Talk:Kosambi–Karhunen–Loève theorem

I've never heard this called the Kosambi-Karhunen-Loeve Theorem
In statistics and machine learning, particularly Gaussian process research, the name Karhunen-Loeve is standard. The article should therefore be renamed as such to make it easier to find. If other fields use the name Kosambi-Karhunen-Loeve, this should be stated in a description and not in the article's default name, because it is likely these decompositions are less-widely used there than in statistics and ML. — Preceding unsigned comment added by 67.241.72.128 (talk) 02:29, 7 February 2024 (UTC)


 * similarly, it would be instructive to learn how "Kosambi" is/was. Not mentioned in the article and no reference has them as author. 141.53.5.110 (talk) 13:29, 11 March 2024 (UTC)
 * I've check the first paper in the references for that name ([1]) and it indeed mentions it under the name Kosambi-Karhunen-Loève by referencing another paper [2] that calls it Karhunen-Loève and doesn't mention Kosambi at all. To me, this sounds like a typo, a bad copy-paste, that propagated.
 * The second paper in the references is behind a paywall.
 * Someone should revert this entry, it creates more confusion than anything else.
 * [1]: http://people.ece.umn.edu/users/sachin/jnl/jetcas11.pdf
 * [2]: https://www.researchgate.net/profile/Sarma-Vrudhula/publication/221061474_Modeling_of_intra-die_process_variations_for_accurate_analysis_and_optimization_of_nano-scale_circuits/links/00b4951dc381d32fa1000000/Modeling-of-intra-die-process-variations-for-accurate-analysis-and-optimization-of-nano-scale-circuits.pdf 2A01:E0A:977:6150:329C:23FF:FE24:9EFF (talk) 11:15, 8 May 2024 (UTC)
 * OK, here is the relevant paper by D. D. Kosambi: http://repository.ias.ac.in/99240/1/Statistics_in_function_space.pdf
 * While it is an interesting paper (certainly very early for what it does!), it doesn't contain the theorem this page is referring to. 2A01:E0A:977:6150:329C:23FF:FE24:9EFF (talk) 11:27, 8 May 2024 (UTC)

too technical tag
i removed the tag. the intro to the article has been edited a bit since then. if you feel the edits still aren't sufficient, feel free to reinsert the tag but please leave some specific suggestions as to what's missing from the article or what you feel is confusing. thanks. Lunch 04:48, 24 September 2006 (UTC)
 * It would be helpful to me if the parallel to the Fourier Transform was better-developed. I'm just a humble computer science major, not a mathematician, and I understand the Fourier transform quite well, but I can get no understanding of what's going on here at all. -- Canar (talk) 22:44, 26 January 2010 (UTC)


 * The article is still too technical. It is pretty much incomprehensible to somebody who isn't already familiar with the transform. The details are fine, but article needs a less-technical introduction: what is this, and why would we want it?Geoffrey.landis (talk) 14:00, 8 July 2016 (UTC)

bracket notation
why does the inner product notation smack of dirac's bracket notation in quantum notation. the whole thing smacks of quantum mechanics and seems vaguely familiar.Godspeed John Glenn! Will 20:36, 21 August 2007 (UTC) .. APPLICATIONS (add) The theorem has been referred to in the article on Multichannel coding.

The theorem has been suggested as a supplement to the Fast Fourier Transform for signal processing for the Search for Extra-Terrestrial Intelligence. The assumption is the KLT would adapt to unknown signal coding and modulation methods not detectable with the FFT. The drawback is increased computation required. Bruno1960 (talk) 02:56, 1 December 2010 (UTC)

weird link to KL Transformation
I think the link in the third paragraph to the "Karhunen-Loève transform" is not really useful because it brings to the very same page. Furthermore, it can bring to misunderstandings with the users regarding the differences between the theorem and the transformation.

Here, I paste the paragraph at issue:

''In contrast to a Fourier series where the coefficients are fixed numbers and the expansion basis consists of sinusoidal functions (that is, sine and cosine functions), the coefficients in the Karhunen–Loève theorem are random variables and the expansion basis depends on the process. In fact, the orthogonal basis functions used in this representation are determined by the covariance function of the process. One can think that the Karhunen–Loève transform adapts to the process in order to produce the best possible basis for its expansion.'' — Preceding unsigned comment added by Gian.steve (talk • contribs) 09:19, 19 June 2018 (UTC)


 * I have unlinked it. Text remains as above. Jheald (talk) 15:07, 11 June 2021 (UTC)