Ingeniero

Proceedings of the 8th WSEAS Int. Conference on Automatic Control, Modeling and Simulation, Prague, Czech Republic, March 12-14, 2006 (pp276-280)

A feed forward sine based neural network for functional approximation
of a waste incinerator emissions
MASSIMO BUSCEMA, STEFANO TERZI, MARCO BREDA
Semeion Research Center of Science of Communication
Via Sersale 117, 00128 Rome
ITALYhttp://www.semeion.it
Abstract: In this paper a new family of neural network named Sine Net (SN) is presented. It is characterized
by the presence of a specific double non-linear relationship on the connections between nodes. This
characteristic has some evident consequences on the properties of this network both on the computed function
and on the behaviour of this network during the learning phase. Thefirst part of the article is the presentation
of SN within a theoretical and mathematical framework, in the last some interesting results on the application
of SN on artificial and real data are illustrated, underlining the most relevant properties of this adaptive
system..
Key-Words: Sine Net, learning law, neural network, adaptive system, non-linear modelling.
Fig. 1 – Conceptualprocessing in classical networks

1 Introduction
The Sine Net (SN) is a family of neural networks
characterized by a specific processing inside each
node, influencing both the output evaluation from
input and the learning phases. This processing can be
applied to existing networks topologies as a
fundamental modification of their learning equations.
That means that the Sine Net represents a newgeneral
learning law. The new learning law demonstrates a
considerable convergence and high extrapolation
capabilities on complex data bases.
This type of ANN family was created in 1999 by M.
Buscema at the Semeion Research Centre of
Communication. Since then it has been applied on
several applications with exciting results.

1

The SN Learning Law

1.1 Philosophical background
In aclassical network each node works as an element
that receives the weighted input from the input nodes,
sums them and filters the result through a non linear
function.
x1

w1

.
.
.
xn

Σ
wn

F

y

The basic idea in the SN processing is to provide each
node with receivers interposed between each input
and the summation.
x1

w1

.
.
.
xn

R
R

Σ

F

y

wnFig. 2 - Conceptual processing in classical Sine Net networks

The receivers appropriately transforms in a non linear
way the input from each input node, before summing
the input contributes into a value to be filtered
through a non linear function. The meaning of the
receivers is the introduction of a quanti-qualitative
process on the input value, in substitution of a merely
quantitativeprocess on it, in analogy to what is done
in biological organisms by chemical ports with
respect to potential ports. The qualitative aspects of
transformation is obtained by using sinusoidal
functions. For each i-th coordinate of the input space,
this allows the introduction of a dependency of each ith transformed value by the spatial position of the
coordinate value with respect a spatialwave of given
wavelength. Input coordinate values, multiplied by
the wavelength, are then transformed into the same
value. The wavelength on each input receiver is
tuned during the learning phase.

1

Proceedings of the 8th WSEAS Int. Conference on Automatic Control, Modeling and Simulation, Prague, Czech Republic, March 12-14, 2006 (pp276-280)

1.2 The algorithm
As stated, the SN familyconsists of quite generally
defined networks, deeply modified in the inner
behaviour of their nodes; this adjustment of the nodes
is taken into account, both in the output evaluation
from input and in the learning phases. The details of
the node processing for classical networks and Sine
Nets are explained in the following.

((

s
[
x [js ] = F G w[ji ] , xi s −1]

(4)

where the...