Paper Info
Title
Solving the minimum sum-of-squares clustering problem by hyperbolic smoothing and partition into boundary and gravitational regions
Abstract
This article considers the minimum sum-of-squares clustering (MSSC) problem. 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 subproblems which gradually approach the original problem. This paper introduces the method of partition of the set of observations into two nonoverlapping groups: ''data in frontier'' and ''data in gravitational regions''. The resulting combination of the two methodologies for the MSSC problem has interesting properties, which drastically simplify the computational tasks.
Year
DOI
Venue
2011
10.1016/j.patcog.2010.07.004
Pattern Recognition
Keywords
Field
DocType
final solution,gravitational region,hyperbolic smoothing,minimum sum-of-squares,low dimension differentiable,min-sum-min problems,smoothing strategy,smoothing,computational task,original problem,cluster analysis,nondifferentiable programming,proposed resolution method,mssc problem,differentiable class function,sum of squares,mathematical model,grouped data
Mathematical optimization,Class function,Differentiable function,Smoothing,Signal classification,Artificial intelligence,Cluster analysis,Explained sum of squares,Partition (number theory),Gravitation,Machine learning,Mathematics
Journal
Volume
Issue
ISSN
44
1
Pattern Recognition
Citations 
PageRank 
References 
11
0.61
8
Authors
2
Name
Order
Citations
PageRank
Adilson Xavier1456.28
Vinicius Layter Xavier2132.01