learning vector quantization

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.T. Kohonen. Self-Organizing Maps. Springer, Berlin, 1997.

An LVQ system is represented by prototypes $W=(w(i),...,w(n))$ 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.{{citation|author=T. Kohonen|contribution=Learning vector quantization|editor=M.A. Arbib|title=The Handbook of Brain Theory and Neural Networks|pages=537–540|publisher=MIT Press|location=Cambridge, MA|year=1995}}

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){{cite journal|author1=P. Schneider |author2=B. Hammer |author3=M. Biehl |title=Adaptive Relevance Matrices in Learning Vector Quantization|journal= Neural Computation|volume=21|issue=10|pages=3532–3561|year=2009|doi=10.1162/neco.2009.10-08-892|pmid=19635012|citeseerx=10.1.1.216.1183|s2cid=17306078}} and references therein.

LVQ can be a source of great help in classifying text documents.{{Citation needed|date=December 2019|reason=removed citation to predatory publisher content}}

Below follows an informal description.

The algorithm consists of three basic steps. The algorithm's input is:

• how many neurons the system will have $M$ (in the simplest case it is equal to the number of classes)
• what weight each neuron has $\backslash vec\{w\_i\}$ for $i\; =\; 0,1,...,M\; -\; 1$
• the corresponding label $c\_i$ to each neuron $\backslash vec\{w\_i\}$
• how fast the neurons are learning $\backslash eta$
• and an input list $L$ containing all the vectors of which the labels are known already (training set).

The algorithm's flow is:

1. For next input $\backslash vec\{x\}$ (with label $y$) in $L$ find the closest neuron $\backslash vec\{w\_m\}$,
   i.e. $d(\backslash vec\{x\},\backslash vec\{w\_m\})\; =\; \backslash min\backslash limits\_i\; \{d(\backslash vec\{x\},\backslash vec\{w\_i\})\}$, where $\backslash ,\; d$ is the metric used ( Euclidean, etc. )

• [http://www.cis.hut.fi/panus/papers/dtwsom.pdf Self-Organizing Maps and Learning Vector Quantization for Feature Sequences, Somervuo and Kohonen. 2004] (pdf)

• [http://www.cis.hut.fi/research/lvq_pak/ lvq_pak] official release (1996) by Kohonen and his team

Category:Artificial neural networks

Category:Classification algorithms