<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, firstly, the fuzzy mathematical model and its types and algorithms of fuzzy numbers are studied. Then, the concept of fuzzy mathematics is added to cluster analysis, and fuzzy cluster analysis is carried out on samples or objects after data standardization and the construction of a similarity matrix. Then, the fuzzy C-mean FCM algorithm is proposed, and the FCM algorithm is improved by introducing the point density of data objects, the maximum minimum distance method of point density sampling, and the reduction of computation to improve the statistical function of clustering high-dimensional data. Finally, the algorithm of this paper is compared with other algorithms by AC, PR, RE, convergence speed, running time, DBI index and other indexes in order to analyze the advantages of the FCM algorithm in high dimensional data clustering statistics. The results show that the F value of the FCM algorithm in the Zoo dataset reaches 0.976, which improves 61% compared to FKM and nearly 12.6% compared to the IIFKM0 algorithm, with the best clustering effect. The DBI index of the FCM algorithm is the lowest in the four datasets, which is basically stabilized in the range of 0.5-0.6. This is better than other algorithms.</p>
</abstract>

In this paper, firstly, the fuzzy mathematical model and its types and algorithms of fuzzy numbers are studied. Then, the concept of fuzzy mathematics is added to cluster analysis, and fuzzy cluster analysis is carried out on samples or objects after data standardization and the construction of a similarity matrix. Then, the fuzzy C-mean FCM algorithm is proposed, and the FCM algorithm is improved by introducing the point density of data objects, the maximum minimum distance method of point density sampling, and the reduction of computation to improve the statistical function of clustering high-dimensional data. Finally, the algorithm of this paper is compared with other algorithms by AC, PR, RE, convergence speed, running time, DBI index and other indexes in order to analyze the advantages of the FCM algorithm in high dimensional data clustering statistics. The results show that the F value of the FCM algorithm in the Zoo dataset reaches 0.976, which improves 61% compared to FKM and nearly 12.6% compared to the IIFKM0 algorithm, with the best clustering effect. The DBI index of the FCM algorithm is the lowest in the four datasets, which is basically stabilized in the range of 0.5-0.6. This is better than other algorithms.

Statistical method for clustering high-dimensional data based on fuzzy mathematical modeling

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this paper, firstly, the fuzzy mathematical model and its types and algorithms of fuzzy numbers are studied. Then, the concept of fuzzy mathematics is added...

Statistical method for clustering high-dimensional data based on fuzzy mathematical modeling

Published Online: Dec 11, 2023

Page range: -

Received: Dec 24, 2022

Accepted: Jun 21, 2023

DOI: https://doi.org/10.2478/amns.2023.2.01452

Keywords
Fuzzy mathematical model, Data clustering, FCM algorithm, DBI index, Fuzzy C-means

© 2023 Changhui Wang, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Statistical method for clustering high-dimensional data based on fuzzy mathematical modeling

Published Online: Dec 11, 2023

Page range: -

Received: Dec 24, 2022

Accepted: Jun 21, 2023

DOI: https://doi.org/10.2478/amns.2023.2.01452

KeywordsFuzzy mathematical model, Data clustering, FCM algorithm, DBI index, Fuzzy C-means

© 2023 Changhui Wang, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Fuzzy mathematical model, Data clustering, FCM algorithm, DBI index, Fuzzy C-means