Abstract
We analyze the influence of the cluster shape on the performance of four cluster validation criteria: AIC, BIC, ICL and NI. First we introduce a method to generate unimodal and radially symmetric clusters whose shape can be interpolated between peaky long-tailed and flat distributions using a single parameter. Normally distributed clusters are obtained as a special case. Then we systematically study the performance of AIC, BIC, ICL and NI when validating clusters of arbitrary shapes. Using problems with two clusters, different inter-cluster distances and different dimensions, we show that, while BIC provides the best results for normally distributed clusters, in a general context with high dimensional data and unknown cluster distributions the use of ICL or NI may be a better choice.
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Notes
- 1.
Note that \(\hat{\beta }(1) = \beta (1)\) as there is only one trivial solution for \(n_{c} = 1\).
- 2.
In the original formulation in [18] there is an additional constant term that has been omitted here for the sake of simplicity. This term depends only on the covariance matrix of the entire data set, which is constant for any particular problem.
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Acknowledgments
This work was funded by grant S2017/BMD-3688 from Comunidad de Madrid, and by Spanish projects MINECO/FEDER TIN2017-84452-R and DPI2015-65833-P (http://www.mineco.gob.es/).
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Lago-Fernández, L.F., Aragón, J., Sánchez-Montañés, M. (2019). Validation of Unimodal Non-Gaussian Clusters. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2019. Lecture Notes in Computer Science(), vol 11507. Springer, Cham. https://doi.org/10.1007/978-3-030-20518-8_50
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