Given a self–dual map on the sphere, the collection of its self– dual permutations generates a transformation group in which the map automorphism group appears as a subgroup of index two. A careful examination of this pairing yields direct constructions of self–dual maps and provides a classification of self–dual maps.

in this paper we address the issue of recognizing farsi handwritten words. two types of gradient features are extracted from a sliding vertical stripe which sweeps across a word image. these are directional and intensity gradient features. the feature vector extracted from each stripe is then coded using the self organizing map (som). in this method each word is modeled using the discrete hidde...

abstract this paper presents a robust approach using artificial neural networks in the form of a self organizing map (som) as a semi-automatic method for analysis and identification of morphometric features in two completely different environments, the man and biosphere reserve “eastern carpathians” (central europe) in a complex mountainous humid area and yardangs in lut desert, iran, a hyper a...

A Hierarchical Extended Kohonen Map (HEKM) learns to associate actions to perceptions under the supervision of a planner: they cooperate to solve path nding problems. We argue for the utility of using the hierarchical version of the KM instead of the \ at" KM. We measure the bene ts of cooperative learning due to the interaction of neighboring neurons in the HEKM. We highlight a bene cial side-...

Many theoretical papers are published about the Kohonen algorithm. It is not easy to understand what is exactly proved, because of the great variety of mathematical methods. Despite all these eeorts, many problems remain without solution. In this small review paper, we intend to sum up the situation.

Abstract : the aim of this paper is to observe the group dynamic of funds’ managers during an interesting period : January 99July 01, which includes many financial events as financial cracks, high speculation on new technologies. We define a strategy as the sensitivity on French stock market indexes. We project strategies on a Kohonen Map. We propose a new approach to analyze the group dynamic ...

The Kohonen Algorithm was extended by (a) a coupling between node and input space based upon gravitational principles and (b) a controling mechanism based upon two-point correlation functions. The extended algorithm avoids optimization of the learning rate and neighbourhood parameters. Applications are given for both a 3-dimensional example data set with mixed topologies and a 13-dimensional da...