Spaceborne Polarimetric SAR and Hyperspectral Data
185
lK
λαα
=.
(8.41)
By normalizing the solutions of
α
k
that belong to non- zero eigenvalues, and the corresponding
vectors in F are also normalized, we get:
1 =
ij
l
i
k
j
k
ij
kk
k
kk
xxK
,
..
..
=
∑
()
()
(
)
=
()
=
()
1
ααϕϕααλαα
(8.42)
To extract the principal components, projection of the image at a point onto the eigenvectors in
F is computed as:
.
Vx
k
ϕ
(
)
(
)
=
i
l
i
k
i
x
=
∑
()
(
)
()
1
αϕϕ
.x
, (8.43)
where,
V
k
= eigenvectors, and
α = column vectors.
Schölkopf, Smola, and Müller (1997) have found that the main advantage of using kernel-
based PCA is that it improves the recognition capability of the non- linear PCA components when
compared with the linear PCA components.
8.3.3.2 MCSM- Based Feature Extraction in ...
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