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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 Claussen1 and Thomas Villmann2 — 1Theoret. Physics, Univ. Kiel — 2Clinic 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.)