Inspired by the reality that collection of fixed/common fixed points can embrace any symmetrical geometric shape comparable to a disc, circle, an elliptic ellipse, or hyperbola, we investigate subsistence point and common study their geometry in partial metric space introducing some novel contractions notions ellipse-like curve which is but entirely different than ellipse Euclidean space. We lo...

We develop an algorithm called bubble clustering which attempts to cover a given set of points with the union of k ellipses of minimum total volume. This algorithm operates by splitting and merging ellipses according to an annealing schedule and does not assume any prior distribution on the data. We compare our algorithm with k-means and the EM algorithm for mixture of Gaussians. Numerical resu...