Neurocomputing in Space - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 116

Chapter 6
Neurocomputing in Space
Abstract The high-dimensional neural network is becoming very popular in almost
every intelligence systemdesign, just to name few, computer vision, robotics, biomet-
ric identification, control, communication system, and forecasting are the scientific
and engineering fields that take advantage of artificial neural networks (ANN) to
emulate intelligent behavior. In computer vision the interpretation of 3D motion, 3D
transformations, and 3D face or object recognition are important tasks. There have
been many methodologies to solve them, but these methods are time consuming and
weak to noise. The advantage of using neural networks for object recognition is the
feasibility of a training system to capture the complex class conditional density of pat-
terns. It will be desirable to explore the capabilities of ANN that can directly process
three-dimensional information. This article discusses the machine learning from the
view points of 3D vector-valued neural network and corresponding applications. The
learning and generalization capacity of high-dimensional ANN is confirmed through
diverse simulation examples.
6.1 3D Vector-Valued Neuron
The advantages with a neural network include robustness, ability to learn, general-
ize, and separate complicated classes [ 1 , 2 ]. In 3D vector-valued neural network, the
input-output signals and threshold are 3D real-valued vectors, while weights asso-
ciated with connections are 3D orthogonal matrices. The weights are assumed to be
orthogonal matrices because this assumption is a natural extension of the weights
of the complex-valued neuron. We will present few illustrative examples to show
how a 3D vector-valued neuron can be used to learn 3D motion and used in 3D face
recognition. The proposed 3D motion interpretation system is trained using only
few set of points lying on a line in the 3D space. The trained system is capable of
interpreting 3D motion consisting of several motion components over unknown 3D
objects. Face recognition is the preferred mode of identity authentication [ 3 - 5 ]. The
facial features have several advantages over other six biometric attributes considered
by Hietmeyer [ 6 ]. It is natural, robust, and uninstructive. It cannot be forgotten or
mislaid like other document of identification. Most of the face recognition techniques