String Tightening as a Self-Organizing Phenomenon: Computation of Shortest Homotopic Path, Smooth Path, and Convex Hull

One of the most well known of The phenomenon of self-organization has been of special such attempts is that of Kohonen's who proposed the interest to the neural network community for decades. In Self-Organizing Map (SOM) [2] inspired by the way in this paper, we study a variant of the Self-Organizing Map which various human sensory impressions are topographically (SOM) that models the phenomenon of self-organization mapped into the neurons of the brain. SOM possesses of the particles forming a string when the string is tightened the capability to extract features from a multidimensional from one or both ends. The proposed variant, called data set by creating a vector quantizer by adjusting the String Tightening Self-Organizing Neural Network weights from common input nodes to M output (STON), can be used to solve certain practical problems, nodes arranged in a two dimensional grid. At convergence, such as computation of shortest homotopic paths, the weights specify the clusters or vector centers smoothing paths to avoid sharp turns, and computation of the set of input vectors such that the point density of convex hull. These problems are of considerable interest function of the vector centers tend to approximate the in computational geometry, robotics path planning, probability density function of the input vectors. Several AI (diagrammatic reasoning), VLSI routing, and geographical authors in different contexts reported different dynamic information systems. Given a set of obstacles versions of SOM [2-11].