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In [[computer science]], '''learning vector quantization''' ('''LVQ''') is a [[prototype|prototype-based]] [[supervised learning|supervised]] [[Statistical classification|classification]] [[algorithm]]. LVQ is the supervised counterpart of [[vector quantization]] systems. LVQ can be understood as a special case of an [[artificial neural network]], more precisely, it applies a [[winner-take-all (computing)|winner-take-all]] [[Hebbian learning]]-based approach. It is a precursor to [[self-organizing map]]s (SOM) and related to [[neural gas]] and the [[k-nearest neighbor algorithm]] (k-NN). LVQ was invented by [[Teuvo Kohonen]].<ref>T. Kohonen. Self-Organizing Maps. Springer, Berlin, 1997.</ref>
== Definition ==
An LVQ system is represented by prototypes <math>W=(w(i),...,w(n))</math> which are defined in the [[feature space]] of observed data. In winner-take-all training algorithms one determines, for each data point, the prototype which is closest to the input according to a given distance measure. The position of this so-called winner prototype is then adapted, i.e. the winner is moved closer if it correctly classifies the data point or moved away if it classifies the data point incorrectly.
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==Algorithm==
The algorithm consists of three basic steps. The algorithm's input is:
* how many neurons the system will have <math>M</math> (in the simplest case it is equal to the number of classes)
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