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I have a handful of N "things" for which I have a NxN symmetric correlation matrix. The correlations are a based on a custom scheme for quantifying similarity between complex things, with a value range 0% to 100%, though the values for the N things are all high (95.4%-97.4%). I want to visualize the similarities and differences using force directed graph visualization [1].

I was going to use 1 minus the correlations as a distance metric. Is this an appropriate for correlations, particularly when values are all high?

Googling hasn't been my friend when searching for the intersection between correlation matrices and graph visualization. My thought is that 1 minus the correlation plots the N things with distances somewhat proportional to their very small differences. An alternative might be to use the reciprocal of the correlation as the distance, but since the values are close to one, the Taylor expansion would show such a distance would be similar to 1 minus the correlation. The two schemes would differ much more for near-zero correlations, where the reciprocal would yield a distance approaching infinity (not practical for graph visualization). I can tweak the 1 minus distance scheme by raising to various powers, greater or less than 1 depending on whether I want to emphasize the small distances or the great distances.

[1] I would be using Matlab's layout tool, which uses Fruchterman & Reingold's "Graph Drawing by Force-directed Placement." Software — Practice & Experience. Vol. 21 (11), 1991, pp. 1129–1164.

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  • $\begingroup$ what you propose is a distance metric, so try it $\endgroup$ – Nikos M. Mar 21 at 10:54
  • $\begingroup$ I've used it years before, though with a correlation metric. I know that a graph will be drawn, but I was more wondering whether the definition of the distance metric makes sense. Is there a reason why one might want to use a different definition of distance? Is there some intuitive motivation for choosing a power for the nonlinear tweaking? Right now, it seems like anything goes. $\endgroup$ – user2153235 Mar 21 at 16:05
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What I have found is that it is not worth sweating the nuances of how distances are represented because they only partially determine the layout. Other factors are geared to generating a pleasing layout so that analysts can recognize gross patterns based on the absence presence of interconnections rather than purely based on distance.

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