Dr. Gilles Labonté, BSc, MSc, PhDProfessor

Department of Mathematics & Computer Science

Present research interests

All aspects of natural and artificial neural networks. Their working principles. Their mathematical properties. Their applications.

Research projects

MATHEMATICAL ANALYSIS of the nature and convergence of the learning algorithms used by neural networks

Complete mathematical analysis of a class of artificial neural networks that can solve sets of linear inequalities.  These networks realize the method of orthogonal projections on the hyperplanes bounding the polytope of solutions.  Published in  "On Solving Systems of Linear Inequalities with Artificial Neural Networks" by G. Labonté, in IEEE Transactions on Neural Networks, 8, 590-600, 1997.

Analysis of a particular version of the algorithm of self-organizing maps of Kohonen.  Our study on the behavior of this algorithm is described in the article "A Neural Network that Performs an Enhanced Nearest-Neighbor Matching" which will appear shortly in the journal Pattern Analysis and Applications.  A complete mathematical analysis of the process and speed of convergence of this algorithm, described in this paper, is presently under completion.

PARTICLE IMAGE VELOCIMETRY  

Design of artificial neural networks for the processing of images and correction of experimental errors in PIV.   PIV is a technique for determining the velocity field of a fluid in motion.  It consists in taking successive photographs of small particles suspended in this fluid.  The velocity of these particles is then readily calculated from the measure of their displacements.  However, these displacements can be measured only when the correspondence problem is solved, that is when it is determined which images, in the different photos, correspond to the same particle.

COMPUTATIONS ON NETWORK PARALLEL COMPUTERS 

Design, analysis and tests of a method for realizing artificial neural networks on a super parallel computer, obtained by configuring an existing  network of computers, such as intranets and the Internet, as a single data processing entity.

AUTONOMOUS ROBOT AIRPLANE 

Design of an intelligent airplane, endowed with sensors, controllers and artificial neural networks.  These neural networks will serve to integrate the data produced by the sensors, assume the command and coordination of the functions of the airplane.  Above all, they will render it able to learn, either by imitation of a teacher or by instrumental conditioning, to take off, to fly in a stable manner and to land.

This link leads to a site belonging to an entity not subject to the Official Languages Act. Information on this site is available in the language of the site.

Visit the International Neural Network Society.