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Convergence Analysis of a New MaxMin-SOMO Algorithm

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Abstract

The convergence analysis of MaxMin-SOMO algorithm is presented. The SOM-based optimization (SOMO) is an optimization algorithm based on the self-organizing map (SOM) in order to find a winner in the network. Generally, through a competitive learning process, the SOMO algorithm searches for the minimum of an objective function. The MaxMin-SOMO algorithm is the generalization of SOMO with two winners for simultaneously finding two winning neurons i.e., first winner stands for minimum and second one for maximum of the objective function. In this paper, the convergence analysis of the MaxMin-SOMO is presented. More specifically, we prove that the distance between neurons decreases at each iteration and finally converge to zero. The work is verified with the experimental results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 11171367 and 61502068), the Fundamental Research Funds for the Central Universities of China (No. 3132014094), the China Postdoctoral Science Foundation (Nos. 2013M541213 and 2015T80239) and Fundacao da Amaro a Pesquisa do Estado de Sao Paulo (FAPESP) Brazil (No. 2012/23329-5).

The authors wish to thank the associate editor and the anonymous reviewers for their helpful and interesting comments. We are very grateful to professor Wu Wei for extremely helpful discussion and comments to improve the quality of the paper. Thanks to professor Ricardo Zorzetto Nicoliello Vêncio for his help to improve the text of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, China

    Atlas Khan & Zheng-Xue Li

  2. School of Information Science and Technology, Dalian Maritime University, Dalian, China

    Yan-Peng Qu

  3. Department of Computing and Mathematics FFCLRP, University of Sao Paulo, Ribeirao Preto, Brazil

    Atlas Khan

Authors
  1. Atlas Khan
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  2. Yan-Peng Qu
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  3. Zheng-Xue Li
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Correspondence to Atlas Khan.

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Recommended by Associate Editor Hong Qiao

Atlas Khan received the B. Sc. and M. Sc. degrees in mathematics from Gomal University DI Khan Pakistan, in 2005 and 2007, respectively, and M.Phil. degree in mathematics from Quaid-i-Azam University, Pakistan in 2010. He obtained the Ph.D. degree from Department of Applied Mathematics, Dalian University of Technology, China in 2013. Since August 2013, he is doing post-docotor in bioinformatics with Department of Computing and Mathematics, University of Sao Paulo, Brazil. He has published a number of papers in international journals and conferences.

His research interests include bioinformatios, computational biology, neural networks and coding theory.

Yan-Peng Qu received the Ph.D. degree in computational mathematics from Dalian University of Technology, China in 2012. He is a lecturer with the Information Science and Technology College at Dalian Maritime University, China.

His research interests include rough and fuzzy set theory, pattern recognition, neural networks, classification and feature selection.

Zheng-Xue Li received the Ph.D. degree in mathematics from Jilin University, Changchun, China in 2001. He is currently an associate professor with Dalian University of Technology, China.

His research interests include nonlinear algorithm analysis and intelligent information processing.

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Khan, A., Qu, YP. & Li, ZX. Convergence Analysis of a New MaxMin-SOMO Algorithm. Int. J. Autom. Comput. 16, 534–542 (2019). https://doi.org/10.1007/s11633-016-0996-0

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