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I have a cloud of points that can be clustered so that each set of points in the cluster can be fitted with an inverse function : $f(x) = cte / x$.

What would be an approach for clustering my dataset when discrimining criteria is fit to an inverse curve. I am on the computational side, I am looking for a simple fitting algorithm for a beautiful display with curves that are fitting the data thus demarcating several cluters of points.

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