A Novel Hyperbolic Smoothing Algorithm for Clustering Large Data Sets
Adilson Elias Xavier, Vinícius Layter Xavier · 2009
The minimum sum-of-squares clustering problem is considered. The mathematical modeling of this problem leads to a min i sum i min formulation which, in addition to its intrinsic bi-level nature, has the signiflcant characteristic of being strongly nondifierentiable. To overcome these di‐culties, the proposed resolution method, called Hyperbolic Smoothing, adopts a smoothing strategy using a special C 1 difierentiable class function. The flnal solution is obtained by solving a sequence of low dimension difierentiable 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 simpliflcation of the computational tasks.