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The centroid of a cluster is defined as centroid. It is defined as the mean of each dimension across all samples of the cluster.

What is the analogous that uses the median of each dimension? As far as I know, a similar concept is the medoid, which needs to be an actual sample of the cluster.

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marked as duplicate by Anony-Mousse clustering Nov 23 '16 at 22:36

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    $\begingroup$ Centroid is multivariate mean, quite univocal concept. Median in multivariate space can be defined differently (e.g. en.wikipedia.org/wiki/Median#Multivariate_median). Medoid is defined univocally up to its formula, but the formula is based on distance in space, and that disctance could be defined differently (e.g. euclidean or manhattan). $\endgroup$ – ttnphns Nov 23 '16 at 15:20
  • $\begingroup$ Thanks @ttnphns. I think that my idea of the centroid-like point is the marginal multivariate median. Although I don't know if the spatial multivariate median could be a better estimate. $\endgroup$ – gc5 Nov 23 '16 at 15:25
  • $\begingroup$ @ttnphns could you please put it as answer? $\endgroup$ – gc5 Nov 23 '16 at 17:29
  • $\begingroup$ fbrundu, thank you. But I don't feel like having given anything special deserving to be an answer. $\endgroup$ – ttnphns Nov 23 '16 at 18:01
  • $\begingroup$ Well, I thought that multivariate median, also with the corresponding description of alternatives, could be a suitable answer. Why wouldn't be it? $\endgroup$ – gc5 Nov 23 '16 at 18:12

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