Abstract
Recently, a particle swarm optimization (PSO) algorithm was used to fit a Gaussian mixture model (GMM). However, this algorithm incorporates an additional step in the optimization process which increases the algorithm complexity and scales badly to a large number of components and large datasets. This study proposes a cooperative approach to improve the scalability and complexity of the PSO approach and illustrates its effectiveness compared to the expectation-maximization (EM) algorithm and the existing PSO approach when applied to a number of clustering problems.
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Notes
- 1.
Also referred to as components.
- 2.
The angle of a rotation in a plane described by two axis.
- 3.
For D dimensions there are \(\tau \) planes wherein a rotation can be applied.
- 4.
A matrix which applies a Givens rotation.
- 5.
A GMM assuming K components.
- 6.
Dua, D. and Graff, C. (2019). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.
- 7.
U(a, b) denotes a uniform distribution over the interval (a, b).
References
Ari, C., Aksoy, S.: Maximum likelihood estimation of Gaussian mixture models using particle swarm optimization. In: Proceedings of the International Conference on Pattern Recognition, pp. 746–749 (2010)
Blömer, J., Bujna, K.: Adaptive seeding for Gaussian mixture models. In: Bailey, J., Khan, L., Washio, T., Dobbie, G., Huang, J.Z., Wang, R. (eds.) PAKDD 2016. LNCS (LNAI), vol. 9652, pp. 296–308. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-31750-2_24
Dasgupta, S.: Learning mixture of Gaussians. In: Proceedings of the 40th Annual Symposium on Foundations of Computer Science, pp. 634–644 (1999)
Duffin, K., Barrett, W.: Spiders: a new user interface for rotation and visualization of n-dimensional point sets. In: Proceedings of the 1994 IEEE Conference on Scientific Visualization, pp. 205–211 (1994)
Engelbrecht, A.P., Van den Bergh, F.: A cooperative approach to particle swarm optimization. Proc. IEEE Trans. Evol. Comput. 8, 225–239 (2004)
Gensler, S.: Finite mixture models. In: Homburg, C., Klarmann, M., Vomberg, A. (eds.) Handbook of Market Research. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-05542-8_12-1
Georgieva, K.: A Computational Intelligence Approach to Clustering of Temporal Data. Master’s thesis, University of Pretoria, South Africa (2015)
Georgieva, K.S., Engelbrecht, A.P.: Dynamic differential evolution algorithm for clustering temporal data. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2013. LNCS, vol. 8353, pp. 240–247. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43880-0_26
Redner, R., Walker, H.: Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev. 26, 195–239 (1984)
Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, pp. 69–73 (1998)
Shi, Y., Eberhart, R.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, vol. 1, pp. 84–88 (2000)
Xie, X., Beni, G.: A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 13, 841–847 (1991)
Acknowledgements
The authors would like to thank the Centre for High Performance Computing for the use of their resources to run the simulations used in this study. As well as the UCI Machine Learning Repository for the real-world datasets used.
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Cilliers, H., Engelbrecht, A.P. (2020). Fitting Gaussian Mixture Models Using Cooperative Particle Swarm Optimization. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2020. Lecture Notes in Computer Science(), vol 12421. Springer, Cham. https://doi.org/10.1007/978-3-030-60376-2_24
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