Image Processing Reference

In-Depth Information

The total scater matrix in kernel 2DPCA can be calculated as

(8)

Thus,

(9)

In kernel 2DPCA, after achieving
B
i
= [
Y
1
i
,
Y
1
i
, …,
Y
d
i
] and
G
t
Φ
, obtaining projecting axes and

the projection and classification procedures are same as in 2DPCA.

4.2 Kernel Mapping in Row and Column Directions and 2DPCA

argument here is that by applying this mapping in different directions (along row and column

directions), we will end up having two different data having different dimensions. To further

elaborate this, let us assume we have
m
×
n
input matrixes (
n
>
m
). By applying the kernel map-

ping function along the row direction (we have
m
rows meaning that there are
m
elements for

the kernel matrix to be made of), the kernel matrix will be (
m
×
m
). In this case, by applying

kernel mapping, we reduce the number of input data and its dimension in kernel space which

is (
n
×
n
). However, if the kernel function is applied along column direction, the kernel matrix

will be (
n
×
n
). In this case, we have expanded the input data to a higher dimensional space

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