Reduced Clustering Method Based on the Inversion Formula Density Estimation

Mantas Lukauskas () and Tomas Ruzgas
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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

Mathematics, 2023, vol. 11, issue 3, 1-15

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.

Keywords: nonparametric density estimation; unsupervised machine learning; clustering; inversion formula; dimensions reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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