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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**Reviewed:****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.

Constrained self organizing maps for data clusters visualization

- Mohebi, Ehsan, Bagirov, Adil

**Authors:**Mohebi, Ehsan , Bagirov, Adil**Date:**2016**Type:**Text , Journal article**Relation:**Neural Processing Letters Vol. 43, no. 3 (2016), p. 849-869**Full Text:**false**Reviewed:****Description:**High dimensional data visualization is one of the main tasks in the field of data mining and pattern recognition. The self organizing maps (SOM) is one of the topology visualizing tool that contains a set of neurons that gradually adapt to input data space by competitive learning and form clusters. The topology preservation of the SOM strongly depends on the learning process. Due to this limitation one cannot guarantee the convergence of the SOM in data sets with clusters of arbitrary shape. In this paper, we introduce Constrained SOM (CSOM), the new version of the SOM by modifying the learning algorithm. The idea is to introduce an adaptive constraint parameter to the learning process to improve the topology preservation and mapping quality of the basic SOM. The computational complexity of the CSOM is less than those with the SOM. The proposed algorithm is compared with similar topology preservation algorithms and the numerical results on eight small to large real-world data sets demonstrate the efficiency of the proposed algorithm. © 2015, Springer Science+Business Media New York.

Modified self-organising maps with a new topology and initialisation algorithm

- Mohebi, Ehsan, Bagirov, Adil

**Authors:**Mohebi, Ehsan , Bagirov, Adil**Date:**2015**Type:**Text , Journal article**Relation:**Journal of Experimental and Theoretical Artificial Intelligence Vol. 27, no. 3 (2015), p. 351-372**Full Text:**false**Reviewed:****Description:**Mapping quality of the self-organising maps (SOMs) is sensitive to the map topology and initialisation of neurons. In this article, in order to improve the convergence of the SOM, an algorithm based on split and merge of clusters to initialise neurons is introduced. The initialisation algorithm speeds up the learning process in large high-dimensional data sets. We also develop a topology based on this initialisation to optimise the vector quantisation error and topology preservation of the SOMs. Such an approach allows to find more accurate data visualisation and consequently clustering problem. The numerical results on eight small-to-large real-world data sets are reported to demonstrate the performance of the proposed algorithm in the sense of vector quantisation, topology preservation and CPU time requirement. © 2014 Taylor & Francis.

Nonsmooth optimization based algorithms in cluster analysis

- Bagirov, Adil, Mohebi, Ehsan

**Authors:**Bagirov, Adil , Mohebi, Ehsan**Date:**2015**Type:**Text , Book chapter**Relation:**Partitional Clustering Algorithms p. 99-146**Full Text:**false**Reviewed:****Description:**Cluster analysis is an important task in data mining. It deals with the problem of organization of a collection of objects into clusters based on a similarity measure. Various distance functions can be used to define the similarity measure. Cluster analysis problems with the similarity measure defined by the squared Euclidean distance, which is also known as the minimum sum-of-squares clustering, has been studied extensively over the last five decades. L1 and L1 norms have attracted less attention. In this chapter, we consider a nonsmooth nonconvex optimization formulation of the cluster analysis problems. This formulation allows one to easily apply similarity measures defined using different distance functions. Moreover, an efficient incremental algorithm can be designed based on this formulation to solve the clustering problems. We develop incremental algorithms for solving clustering problems where the similarity measure is defined using the L1; L2 and L1 norms. We also consider different algorithms for solving nonsmooth nonconvex optimization problems in cluster analysis. The proposed algorithms are tested using several real world data sets and compared with other similar algorithms.**Description:**Cluster analysis is an important task in data mining. It deals with the problem of organization of a collection of objects into clusters based on a similarity measure. Various distance functions can be used to define the similarity measure. Cluster analysis problems with the similarity measure defined by the squared Euclidean distance, which is also known as the minimum sum-of-squares clustering, has been studied extensively over the last five decades. However, problems with the L

A convolutional recursive modified Self Organizing Map for handwritten digits recognition

- Mohebi, Ehsan, Bagirov, Adil

**Authors:**Mohebi, Ehsan , Bagirov, Adil**Date:**2014**Type:**Text , Journal article**Relation:**Neural Networks Vol. 60, no. (2014), p. 104-118**Relation:**http://purl.org/au-research/grants/arc/DP140103213**Full Text:**false**Reviewed:****Description:**It is well known that the handwritten digits recognition is a challenging problem. Different classification algorithms have been applied to solve it. Among them, the Self Organizing Maps (SOM) produced promising results. In this paper, first we introduce a Modified SOM for the vector quantization problem with improved initialization process and topology preservation. Then we develop a Convolutional Recursive Modified SOM and apply it to the problem of handwritten digits recognition. The computational results obtained using the well known MNIST dataset demonstrate the superiority of the proposed algorithm over the existing SOM-based algorithms.

CR-Modified SOM to the problem of handwritten digits recognition

- Mohebi, Ehsan, Bagirov, Adil

**Authors:**Mohebi, Ehsan , Bagirov, Adil**Date:**2014**Type:**Text , Conference proceedings**Relation:**34th SGAI International Conference on Innovative Techniques and Applications of Artcificial Intelligence; Cambridge, England; 9th-11th December 2014; published in Research and Development in Intelligent Systems XXXI (Incorporating Applications and Innovations in Intelligent Systems XXII) p. 225-238**Full Text:**false**Reviewed:****Description:**Recently, researchers show that the handwritten digit recognition is a challenging problem. In this paper first, we introduce a Modified Self Organizing Maps for vector quantization problem then we present a Convolutional Recursive ModifiedSOMto the problem of handwritten digit recognition. TheModifiedSOMis novel in the sense of initialization process and the topology preservation. The experimental result on the well known digit database of MNIST, denotes the superiority of the proposed algorithm over the existing SOM-based methods.

A new modification of Kohonen neural network for VQ and clustering problems

- Mohebi, Ehsan, Bagirov, Adil

**Authors:**Mohebi, Ehsan , Bagirov, Adil**Date:**2013**Type:**Text , Conference paper**Relation:**Proceedings of the 11-th Australasian Data Mining Conference (AusDM'13) Vol. 146, p. 81-88**Full Text:**false**Reviewed:****Description:**Vector Quantization (VQ) and Clustering are significantly important in the field of data mining and pattern recognition. The Self Organizing Maps has been widely used for clustering and topology visualization. The topology of the SOM and its initial neurons play an important role in the convergence of the Kohonen neural network. In this paper, in order to improve the convergence of the SOM we introduce an algorithm based on the split and merging of clusters to initialize neurons. We also introduce a topology based on this initialization to optimize the vector quantization error. Such an approach allows one to find global or near global solution to the vector quantization and consequently clustering problem. The numerical results on 4 small to large real-world data sets are reported to demonstrate the performance of the proposed algorithm.

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