A New Clustering Method Based on the Inversion Formula
Data clustering is one area of data mining that falls into the data mining class of unsupervised learning. Cluster analysis divides data into different classes by discovering the internal structure of data set objects and their relationship. This paper presented a new density clustering method based...
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| Format: | Article |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2559 |
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| author | Mantas Lukauskas Tomas Ruzgas |
| author_facet | Mantas Lukauskas Tomas Ruzgas |
| author_sort | Mantas Lukauskas |
| collection | DOAJ |
| description | Data clustering is one area of data mining that falls into the data mining class of unsupervised learning. Cluster analysis divides data into different classes by discovering the internal structure of data set objects and their relationship. This paper presented a new density clustering method based on the modified inversion formula density estimation. This new method should allow one to improve the performance and robustness of the k-means, Gaussian mixture model, and other methods. The primary process of the proposed clustering algorithm consists of three main steps. Firstly, we initialized parameters and generated a T matrix. Secondly, we estimated the densities of each point and cluster. Third, we updated mean, sigma, and phi matrices. The new method based on the inversion formula works quite well with different datasets compared with K-means, Gaussian Mixture Model, and Bayesian Gaussian Mixture model. On the other hand, new methods have limitations because this one method in the current state cannot work with higher-dimensional data (d > 15). This will be solved in the future versions of the model, detailed further in future work. Additionally, based on the results, we can see that the MIDEv2 method works the best with generated data with outliers in all datasets (0.5%, 1%, 2%, 4% outliers). The interesting point is that a new method based on the inversion formula can cluster the data even if data do not have outliers; one of the most popular, for example, is the Iris dataset. |
| first_indexed | 2024-03-09T12:23:41Z |
| format | Article |
| id | doaj.art-64c4cc39d04346109025a9fcb3ef2a9d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T12:23:41Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-64c4cc39d04346109025a9fcb3ef2a9d2023-11-30T22:37:13ZengMDPI AGMathematics2227-73902022-07-011015255910.3390/math10152559A New Clustering Method Based on the Inversion FormulaMantas Lukauskas0Tomas Ruzgas1Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, LithuaniaDepartment of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, LithuaniaData clustering is one area of data mining that falls into the data mining class of unsupervised learning. Cluster analysis divides data into different classes by discovering the internal structure of data set objects and their relationship. This paper presented a new density clustering method based on the modified inversion formula density estimation. This new method should allow one to improve the performance and robustness of the k-means, Gaussian mixture model, and other methods. The primary process of the proposed clustering algorithm consists of three main steps. Firstly, we initialized parameters and generated a T matrix. Secondly, we estimated the densities of each point and cluster. Third, we updated mean, sigma, and phi matrices. The new method based on the inversion formula works quite well with different datasets compared with K-means, Gaussian Mixture Model, and Bayesian Gaussian Mixture model. On the other hand, new methods have limitations because this one method in the current state cannot work with higher-dimensional data (d > 15). This will be solved in the future versions of the model, detailed further in future work. Additionally, based on the results, we can see that the MIDEv2 method works the best with generated data with outliers in all datasets (0.5%, 1%, 2%, 4% outliers). The interesting point is that a new method based on the inversion formula can cluster the data even if data do not have outliers; one of the most popular, for example, is the Iris dataset.https://www.mdpi.com/2227-7390/10/15/2559artificial intelligenceunsupervised machine learningclusteringnonparametric density estimationinversion formula |
| spellingShingle | Mantas Lukauskas Tomas Ruzgas A New Clustering Method Based on the Inversion Formula Mathematics artificial intelligence unsupervised machine learning clustering nonparametric density estimation inversion formula |
| title | A New Clustering Method Based on the Inversion Formula |
| title_full | A New Clustering Method Based on the Inversion Formula |
| title_fullStr | A New Clustering Method Based on the Inversion Formula |
| title_full_unstemmed | A New Clustering Method Based on the Inversion Formula |
| title_short | A New Clustering Method Based on the Inversion Formula |
| title_sort | new clustering method based on the inversion formula |
| topic | artificial intelligence unsupervised machine learning clustering nonparametric density estimation inversion formula |
| url | https://www.mdpi.com/2227-7390/10/15/2559 |
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