Information Technology Reference
In-Depth Information
into 2
2
=
4) equal sections. Now, neural network dealing with complex numbers
are not the new entrants to the field of neural networks; they have established the
basic theories, yet they require more exploration in new coming applications. A brief
survey into the CVNN brings out the fact that it provides faster convergence with
better results, reduction in learning parameters (network topology), and the ability to
learn two-dimensional motion of signal [
3
,
8
]. The weight update rule for the CVNN
is exactly same as the one used to training networks using the most popular error
correction learning.
(
ʴ
E
)
w
(
t
+
1
)
=
w
(
t
)
+
ʷ
(2.3)
ʴ
w
(
t
)
where
w
is the weight that get updated as the algorithm runs iteratively, E is the Error
Function that gets minimized in the process of weight update and
ʷ
is the learning
rate. The difference of course lies in the fact that the weights are complex numbers,
while the error function and learning constant are positive real numbers. All the
signals that the neurons fire in response to aggregation and activation functions are all
complex in nature. It must be emphasized here that continuity and differentiability of
a function in complex domain play a central role in development of complex variable
based neural networks. It is hence obvious that a thorough discussion of complex
variables and complex mappings is essential to comprehend the mechanism by which
a CVNN operates. The definitions discussed here are required to prepare the ground
for a systematic study to develop a theory for analysis.
2.4 Neurocomputing with Three Dimensional Parameters
Artificial neural networks have been studied for many years in the hope of achiev-
ing human like flexibility in processing typical information. Some of the recent
researches in neurocomputing concerns the development of neurons dealing with
three-dimensional parameters [
9
] and their applications to the problems, which deals
with three-dimensional information. There has been rapid development in the field
of 3D imaging, computer vision, and robotics in last few years. These are multidisci-
plinary fields, which encompasses various research areas and deal with information
processing through modern neurocomputing paradigm. They are at their infancy
[
10
-
12
] and requires to explore methods based on neural networks. The 3D motion
interpretation and 3D feature recognition are essential part of high level analysis,
and found wide practical uses in the system development of these fields. Although,
there are many methodologies [
10
,
11
,
13
,
14
] to solve them, they instead use exten-
sive mathematics and are time consuming. They are also weak to noise. Therefore,
it is desirable for realistic system to consider iterative methods, which can adapt
system for three-dimensional applications. This topic is aimed at presenting relevant
theoretical and experimental framework based on multilayer neural networks of 3D
3D geometric point set (point cloud) representation of objects. The method described
Search WWH ::
Custom Search