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A New Clustering Method Based on the Inversion Formula

Author

Listed:
  • 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

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.

Suggested Citation

  • Mantas Lukauskas & Tomas Ruzgas, 2022. "A New Clustering Method Based on the Inversion Formula," Mathematics, MDPI, vol. 10(15), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2559-:d:869433
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    References listed on IDEAS

    as
    1. Jonas Rothfuss & Fabio Ferreira & Simon Walther & Maxim Ulrich, 2019. "Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks," Papers 1903.00954, arXiv.org, revised Apr 2019.
    2. 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.
    3. Kemal Polat, 2012. "Classification of Parkinson's disease using feature weighting method on the basis of fuzzy C-means clustering," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(4), pages 597-609.
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    Cited by:

    1. Mantas Lukauskas & Tomas Ruzgas, 2023. "Reduced Clustering Method Based on the Inversion Formula Density Estimation," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    2. 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.
    3. Jinshi Yu & Qi Duan & Haonan Huang & Shude He & Tao Zou, 2023. "Effective Incomplete Multi-View Clustering via Low-Rank Graph Tensor Completion," Mathematics, MDPI, vol. 11(3), pages 1-18, January.

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