# Dresden 2003 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 36: Nonlinear dynamics II

### DY 36.3: Vortrag

### Mittwoch, 26. März 2003, 17:00–17:15, G\"OR/226

**Winner-Relaxing and Winner-Enhancing in Self-Organizing Map and Neural Gas: Nonlocal magnification control from modifying the learning rule of the winner** — •Jens Christian Claussen^{1} and Thomas Villmann^{2} — ^{1}Theoret. Physics, Univ. Kiel — ^{2}Clinic of Psychotherapy, University Leipzig, Germany

Self-Organizing Maps (SOM) are rather widely considered in applications, despite the origin of the Kohonen model was in aim of biological modeling. The lack of an energy function for the Kohonen model has lead to a variety of other models, e.g. the approach of an elastic net feature map [1] and of voronoi border corrections to the learning rule [2] that were generalized [3] giving a SOM with adjustable magification and therefore adjustable information transfer.

In [3] this approach is applied also to the Neural Gas (NG) Algorithm
giving a magnification control without local bookkeeping of firing
rate and reconstruction error.
The dimension-dependence of the winner-relaxing prefactor
can be derived analytically [4] and allows for
an a-priori parameter preset if the data dimension is
known approximately.
While for *D*≪1 the NG already is near to magnification
exponent 1, the (computationally) simple Winner-Relaxing term enhances
the entropy of the resulting map significantly esp. for
the lowdimensional (*D*=2…5) case.

[1] J. C. Claussen and H.G.Schuster, Proc. ICANN’2002, Springer LNCS.

[2] T. Kohonen, in: Artificial Neural Networks, ed. Kohonen et.al. 1991.

[3] J. C. Claussen, cond-mat/0208414, submitted to Neural Computation.

[4] J. C. Claussen and Th. Villmann, Proc. ESANN 2003 (subm.)