Name
Abstract | ||
|---|---|---|
. The self-organizing map (SOM), a widely used algorithm for the unsupervised learning of neural maps, can be formulated in
a low-dimensional ‘feature map’ variant which requires prespecified parameters (‘features’) for the description of receptive
fields, or in a more general high-dimensional variant which allows self-organization of the structure of individual receptive
fields as well as their arrangement in a map. We present here a new analytical method for deriving conditions for the emergence
of structure in SOMs which is particularly suited for the as yet inaccessible high-dimensional SOM variant. Our approach is
based on an evaluation of a map distortion function. It involves only an ansatz for the way stimuli are distributed among
map neurons; the receptive fields of the map need not be known explicitly. Using this method we first calculate regions of
stability for four possible states of SOMs projecting from a rectangular input space to a ring of neurons. We then analyze
the transition from nonoriented to oriented receptive fields in a SOM-based model for the development of orientation maps.
In both cases, the analytical results are well corroborated by the results of computer simulations. |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1007/s004220050305 | Biological Cybernetics |
Keywords | Field | DocType |
Phase Transition,Computer Simulation,Receptive Field,Input Space,Unsupervised Learning | Receptive field,Ansatz,Phase transition,Distortion function,Quasi-open map,Self-organizing map,Unsupervised learning,Artificial intelligence,Machine learning,Mathematics | Journal |
Volume | Issue | ISSN |
75 | 5 | 0340-1200 |
Citations | PageRank | References |
9 | 1.55 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Maximilian Riesenhuber | 1 | 761 | 59.73 |
| Hans-ulrich Bauer | 2 | 236 | 38.94 |
| Theo Geisel | 3 | 314 | 40.09 |