Login

 


Plenary Lecture

Real Model Geometric Characterization using Gram-Schmidt Orthogonalization Concept

Professor Benabdellah Yagoubi
Laboratory of Signals and systems
Department of Electrical Engineering
University of Mostaganem
Algeria
E-mail: yagoubibenabdellah@yahoo.com

Abstract: It is well known that modeling is to look for an adequate mathematical model to represent the real model by linking, mathematically, the inputs to the output data of the real model. In the case of a linear model, this relation is, usually, performed using a different kind of mathematical models, which are used to estimate the coefficients of the closest linear model to the real one. This sort of models are, usually, obtained by the LMS algorithm or the minimum square error (MSE) which suggests that the best linear approximation of any real model output corresponds to the minimum of the estimation error or, equivalently, must be, geometrically, orthogonal to the linear input space. The determination of the non linear model is, however, one of the most difficult tasks in modeling. In contrast to a linear model corresponding, geometrically, to a hyper plane with only a zero Riemannian curvature, a non linear model corresponds to a many possible variable Riemannian curvatures. The crucial question is, therefore, how to select the right mathematical non linear model to fit the real one. Theoretically, we have an infinite number of possible non linear models, but if we have, however, any faire indication about the real model curvature or non linearity, then the selected mathematical model could be restricted, accordingly, to a limited range of possible models to represent the real one. The selected model is, obviously, the one that has the least modeling error. This is indeed what we, usually, attempt to do, particularly, in neural networks field. This selected model, unfortunately, may not be the decisive one since we could not try all the mathematical models.
In the algebraic methods of modeling, we do not, usually, look how a real model is being constituted and what are its geometric components. We believe, therefore, that it is very important to represent a real model, geometrically, by its main components in order to see how they are, naturally, related to each other. As a result, we can understand how it is possible to obtain a better approximation for the real system (or model) In this talk, we try, thus, to discuss the main characteristics of a real model, in general, using geometric approach based on Gram-Schmidt concept. Some examples such as Autoregressive models, Kalmann algorithm and so on, are reviewed to clarify this geometric representation of a real model.

Brief Biography of the Speaker: Dr B. Yagoubi received the M. Sc degree in Electrical Engineering in 1985 from Bel-Abbes University, Algeria and the Ph. D degree (thin films) (1986-1989) in the Faculty of Sciences from Brunel University (UK). He was the head of the Signals and Systems Laboratory (1999-2003) and the head of the Department of Electrical Engineering (2005-2006). He is lecturing the theory of digital signal, systems modeling and identification, random processes and detection (1996-2013) at Mostaganem University, Algeria. Currently, he is involved in some national projects; forest fire detection, heart rate variability in the LF and HF bands to characterize the autonomous nervous system, and study and application of random processes. Further research interests are in real signals and models geometric representation based on Gram-Schmidt orthogonalization concept, as well as using a relative geometric space of observation.

Bulletin Board

Currently:

The Conference Program is online.

The Conference Guide is online.

The paper submission deadline has expired. Please choose a future conference to submit your paper.


WSEAS Main Site


NAUN Main Site

Publication Ethics and Malpractice Statement