Wikipedia:Articles for deletion/Łukaszyk–Karmowski metric

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was keep. Whilst I note that some contributors have limited contributions elsewhere, and there are potential COI issues, it seems clear to me that there is coverage and references, as evidenced by User:Guswen, the author (of both the article and the metric). Stifle (talk) 15:53, 13 July 2022 (UTC)

Łukaszyk–Karmowski metric

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Łukaszyk–Karmowski metric (edit | talk | history | protect | delete | links | watch | logs | views) – (View log | edits since nomination)

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Fails notability. Article was written by Łukaszyk himself to promote his work. It was already deleted back in 2009 for these reasons, after which Łukaszyk restored the article. The paper upon which has been cited a couple of times, as in Refs [4] and [5], but these are only passing mentions. I did managed to find a source that discusses it in detail [1], but the conclusion is that it is a misconception.

Moreover, the author has been hard at work to include mentions to his work everywhere in Wikipedia, including Inverse distance weighting, Quantum geometry, Wigner's friend, Statistical distance, and Metric (mathematics). Tercer (talk) 08:11, 4 July 2022 (UTC)

• Delete - no evidence of sufficient coverage in independent sources. PianoDan (talk) 15:36, 4 July 2022 (UTC)
• Keep

I do believe that science is among us not for self-promotion but for inspiring the evolution of further research. Thus, I created the Łukaszyk–Karmowski metric article, covering the subject of my PhD thesis, defended in 2003 at Tadeusz Kościuszko University of Technology in good faith.

Since then, the paper , concerning this distance function and published by Springer-Verlag in 2004 has been cited 133 times, according to Google Scholar.

In particular, the LK-metric enables avoiding singularities and ill-conditioning present in various approximation and interpolation methods (in particular inverse distance weighting and radial basis function interpolation), due to overlapping data points, as it can be fine-tuned to be always greater than zero. Thus, in [2], for example, LK-metric has been classified as an example of a "diffuse metric".

The concept of the LK-metric has been successfully applied, for example, in the fields of:

• engineering ([3], [4], [5], [6], [7], [8]);
• hydrochemistry, geophysics, environmental interference, and ecology ([9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]);
• machine learning ([20], [21], [22], [23]);
• medicine and neuroscience ([24], [25], [26], [27]);
• navigation ([28], [29]); and
• speech synthesis ([30]).

Therefore, User:Tercer first claim that the LK-metric lack WP:N, as it has been cited a couple of times, as in Refs [4] and [5], and only in passing mentions is false. Similarly User:PianoDan claim that there is no evidence of sufficient coverage of this concept in independent sources.

User:Tercer second claim that this distance function is a misconception is based on the preprint in the field of econometrics, whose author admits (p. 12) that his consideration does not greatly affect the merit of the article, where otherwise conclusive results in applied physics are presented.

Indeed, I included mentions of the LK-metric in other Wikipedia articles. But, again, I did it not to promote myself but to promote this concept, which I find interesting.

Finally, this concept is not the only one that invalidates the identity of indiscernibles ontological principle proposed by the German philosopher Gottfried Wilhelm Leibniz. This principle is invalid, for example, also due to the Ugly duckling mathematical theorem derived by Satosi Watanabe in 1969.

Guswen (talk) 11:51, 5 July 2022 (UTC)

• Note: This discussion has been included in the list of Mathematics-related deletion discussions. –LaundryPizza03 (dc̄) 14:04, 5 July 2022 (UTC)

Thank you for acknowledging your WP:COI. I have added a notice to the talk page of the article to that effect. In accordance with that policy, you should refrain from further edits to the article if it survives this AfD. PianoDan (talk) 15:38, 5 July 2022 (UTC)

The number of citations is irrelevant. I have several papers with more than 133 citations, I still don't go around creating an Wikipedia article for each of them. What is relevant is whether there are reliable, independent sources that describe the content. I skimmed a couple of the references you just posted, and found only passing mentions. I'm not going to go through each one in this huge list showing that the don't discuss the subject. The onus is on you to find relevant references, if they exist at all. Moreover, the "identity of indiscernibles" in this context is not a philosophical principle that can be valid or not. It is just a part of the mathematical definition of what is a metric. Since your function does not satisfy it, it is not a metric. And, as [31] shows, if you had done it correctly it would satisfy the "identity of indiscernibles" and would be a metric. Tercer (talk) 17:46, 5 July 2022 (UTC)

Of course, the LK-metric is not a metric! It cannot be a metric, as it does not satisfy the 1st axiom of the metric. That is why I proposed to change the title of this article to Łukaszyk–Karmowski distance (but I failed).

It is an example of a diffuse metric according to definition 4.9 of this article. The MICo distance disclosed in this article is another example.

What haven’t I done correctly? How do you define correctness in science? As I showed above, the LK-metric has proven to have plenty practical applications and may be considered as a distance between quantum mechanics particles described by wavefunctions ψ, where the probability dP that given particle is present in given volume of space dV amounts:

$dP=|\psi (x,y,z)|^{2}dV$

The author of the econometrics preprint that you quote, himself admits that his consideration does not greatly affect the merit of the article, where otherwise conclusive results in applied physics are presented. Guswen (talk) 06:47, 6 July 2022 (UTC)

Metric and distance are synonyms in mathematics, your function is not a distance either. Tercer (talk) 07:24, 6 July 2022 (UTC)

What is it then? A "misconception"? Is my PhD thesis defended almost 20 years ago at a renowned university a misconception? Guswen (talk) 09:01, 6 July 2022 (UTC)

"distance" is an informal term; a pseudometric could be called a distance too in the right context, as it is one way of generalising it. 1234qwer1234qwer4 10:38, 11 July 2022 (UTC)

But pseudometric satisfies the 1st metric axiom, while LK-metric does not (in general).Guswen (talk) 11:53, 11 July 2022 (UTC)

True. I missed your point. If you argue that an informal term of "distance" encompasses all mathematically conceivable functions yielding "distances", including generalized metrics, I agree. Guswen (talk) 13:21, 11 July 2022 (UTC)

• Delete This expression has been sometimes mentioned, occasionally calculated, but not analyzed. To justify a page about it, we need surveys, review articles, textbooks, etc., that have done the work of explaining the motivation, assessing the advantages and the drawbacks, comparing and contrasting with related quantities, and all that. (Think of the discussion of trace distance and fidelity in chapter 9 of Mike and Ike.) We simply don't have that here — or rather, the closest approach is a single not-yet-peer-reviewed paper which claims it wasn't done right. Wikipedia is not the place for inspiring the evolution of further research, but rather a place to explain research that has already been done, and whose merit is already clear. XOR'easter (talk) 20:12, 5 July 2022 (UTC)

This "expression" has been analyzed in my PhD 20 years ago. And it has been analyzed thereafter. In “Introduction to Uncertainty Quantification” by T.J. Sullivan, for example, it was shown that the LK-metric is the upper bound of the Wasserstein metric.

Indeed, Wikipedia is a place to explain research that has already been done (20 years ago in this case), and whose merit is already clear (as confirmed by the publications that I quoted above). I used my belief that science should inspire the evolution of further research to justify my good faith in creating this article 13 years ago. Guswen (talk) 06:47, 6 July 2022 (UTC)

Two homework problems about it (Exercises 5.10 and 5.11) are hardly substantial enough to serve for our purposes here. And even taking them for all they're worth, they rather indicate that if we were to cover this topic, it doesn't deserve an article of its own; for Sullivan, it is of ancillary interest to the $p$-Wasserstein distances. XOR'easter (talk) 14:45, 6 July 2022 (UTC)

No study shows that LK-metric is useful in quantum computation, like trace distance and fidelity discussed by Mike and Ike. On the contrary, LK-metric has been shown to be useful in classical computation, such as inverse distance weighting and radial basis function interpolation by removing ill-conditioning. Mike and Ike is a profound study, yet irrelevant in this discussion. Guswen (talk) 10:39, 7 July 2022 (UTC)

This completely misses the point of my comment. I pointed to a discussion of distance measures between classical probability distributions as illustrative of the type of coverage we would need in order to justify having this article. We don't have that coverage, so we shouldn't have this article. Passing mentions like those provided by Google Scholar ("Other modifications to IDW include using a probability metric instead of Euclidean distance...") don't cut it. XOR'easter (talk) 14:58, 7 July 2022 (UTC)

Now I'm confused. Jean Raimbault (talk · contribs) claims that "the content of the article is entirely trivial (...) the work it describes (...) should be named "expected distance between two random variables", and [consists in] computing some easy examples". And he is right, in a way, as this concept is, indeed, pretty simple (though published only in 2003). Therefore, no coverage other than my PhD thesis should be required. On the other hand, you seem to turn it into some kind of rocket science. It's at least a useful tool enabling to avoid ill-conditioning of various deterministic algorithms, which tool initially found applications in experimental mechanics and later on in other fields, such as e.g. pursuit-evasion games. Guswen (talk) 17:12, 7 July 2022 (UTC)

I didn't say it was simple; I didn't say it was complicated. I said that we had insufficient evidence that people have cared enough about it for us to write an article. Even if it were "simple", we would need more than your PhD thesis. We also need evidence that this topic stands on its own to a sufficient extent to warrant a page devoted to it, instead of being only thought of as a bound on something else or a calculational step in some procedure. Everything you have provided turned up in my own searches, and I remain unconvinced. XOR'easter (talk) 14:57, 8 July 2022 (UTC)

I hope that the list of the publications to support the LK-metric coverage in independent reliable sources (below) will help in convincing you.Guswen (talk) 15:04, 8 July 2022 (UTC)

I saw the list and evaluated them before I wrote my comment above. XOR'easter (talk) 15:07, 8 July 2022 (UTC)

• Keep Mere google search for "lukaszyk-karmowski metric" reveals about 1400 results. One cannot say that LK-metric lack WP:N --Zvid (talk) 07:39, 7 July 2022 (UTC)

— Zvid (talk • contribs) has made few or no other edits outside this topic.

That's not a substantial argument. XOR'easter (talk) 15:24, 7 July 2022 (UTC)

But it it is an argument nevertheless (cf. WP:GOOGLE). Guswen (talk) 16:44, 7 July 2022 (UTC)

On my PC Bing reports 12,600 and Yahoo about 84,300,000 search results for the words lukaszyk-karmowski metric.Guswen (talk) 16:51, 7 July 2022 (UTC)

The very page you point to says Hit-count numbers alone can only rarely "prove" anything about notability. XOR'easter (talk) 17:02, 7 July 2022 (UTC)

True. Let us then not count hit-numbers alone. --Guswen (talk) 17:18, 7 July 2022 (UTC)

• Keep The described metric is applicable in calculations as evidenced by citations in the scientific literature [32]. The described metric was the subject of a doctoral dissertation successfully defended at Cracov University of Technology, one of the leading universities in Poland. It has practical applications in calculations in the fields of metrology and quantum mechanics. The ongoing scientific discussion on it should not prejudge its encyclopedic nature. However, in my opinion, its applications described in the works cited above indicate the advisability of leaving the article. PawełMM (talk) 07:16, 7 July 2022 (UTC)

  I have a doctorate. Does that mean the subject of my dissertation is inherently notable? Of course not. The subject of my doctorate is an obscure piece of specialist equipment with no coverage in secondary sources. I'm very proud of it, and I hope it is of some use to the users of the device. But it does NOT deserve a Wikipedia article.

  Can we stop saying "this was the subject of a doctoral dissertation" as if that were in any way meaningful? 99.9999% of doctoral dissertations are not notable. PianoDan (talk) 17:36, 7 July 2022 (UTC)

True. The most of doctral dissertations lack notability. But the list of independent publications below supports the claim that this is not the case here.

I do hope that your specialist equipment will also gain notability in the future. Guswen (talk) 11:48, 8 July 2022 (UTC)

• Keep I believe Guswen proved above that this metric was applied many times by many independent researchers, so it has the required notability. The accusation in the deletion request "I did managed to find a source that discusses it in detail [33], but the conclusion is that it is a misconception." is invalid, the quality of a probabilistic metric is not a subject of this discussion and not a reason for deletion. This sentence, however, explains why the other accusation, that this metric hasn't been analyzed in independent papers is false. The conflict of interest of the author is not a reason to delete an article on a notable subject. So I can't see any reason to delete this article. Olaf (talk) 10:51, 7 July 2022 (UTC)

   — Note: An editor has expressed a concern that editors have been canvassed to this discussion. (diffs: [34], [35], [36])— Preceding unsigned comment added by Tercer (talk • contribs) 12:06, 7 July 2022 (UTC)
   — Comment: In my opinion, the content of the article deals with a rather hermetic field such as higher mathematics. The links cited above appeared in the Polish Wikipedia on pages designed to discuss articles. I see no justification here for the accusation of canvasing, since discussing such specialized issues as the article raises should be done by those with expertise in the field under discussion and therefore able to assess its notability. PawełMM (talk) 13:19, 7 July 2022 (UTC)
   The text of the notifications clearly violates our rules for such comments, which expressly prohibit posting a notification of discussion that presents the topic in a non-neutral manner and recruiting editors perceived as having a common viewpoint. XOR'easter (talk) 15:04, 7 July 2022 (UTC)

• Delete There is no convincing opposition to the the arguments of Tercer (talk · contribs) in the !votes above, as witnessed by the current state of the article where no description of a serious application is given, just references. On the other hand the mathematical content of the article is entirely trivial, judging from the article itself the work it describes consists in putting one's name on (a particular case of) what should be named "expected distance between two random variables", and computing some easy examples. I don't see any reason to keep the article. jraimbau (talk) 13:03, 7 July 2022 (UTC)

In my opinion the opposition to the arguments of Tercer (talk · contribs) is strong: WP:N is void, while the alleged misconception is based on a single preprint in the field of econometrics, whose author admits that his (possibly false) considerations do not affect the merit of this concept.

Current state of the article certainly needs improvement to include applications of LK-metric. Unfortunately, I am not in a position to do this due to clear WP:COI.

The mathematical content of the article is based on my PhD thesis.

I did not want to put my, nor the supervisor of my thesis, name on this concept. I was, in a way, forced to in 2009, while creating this article.

Novelty and usefulness of a concept are unrelated to its simplicity (or triviality). Even more so, simple concepts frequently turn out to be more useful than complicated ones. Take Shannon entropy as an example. Furthermore, often a concept seems trivial after it has been disclosed. However, it remained undiscovered prior to disclosure. Take could vs. would approach used by the European Patent Office to ascertain the inventive step of a patentable invention as an example. Guswen (talk) 13:37, 7 July 2022 (UTC)

Novelty and usefulness are also unrelated to notability. Let's try not to get distracted - if the concept has sufficient coverage in independent reliable sources, it's notable. If it doesn't, it isn't. PianoDan (talk) 17:45, 7 July 2022 (UTC)

"the opposition to the arguments of is strong" : that seems false in view of the discussion above, not one substantial application has been described and the arguments are reduced to "there are citations" which as pointed out does not mean anything for notability if these citations do not directly relate to the topic. This is the main point made by Tercer which so far has not been seriously countered either in this discussion or by adding content to the article (you may not be allowed to edit the article but the other persons who claim that substantial applications exist certainly can).

regarding comments on triviality and novelty: while i agree that in general mathematical sophistication is not relevant at all to notability, 90% of this article is spent on mathematical trivialities, while the "applications" section is essentially empty, so it seems to me to be relevant to comment on it. It is also relevant in view of the clumsy appeal to authority in the comment on the canvassing observation above. jraimbau (talk) 06:21, 8 July 2022 (UTC)

Would you kindly advise, how should I seek for help in expanding the applications section of this article, not to be accused of WP:CANVASING again ? Guswen (talk) 12:01, 8 July 2022 (UTC)

WP:COIREQ gives guidance for how editors with a conflict of interest should request changes to pages. You would place a "conflict of interest edit request" on the talk page for the article, and then wait for a neutral editor to evaluate the proposed change. PianoDan (talk) 04:29, 10 July 2022 (UTC)

Certain publications to support the LK-metric coverage in independent reliable sources:

• X. Pan, et al. "Theoretical Analysis of Image-to-Image Translation with Adversarial Learning" (19 Jun 2018)

The LK-metric is used as divergence in the definition of Generalization w.r.t Generator. It brings convenience for analysis and requires only several technical steps to satisfy Lipschitz condition.

• X. Pan, et al. "A Geometrical Perspective on Image Style Transfer with Adversarial Learning" (23 Jul 2020)

A metric (21) similar to the LK-metric is derived. Two theorems involving the LK-metric are provided.

• P. Castro, et al. "MICo: Improved representations via sampling-based state similarity for Markov decision processes"

The LK-metric is found to be an example of a diffuse metric on probability measures defined in this article and used in a definition of a diffuse metric space. "Diffuse" as the non-zero self distances arise from a point being spread across a probability distribution. Another distance, the MICo distance $U^{\pi }(x,y)$, is then defined in terms of the LK-metric. It is shown that a state $x\in \chi$ has zero self-distance iff the Markov chain induced by $\pi$ initialized at $x$ is deterministic, and the magnitude of a state’s self-distance is indicative of the amount of “dispersion” in the distribution.

It is also shown, that in general $U^{\pi }(x,x)\neq U^{\pi }(y,y)$ for distinct states $x,y\in \chi$.

• M. Mio, et. al "Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning"

The diffuse metric space is investigated. An extension of the quantitative algebra framework allowing to reason on generalized metric spaces and on algebraic operations that are nonexpansive up to a lifting is presented, allowing for the axiomatization of the LK-metric.

• C. Hazard, et al. "Natively Interpretable Machine Learning and Artificial Intelligence: Preliminary Results and Future Directions"

It is found that using the residuals in the k-nearest neighbors system with the LK-metric, calculating new residuals, and then feeding these back in, generally yields convergence of the residual values with notable convergence after only 3 or 4 iterations.

• M. Lake, et. al. "Generalised uncertainty relations from superpositions of geometries"

The LK-metric is generalized from probability-weighted measure to amplitude-weighted sums, a la canonical path-integral techniques. The associated amplitudes are not interpreted as the wave functions of quantum particles on classical backgrounds but represent the weights associated with spatial points in an entangled superposition of geometries, represented by a higher dimensional phase space.

• L. Pronzato, et al. "Bregman divergences based on optimal design criteria and simplicial measures of dispersion"

The dispersion measure is defined and it is shown that the directional derivative thereof includes the LK-metric.

• F. Angiulli, et al. "Uncertain Nearest Neighbor Classification"

Various concepts of similarity between uncertain objects are thoroughly discussed in the context of uncertain data.

• P. Durdevic, et al. "Cost-Effective ERT Technique for Oil-in-Water Measurement for Offshore Hydrocyclone Installations"
• S. Pedersen, et al. "Online Slug Detection in Multi-phase Transportation Pipelines Using Electrical Tomography"

Adaptations (novel forms) of the LK-metric are provided. It is shown that the application of the LK-metric leads to more smooth results.

• B. Brutovsky, et al. "Towards inverse modeling of intratumor heterogeneity"

The Markovian-based conceptualization outlined in the paper links uncertainty of environment with intratumor heterogeneity, both expressed in probabilistic terms. The evolutionary nature of carcinogenesis is respected, as the transition probabilities correlate with statistical match between environment and the attractors of the respective states, which corresponds to the bet-hedging strategy, evolved in biological populations that face time-varying environment.

A Regularization of Hellinger distance for a pair of gaussian distributions is provided highlighting the interesting connection between traditional geometric and functional distance measures. It is shown that the consequences of random switching could be readily quantified using the LK-metric which specifies geometric distance of the points with coordinates known up to the respective probability distributions.

Guswen (talk) 11:09, 8 July 2022 (UTC)

The list seems to support my initial claim that the LK-metic inspired the evolution of further research.Guswen (talk) 11:58, 8 July 2022 (UTC)

I do not agree with this assessment. A brief look at some of these papers or preprints shows that lots of them cite the paper without using it. The work of Castro et al. is a bit different, they refer to this metric as an example of a "diffuse metric", but without using the contents of the original paper at all otherwise. Moreover wikipedia does not have an article on "diffuse metrics" so this article existing on the basis of being an example of one makes no sense. jraimbau (talk) 11:18, 11 July 2022 (UTC)

Would you please specify, which of the above papers cite the paper about the LK-metric without using it? For example:

X. Pan, et al. use the LK-metric in as a divergence in a definition of a generator (i.e. an adaptive model that maps a gaussian noise to a fake sample) and derive two theorems concerning such generator in theoretical analysis of image-to-image translation. Similarly, X. Pan, et al. use the LK-metric $D_{LK}$ in as a divergence in a definition of a generator (this time a mapping between manifolds).

M. Lake, et. al. investigates further applications of the Lk-metric in quantum physics.

L. Pronzato, et al. recovers the Lk-metric in a directional derivative of a dispersion measure and defines a Bregman divergence on this basis.

P. Durdevic, et al. and S. Pedersen, et al. provide novel forms of the LK-metric $D_{Luk}$ (for independent marginal distributions) and show that its application leads to more smooth results in a minimum distance algorithm.

B. Brutovsky, et al. apply the LK-metric in the Markovian framework to relate population heterogeneity to the statistics of the environment in anticancer therapies. The generalized distance-based concept is applied to express distances between probabilistically described cell states and environmental conditions, respectively. It is shown that where small noise perturbations induce random switching between (stable) coexisting point attractors of different relative depth, the consequences of this switching can be readily quantified using the LK-metric.

And this is not an exhaustive list of publications, in which the LK-metric was successfully used, analysed, adapted, recovered, etc. (cf. e.g. additional publications listed in the practical applications section of this article and at the onset of this discussion page). Guswen (talk) 12:59, 11 July 2022 (UTC)

Furthermore, on the contrary, P. Castro, et al. use the LK-metric $d_{LK}(U^{\pi })(P_{x}^{\pi },P_{y}^{\pi })$ to define their MICo distance $U^{\pi }(x,y)$. Therefore, they use the contents of the original paper (cf. p. 6, l. 16-22 of P. Castro, et al.). Perhaps, it's time to create a Wikipedia article on "diffuse metrics"? Guswen (talk) 19:26, 11 July 2022 (UTC)

it's time to create a Wikipedia article on "diffuse metrics" that's another discussion.

i had a brief look at two of the papers you quote (first and last ones). the first is not concerned with the LK distance, at best they use it as a technical tool. The second seems to analyse the properties of statistical tools based on a formula similar to yours but the actual contents do not bear much resemblance to the current article. jraimbau (talk) 20:14, 11 July 2022 (UTC)

Brutovsky and Horvath use a different distance between probability distributions and say that the topic of this article "should also be mentioned" in the last two lines of the appendix. XOR'easter (talk) 20:29, 12 July 2022 (UTC)

• Keep The discussion above clearly shows that this topic is notable. Numerous literature references prove that It has been successfully applied, researched, classified, extended, and modified. And, obviously, the fact that it is now called "Łukaszyk–Karmowski metric", not “Probability metric”, as in the author’s Ph.D. dissertation has nothing to do with the reliability of these references. Jilaszczuk (talk) 20:24, 10 July 2022 (UTC)

  I will point out that this is Jilaszczuk's only edit to the English Wikipedia. They appear to have edited their personal page on the Polish site, but made no other contributions. PianoDan (talk) 22:25, 10 July 2022 (UTC)

• Comment Looking through the discussion pointed to above and examining the literature, it appears that the article's creator invented the name "Łukaszyk–Karmowski metric" and every mention in the literature got the name from Wikipedia. Citogenesis, in other words. I'm tempted to call any paper whose authors learned about their topic from Wikipedia unreliable de facto, but that's only because I'm familiar with Wikipedia. XOR'easter (talk) 14:38, 9 July 2022 (UTC)

  On further reflection, I'd like to amplify what I said before. Forget the "tempted" part. It would be unethical for us to allow a term to be invented on Wikipedia and then use papers based on Wikipedia to justify keeping the article that originated the term. XOR'easter (talk) 00:15, 11 July 2022 (UTC)

Would you please elaborate, on why would it be unethical to keep this article under this name? Would you withdraw this objection if we rolled back to "Metric on random variables or random vectors", as proposed by User:Melcombe in May 2009? Guswen (talk) 04:54, 11 July 2022 (UTC)

I don't think what I wrote needs elaboration: inventing new ideas, or even new terminology, is not Wikipedia's purpose, and we would fail as a community if we let that stand. The proposed alternative is completely awkward and unworkable on its own merits. XOR'easter (talk) 15:58, 11 July 2022 (UTC)

This distance function was discovered by me (Łukaszyk) and revised by the supervisor of my PhD dissertation (Karmowski). That is why it can be called Łukaszyk-Karmowski distance function (or Łukaszyk-Karmowski metric), not because such term was invented on Wikipedia. Furthermore, this concept exists in the literature under various names. For example:

* [37] uses "Łukaszyk–Karmowski distance on probability distributions",

* [38], [39], [40] use the original term "probability metric",

* [41], [42], and [43] use "Łukaszyk–Karmowski distance",

* [44] uses "expected distance",

* [45] uses "probabilistic concept",

* [46] uses "Łukaszyk distance measure",

* [47] uses simply "Łukaszyk-Karmovski", while

* [48] and [49] use "Lukaszyk-Karmowski probability metric".

I have no objections to change the name of this article to any of the names above or, perhaps, some new one.

We may fail as a community for quite different reasons, that I would not want to delve into at this very moment. Guswen (talk) 16:44, 11 July 2022 (UTC)

The purpose of Wikipedia is not to name things after oneself. Particularly things that already existed.

I could maybe, maybe, see the merit in an article called something like "Expected distance between random variables", but even that would require blowing up this page and starting from scratch to cover the long history of quadratic dissimilarity measures in ecology [50], bounds on the Wasserstein distance [51], etc. And seeing how these quantities are used, I'm still not convinced that a dedicated page would be the proper presentation of the topic. XOR'easter (talk) 19:24, 11 July 2022 (UTC)

The expected distance between two regions $\int \int ||x-y||dP(x)dQ(y)$ (disclosed in p. 3(36) of your reference), where P and Q are probability measures in $\mathbb {R} ^{2}$ is not the same as $\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }|x-y|f(x)f(y)dxdy$ (Eq. (4.3) of the LK-metric disertation; particular version of the LK-metric between independent continuous random variables), where f and g are probability density functions. As stated in your reference (p. 3(36)) "Even in the most simple case of uniform distributions, the evaluation of these (the former) formulae, when possible, is very time-consuming", whereas computational complexity required to calculate the latter formula (4.25) (or (4.24)) of the LK-metric disertation (p. 29) for uniform distributions is insignificant. Guswen (talk) 09:15, 12 July 2022 (UTC)

It's the same idea, apart from being defined on the plane instead of only on the line. The complexity they're talking about is due to the shapes of the regions on which the densities have uniform support. It has nothing to do with "computational complexity" in the algorithmic sense and everything to do with integrals being hard to do by hand. XOR'easter (talk) 18:58, 12 July 2022 (UTC)

True. After your explanation I see that the expected distance between two regions $\int \int ||x-y||dP(x)dQ(y)$ corresponds to the 2-dimensional form of the LK-metric of mutually independent random vectors (4.39), (4.42) (p. 34). I was not aware of that study until you put it on the table (and I was not aware in 2000). Seemingly, neither the reviewers of my PhD dissertation (2003), nor the reviewers of the Springer article (2004) were. Thank you. It certainly needs to be cited in the Wikipedia article (perhaps long with this paper, also published by Springer) in the "Earlier research" section. Yet, this study, for example:

• considers only 2-dimensional convex regions supporting independent probability measures, not arbitrary (and possibly unbounded) probability density functions (probability measure is not precisely the same as probability density function);
• does not extend this idea to other dimensionalities (Which could be called obvious. But, again, could vs. would);
• does not prove that this expected distance satisfies the triangle inequality (4.46) (p. 36) (the proof of symmetry is trivial);
• does not prove that this expected distance reduces to the metric for the Dirac delta distributions;
• does not derive particular forms ((4.15), (4.16); (4.20), (4.21); (4.24), (4.25); (4.28), (4.29); (4.35), (4.36)) of this expected distance for various probability density functions;
• does not provide a simplified form of distance (4.48) (p. 37) between random vectors that uses these derived particular forms and thus, enables to avoid time-consumming evaluations due to - as you point out - integrals being hard to do by hand;
• does not discuss physical interpretations of such an expected distance in quantum mechanics.

Guswen (talk) 22:12, 12 July 2022 (UTC)

So you propose to blow up this page and start from scratch to establish a historical background, in order arrive at my PhD disertation defended almost 20 years ago? And perhaps move it further to include further research [52], [53], [54], [55], etc.? Why not just add sections "Historical background" and "Further research" at the top and at the end of the existing article? Guswen (talk) 19:36, 11 July 2022 (UTC)

Because the COI issues are irreparable, we have no reliable indication that the content currently in the article reflects a justifiable choice of topics, and we have no reason to say that prior work was merely "background" to your PhD thesis. XOR'easter (talk) 20:11, 11 July 2022 (UTC)

The content, currently in the article reflects my PhD disertation. And it was you who said that this content has to cover the long history of quadratic dissimilarity measures in ecology, bounds on the Wasserstein distance, etc.

By no means did I want to say that prior work is merely a "background" to my PhD thesis. It seemed to me that you wanted to add some "historical background" to it. Guswen (talk) 20:41, 11 July 2022 (UTC)

And I'll do my best to present someone with my WP:COI issue in a hope that s/he's able to improve this article pursuant to your guidelines. Guswen (talk) 21:04, 11 July 2022 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.