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Suppose we have similarity values between some data point in the interval $[0, 1]$. How can I transform this similarity values into a dissimilarity values in the interval $[0, ∞]$?

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  • $\begingroup$ Would simply taking the inverse work? This would give you values in the range 1 to infinity, so if you want the lower bound to be zero you can simply subtract 1. $\endgroup$
    – Oxbowerce
    Dec 28, 2021 at 17:39
  • $\begingroup$ I find it strange that you want to convert a normalized value to a non-normalized one. Why not just use the normalized dissimilarity $1-x$? $\endgroup$
    – Erwan
    Dec 29, 2021 at 0:07

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You can use $-\ln x$ as transformation. It will map the interval $(0, 1]$ to the interval $[0, \infty)$.

As proposed in the comments it would be much easier to convert the normalized similarity value $x$ to a dissimilarity value by $1-x$.

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