Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich.
mehr Informationen...
About the Multidimensional Competitive Learning Vector Quantization Algorithm with Constant Gain
Ist Teil von
The Annals of applied probability, 1997-08, Vol.7 (3), p.679-710
Ort / Verlag
Institute of Mathematical Statistics
Erscheinungsjahr
1997
Link zum Volltext
Quelle
Project Euclid Complete
Beschreibungen/Notizen
The competitive learning vector quantization (CLVQ) algorithm with constant step $\varepsilon > 0$--also known as the Kohonen algorithm with 0 neighbors--is studied when the stimuli are i.i.d. vectors. Its first noticeable feature is that, unlike the one-dimensional case which has n! absorbing subsets, the CLVQ algorithm is "irreducible on open sets" whenever the stimuli distribution has a path-connected support with a nonempty interior. Then the Doeblin recurrence (or uniform ergodicity) of the algorithm is established under some convexity assumption on the support. Several properties of the invariant probability measure νεare studied, including support location and absolute continuity with respect to the Lebesgue measure. Finally, the weak limit set of νεas ε → 0 is investigated.