Fuzzy Clustering Algorithm Based on Improved Global Best-Guided Artificial Bee Colony with New Search Probability Model for Image Segmentation
Abstract
:1. Introduction
2. Related Work
3. FCM
4. The Original Artificial Bee Colony (ABC)
5. Improved Global Best-Guided Artificial Bee Colony Algorithm (IABC) Based on a New Probability Model
5.1. IABC
5.2. IABC-Based New Probability Model
Algorithm 1: PIABC |
Initialization |
1: The centroids value is initialized by Equation (3) |
2: Cycle= |
3: For each food source(i) |
4: Counter(i) = 0 |
5: End |
Repeat Employee phase |
6: FOR each employee bee(i) |
7: Generate new solutions vij in the neighbourhood of xij |
Using “Equation (7) |
8: If fit(vij) ≥ fit(xij) |
Change xij by vij |
Counter(i) = 0 |
9: Else |
Counter(i)= Counter(i) + 1 |
End if |
End for |
Onlooker Phase |
10: “Calculate probability P(xi) for the solutions |
by Equation (13). |
11: FOR each food source(i) |
12: Select a solution depending on P(xi). |
13: Generate new solution vij(o) in the neighbourhood of xij(o) |
Using “Equation (12). |
Evaluate new solution vij(o) |
If fit(vij(o)) ≥ fit(xij(o)) |
14: Change xij(o) by vij(o) |
15: Counter(i) = 0 |
Else |
“Counter(i) = Counter(i) + 1 |
16: End if |
End for |
Scouts phase |
17: FOR each food source(i) |
18: If Counter(i) > limit |
19: Abandon the food source(i) |
20: Generate new solutions using Equation (3) |
21: Memorize the best solution achieved so far. |
22: Cycle = Cycle + 1 |
23: Until termination criteria are reached |
6. The Proposed Approach (PIABC-FCM)
6.1. Initialization
6.2. Employed Bees Phase
6.3. Onlooker Bees Phase
6.4. Scout Bees Phase
6.5. Segmentation
Algorithm 2: PIABC-FCM |
Initialization |
1: The centroids value is initialized by Equation (14) |
2: Cycle = 1 |
3: For each food source(i) |
4: Counter(i) = 0 |
5: End |
Repeat Employee phase |
6: FOR each employee bee(i) |
7: Generate new solutions vij in the neighbourhood of xij” |
using Equation (7) |
8: Calculate the membership matrix hkj using Equation (2) |
Calculate the fitness value fit for the new solution |
by Equation (1) and Equation (16) |
9: If fit(vij) ≥ fit(xij) |
10: Change xij by vij |
11: Counter(i) = 0 |
12: Else |
13: Counter(i) = Counter(i) + 1 |
14: End if |
15: End for |
Onlooker Phase |
16: Calculate probability P(xi) for the solutions |
by Equation (13). |
17: FOR each food source(i) |
18: Select a solution depending on P(xi). |
19: “Generate new solution vij(o) in the neighbourhood of xij(o) |
Using Equation (12). |
Evaluate new solution vij(o) |
Calculate the membership matrix hkj using Equation (2) |
20: Calculate the fitness value fit for the new solution |
21: by Equation (1)and Equation (16) |
22: If fit(vij(o)) ≥ fit(xij(o)) |
23: Change xij(o) by vij(o) |
24: Counter(i) = 0 |
25: Else |
26: Counter(i) = Counter(i)+ 1 |
27: End if |
28: End for |
29: Scouts phase |
30: FOR each food source(i) |
31: If Counter(i) > limit |
32: Abandon the food source(i) |
33: Generate new solutions using Equation (14) |
34: Memorize the best solution achieved so far. |
35: Cycle = Cycle + |
36: Until termination criteria are reached |
37: “Do the segmentation image by |
“The optimal cluster centres for FCM. |
7. Experiments and Results
7.1. Cluster Validity Indices
7.2. Natural Images
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Approach | Population Size SN (Np) | Limit | Maximum Cycle Number (MCN) | Nonnegative Constant Parameter Z | Weighting Exponent m |
---|---|---|---|---|---|
PIABC-FCM | 100 | 100 | 2000 | 1.43 | 2 |
ABC-FCM [35] | 100 | 100 | 2000 | 1.43 | 2 |
MABC-FCM [35] | 100 | 100 | 2000 | 1.43 | 2 |
MoABC-FCM [35] | 100 | 100 | 2000 | 1.43 | 2 |
ABC-SFCM [53] | 20 | 100 | 2000 | NA | 2 |
Images | Algorithms | CE | SC | PC | S |
---|---|---|---|---|---|
LENA C = 5 | FCM | 0.9850 | 1.0684 | 0.5316 | 1.0742 × 10−4 |
PSO-FCM | 2.0900 | 5.3410 | 0.3925 | 1.4035 | |
ABC-FCM | 1.3544 | 0.5670 | 0.0608 | 0.1458 | |
MABC-FCM | 0.4714 | 0.5129 | 0.7364 | 0.5962 | |
MoABC-FCM | 0.4712 | 0.4840 | 0.7364 | 0.7261 | |
EBO–FCM | 0.4335 | 0.0273 | 0.7745 | 0.0591 | |
BBO–FCM | 0.4335 | 0.0266 | 0.7745 | 0.059 | |
IABC-FCM | 0.2619 | 0.0348 | 0.7125 | 1.025 | |
PIABC-FCM | 0.1128 | 0.0215 | 0.8144 | 1.2370 |
Images | Algorithms | CE | SC | PC | S |
---|---|---|---|---|---|
Baboon C = 4 | FCM | 0.5897 | 0.8642 | 0.7063 | 0.1862 |
PSO-FCM | 0.5372 | 0.9271 | 0.7509 | 1.0964 | |
ABC-FCM | 0.5316 | 0.3460 | 0.7510 | 1.6614 | |
MABC-FCM | 0.4388 | 0.1522 | 0.7511 | 2.9273 | |
MoABC-FCM | 0.4372 | 0.1003 | 0.7524 | 1.8163 | |
BBO–FCM | 0.4294 | 0.0260 | 0.7763 | 0.0569 | |
EBO–FCM | 0.6186 | 0.0355 | 0.6532 | 15.6874 | |
IABC-FCM | 0.3903 | 0.0370 | 0.7721 | 2.6155 | |
PIABC-FCM | 0.1790 | 0.0201 | 0.7917 | 2.9803 |
Images | Algorithms | CE | SC | PC | S |
---|---|---|---|---|---|
Cameraman C = 5 | FCM | 0.3104 | 0.1960 | 0.7515 | 0.0031 |
PSO-FCM | 0.3086 | 0.1441 | 0.7564 | 1.1370 | |
ABC-FCM | 0.3052 | 0.1108 | 0.7574 | 0.7516 | |
MABC-FCM | 0.2968 | 0.0995 | 0.7583 | 0.2269 | |
MoABC-FCM | 0.2964 | 0.0931 | 0.7868 | 0.3214 | |
BBO–FCM | 0.4326 | 0.0264 | 0.7748 | 0.0598 | |
EBO–FCM | 0.4326 | 0.0261 | 0.7745 | 0.0571 | |
IABC-FCM | 0.2670 | 0.3194 | 0.0772 | 0.7924 | |
PIABC-FCM | 0.1981 | 0.0202 | 0.7990 | 0.8690 |
Images | Algorithms | CE | SC | PC | S |
---|---|---|---|---|---|
Pepper C = 5 | FCM | 0.4896 | 0.9661 | 0.7249 | 0.0262 |
PSO-FCM | 0.4852 | 0.9725 | 0.7326 | 0.8170 | |
ABC-FCM | 0.4824 | 0.4251 | 0.7330 | 0.9293 | |
MABC-FCM | 0.4810 | 0.2537 | 0.7343 | 2.2715 | |
MoABC-FCM | 0.4810 | 0.1981 | 0.7344 | 1.0421 | |
BBO–FCM | 0.4324 | 0.0262 | 0.7748 | 0.0569 | |
EBO–FCM | 0.4326 | 0.0349 | 0.6991 | 0.0571 | |
IABC-FCM | 0.4051 | 0.2273 | 0.7410 | 1.9552 | |
PIABC-FCM | 0.2539 | 0.0182 | 0.7869 | 2.9160 |
Images | Algorithms | CE | SC | PC | S |
---|---|---|---|---|---|
Airplane C = 5 | FCM | 0.3848 | 0.5172 | 0.7237 | 0.0016 |
PSO-FCM | 0.2858 | 0.3640 | 0.7466 | 0.1520 | |
ABC-FCM | 0.2831 | 0.2257 | 0.7470 | 0.0317 | |
MABC-FCM | 0.2825 | 0.1868 | 0.7567 | 0.0954 | |
MoABC-FCM | 0.2810 | 0.0935 | 0.7567 | 0.0982 | |
BBO–FCM | 0.4323 | 0.0258 | 0.7748 | 0.0576 | |
EBO–FCM | 0.4323 | 0.0258 | 0.7748 | 0.0578 | |
IABC-FCM | 0.2004 | 0.0164 | 0.7841 | 0.1123 | |
PIABC-FCM | 0.1308 | 0.0115 | 0.7990 | 0.1164 |
Algorithm | Mean Rank |
---|---|
PIABC_FCM | 1 |
IABC_FCM | 2 |
MoABC_FCM | 4.1 |
MABC_FCM | 4.9 |
EBO–FCM | 5.3 |
ABC_FCM | 6.2 |
BBO–FCM | 6.7 |
PSO_FCM | 7.2 |
FCM | 7.6 |
Algorithm | Mean Rank |
---|---|
PIABC_FCM | 1 |
BBO–FCM | 2.7 |
EBO–FCM | 2.7 |
MoABC_FCM | 4.6 |
IABC_FCM | 4.8 |
MABC_FCM | 5.8 |
ABC_FCM | 6.8 |
FCM | 8.2 |
PSO_FCM | 8.4 |
Algorithm | Mean Rank |
---|---|
PIABC_FCM | 9 |
EBO–FCM | 7.4 |
MoABC_FCM | 6 |
IABC_FCM | 5.4 |
MABC_FCM | 5 |
BBO–FCM | 4.4 |
ABC_FCM | 3.2 |
PSO_FCM | 2.6 |
FCM | 2 |
Algorithm | Mean Rank |
---|---|
PIABC_FCM | 8.2 |
IABC_FCM | 6.8 |
PSO_FCM | 6.8 |
MABC_FCM | 5.8 |
MoABC_FCM | 5.6 |
ABC_FCM | 4.2 |
BBO–FCM | 4 |
EBO–FCM | 2.4 |
FCM | 1.2 |
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Alomoush, W.; Khashan, O.A.; Alrosan, A.; Houssein, E.H.; Attar, H.; Alweshah, M.; Alhosban, F. Fuzzy Clustering Algorithm Based on Improved Global Best-Guided Artificial Bee Colony with New Search Probability Model for Image Segmentation. Sensors 2022, 22, 8956. https://doi.org/10.3390/s22228956
Alomoush W, Khashan OA, Alrosan A, Houssein EH, Attar H, Alweshah M, Alhosban F. Fuzzy Clustering Algorithm Based on Improved Global Best-Guided Artificial Bee Colony with New Search Probability Model for Image Segmentation. Sensors. 2022; 22(22):8956. https://doi.org/10.3390/s22228956
Chicago/Turabian StyleAlomoush, Waleed, Osama A. Khashan, Ayat Alrosan, Essam H. Houssein, Hani Attar, Mohammed Alweshah, and Fuad Alhosban. 2022. "Fuzzy Clustering Algorithm Based on Improved Global Best-Guided Artificial Bee Colony with New Search Probability Model for Image Segmentation" Sensors 22, no. 22: 8956. https://doi.org/10.3390/s22228956