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 $\nu^{\varepsilon}$ are
studied, including support location and absolute continuity with respect to the
Lebesgue measure. Finally, the weak limit set of $\nu^{\varepsilon}$ as
$\varepsilon \to 0$ is investigated.
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