Talk:Medoid

Is this just the median, as in the point with minimal total distance to the rest of the points? -- Nils Grimsmo 13:16, 3 April 2006 (UTC)

It is the Median but I *think* it might be for vector values, (non-scalar values - 1 dimensional).

On multidimensional / vector points, the median is not consistently defined (see below for one specific definition), but one common meaning of median is "the point that is constructed by taking the median of each definition". By that definition, the medoid is definitely not the same thing.

It seems to be the synonym of a geometric median. Semifinalist (talk) 14:54, 29 June 2010 (UTC)

It isn't the same as a geometric median; a medoid must be an actual point from the dataset, where a geometric median does not necessarily have to be one of the original points. SeparateWays (talk) 21:52, 12 October 2010 (UTC)

Specific distance function in Algorithms section?

While the definition talks about general distance function which is great. Yet the Algorithms section assumes specific distance function without being explicit. Royi A (talk) 11:10, 15 October 2019 (UTC)

That section seems to have been added in this group of edits and that user account no longer seems to be active. Wclark (talk) 04:07, 1 January 2020 (UTC)

Manhattan or Euclidean?

This edit states that the median is determined by seeking to minimize the distance according to the Taxicab geometry, but the article on Median states: "A median is only defined on ordered one-dimensional data, and is independent of any distance metric." Since in one dimension the Manhattan distance and Euclidean distance are equivalent, and since the geometric median generalizes the concept using the Euclidean distance, I propose we use that as the example (but note that it's actually independent of distance metric.) This is all original research on my part however, using definitions from within our own articles primarily, and the original statements were never sourced either, so I wanted to ask here before making changes. Wclark (talk) 04:44, 1 January 2020 (UTC)

I've received some clarification on the claims in these edits and believe this article would be best served by editing the statement about distance metrics to clarify that it's not just the aggregate distance under the Manhattan distance / Taxicab geometry that's minimized, but any strictly additive metric in a single dimension (all of which are equivalent, up to scaling.) This is not the case for other strictly subadditive metrics, which may also be worth mentioning. For instance, the mode is the member of a set that minimizes the aggregate distance to all other members of the set, under the zero-one loss function (taken as a distance/dissimilarity metric.) I'm awaiting some feedback on other related articles (so that I can try to harmonize this point across all of them) and would appreciate any here, if anybody is so inclined. Thanks! Wclark (talk) 18:51, 3 January 2020 (UTC)