Why doesn't the scatter plot change when I perform multidimensional scaling on distance or similarity matrix?
This figure uses similarity matrix
And this figure use distance matrix (sqrt(1-similarity))
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4$\begingroup$ 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. $\endgroup$– ttnphnsCommented Feb 26, 2013 at 18:30
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4$\begingroup$ That's not a bug, it's a feature! :-). Seriously, isn't this a desirable behavior? $\endgroup$– Peter FlomCommented Feb 26, 2013 at 19:21
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1$\begingroup$ @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. $\endgroup$– ttnphnsCommented Feb 26, 2013 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.
answered Jun 26, 2018 at 14:22