10,078 research outputs found
On the use of self-organizing maps to accelerate vector quantization
Self-organizing maps (SOM) are widely used for their topology preservation
property: neighboring input vectors are quantified (or classified) either on
the same location or on neighbor ones on a predefined grid. SOM are also widely
used for their more classical vector quantization property. We show in this
paper that using SOM instead of the more classical Simple Competitive Learning
(SCL) algorithm drastically increases the speed of convergence of the vector
quantization process. This fact is demonstrated through extensive simulations
on artificial and real examples, with specific SOM (fixed and decreasing
neighborhoods) and SCL algorithms.Comment: A la suite de la conference ESANN 199
Magnification Control in Self-Organizing Maps and Neural Gas
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: 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.Comment: 24 pages, 4 figure
Batch and median neural gas
Neural Gas (NG) constitutes a very robust clustering algorithm given
euclidian data which does not suffer from the problem of local minima like
simple vector quantization, or topological restrictions like the
self-organizing map. Based on the cost function of NG, we introduce a batch
variant of NG which shows much faster convergence and which can be interpreted
as an optimization of the cost function by the Newton method. This formulation
has the additional benefit that, based on the notion of the generalized median
in analogy to Median SOM, a variant for non-vectorial proximity data can be
introduced. We prove convergence of batch and median versions of NG, SOM, and
k-means in a unified formulation, and we investigate the behavior of the
algorithms in several experiments.Comment: In Special Issue after WSOM 05 Conference, 5-8 september, 2005, Pari
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