Talk:Wasserstein metric

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Contents 1 Wasserstein vs.Vasershtein 2 Hutchinson Metric 3 Conversion to mathematics format 4 Lip - Changes by Doetoe

[edit] Wasserstein vs.Vasershtein

Rather obviously, the cyrillic lettering is a transcription of the German "Wasserstein". Therefore, it is quite natural to write "Wasserstein" instead of the more formal "Vasershtein" transliteration in latin script.--Trigamma 22:03, 15 January 2007 (UTC)

As I understand, "Vasershtein" is a form of transliteration while "Wasserstein" is a form of transcription. The latter is not a form to transform the cyrillic writing to Latin characters but an attempt to write the name, being of German origin, in Latin characters according to German rules. But I don't insist.--Trigamma 06:49, 16 January 2007 (UTC)

This is an interesting one. :-) The name is of Germanic origin, so somehow "Wasserstein" (or possibly "Waßerstein") seems to be the "correct" spelling. The issue is complicated by the fact that, although his name was of Germanic origin, Vasershtein/Wassertein was himself Russian! So now we are in the situation of discussing someone whose name should be written in Cyrillic characters as a transliteration of the original German name. My original reference to transliteration in the article was to the problem of transliterating from the Russian, not into it; my point there was that a German would simply transliterate back to the original "Wasserstein"), whereas another reader might transliterate the Cyrillic characters according to some correspondence between Russian and English phonemes to get "Vasershtein". It's a little bit of a tangled web: perhaps we can come up with some suitable explanation to include in the article?

By the way, thank you for your civil words. After witnessing several edit wars in recent days and weeks, this is a breath of fresh air. Sullivan.t.j 10:46, 16 January 2007 (UTC)

I am myself a German. Maybe the problem is, that in German the meaning of the word "transliteration" is more restrict than in English. It is only used when there is a one-to-one correspondence between the original an the transliteration, so that the original spelling can be reconstructed from the transliteration. In all other cases, in German the word "Transcription" is used. --Trigamma 16:43, 16 January 2007 (UTC)

I see. Interesting. At least according to my understanding, the correspondence "Ш"<-->"sh" would still count as transliteration in the English usage of the word, even though the number of characters is different in each string. Sullivan.t.j 17:12, 16 January 2007 (UTC)

The same in German, I think. But writing "Wasserstein" because of the German origin, would certainly not be called a transliteration. At least the Ш would have to be written as "sch". But I am a mathematician, not an expert in linguistics.--Trigamma 17:25, 16 January 2007 (UTC)

Coming back to the article. What about:

"The usage of "Wasserstein" can be attributed to the fact that the name "Vasershtein" is of Germanic origin. "Wasserstein" is the German spelling." --Trigamma 17:32, 16 January 2007 (UTC)

[edit] Hutchinson Metric

Is it just me, or is the 1st Wasserstein metric precisely the same thing as the Hutchinson metric? (See M. F. Barnsley, "Fractals Everywhere") 217.44.217.128 20:48, 31 January 2007 (UTC)

I suppose, you are speaking of the Wasserstein metric W₁. As mentioned in the text, this metric is only a special case of the whole family of Wasserstein metrics. As far as I know, Hutchinson uses this metric in his work on fractals. He himself calls it the "Monge-Kantorovitch metric" (according to my lecture notes).

As far as I know the name Wasserstein metric is more widely used for W₂.--Trigamma 19:18, 12 February 2007 (UTC)

That would explain why Barnsley uses that name in his new fractal geometry book. Thanks for the pointer. 217.44.217.128 18:52, 15 February 2007 (UTC)

[edit] Conversion to mathematics format

The text is atrocious in that it is left as LaTeX. It needs to be cleaned up and presented in a readable format. —The preceding unsigned comment was added by 71.132.145.120 (talk) 16:26, 19 March 2007 (UTC).

[edit] Lip - Changes by Doetoe

As far as I can see, the "corrections" made by Doetoe are wrong. I remove them. --Trigamma 08:09, 6 June 2007 (UTC)

The norm called the "bounded Lipschitz norm" by Doetoe is better known as the C^{0,1} norm. It is different from the optimal Lipschitz constant Lip (f). With Lip(f) replaced by the C^{0,1} norm, one does not get the W_1 Wasserstein metric but the so-called "flat metric" (cf. Herbert Federer, Geometric Measure Theory, Springer Verlag, p. 367, paragraph 4.1.12).--Trigamma 08:23, 6 June 2007 (UTC)

Thanks, you're totally right. Doetoe 19:45, 30 August 2007 (UTC)