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We consider quantizing an $Ld$-dimensional sample, which is obtained byconcatenating $L$ vectors from datasets of $d$-dimensional vectors, to a$d$-dimensional cluster center. The distortion measure is the weighted sum of$r$th powers of the distances between the cluster center and the samples. For$L=1$, one recovers the ordinary center based clustering formulation. Thegeneral case $L>1$ appears when one wishes to cluster a dataset through $L$noisy observations of each of its members. We find a formula for the averagedistortion performance in the asymptotic regime where the number of clustercenters are large. We also provide an algorithm to numerically optimize thecluster centers and verify our analytical results on real and artificialdatasets. In terms of faithfulness to the original (noiseless) dataset, ourclustering approach outperforms the naive approach that relies on quantizingthe $Ld$-dimensional noisy observation vectors to $Ld$-dimensional centers.

Quantizing Multiple Sources to a Common Cluster Center: An Asymptotic Analysis