming is used. In PCA, it is ensured that the transferred data are uncorrelated, and
only preserve maximally the second-order statistics of the original data, which is why PCA
is known as insensitive to the dependencies of multiple features of the pattern. In KPCA, the
mentioned problem has been overcome as it is not a linear method. In KPCA, however, it is
essential that which kernel mapping function is chosen to be used. It could be considered very
important due to the fact that each kernel mapping has particular characteristics and the data
after being mapped will be in a totally different and high-dimensional space where it could be
too complicated to extract the valuable features. As PCA is a well-known method of dimen-
sionality reduction, the combination of PCA and kernel mapping will lead to a more reliable
system. This work is an extension of the work of Damavandinejadmonfared and Varadharajan
[ 21 ] presented in IPCV 2014 conference. There are several different types of kernel mapping
which have been proven to be novel in different machine learning algorithms. In this research,
well use four famous kernel mappings such as polynomial, Gaussian, exponential, and Lapla-
cian as they have an extensive use within image processing related algorithms. Comparison
in this paper is between different types of KPCA using the mentioned four kernel functions to
map the data to achieve a twofold contribution; first, KPCA is appropriate enough to be used
in finger vein area, and second, which kernel mapping function is the most superior one.
The remainder of this paper is organized as follows:
In Section 2 , image acquisition is explained. In Section 3 , PCA is explained. In Section 4 ,
KPCA is introduced. In Section 5 , experimental results on the finger vein database are given.
Finally, Section 6 concludes the paper.
2 Image Acquisition
Based on the proven scientific fact that the light rays can be absorbed by deoxygenated hemo-
globin in the vein, absorption coefficient of the vein is higher than other parts of finger. In or-
der to provide the finger vein images, four low-cost prototype devices are needed such as an
infrared (IR) LED and its control circuit with wavelength 830 nm, a camera to capture the im-
ages, a microcomputer unit to control the LED array, and a computer to process the images.
The webcam has an IR blocking filter; hence, it is not sensitive to the IR rays. To solve this
problem, an IR blocking filter is used to prevent the infrared rays from being blocked ( Figure
1 ) .
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