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Using the Gini Index for a Gaussian Mixture Model

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Advances in Computational Intelligence (MICAI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12469))

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Abstract

A Gaussian mixture model is a weighted sum of parametric Gaussian components. These parametric density functions are widely used in data mining and pattern recognition. In this work we propose an efficient method to model a density function as a Gaussian mixture through an iterative algorithm that allow us to estimate the parameters of the model for a given data set. For this purpose we use the Gini Index, a measure of the inequality degree between two probability distributions. The Gini Index is obtained by finding the solution of an optimization problem. Our model consists in minimizing the Gini Index between an empirical distribution and a parametric distribution that is a Gaussian mixture. We will show some simulated examples and real data examples, with two widely used datasets, to observe the efficiency and properties of our model.

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Notes

  1. 1.

    https://archive.ics.uci.edu/ml/index.php.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Veracruz, Xalapa, Veracruz, Mexico

    Adriana Laura López-Lobato & Martha Lorena Avendaño-Garrido

Authors
  1. Adriana Laura López-Lobato
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  2. Martha Lorena Avendaño-Garrido
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Corresponding author

Correspondence to Adriana Laura López-Lobato .

Editor information

Editors and Affiliations

  1. Facultad de Ingeniería, Universidad Panamericana, Mexico City, Mexico

    Lourdes Martínez-Villaseñor

  2. Universidad Autónoma Metropolitana, Mexico City, Mexico

    Oscar Herrera-Alcántara

  3. Facultad de Ingeniería, Universidad Panamericana, Mexico City, Mexico

    Hiram Ponce

  4. Universidad Autónoma del Estado de Hidalgo, Hidalgo, Mexico

    Félix A. Castro-Espinoza

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López-Lobato, A.L., Avendaño-Garrido, M.L. (2020). Using the Gini Index for a Gaussian Mixture Model. In: Martínez-Villaseñor, L., Herrera-Alcántara, O., Ponce, H., Castro-Espinoza, F.A. (eds) Advances in Computational Intelligence. MICAI 2020. Lecture Notes in Computer Science(), vol 12469. Springer, Cham. https://doi.org/10.1007/978-3-030-60887-3_35

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  • DOI: https://doi.org/10.1007/978-3-030-60887-3_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-60886-6

  • Online ISBN: 978-3-030-60887-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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