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New diagonal bundle method for clustering problems in large data sets

Author

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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. A. Bagirov & B. Ordin & G. Ozturk & A. Xavier, 2015. "An incremental clustering algorithm based on hyperbolic smoothing," Computational Optimization and Applications, Springer, vol. 61(1), pages 219-241, May.
    2. Santi, Éverton & Aloise, Daniel & Blanchard, Simon J., 2016. "A model for clustering data from heterogeneous dissimilarities," European Journal of Operational Research, Elsevier, vol. 253(3), pages 659-672.
    3. 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.
    4. 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.
    5. 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.
    6. A. Bagirov & A. Rubinov & N. Soukhoroukova & J. Yearwood, 2003. "Unsupervised and supervised data classification via nonsmooth and global optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 1-75, June.
    7. Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Introduction to Nonsmooth Optimization," Springer Books, Springer, edition 127, number 978-3-319-08114-4, June.
    8. Napsu Karmitsa, 2015. "Diagonal Bundle Method for Nonsmooth Sparse Optimization," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 889-905, September.
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    Cited by:

    1. Veronica Piccialli & Antonio M. Sudoso & Angelika Wiegele, 2022. "SOS-SDP: An Exact Solver for Minimum Sum-of-Squares Clustering," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2144-2162, July.
    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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