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Reduced Clustering Method Based on the Inversion Formula Density Estimation

Author

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  • Mantas Lukauskas

    (Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania)

  • Tomas Ruzgas

    (Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania)

Abstract

Unsupervised learning is one type of machine learning with an exceptionally high number of applications in various fields. The most popular and best-known group of unsupervised machine learning methods is clustering methods. The main goal of clustering is to find hidden relationships between individual observations. There is great interest in different density estimation methods, especially when there are outliers in the data. Density estimation also can be applied to data clustering methods. This paper presents the extension to the clustering method based on the modified inversion formula density estimation to solve previous method limitations. This new method’s extension works within higher dimensions (d > 15) cases, which was the limitation of the previous method. More than 20 data sets are used in comparative data analysis to prove the effectiveness of the developed method improvement. The results showed that the new method extension positively affects the data clustering results. The new reduced clustering method, based on the modified inversion formula density estimation, outperforms popular data clustering methods on test data sets. In cases when the accuracy is not the best, the data clustering accuracy is close to the best models’ obtained accuracies. Lower dimensionality data were used to compare the standard clustering based on the inversion formula density estimation method with the extended method. The new modification method has better results than the standard method in all cases, which confirmed the hypothesis about the new method’s positive impact on clustering results.

Suggested Citation

  • Mantas Lukauskas & Tomas Ruzgas, 2023. "Reduced Clustering Method Based on the Inversion Formula Density Estimation," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:661-:d:1049272
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    References listed on IDEAS

    as
    1. Mantas Lukauskas & Vaida Pilinkienė & Jurgita Bruneckienė & Alina Stundžienė & Andrius Grybauskas & Tomas Ruzgas, 2022. "Economic Activity Forecasting Based on the Sentiment Analysis of News," Mathematics, MDPI, vol. 10(19), pages 1-22, September.
    2. Mantas Lukauskas & Tomas Ruzgas, 2022. "A New Clustering Method Based on the Inversion Formula," Mathematics, MDPI, vol. 10(15), pages 1-16, July.
    3. Zura Kakushadze & Willie Yu, 2017. "*K-means and Cluster Models for Cancer Signatures," Papers 1703.00703, arXiv.org, revised Jul 2017.
    4. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
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