TY - JOUR
T1 - Unconstrained Fuzzy C-Means Algorithm
AU - Nie, Feiping
AU - Zhang, Runxin
AU - Yu, Weizhong
AU - Li, Xuelong
N1 - Publisher Copyright:
© 1979-2012 IEEE.
PY - 2025
Y1 - 2025
N2 - 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.
AB - 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.
KW - Fuzzy C-Means
KW - gradient descent
KW - local minimum
KW - membership matrix
UR - http://www.scopus.com/inward/record.url?scp=105003047747&partnerID=8YFLogxK
U2 - 10.1109/TPAMI.2025.3532357
DO - 10.1109/TPAMI.2025.3532357
M3 - 文章
C2 - 40031209
AN - SCOPUS:105003047747
SN - 0162-8828
VL - 47
SP - 3440
EP - 3451
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
IS - 5
ER -