Due to the uncertainty and fuzziness of information, the traditional clustering analysis method sometimes cannot meet the requirement in practice. The clustering method based on intuitionistic fuzzy set has attracted more and more scholars attention nowadays. This paper discusses the intuitionistic fuzzy C-means clustering algorithm. There are a number of clustering techniques developed in the past using different distance/similarity measure. In this paper, we proposed a improved edge density minimal spanning tree initilization method using LINEX hellinger distance based weighted LINEX intuitionistic fuzzy c means clustering. IFCM considered an uncertainty parameter called hesitation degree and incorporated a new objective function which is based upon intutionistic fuzzy entropy in the conventional Fuzzy C-means. The clustering algorithm has membership and non membership degrees as intervals. Information regarding membership and typicality degrees of samples to all clusters is given by algorithm. Furthermore, the algorithm is extended for calculating membership and updating prototypes by minimizing the new objective function of weighted LINEX intuitionistic fuzzy c-means. Finally, the developed algorithms are illustrated through conducting experiments on random dataset, partition coefficient and validation function are used to evaluate the validity of clustering also this paper compares the results of proposed method with the results of existing basic intuitionistic fuzzy c-means.
Published in | Journal of Electrical and Electronic Engineering (Volume 12, Issue 2) |
DOI | 10.11648/j.jeee.20241202.12 |
Page(s) | 36-47 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Intuitionistic Fuzzy C-means, Edge Density, Minimal Spanning Tree, Hellinger Distance, LINEX Function
Data | Intensity | Data | Intensity | ||||
---|---|---|---|---|---|---|---|
S. No | X | Y | I (v) | S. No | X | Y | I (v) |
1 | 2.50 | 3.00 | 0.75 | 11 | 15.80 | 20.50 | 0.25 |
2 | 3.80 | 3.50 | 0.50 | 12 | 11.80 | 12.50 | 0.35 |
3 | 7.00 | 1.80 | 0.15 | 13 | 15.50 | 14.50 | 0.80 |
4 | 3.10 | 4.80 | 0.18 | 14 | 5.50 | 10.50 | 0.70 |
5 | 5.50 | 7.50 | 0.45 | 15 | 18.50 | 19.50 | 0.40 |
6 | 8.50 | 9.50 | 0.75 | 16 | 12.50 | 13.80 | 0.25 |
7 | 10.80 | 11.50 | 0.60 | 17 | 21.80 | 12.50 | 0.95 |
8 | 4.20 | 3.80 | 0.25 | 18 | 19.80 | 20.50 | 0.25 |
9 | 2.80 | 1.80 | 0.45 | 19 | 19.00 | 20.00 | 0.60 |
10 | 12.50 | 20.50 | 0.65 | 20 | 11.00 | 12.00 | 0.30 |
S. No | Co-ordinate | intensity | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
x | y | I (v) | vertex | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
1 | 2.50 | 3.00 | 0.75 | 1 | 0.0000 | 0.0408 | 0.2892 | 0.0942 | 0.3091 | 0.6035 | 0.8693 | 0.0867 | 0.0449 | 1.5020 |
2 | 3.80 | 3.50 | 0.50 | 2 | 0.0000 | 0.1761 | 0.0490 | 0.1841 | 0.4338 | 0.6711 | 0.0140 | 0.0780 | 1.3012 | |
3 | 7.00 | 1.80 | 0.15 | 3 | 0.0000 | 0.2876 | 0.3871 | 0.5657 | 0.7566 | 0.1521 | 0.2048 | 1.4524 | ||
4 | 3.10 | 4.80 | 0.18 | 4 | 0.0000 | 0.1455 | 0.4181 | 0.6427 | 0.0337 | 0.1618 | 1.2158 | |||
5 | 5.50 | 7.50 | 0.45 | 5 | 0.0000 | 0.1029 | 0.2566 | 0.1525 | 0.4303 | 0.7407 | ||||
6 | 8.50 | 9.50 | 0.75 | 6 | 0.0000 | 0.0539 | 0.3941 | 0.7374 | 0.4416 | |||||
7 | 10.80 | 11.50 | 0.60 | 7 | 0.0000 | 0.6146 | 1.0036 | 0.2621 | ||||||
8 | 4.20 | 3.80 | 0.25 | 8 | 0.0000 | 0.1144 | 1.2360 | |||||||
9 | 2.80 | 1.80 | 0.45 | 9 | 0.0000 | 1.6847 | ||||||||
10 | 12.50 | 20.50 | 0.65 | 10 | 0.0000 |
S. No | Edges | LINEX HELLINGER distance | S. No | Edges | LINEX HELLINGER distance |
---|---|---|---|---|---|
1 | (1, 2) | 0.0408 | 11 | (20, 12) | 0.0051 |
2 | (2, 8) | 0.0140 | 12 | (12, 16) | 0.0120 |
3 | (8, 4) | 0.0337 | 13 | (16, 13) | 0.0714 |
4 | (8, ) | 0.1144 | 14 | (13, 15) | 0.1204 |
5 | (8, 3) | 0.1521 | 15 | (15, 19) | 0.0064 |
6 | (8, 5) | 0.1525 | 16 | (15, 18) | 0.0124 |
7 | (5, 14) | 0.0619 | 17 | (15, 11) | 0.0313 |
8 | (14, 6) | 0.0767 | 18 | (11, 10) | 0.0635 |
9 | (6, 7) | 0.0539 | 19 | (11, 17) | 0.3183 |
10 | (7, 20) | 0.0136 |
S. No | Degree of MST | S. No | Degree of MST |
---|---|---|---|
1 | 1 | 11 | 3 |
2 | 2 | 12 | 2 |
3 | 1 | 13 | 2 |
4 | 1 | 14 | 2 |
5 | 2 | 15 | 4 |
6 | 2 | 16 | 2 |
7 | 2 | 17 | 1 |
8 | 5 | 18 | 1 |
9 | 1 | 19 | 1 |
10 | 1 | 20 | 2 |
S. No | Edges | Edge density | S. No | Edges | Edge density |
---|---|---|---|---|---|
1 | (1, 2) | 0.0577 | 11 | (20, 12) | 0.0102 |
2 | (2, 8) | 0.0443 | 12 | (12, 16) | 0.0240 |
3 | (8, 4) | 0.0754 | 13 | (16, 13) | 0.1428 |
4 | (8, 9) | 0.2558 | 14 | (13, 15) | 0.3405 |
5 | (8, 3) | 0.3401 | 15 | (15, 19) | 0.0128 |
6 | (8, 5) | 0.4822 | 16 | (15, 18) | 0.0248 |
7 | (5, 14) | 0.1238 | 17 | (15, 11) | 0.1084 |
8 | (14, 6) | 0.1534 | 18 | (11, 10) | 0.1100 |
9 | (6, 7) | 0.1078 | 19 | (11, 17) | 0.5513 |
10 | (7, 20) | 0.0272 |
Co-ordinate (x, y) | intensity | appropriate cluster | |||||
---|---|---|---|---|---|---|---|
S. No | x | y | I (v) | Mem-1 | Mem-2 | Mem-3 | |
1 | 2.50 | 3.00 | 0.75 | 1 | 0.9213 | 0.0523 | 0.0265 |
2 | 3.80 | 3.50 | 0.50 | 2 | 0.9895 | 0.0072 | 0.0032 |
3 | 7.00 | 1.80 | 0.15 | 1 | 0.7820 | 0.1444 | 0.0736 |
4 | 3.10 | 4.80 | 0.18 | 1 | 0.8808 | 0.0830 | 0.0362 |
5 | 5.50 | 7.50 | 0.45 | 2 | 0.4630 | 0.4292 | 0.1077 |
6 | 8.50 | 9.50 | 0.75 | 2 | 0.0794 | 0.8548 | 0.0658 |
7 | 10.80 | 11.50 | 0.60 | 2 | 0.0046 | 0.9858 | 0.0096 |
8 | 4.20 | 3.80 | 0.25 | 5 | 0.9710 | 0.0202 | 0.0087 |
9 | 2.80 | 1.80 | 0.45 | 1 | 0.9149 | 0.0551 | 0.0299 |
10 | 12.50 | 20.50 | 0.65 | 1 | 0.0559 | 0.2632 | 0.6809 |
11 | 15.80 | 20.50 | 0.25 | 3 | 0.0199 | 0.0788 | 0.9013 |
12 | 11.80 | 12.50 | 0.35 | 2 | 0.0269 | 0.8865 | 0.0866 |
13 | 15.50 | 14.50 | 0.80 | 2 | 0.0480 | 0.3319 | 0.6201 |
14 | 5.50 | 10.50 | 0.70 | 2 | 0.2367 | 0.6315 | 0.1318 |
15 | 18.50 | 19.50 | 0.40 | 4 | 0.0026 | 0.0093 | 0.9882 |
16 | 12.50 | 13.80 | 0.25 | 2 | 0.0490 | 0.7068 | 0.2442 |
17 | 21.80 | 12.50 | 0.95 | 1 | 0.0852 | 0.2753 | 0.6395 |
18 | 19.80 | 20.50 | 0.25 | 1 | 0.0161 | 0.0513 | 0.9326 |
19 | 19.00 | 20.00 | 0.60 | 1 | 0.0050 | 0.0171 | 0.9779 |
20 | 11.00 | 12.00 | 0.30 | 2 | 0.0171 | 0.9420 | 0.0410 |
No. of iterations | No. of clusters | |
---|---|---|
FCM | 11 | 3 |
KFCM | 8 | 3 |
Edge density MST initialization method based LINEX Hellingerdistance based Intuitionistic FCM | 3 | 3 |
V_{pc} | V_{p} | |
---|---|---|
FCM | 0.8325 | 0.1825 |
KFCM | 0.8238 | 0.1720 |
MST initialization method based LINEX Hellinger Intuitionistic FCM | 0.8889 | 0.0661 |
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APA Style
M., N., Balasubramaium, K. B., S., S. (2024). MST Initialization Based Intuitionistic Fuzzy c Means Clustering Using LINEX Hellinger Distance and Its Applications. Journal of Electrical and Electronic Engineering, 12(2), 36-47. https://doi.org/10.11648/j.jeee.20241202.12
ACS Style
M., N.; Balasubramaium, K. B.; S., S. MST Initialization Based Intuitionistic Fuzzy c Means Clustering Using LINEX Hellinger Distance and Its Applications. J. Electr. Electron. Eng. 2024, 12(2), 36-47. doi: 10.11648/j.jeee.20241202.12
AMA Style
M. N, Balasubramaium KB, S. S. MST Initialization Based Intuitionistic Fuzzy c Means Clustering Using LINEX Hellinger Distance and Its Applications. J Electr Electron Eng. 2024;12(2):36-47. doi: 10.11648/j.jeee.20241202.12
@article{10.11648/j.jeee.20241202.12, author = {Nithya M. and K. Bhuvaneswari Balasubramaium and Senthil S.}, title = {MST Initialization Based Intuitionistic Fuzzy c Means Clustering Using LINEX Hellinger Distance and Its Applications }, journal = {Journal of Electrical and Electronic Engineering}, volume = {12}, number = {2}, pages = {36-47}, doi = {10.11648/j.jeee.20241202.12}, url = {https://doi.org/10.11648/j.jeee.20241202.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jeee.20241202.12}, abstract = {Due to the uncertainty and fuzziness of information, the traditional clustering analysis method sometimes cannot meet the requirement in practice. The clustering method based on intuitionistic fuzzy set has attracted more and more scholars attention nowadays. This paper discusses the intuitionistic fuzzy C-means clustering algorithm. There are a number of clustering techniques developed in the past using different distance/similarity measure. In this paper, we proposed a improved edge density minimal spanning tree initilization method using LINEX hellinger distance based weighted LINEX intuitionistic fuzzy c means clustering. IFCM considered an uncertainty parameter called hesitation degree and incorporated a new objective function which is based upon intutionistic fuzzy entropy in the conventional Fuzzy C-means. The clustering algorithm has membership and non membership degrees as intervals. Information regarding membership and typicality degrees of samples to all clusters is given by algorithm. Furthermore, the algorithm is extended for calculating membership and updating prototypes by minimizing the new objective function of weighted LINEX intuitionistic fuzzy c-means. Finally, the developed algorithms are illustrated through conducting experiments on random dataset, partition coefficient and validation function are used to evaluate the validity of clustering also this paper compares the results of proposed method with the results of existing basic intuitionistic fuzzy c-means. }, year = {2024} }
TY - JOUR T1 - MST Initialization Based Intuitionistic Fuzzy c Means Clustering Using LINEX Hellinger Distance and Its Applications AU - Nithya M. AU - K. Bhuvaneswari Balasubramaium AU - Senthil S. Y1 - 2024/08/27 PY - 2024 N1 - https://doi.org/10.11648/j.jeee.20241202.12 DO - 10.11648/j.jeee.20241202.12 T2 - Journal of Electrical and Electronic Engineering JF - Journal of Electrical and Electronic Engineering JO - Journal of Electrical and Electronic Engineering SP - 36 EP - 47 PB - Science Publishing Group SN - 2329-1605 UR - https://doi.org/10.11648/j.jeee.20241202.12 AB - Due to the uncertainty and fuzziness of information, the traditional clustering analysis method sometimes cannot meet the requirement in practice. The clustering method based on intuitionistic fuzzy set has attracted more and more scholars attention nowadays. This paper discusses the intuitionistic fuzzy C-means clustering algorithm. There are a number of clustering techniques developed in the past using different distance/similarity measure. In this paper, we proposed a improved edge density minimal spanning tree initilization method using LINEX hellinger distance based weighted LINEX intuitionistic fuzzy c means clustering. IFCM considered an uncertainty parameter called hesitation degree and incorporated a new objective function which is based upon intutionistic fuzzy entropy in the conventional Fuzzy C-means. The clustering algorithm has membership and non membership degrees as intervals. Information regarding membership and typicality degrees of samples to all clusters is given by algorithm. Furthermore, the algorithm is extended for calculating membership and updating prototypes by minimizing the new objective function of weighted LINEX intuitionistic fuzzy c-means. Finally, the developed algorithms are illustrated through conducting experiments on random dataset, partition coefficient and validation function are used to evaluate the validity of clustering also this paper compares the results of proposed method with the results of existing basic intuitionistic fuzzy c-means. VL - 12 IS - 2 ER -