CONVERGENCE OF SELF-ORGANIZING NEURAL ALGORITHMS

Cottrell-Fort's model and some self-organizing neural algorithms are analyzed in this paper In the one-dimensional case, the almost sure convergence for Cottrell-Fort's algorithm is obtained when the probability distribution of stimulus center is not uniform. A new algorithm is designed which is the combination of Kohonen and Cottrell-Fort's algorithms. In the two-dimensional case, another new training algorithm is provided which is different from Cottrell-Fort's. It also has almost sure convergence for rather general stimulus distributions. An interaction parameter is introduced to make the model more flexible. For any boundary condition, the algorithm is convergent when suitable stimulus distributions are applied. The self-organized map depends on the stimulus distribution and the boundary conditions but not on the initial map. It shows some relation between the statistical distribution of the stimulus and the connection structure in the neural maps. The system is robust and reliable. An example in the one-dimensional case shows that even if some nodes have zero stimulus probability the system can still form an ordered map from an unordered initial map.