# Clustering cloud fitting inverse functions

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.

• what does "cte" mean? – EngrStudent Aug 1 '13 at 0:13
• one constant ex. C=0.3 – kiriloff Aug 1 '13 at 11:00
• so you have a mixture of radial basis cluster components. – EngrStudent Aug 2 '13 at 20:52

so you have a mixture of radial basis cluster components.

A finite mixture model with exponential radial basis functions instead of gaussian components should do the job. I would initialize with gaussian mixture components, because that will give good count of components, approximate means, and approximate variances. I would then separate out the data by gaussian cluster membership, fit the radial basis function (to improve parameter estimates) and recompute cluster membership.

Borders will be where probability of membership is equal.

Some toolboxes:

Some references:

Associated concept is regression clustering: joint clustering using a set of functions the data can be optimally regressed to, and regression.

See for example

Estimation and Selection in Regression Clustering

Guoqi Qian1,∗, Yuehua Wu2