TY - JOUR
T1 - Magnification control in self-organizing maps and neural gas
AU - Villmann, Thomas
AU - Claussen, Jens Christian
N1 - © 2005 Massachusetts Institute of Technology
PY - 2006/2/1
Y1 - 2006/2/1
N2 - We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms that are localized learning, concave-convex learning, and winner-relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case, the results hold only for the one-dimensional case.
AB - We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms that are localized learning, concave-convex learning, and winner-relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case, the results hold only for the one-dimensional case.
UR - http://www.scopus.com/inward/record.url?scp=33644899424&partnerID=8YFLogxK
UR - https://www.mitpressjournals.org/doi/10.1162/089976606775093918
U2 - 10.1162/089976606775093918
DO - 10.1162/089976606775093918
M3 - Article
C2 - 16378522
AN - SCOPUS:33644899424
SN - 0899-7667
VL - 18
SP - 446
EP - 469
JO - Neural Computation
JF - Neural Computation
IS - 2
ER -