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Median independent of distance metric

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I know this is an ancient edit, but I was wondering if I could ask you about this change to the median article, in particular the statement that "A median is only defined on one-dimensional data, and is independent of any distance metric." This directly contradicts the statement in the medoid article that "A median is only defined on 1-dimensional data, and it only minimizes dissimilarity to other points for a specific distance metric (Manhattan norm)." I believe your claim is correct (that the median is independent of the choice of distance metric) but I can't find any citations to that effect. Do you have any idea where you came across that? Wclark (talk) 06:16, 1 January 2020 (UTC)[reply]

The two statements are not contradictory. The median is uniquely defined for any one-dimensional data set, but it will minimize dissimilarity only for certain distance metrics. Urhixidur (talk) 13:59, 1 January 2020 (UTC)[reply]
Are you sure? Can you give an example of a distance metric in one dimension that the median doesn't minimize? [EDIT: Any metric where the triangle inequality is not a strict equality.] At the very least, it also minimizes Euclidean distance and not just the Manhattan norm. I'd like to update one/both articles to give more detail on this point, but would like to make sure I'm citing a proper source.. do you know of any particular textbooks / other references that address this? I've read various articles that take it as given that the median will minimize Euclidean distance (or provide their own proof, but none of these are proper sources I can cite here) but never a discussion of other distance metrics with respect to the median. Thanks, Wclark (talk) 16:28, 1 January 2020 (UTC)[reply]
Now I’m even more confused by the statement in the Euclidean distance article that “In one dimension, there is a single homogeneous, translation-invariant metric (in other words, a distance that is induced by a norm), up to a scale factor of length, which is the Euclidean distance. In higher dimensions there are other possible norms.” I had just convinced myself that perhaps there ‘’were’’ other metrics (in a single dimension) that the median did ‘’not’’ minimize, but now I’m back to thinking it’s actually independent of any distance metric (per your original edit) — but because ‘’all’’ distance metrics in one dimension are in fact equivalent. Wclark (talk) 16:46, 1 January 2020 (UTC)[reply]
Thinking through it more, I think it's true that (up to scaling) there is only one metric in the single dimensional case. In a single dimension, the triangle inequality necessarily becomes an equality relation, and so the median will always be a point that minimizes the sum of the distances to all the other points (given the standard proof.) Thus I think both articles are somewhat misleading, since the median isn't actually independent of the choice of distance metric in any meaningful sense (since there is actually only one distance metric in a single dimension) and it's an unusual choice to pick the Manhattan distance as the representative for that single metric -- the Euclidean distance would be more natural, especially given that it's the one used in some higher dimensional generalizations such as the geometric median. There are other values that we can seek to minimize, such as the zero-one loss function or the squared euclidean distance (which give the mode and mean, respectively) but these are not actually metrics in the single-dimension case, because they violate the triangle inequality. Does this sound right to you, and do you have any idea where I could find a source to cite for this? Thanks again for hearing me out, Wclark (talk) 19:38, 1 January 2020 (UTC)[reply]
Thinking through it even more I see that there are a variety of different subadditive metrics in a single dimension, and experimenting some have found plenty of cases where the median is not the point that minimizes the aggregate distance. I'm not sure what the Euclidean distance article is claiming though, since the other subadditive metrics are most definitely not equivalent to the euclidean distance. I still think referring to the Manhattan distance is misleading (since in one dimension that is equivalent to the euclidean distance, and that makes the generalization to higher dimensions in the geometric median more intuitive) and may add some explanation there. I'll follow up elsewhere to see what's going on with the claim on the Euclidean distance article. Thanks! Wclark (talk) 19:58, 2 January 2020 (UTC)[reply]

Administrators' newsletter – January 2020

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News and updates for administrators from the past month (December 2019).

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Administrators' newsletter – February 2020

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I have sent you a note about a page you started

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Hello, Urhixidur

Thank you for creating Information behavior.

User:Doomsdayer520, while examining this page as a part of our page curation process, had the following comments:

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Administrators' newsletter – March 2020

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News and updates for administrators from the past month (February 2020).

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March 2020

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Information icon Please refrain from making unconstructive edits to Wikipedia, as you did at Jean Giraud. Your edits appear to constitute vandalism and have been reverted. If you would like to experiment, please use the sandbox. Repeated vandalism may result in the loss of editing privileges. Thank you. TonyTheTiger (T / C / WP:FOUR / WP:CHICAGO / WP:WAWARD) 02:30, 13 March 2020 (UTC)[reply]

@TonyTheTiger: Urhixidur (talk) 03:22, 13 March 2020 (UTC)[reply]
I would obviously dispute your judgement, but as the edits have been removed from the page's history, I'm not sure what you took exception to. Please explain constructively. Urhixidur (talk) 03:14, 13 March 2020 (UTC)[reply]
I suspect you mean my edit to {{Jean Giraud}}, where I added a placeholder for one of Giraud's major works, Le Bandard fou, known in English as The Horny Goof. This is factual, not vandalism. See e.g. https://www.goodreads.com/book/show/270771.The_Forbidden_Work_Vol_0 Urhixidur (talk) 03:20, 13 March 2020 (UTC)[reply]
When the article is no longer a redlink, you can add it back.-TonyTheTiger (T / C / WP:FOUR / WP:CHICAGO / WP:WAWARD) 11:26, 16 March 2020 (UTC)[reply]
No apology? Hrmph. Urhixidur (talk) 02:47, 24 March 2020 (UTC)[reply]

do we use Herget or Schmadel for etymology of asteroids?

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Hi Urhixidur,

I noticed our list said 770 Bali is named after the Mahabali but the article said it's named after the island. I see the difference came in here, where you changed a guess that the asteroid was named after the island to a cited claim, based on Herget, that it's the Mahabali. But Schmadel, who our intro says is based on Herget, also says it's the island. There's s.t. similar with 681 Gorgo, going from an unref'd claim it's the Gorgon, to [H] saying it's some king or queen (with a comment that H seems a bit garbled) to [S] saying it's the Gorgon again. The items in the list unfortunately no longer note which source they're following. Should we take one of the sources as more reliable than the other?

BTW, how would we say 'Urhixidur'? (I stress the 'hix' in my mind.) — kwami (talk) 15:10, 14 March 2020 (UTC)[reply]

We should cite both. Hopefully, Schmadel explains why he diverges from Herget when that happens. As for the pronunciation of Urhixidur, the word is originally German for what it's worth. Stressing the 'hix' sounds about right. I pronounce it in French: \y.ʁi.ksi.dyʁ\. :-) Urhixidur (talk) 18:17, 14 March 2020 (UTC)[reply]

No mention of [H], unlike (769) or (771), which are both cited to him. For (770), LDS just says "this planet was obviously named after [the island]. The discoverer repeatedly named planets after geographic items of Indonesia (cf. planets (732) and (772))." Similarly, for (681), LDS says "Gorgo is the German word for Gorgon," and doesn't mention [H]. If I had to guess, LDS repeats H where he doesn't have any better idea, but not where he thinks he's wrong. Maybe there some where he has both? — kwami (talk) 23:35, 14 March 2020 (UTC)[reply]

I looked up my copy of [H]. For 770 Bali we have "In Hindu mythology, Bali was king of the Daityas." No source. This probably means it is merely an observation by Herget. For 681 Gorgo we have "King of Salamine, in the 5th century B.C., who accompanied Xerxes in Greece." Sources IG (Ingrid van Houten-Groeneveld) and AP (Antonio Paluzie-Borrell). Urhixidur (talk) 23:59, 14 March 2020 (UTC)[reply]
Entries updated accordingly. Urhixidur (talk) 00:14, 15 March 2020 (UTC)[reply]

Thanks!

I noticed there are quite a few more names by Wolf, Kopff & Metcalf that look like they were inspired their provisional designation than we note, e.g. 580 Selene 1905 SE, 590 Tomyris 1906 TO, 604 Tekmessa 1906 TK, 645 Agrippina 1907 AG, 647 Adelgunde 1907 AD, 650 Amalasuntha 1907 AM, 651 Antikleia 1907 AN, 653 Berenike 1907 BK, 660 Crescentia 1908 CC, 661 Cloelia 1908 CL, 673 Edda 1908 EA, 682 Hagar 1909 HA -- and more if we allow for letter correspondences among German, Latin and Greek, e.g. 586 Thekla 1906 TC, 627 Charis 1907 XS, 680 Genoveva 1909 GW. (678 Fredegundis [1909 FS] and 685 Hermia [1909 HE] may be coincidence, as they had different discoverers.) If you allow the letter order to reverse, there are of course even more (e.g. 597 Bandusia 1906 UB, 600 Musa 1906 UM, 601 Nerthus 1906 UN, 609 Fulvia 1906 VF, 646 Kastalia 1907 AC, 663 Gerlinde 1908 DG), which you'd expect just as coincidence but would also be likely to suggest names to the discoverers. Outside of the years 1905–1909, there are practically no matches (only a very few such as 507 Laodica 1903 LO before and 769 Tatjana 1913 TA after), even allowing for Latin/Greek and metathesis, so I doubt these are all coincidence. — kwami (talk) 03:34, 15 March 2020 (UTC)[reply]

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An automated process has detected that when you recently edited Rings of Saturn, you added links pointing to the disambiguation pages William Bond and George Bond (check to confirm | fix with Dab solver).

(Opt-out instructions.) --DPL bot (talk) 11:00, 24 March 2020 (UTC)[reply]

 Done

Administrators' newsletter – April 2020

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Your thread has been archived

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Hi Urhixidur! The thread you created at the Wikipedia:Teahouse, Heat death of the universe, has been archived because there was no discussion for a few days (usually at least two days, and sometimes four or more). You can still find the archived discussion here. If you have any additional questions that weren't answered then, please feel free to create a new thread.


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Happy Adminship Anniversary!

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