Document Type: Original Research Paper


1 Department of Computer Engineering, Alzahra University

2 Qazvin Islamic Azad Branch


Data visualization is the process of transforming data, information, and knowledge into visual form, making use of humans’ natural visual capabilities which reveals relationships in data sets that are not evident from the raw data, by using mathematical techniques to reduce the number of dimensions in the data set while preserving the relevant inherent properties. In this paper, we formulated data visualization as a Quadric Assignment Problem (QAP), and then presented an Artificial Bee Colony (ABC) to solve the resulted discrete optimization problem. The idea behind this approach is to provide mechanisms based on ABC to overcome trapped in local minima and improving the resulted solutions. To demonstrate the application of ABC on discrete optimization in data visualization, we used a database of electricity load and compared the results to other popular methods such as SOM, MDS and Sammon's map. The results show that QAP-ABC has high performance with compared others.


Main Subjects

1. L. Xu, Y. Xu, T. W. S. Chow, "PolSOM: A new method for multidimensional data visualization", Pattern Recognition, Volume 43, Issue 4, pp. 1668–1675, 2010.
2. Y. Xu, L. Xu, T. W. S. Chow, "PPoSOM: A new variant of PolSOM by using probabilistic assignment for multidimensional data visualization", Neurocomputing, Volume 74, Issue 11, pp. 2018–2027, 2011.
3. F. S. Tsai, "Dimensionality reduction techniques for blog visualization", Expert Systems with Applications, Volume 38, Issue, pp. 2766–2773, 2011.
4. R. Abbiw-Jackson, B. Golden, S. Raghavan, and E. Wasil, "A divide-and-conquer local search heuristic for data visualization", Computers and operations research, Volume 33, Issue 11, pp. 3070–3087, 2006.
5. M. H. Ghaseminezhad, A. Karami, "A novel self-organizing map (SOM) neural network for discrete groups of data clustering", Applied Soft Computing, Volume 11, Issue 4, pp. 3771–3778, 2011.
6. P. Klement, V. Snášel, "Using SOM in the performance monitoring of the emergency call-taking system", Simulation Modelling Practice and Theory, Volume 19, Issue 1, pp. 98–109, 2011.
7. J. W. Sammon, "A nonlinear mapping for data structure analysis", IEEE Transactions on computers, Volume 18, Issue 5, pp. 401–409, 1969.
8. J. Sun, C. Fyfe, M. Crowe, "Extending Sammon mapping with Bregman divergences", Information Sciences, Volume 187, pp. 72–92, 2012.
9. G. Gan, C. Ma, J. Wu, Data Clustering: Theory, Algorithms, and Applications, Society for Industrial and Applied Mathematics, 2007.
10. P. A. De Mazière, M. M. Van Hulle, "A clustering study of a 7000 EU document inventory using MDS and SOM", Expert Systems with Applications, Volume 38, Issue 7, pp. 8835–8849, 2011.
11. M. Ghanbari, "Visualization Overview", Thirty-Ninth Southeastern Symposium on System Theory, pp. 115–119, 2007.
12. S.-H. Bae, J. Qiu, G. Fox, "Adaptive interpolation of multidimensional scaling", Procedia Computer Science, Volume 9, pp. 393–402, 2012.
13. A. M. Lopes, J. A. Tenreiro Machado, C. M. A. Pinto, and A. M. S. F. Galhano, "Fractional dynamics and MDS visualization of earthquake phenomena", Computers & Mathematics with Applications, Volume 66, Issue 5, pp. 647–658, 2013.
14. T. Kohonen, "The self-organizing map", Neurocomputing, Volume 21, Number 1-3, pp. 1–6, 1998.
15. H. T. Jadhav, R. Roy, "Gbest guided artificial bee colony algorithm for environmental/economic dispatch considering wind power", Expert Systems with Applications, Volume 40, Issue 16, pp. 6385–6399, 2013.
16. A. P. Engelbrecht, Computational Intelligence: An Introduction, Wiley, 2007.
17. C. B. Kalayci, S. M. Gupta, "Artificial bee colony algorithm for solving sequence-dependent disassembly line balancing problem", Expert Systems with Applications, Volume 40, Issue 18, pp. 7231–7241, 2013.
18. H.-C. Tsai, "Integrating the artificial bee colony and bees algorithm to face constrained optimization problems", Information Sciences, Volume 258, pp. 80–93, 2013.
19. J.-Y. Park, S.-Y. Han, "Application of artificial bee colony algorithm to topology optimization for dynamic stiffness problems", Computers & Mathematics with Applications, Volume 66, Issue 10,, pp. 1879–1891, 2013.
20. M. Rani, H. Garg, S. P. Sharma, "Cost minimization of butter-oil processing plant using artificial bee colony technique", Mathematics and Computers in Simulation, Volume 97, pp. 94–107, 2014.
21. V. Golmah, J. Parvizian, "Visualization and the understanding of multidimensional data using Genetic Algorithms: Case study of load patterns of electricity customers", International Journal of Database Theory & Application, Volume 3, Issue 4, pp. 41–56, 2010.
22. J. Vesanto, J. Himberg, E. Alhoniemi, J. Parhankangas, S. Team, and L. Oy, "Som toolbox for matlab 5", Technical Report A57, Helsinki University of Technology, Neural Networks Research Centre, 2000.
23. A. Alizadegan, B. Asady, M. Ahmadpour, "Two modified versions of artificial bee colony algorithm", Applied Mathematics and Computation, Volume 225, pp. 601–609, 2013