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Limited Memory Bundle Method for Solving Large Clusterwise Linear Regression Problems

Napsu Karmitsa, Adil Bagirov, Sona Taheri, Limited Memory Bundle Method for Solving Large Clusterwise Linear Regression Problems. TUCS Technical Reports 1172, TUCS, 2016.

Abstract:

A clusterwise linear regression problem consists of finding a number of linear functions each approximating a subset of the given data. In this paper, the limited memory bundle method [Haarala et.al. {\em Math.\ Prog.}, Vol.\ 109, No.\ 1, pp.\ 181--205, 2007] is modified and combined with the incremental approach to solve this problem using its nonsmooth optimization formulation. The proposed algorithm is tested on small and large real world data sets and compared with other algorithms for clusterwise linear regression. Numerical results demonstrate that the proposed algorithm is especially efficient in data sets with large numbers of instances and input variables.

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BibTeX entry:

@TECHREPORT{tKaBaTa16c,
  title = {Limited Memory Bundle Method for Solving Large Clusterwise Linear Regression Problems},
  author = {Karmitsa, Napsu and Bagirov, Adil and Taheri, Sona},
  number = {1172},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2016},
  keywords = {Clusterwise linear regression; Nonsmooth optimization; Nonconvex problems; Bundle methods; Limited memory methods.},
  ISBN = {978-952-12-3488-0},
}

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

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