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New diagonal bundle method for clustering problems in large data sets

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  • Karmitsa, Napsu
  • Bagirov, Adil M.
  • Taheri, Sona

Abstract

Clustering is one of the most important tasks in data mining. Recent developments in computer hardware allow us to store in random access memory (RAM) and repeatedly read data sets with hundreds of thousands and even millions of data points. This makes it possible to use conventional clustering algorithms in such data sets. However, these algorithms may need prohibitively large computational time and fail to produce accurate solutions. Therefore, it is important to develop clustering algorithms which are accurate and can provide real time clustering in large data sets. This paper introduces one of them. Using nonsmooth optimization formulation of the clustering problem the objective function is represented as a difference of two convex (DC) functions. Then a new diagonal bundle algorithm that explicitly uses this structure is designed and combined with an incremental approach to solve this problem. The method is evaluated using real world data sets with both large number of attributes and large number of data points. The proposed method is compared with two other clustering algorithms using numerical results.

Suggested Citation

  • Karmitsa, Napsu & Bagirov, Adil M. & Taheri, Sona, 2017. "New diagonal bundle method for clustering problems in large data sets," European Journal of Operational Research, Elsevier, vol. 263(2), pages 367-379.
    • Handle: RePEc:eee:ejores:v:263:y:2017:i:2:p:367-379
    DOI: 10.1016/j.ejor.2017.06.010
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    References listed on IDEAS

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    1. Carrizosa, Emilio & Mladenović, Nenad & Todosijević, Raca, 2013. "Variable neighborhood search for minimum sum-of-squares clustering on networks," European Journal of Operational Research, Elsevier, vol. 230(2), pages 356-363.
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    5. Rabello, Rômulo Louzada & Mauri, Geraldo Regis & Ribeiro, Glaydston Mattos & Lorena, Luiz Antonio Nogueira, 2014. "A Clustering Search metaheuristic for the Point-Feature Cartographic Label Placement Problem," European Journal of Operational Research, Elsevier, vol. 234(3), pages 802-808.
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    7. Napsu Karmitsa, 2015. "Diagonal Bundle Method for Nonsmooth Sparse Optimization," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 889-905, September.
    8. Bagirov, Adil M. & Yearwood, John, 2006. "A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems," European Journal of Operational Research, Elsevier, vol. 170(2), pages 578-596, April.
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    Cited by:

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    2. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.

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