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Diagonal Bundle Method for Solving the Minimum Sum-of-Squares Clustering Problems

Napsu Karmitsa, Adil Bagirov, Sona Taheri, Diagonal Bundle Method for Solving the Minimum Sum-of-Squares Clustering Problems. TUCS Technical Reports 1156, TUCS, 2016.

Abstract:

Clustering is among most important tasks in data mining. This problem in very large data sets is challenging for most existing clustering algorithms. It is important to develop clustering algorithms which are accurate and can provide real time clustering in such data sets. This paper introduces one such algorithm. Using nonsmooth optimization formulation of the clustering problem the objective function in this problem is represented as a difference of two convex functions. Then a new diagonal bundle method that explicitly utilizes this structure is designed to solve this problem. The method is evaluated using real world data sets with both the large number of attributes and/or large number of data points. The new algorithm is also compared with an other algorithm based on difference of convex representations.

BibTeX entry:

@TECHREPORT{tKaBaTa16a,
  title = {Diagonal Bundle Method for Solving the Minimum Sum-of-Squares Clustering Problems},
  author = {Karmitsa, Napsu and Bagirov, Adil and Taheri, Sona},
  number = {1156},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2016},
  keywords = {Cluster analysis, Nonsmooth optimization, Nondifferentiable optimization, DC-function, Nonconvex problems, Bundle methods.},
  ISBN = {978-952-12-3384-5},
}

Belongs to TUCS Research Unit(s): Turku Optimization Group (TOpGroup)

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