Talk:Bhattacharyya distance

message: The articles do seem to be about the same thing. One problem may be the title to adopt. Should "distance" be used, considering that it isn't a "distance" in the metric sense? So what is the common usage? Melcombe (talk) 16:31, 15 May 2008 (UTC)
replies: text: Google seems to prefer distance (13,000 versus 3,000 hits). Btyner (talk) 20:14, 10 May 2009 (UTC)

text: It is a measure of dissimilarity, even though it does not obey the triangle inequality (see Kailath's paper, referenced in the main article).Jrvz (talk) 16:54, 8 November 2010 (UTC)
thread_title:  Merger question 

message: There is no article on battacharyya bound!! — Preceding unsigned comment added by 165.91.166.94 (talk) 22:56, 26 November 2006
 Note: in article's Definition section, in paragraph
 relating it to Mahalanobis distance, figures are 
 mentioned but none are present. 
128.101.106.11 (talk) 23:37, 7 March 2013 (UTC)
thread_title: Comments from [[Talk:Bhattacharya coefficient]]

message: In the definition based on mean and variance: "where sigma_p is the variance of the p-th distribution," -> is sigma really the variance, shouldn't it be the standard deviation? Since sigma^2 is used everywhere in the formula, I'm not sure but I suspect that it should be "where sigma^2_p is the variance of the p-th distribution". Can someone confirm or refute that please?
82.67.136.228 (talk) 16:05, 5 April 2013 (UTC)
replies: text: Using Maxima I can quickly derive Bhattacharyya distance for normal distributions directly like that: 
N[m,s](x) := 1/(s*sqrt(2*%pi)) * exp(-(x-m)**2/(2*s**2)) $
assume(sp > 0, sq > 0) $
-log(integrate(sqrt(N[mp,sp](x) * N[mq,sq](x)), x, -inf, inf));
 Which gives 
-\log \left({{\sqrt{2}\,\sqrt\,\sqrt\,e^ {- {{
 {\it mq}^2-2\,{\it mp}\,{\it mq}+{\it mp}^2}\over{4\,{\it sq}^2+4\,
 {\it sp}^2}} }}\over{\sqrt{{\it sq}^2+{\it sp}^2}}}\right)
 where sp and sq stand for standard deviations. Substituting the usual symbols, i.e. \sigma_p for sp, etc, and simplifying this is 
\frac{1}{2}\log\left(\frac{\sigma_p^2+\sigma_q^2}{2\sigma_p\sigma_q}\right) +
\frac{1}{4}\frac{(\mu_p-\mu_q)^2}{\sigma_p^2+\sigma_q^2}
 which is essentially the same formula as the one in the article (except that the first term is further rewritten so that sigmas appear only squared, perhaps for numerical reasons). So I conclude that indeed variance is, as usual, written \sigma^2 in it. Wherever the mistake comes from, it's an obvious typo so I'm fixing it. — mwgamera (talk) 10:51, 16 March 2016 (UTC)
thread_title:  Error in simplified formula? 

message: How am I to understand the sentence "the Mahalanobis distance is a particular case of the Bhattacharyya distance when the standard deviations of the two classes are the same"? We are not talking mathematical equivalency since D_{B}={1 \over 8} {D_{M}}^2. 
I understand the Mahalanobis distance to measure the distance between a point and a distribution in standard deviations. What would the equivalent measurement unit for Bhattacharyya distance be?
129.247.247.239 (talk) 14:53, 23 July 2019 (UTC)
replies: text: I wanted to ask the same. Imo this is incomplete or wrong --84.112.248.63 (talk) 12:53, 26 June 2020 (UTC)
thread_title:  A particular case?