Unconstrained Fuzzy C-Means Algorithm
Fuzzy C-Means algorithm (FCM) is one of the most commonly used fuzzy clustering algorithm, which uses the alternating optimization algorithm to update the membership matrix and the cluster center matrix. FCM achieves effective results in clustering tasks. However, due to many constraints, the object...
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| Published in: | IEEE transactions on pattern analysis and machine intelligence Vol. 47; no. 5; pp. 3440 - 3451 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01.05.2025
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| ISSN: | 0162-8828, 1939-3539, 2160-9292, 1939-3539 |
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| Abstract | Fuzzy C-Means algorithm (FCM) is one of the most commonly used fuzzy clustering algorithm, which uses the alternating optimization algorithm to update the membership matrix and the cluster center matrix. FCM achieves effective results in clustering tasks. However, due to many constraints, the objective function is inconvenient to optimize directly and is prone to converges to a suboptimal local minimum, which affects the clustering performance. In this paper, we propose a minimization problem equivalent to FCM. Firstly, we use the optimal solution when fixing the cluster center matrix to replace the membership matrix, transforming the original constrained optimization problem into an unconstrained optimization problem, thus reducing the number of variables. We then use gradient descent instead of alternating optimization to solve the model, so we call this model UC-FCM. Extensive experimental results show that UC-FCM can obtain better local minimum and achieve superior clustering performance compared to FCM under the same initialization. Moreover, UC-FCM is also competitive compared with other advanced clustering algorithms. |
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| AbstractList | Fuzzy C-Means algorithm (FCM) is one of the most commonly used fuzzy clustering algorithm, which uses the alternating optimization algorithm to update the membership matrix and the cluster center matrix. FCM achieves effective results in clustering tasks. However, due to many constraints, the objective function is inconvenient to optimize directly and is prone to converges to a suboptimal local minimum, which affects the clustering performance. In this paper, we propose a minimization problem equivalent to FCM. Firstly, we use the optimal solution when fixing the cluster center matrix to replace the membership matrix, transforming the original constrained optimization problem into an unconstrained optimization problem, thus reducing the number of variables. We then use gradient descent instead of alternating optimization to solve the model, so we call this model UC-FCM. Extensive experimental results show that UC-FCM can obtain better local minimum and achieve superior clustering performance compared to FCM under the same initialization. Moreover, UC-FCM is also competitive compared with other advanced clustering algorithms. Fuzzy C-Means algorithm (FCM) is one of the most commonly used fuzzy clustering algorithm, which uses the alternating optimization algorithm to update the membership matrix and the cluster center matrix. FCM achieves effective results in clustering tasks. However, due to many constraints, the objective function is inconvenient to optimize directly and is prone to converges to a suboptimal local minimum, which affects the clustering performance. In this paper, we propose a minimization problem equivalent to FCM. Firstly, we use the optimal solution when fixing the cluster center matrix to replace the membership matrix, transforming the original constrained optimization problem into an unconstrained optimization problem, thus reducing the number of variables. We then use gradient descent instead of alternating optimization to solve the model, so we call this model UC-FCM. Extensive experimental results show that UC-FCM can obtain better local minimum and achieve superior clustering performance compared to FCM under the same initialization. Moreover, UC-FCM is also competitive compared with other advanced clustering algorithms.Fuzzy C-Means algorithm (FCM) is one of the most commonly used fuzzy clustering algorithm, which uses the alternating optimization algorithm to update the membership matrix and the cluster center matrix. FCM achieves effective results in clustering tasks. However, due to many constraints, the objective function is inconvenient to optimize directly and is prone to converges to a suboptimal local minimum, which affects the clustering performance. In this paper, we propose a minimization problem equivalent to FCM. Firstly, we use the optimal solution when fixing the cluster center matrix to replace the membership matrix, transforming the original constrained optimization problem into an unconstrained optimization problem, thus reducing the number of variables. We then use gradient descent instead of alternating optimization to solve the model, so we call this model UC-FCM. Extensive experimental results show that UC-FCM can obtain better local minimum and achieve superior clustering performance compared to FCM under the same initialization. Moreover, UC-FCM is also competitive compared with other advanced clustering algorithms. |
| Author | Yu, Weizhong Li, Xuelong Zhang, Runxin Nie, Feiping |
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| SubjectTerms | Clustering algorithms Convergence Fuzzy C-Means gradient descent Linear programming local minimum membership matrix Noise Optimization Sensitivity Symbols Time complexity Vectors |
| Title | Unconstrained Fuzzy C-Means Algorithm |
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