Learning vector quantization: Difference between revisions

Revision as of 01:01, 26 October 2016

Revision as of 21:40, 18 May 2017

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Below follows an informal description.<br>

The algorithm consists of 3 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)

* what weight each neuron has <math>\vec{W_iw_i}</math> for <math>i = 0,1,...,M - 1 </math>

* howthe fastcorresponding thelabel <math>c_i</math> neuronsto areeach learningneuron <math> \etavec{w_i} </math>.

* andhow anfast inputthe listneurons containingare vectors to train the neuronslearning <math> L\eta </math>

* and an input list containing tuples of vectors with labels to train the neurons <math> L </math>

The algorithm's flow is:

# For next input <math>(\vec{Xx},c)</math> in <math> L </math> find the neuronneurons <math>\vec{W_mw_m}</math> atwith the same Label and take the one whichso that <math>d(\vec{Xx},\vec{W_mw_m})</math> gets its minimum value, where <math>\, d\, </math> is the metric used ( [[Euclidean distance|Euclidean]], etc. ).

# Update <math>\vec{W_mw_m}</math>. A better explanation is get <math>\vec{W_mw_m}</math> closer to the input <math>\vec{Xx}</math>.<br><math> \vec{W_mw_m} \gets \vec{W_mw_m} + \eta \cdot \left( \vec{Xx} - \vec{W_mw_m} \right) </math>.

# While there are vectors left in <math> L </math> go to step 1, else terminate.

Note: <math>\vec{W_iw_i}</math> and <math>\vec{Xx}</math> are [[vector space|vectors]] in feature space.<br>

A more formal description can be found here: http://jsalatas.ictpro.gr/implementation-of-competitive-learning-networks-for-weka/