Name
Abstract | ||
|---|---|---|
We discuss the property of a.e. and in mean convergence of the Kohonen algorithm considered as a stochastic process. The various conditions ensuring a.e. convergence are described and the connection with the rate decay of the learning parameter is analyzed. The rate of convergence is discussed for different choices of learning parameters. We prove rigorously that the rate of decay of the learning parameter which is most used in the applications is a sufficient condition for a.e. convergence and we check it numerically. The aim of the paper is also to clarify the state of the art on the convergence property of the algorithm in view of the growing number of applications of the Kohonen neural networks. We apply our theorem and considerations to the case of genetic classification which is a rapidly developing field. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.mcm.2006.04.004 | Mathematical and Computer Modelling |
Keywords | Field | DocType |
sufficient condition,convergence property,kohonen neural network,neighborhood function,rate decay,various condition,learning parameter,different choice,genetic classification,genetics,stochastic process,up modulated genes,microarrays,mean convergence,kohonen algorithm,almost everywhere convergence,quantitative method,rate of convergence | Convergence (routing),Mathematical optimization,Algorithm,Stochastic process,Self-organizing map,Kohonen neural network,Convergence acceleration,Rate of convergence,Artificial neural network,Numerical analysis,Mathematics | Journal |
Volume | Issue | ISSN |
45 | 1-2 | Mathematical and Computer Modelling |
Citations | PageRank | References |
5 | 0.43 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniela Bianchi | 1 | 13 | 1.80 |
| Raffaele A Calogero | 2 | 66 | 5.28 |
| B. Tirozzi | 3 | 30 | 6.31 |