An algorithm for clustering using L1-norm based on hyperbolic smoothing technique

- Bagirov, Adil, Mohebi, Ehsan

  • Authors: Bagirov, Adil , Mohebi, Ehsan
  • Date: 2016
  • Type: Text , Journal article
  • Relation: Computational Intelligence Vol. 32, no. 3 (2016), p. 439-457
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
  • Full Text: false
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  • Description: Cluster analysis deals with the problem of organization of a collection of objects into clusters based on a similarity measure, which can be defined using various distance functions. The use of different similarity measures allows one to find different cluster structures in a data set. In this article, an algorithm is developed to solve clustering problems where the similarity measure is defined using the L1-norm. The algorithm is designed using the nonsmooth optimization approach to the clustering problem. Smoothing techniques are applied to smooth both the clustering function and the L1-norm. The algorithm computes clusters sequentially and finds global or near global solutions to the clustering problem. Results of numerical experiments using 12 real-world data sets are reported, and the proposed algorithm is compared with two other clustering algorithms. ©2015 Wiley Periodicals, Inc.

An incremental piecewise linear classifier based on polyhedral conic separation

- Ozturk, Gurkan, Bagirov, Adil, Kasimbeyli, Refail

  • Authors: Ozturk, Gurkan , Bagirov, Adil , Kasimbeyli, Refail
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Machine Learning Vol. 101, no. 1-3 (2015), p. 397-413
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
  • Full Text: false
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  • Description: In this paper, a piecewise linear classifier based on polyhedral conic separation is developed. This classifier builds nonlinear boundaries between classes using polyhedral conic functions. Since the number of polyhedral conic functions separating classes is not known a priori, an incremental approach is proposed to build separating functions. These functions are found by minimizing an error function which is nonsmooth and nonconvex. A special procedure is proposed to generate starting points to minimize the error function and this procedure is based on the incremental approach. The discrete gradient method, which is a derivative-free method for nonsmooth optimization, is applied to minimize the error function starting from those points. The proposed classifier is applied to solve classification problems on 12 publicly available data sets and compared with some mainstream and piecewise linear classifiers. © 2014, The Author(s).

Clustering in large data sets with the limited memory bundle method

- Karmitsa, Napsu, Bagirov, Adil, Taheri, Sona

  • Authors: Karmitsa, Napsu , Bagirov, Adil , Taheri, Sona
  • Date: 2018
  • Type: Text , Journal article
  • Relation: Pattern Recognition Vol. 83, no. (2018), p. 245-259
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
  • Full Text: false
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  • Description: The aim of this paper is to design an algorithm based on nonsmooth optimization techniques to solve the minimum sum-of-squares clustering problems in very large data sets. First, the clustering problem is formulated as a nonsmooth optimization problem. Then the limited memory bundle method [Haarala et al., 2007] is modified and combined with an incremental approach to design a new clustering algorithm. The algorithm is evaluated using real world data sets with both the large number of attributes and the large number of data points. It is also compared with some other optimization based clustering algorithms. The numerical results demonstrate the efficiency of the proposed algorithm for clustering in very large data sets.

A difference of convex optimization algorithm for piecewise linear regression

- Bagirov, Adil, Taheri, Sona, Asadi, Soodabeh

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