Valeria Belmonti, junior student in 2003/2004, CSI/CUNY

Faculty Mentor: Dr. Natacha Gueorguieva, Associate Professor, Department of CS, CSI/CUNY

School: College of Staten Island/City University of New York (CSI/CUNY)
Address: 2800 Victory Blvd, Staten Island, NY 10314

Valeria Belmonti, junior student in 2003/2004, CSI/CUNY

School: College of Staten Island/City University of New York (CSI/CUNY)

Address: 2800 Victory Blvd, Staten Island, NY 10314

Goals and Purpose of the Project

         Analysis of large sets of data is an important task in many scientific research areas. This unavoidably involves clustering [1], which becomes a difficult task when the data space is high dimensional, i.e. when the number of features that characterize each point is very large. The goal of clustering analysis is usually to obtain a symbolic description of the problem and from this an identification procedure. In such situations, it might be useful to rely solely on the distances between the data points. This is the basis of many clustering methods that use these distances as a dissimilarity measure (resemblance or dissemblance). Under the assumption that points within a cluster are closer to one another than to points in other clusters, clustering becomes equivalent to searching for groups of points where the distances within each group cluster, are much smaller than the distances between points in different clusters. Special attention is given to the dynamic clustering methods, which handles adaptively a partition in clusters and a set of symbolic representations of the clusters.

         We propose to design algorithms for data clustering based on spiking neurons dynamics. The neuronal signal consists of short voltage pulses called action potentials or spikes. These pulses travel along the axon and are distributed to several postsynaptic neurons where they evoke postsynaptic potentials [2, 3]. If a postsynaptic neuron receives several spikes from several presynaptic neurons within a short time window, its membrane potential may reach a critical value and an action potential is triggered. This action potential is the output signal, which is, in turn, transmitted to other neurons.

Process Steps Used in Completing the Research

1. Four seminars have been organized during Fall'03. During the first two seminars the PI presented "Overview And Analysis Of Olfactory Bulb Models" and "A Spiking Neuron Model Of Olfactory Bulb Dynamics". During the last two seminars, Valeria and Marina discussed "Elements Of Neuron Systems", "Neural Networks Based On Spiking Neurons" and presented some approaches in building neural networks. They proposed their own ideas and developed the basic steps in spiking neural network design. More details can be found on the project web site given below.
2. Four formal seminars and several informal meetings took place during the Spring'04. Their purpose was to share the achieved results, to discuss the proposed algorithms and the developed neural network topologies, to set the simulation parameters. Because of family circumstances Valeria Belmonti left the team and we invited two male undergraduate student participants who work on voluntarily base. This allowed us to complete the project goals.
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 and analysis of the dynamics of the Hodgkin-Huxley model for different types of input: pulse input, constant input, step current input, and time-dependent input as well as the influence of the neuron geometry on synaptic integration.
• Mastered their knowledge in C++ programming language, Data Structure, Object-Oriented Programming, Linear Algebra and Matlab programming package.
• Designed the basic topologies of the neural networks based on spiking neurons as well as learning algorithms for these topologies.
• Proposed experiments with novel approaches, which can be a basis for a future research and investigated the dependence of the proposed method and algorithms with different sets of parameters.
• Wrote two papers and presented them on traditional CUNY/CSI Undergraduate Research Conference held in April, 22, 2004.
• Created and maintained a project web site.

Publications

1. Kogan M., and Gueorguieva N., Coding and Computation with Spiking Neurons. Undergraduate Research Conference of the City University of New York / College of Staten Island, April 22, 2004. Book of Abstracts, pp. 11.
2. Sabzposh S. Yaris A, Sabzposh Syed-Areeb A., and Natacha Gueorguieva, Reliability of Spike Timing in Brain Modeling. Undergraduate Research Conference of the City University of New York / College of Staten Island on April 22, 2004, Book of Abstracts, pp. 14.

Project web site:

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

http://www.cs.csi.cuny.edu/~natacha/Projects/neurons/

References

[1] Duda R., Hart T., and Stork D., Pattern Classification, 2/e, Wiley-InterScience, 2001.
[2] Gerstner W., Kirstler W., Spiking Neuron Models, Cambridge, 2002.
[3] Maas W., and Ruf B., On Computation with Pulses. Information and Computation, 148:202-218, 1999.