A Novel Hyperbolic Smoothing Algorithm for Clustering Large Data Sets

The minimum sum-of-squares clustering problem is considered. The mathematical modeling of this problem leads to a min − sum −min formulation which, in addition to its intrinsic bi-level nature, has the significant characteristic of being strongly nondifferentiable. To overcome these difficulties, the proposed resolution method, called Hyperbolic Smoothing, adopts a smoothing strategy using a special C∞ differentiable class function. The final solution is obtained by solving a sequence of low dimension differentiable unconstrained optimization This paper presents an extended method based upon the partition of the set of observations in two non overlapping parts. This last approach engenders a drastic simplification of the computational tasks.