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Wikipedia / Learning vector quantization

In computer science, learning vector quantization (LVQ) is a prototype-based supervised 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 Hebbian learning-based approach. It is a precursor to self-organizing maps (SOM) and related to neural gas and the k-nearest neighbor algorithm (k-NN). LVQ was invented by Teuvo Kohonen.

Definition

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.

An advantage of LVQ is that it creates prototypes that are easy to interpret for experts in the respective application domain. LVQ systems can be applied to multi-class classification problems in a natural way.

A key issue in LVQ is the choice of an appropriate measure of distance or similarity for training and classification. Recently, techniques have been developed which adapt a parameterized distance measure in the course of training the system, see e.g. (Schneider, Biehl, and Hammer, 2009) and references therein.

LVQ can be a valuable aid in classifying text documents.

Algorithm

The algorithms are presented as in.

Set up:

  • .

  • .

  • .

  • .

  • .

LVQ1

Initialize several code vectors per label. Iterate until convergence criteria is reached.

  1. falls within the Voronoi cell.

  2. .

LVQ2

have the same class, then nothing happens.

LVQ3

Initialize several code vectors per label. Iterate until convergence criteria is reached.

  1. closest to it.

  2. .

, then

  • .

  • .

  • .

  • have different classes, then the original paper simply does not explain what happens in this case, but presumably nothing happens in this case.

  • Otherwise, skip.

falls between two Apollonian spheres.

References

Further reading

  • lvq_pak official release (1996) by Kohonen and his team