Higher-Order Computational Model for Novel Neurons - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 79

Chapter 4
Higher-Order Computational Model
for Novel Neurons
Abstract Artificial neural network (ANN) has attracted a tremendous amount of
interest for the solution of many complicated engineering and real-life problems.
A small complexity, quick convergence, and robust performance are vital for its
extensive applications. These features are pertinent upon the architecture of the basic
working unit or neuron model, used in neural network. The computational capabil-
ity of a neuron governs the architectural complexity of its neural network, which
in turn defines the number of nodes and connections. Therefore, it is imperative to
look for some neuron models, which yield ANN having small complexity in terms
of network topology, number of learning parameters (connection weights) and at the
same time they should possess fast learning, and superior functional capabilities.
The conventional artificial neurons compute its internal state as the sum of contribu-
tions (aggregation) from impinging signals. For a neuron to respond strongly toward
correlation among inputs, one must include higher-order relation among a set of
inputs in their aggregation. A wide survey into design of artificial neurons brings
out the fact that a higher-order neuron may generate an ANN which can have better
classification and functional mapping capabilities with comparatively less number of
neurons. Adequate functionality of ANN in a complex domain has also been observed
in recent researches. This chapter presents higher-order computational models for
novel neurons with well-defined learning procedures. Their implementation in a
complex domain will provide a powerful scheme for learning input/output mapping
in complex as well as in real domain along with better accuracy in wide spectrum of
applications. The real domain implementationmay be realized as its special case. The
purpose of investigation in this chapter is to present the suitability and sustainability
of higher-order neurons for readers, which can serve as a basis of the formulation
for powerful ANN.
4.1 Biological Neuron
The human nervous system is a tremendously complicated structure consisting of
about 10 11 neuron units. The basic building block of biological information process-
ing system, the neuron, consists of three basic components viz dendrites, soma, and