A simulated annealing-based maximum-margin clustering algorithm
- Authors: Seifollahi, Sattar , Bagirov, Adil , Borzeshi, Ehsan , Piccardi, Massimo
- Date: 2019
- Type: Text , Journal article
- Relation: Computational Intelligence Vol. 35, no. 1 (2019), p. 23-41
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- Description: Maximum-margin clustering is an extension of the support vector machine (SVM) to clustering. It partitions a set of unlabeled data into multiple groups by finding hyperplanes with the largest margins. Although existing algorithms have shown promising results, there is no guarantee of convergence of these algorithms to global solutions due to the nonconvexity of the optimization problem. In this paper, we propose a simulated annealing-based algorithm that is able to mitigate the issue of local minima in the maximum-margin clustering problem. The novelty of our algorithm is twofold, ie, (i) it comprises a comprehensive cluster modification scheme based on simulated annealing, and (ii) it introduces a new approach based on the combination of k-means++ and SVM at each step of the annealing process. More precisely, k-means++ is initially applied to extract subsets of the data points. Then, an unsupervised SVM is applied to improve the clustering results. Experimental results on various benchmark data sets (of up to over a million points) give evidence that the proposed algorithm is more effective at solving the clustering problem than a number of popular clustering algorithms.
An algorithm for clustering using L1-norm based on hyperbolic smoothing technique
- 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
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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.