Talk:Distance matrix

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I disagree with the merger. Adjacency matrices are simply a way to tell whether two vertices are connected or not, and by how many paths. Distance matrices give the distances between two vertices, not whether they are connected or not.

I disagree with the propsed merger with adjacency matrix. These are different concepts. Charles Matthews 13:58, 21 February 2006 (UTC)[reply]

I also disagree with the merger. However, these topics are somewhat related and there should be a sentence or two describing their relationship. -- BAxelrod 13:54, 23 February 2006 (UTC)[reply]

Too bad no one of you added any information about adjacency matrices to the article - at least that should have been done before removing the tags... --Abdull 18:03, 30 April 2006 (UTC)[reply]

I also disagree with the merger. This would leave out the important Mahalanobis distance, which see. Pmanleycooke (talk) 08:13, 12 August 2008 (UTC)[reply]

Merging with Distance matrix methods

These topic are closely related. Could we merged them in some way?

Distance matrix should be symmetric.

Unlike a Euclidean distance matrix, the matrix does not need to be symmetric—that is, the values xi,j do not necessarily equal xj,i.

From a mathematical perspective, if it's not symmetric, it's not really a distance matrix. Intuitively, distance implies the distance from a to b should be equivalent to the distance from b to a. If this doesn't hold, I don't think it should be called a distance matrix. This property is not exclusive to Euclidean space either. Djh901 (talk) 17:59, 13 October 2015 (UTC)[reply]

This article is a bit of a mess. The opening sentence clearly talks about distance as a metric, but the applications in bioinformatics and related fields use distance with a looser non-metric meaning (and while they even talk about metrics, these are not the mathematically defined terms). In these applications, distances can be negative and don't have to be symmetric. I could help fixing up the mathematical side of this topic, but the other applications are beyond my ken. Bill Cherowitzo (talk) 05:30, 14 October 2015 (UTC)[reply]

Can you think of applications that use the term loosely? In my experience, distance implies some structure in the matrix that can then be used by algorithms for clustering or tree building. If a matrix doesn't actually have any of this structure, I don't think the term distance should be used. Maybe in the math definition non-negativity is too restrictive because transformations can usually resolve this, but I think asymmetry should at least hold. Djh901 (talk) 16:36, 17 October 2015 (UTC)[reply]

References to check out

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. Academic Press.
Borg, I. and Groenen, P. (1997) Modern Multidimensional Scaling. Theory and Applications. Springer.

Djh901 (talk) 18:20, 13 October 2015 (UTC)[reply]

The section "Comparison with Euclidean distance matrix" contradicts the "Formalization" section completely

It makes the claim that the matrix need not be symmetric and that it need not be hollow. The rules 2 and 3 under formalization directly contradict this. They state precisely in no uncertain terms that the matrix must be both symmetric and hollow. It also seems to want to allow for complex valued metrics which is not in line with the standard definition of a metric.--2003:69:CD3F:B01:2876:80EC:DC6E:7C68 (talk) 12:19, 20 October 2015 (UTC)[reply]