Goals and Purpose of the Project

Multilayer Perceptrons (MLP) and Radial Basis Function (RBF) networks are commonly used to solve classifica-tion problems. MLP are feed forward networks with one or more hidden layers of nonlinear perceptron elements. They usu-ally employ sigmoid functions as nonlinearities and a variation of delta training algorithm. RBF networks commonly have one hidden layer, the elements of which compute the values of radial basis functions. These nonlinearities are normally Gaussian functions with local influence around their centers. The RBF neural networks compared to MLPs have an advan-tage that their training is much less computationally intensive. Normally one-tenth of the time that is needed for the training of a MLP network, is needed for the training of a RBF network. Also the RBF networks have the best approximation ability.

RBF networks create a global approximation to a target function as a linear combination of the local nonlinearities in the hidden layer. It is difficult to find good parameters for the basis function centers and their variances, while the number of centers is small. In order to fill out a high dimensional hidden space many basis function centers are needed and this number grows exponentially with the dimension of the hidden space. A large number of basis functions leads to a large number of needed training examples. Finding a suitable network size and fitting parameters still remains an open problem.

The goal of this project is to develop supervised learning algorithms for feed forward and RBF neural networks and a novel method for data clustering which performs classification based on a set of potential fields synthesized over the domain of input space by a number of potential function units.

This project represents on-going research conducted by the faculty-applicant. Preliminary results were published and presented at the 13th International Symposium on Computer and Information Sciences ISCIS.98 [5]. Substantial theo-retical findings have been submitted to ANNIE.02 .Smart Engineering System Design: Neural Networks, Fuzzy logic, Evo-lutionary Programming, Data Mining, and Complex Systems. refereed conference honored with Best Paper Award in Theo-retical Developments in Computational Intelligence category (http://web.umr.edu/~annie/bpa02.htm). This proposal was a continuation and was built upon the developed theoretical basis.

Process Steps Used in Completing the Research

1. Seven seminars have been organized during Fall.02. During the first four seminars the PI presented the potential functions and their application in solving pattern recognition problems; how to construct multivatiate functions based on orthonormal polynomials; basic principles in development of supervised learning with radial-basis func-tions using potential functions. During the last three seminars, student-participants discussed some approaches in building neural networks, proposed their own ideas and presented the basic steps in neural network design. More details can be found on the project web site given below.
   http://www.cs.csi.cuny.edu/~natacha/Projects/Pfnn/seminars.htm
2. Three formal seminars and several informal meetings took place during the Spring.03. Their purpose was to share the achieved results, to discuss the content of the papers submitted to two conferences and the prepared presenta-tions, to update the web site.
3. A final meeting was scheduled on May 27 to discuss the final reports and update the project web site.

Conclusions and Results Achieved

The student-participants

• Made a research of the current state of the art of the problem domain and extended their knowledge in design of neural networks.
• Mastered their knowledge in C++/Java programming language, Data Structure, Object-Oriented Programming, Linear Algebra and Matlab programming package.
• Designed the basic topologies of the feed forward and RBF neural networks as well as learning algorithms for super-vised learning with potential functions.
• Proposed experiments with novel approaches, which can be a basis for a future research and investigated the depend-ence of the proposed method and algorithms on different parameters and apply different strategies to several data sets.
• Wrote four papers and presented them on traditional CSI/CUNY Undergraduate Research Conference on April, 10, 2003 and American Society for Engineering Education (ASEE) Mid-Atlantic Region Conference on April 11 . 12, 2003..
• Created and maintained a project web site.

Publications

1. Fiorentino A., Gueorguieva N., Supervised Learning based on Multilayer Feedforward Potential Function Ap-proach. Second Annual Undergraduate Research Conference of the City University of New York / College of Staten Island on April 10, 2003, Book of Abstracts, pp. 18.

2. Wang A., Gueorguieva N., New Approach To Design Of Radial Basis Functions Neural Networks. Second Annual Undergraduate Research Conference of the City University of New York / College of Staten Island on April 10, 2003, Book of Abstracts, pp. 39.

3. Zhang H., Gueorguieva N., Neural Network Learning and Classification: A Potential Functions Approach. Second Annual Undergraduate Research Conference of the City University of New York / College of Staten Island on April 10, 2003, Book of Abstracts, pp. 43.

4. Fiorentino A., Wang A., Zhang H.,Gueorguieva N., Supervised Learning Neural Networks Based on Potential Functions Approach. Proceedings of the Mid-Atlantic Conference, organized by the American Society for Engi-neering Education (ASEE), Kean Univesity, Union, NJ April 11 . 12, 2003, CD # AESS_Kean 2003. The Pro-ceedings of the Mid

Project web site:

http://www.cs.csi.cuny.edu/~natacha/Projects/ProjectGrant.htm
http://www.cs.csi.cuny.edu/~natacha/Projects/Pfnn/index.htm