  Motivated by the problem of effectively executing clustering algorithms on
very large data sets, we address a model for large scale distributed clustering
methods. To this end, we briefly recall some standards on the quantization
problem and some results on the almost sure convergence of the Competitive
Learning Vector Quantization (CLVQ) procedure. A general model for linear
distributed asynchronous algorithms well adapted to several parallel computing
architectures is also discussed. Our approach brings together this scalable
model and the CLVQ algorithm, and we call the resulting technique the
Distributed Asynchronous Learning Vector Quantization algorithm (DALVQ). An
in-depth analysis of the almost sure convergence of the DALVQ algorithm is
performed. A striking result is that we prove that the multiple versions of the
quantizers distributed among the processors in the parallel architecture
asymptotically reach a consensus almost surely. Furthermore, we also show that
these versions converge almost surely towards the same nearly optimal value for
the quantization criterion.
