Information Technology Reference
In-Depth Information
this section using split nonlinearity. We perform maximization of entropy surface by
complex gradient ascent which result in faster convergence. This is achieved through
the complex extension of the natural gradient. In
C
ICA-based feature extraction, we
assume that the image data X is a linear mixture of M statistically independent
complex-valued sources S, then Y =
f
C
(U=WX),whereU,W,X
C
. The basic
steps in
C
ICA algorithm for feature extraction in image database can be summarized
as follows:
∈
1. Collect the images in data matrix X (M by N) so that images are in rows and
pixels are in column.
2. Apply
R
PCA. The PCA basis vectors in
E
T
are analyzed for independent com-
ponents, where
E
(N by M
) be the matrix of M
eigenvectors.
3. Apply whitening (sphering) of data. Final transformation matrix will be the prod-
uct of whitening matrix and optimal unmixing matrix.
4. Sources are modeled as complex random vectors. Take sigmoidal complex func-
5. Derive a contrast function
h
from CVNN point of view. Performmaximization of
joint entropy
h
. This can be achieved using extension of the natural gradient
in a complex domain.
6. Perform complex infomax on PCA basis
X
. Find an optimal matrix W such that:
MAX [
h
(
Y
)
{
)
}
f
C
(
WX
], this can be done as:
{
)
}
•
Define a surface
h
f
C
(
U
•
∇
∝∇
Find the gradient
h
with respect to W and ascent it,
W
h
, then
W
T
−
1
X
T
M
f
C
(
1
M
u
)
W
=
η
+
,
u
∈
U
.
(7.19)
f
C
(
)
u
i
=
1
f
C
(
f
(
(
jf
(
(
u
)
u
))(
1
−
2
f
(
(
u
)))
−
u
))(
1
−
2
f
(
(
u
)))
where
=
.
f
C
(
f
(
(
f
(
(
u
)
2
(
u
))
+
u
)))
(7.20)
•
When function
h
ismaximumor magnitude of gradient of function h converges
toward zero, W is
W
OPT
. done! At a maximum in h the gradient magnitude
should be zero.
7. Maximizing joint entropy of outputs also minimizes the mutual information
between the individual outputs, ie basis images in U. That will let us know how
much the extracted signals in U are close to being independent. Thus,
C
ICA algo-
rithm produces transformation matrix
W
t
=
W
t
E
T
.
8.LetR=X
E
be the PC representation of images in X, also approximation of
X=R
E
T
. Assumption that
W
t
is invertible, we get
E
T
W
OPT
×
W
w
, such that
U
=
W
−
1
t
=
RW
−
t
U
. The estimation of IC representation of images is therefore based on the
independent basis images in U.
=
U
. Hence
X
Search WWH ::
Custom Search