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Why doesn't the scatter plot change when I perform multidimensional scaling on distance or similarity matrix?

This figure uses similarity matrix

enter image description here

And this figure use distance matrix (sqrt(1-similarity))

enter image description here

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    $\begingroup$ This is because MDS software which converts similarities into dissimilarities do it other way than by formula sqrt(1-similarity). That formula - precisely, sqrt[2(1-similarity)] -- is best to convert Pearson correlation or cosine into euclidean distance, so it isn't universal. $\endgroup$ – ttnphns Feb 26 '13 at 18:30
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    $\begingroup$ That's not a bug, it's a feature! :-). Seriously, isn't this a desirable behavior? $\endgroup$ – Peter Flom - Reinstate Monica Feb 26 '13 at 19:21
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    $\begingroup$ @Dzung, you should consult your software documentation. MDS implementations vary in how they preprocess input proximity matrices, How and when they convert a similarity into a distance etc. $\endgroup$ – ttnphns Feb 26 '13 at 19:37
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Answer from comments:

That's not a bug, it's a feature! :-). Seriously, isn't this a desirable behavior? – Peter Flom (which I wholeheartedly agree with)

For more details, you really need to consult your software's documentation. You didn't mention which software, and we cannot mindread.

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