Variable-weighted multi-view collaborative fuzzy clustering with consideration of entropy and separability

Collaborative clustering methods have been widely applied in complex object classification tasks. However, as data complexity increases, the relative importance of view clustering results often varies across different scenarios of multi-view collaborative analysis. To address this issue, this paper proposes an improved mathematical model for multi-view collaborative fuzzy clustering, which incorporates variable weights and considers both entropy and separability. To solve this problem, an enhanced variable-weighted multi-view collaborative fuzzy clustering method (abbreviated as VW-CoFKM) algorithm is proposed. Initially, this paper discusses fuzzy C-means clustering (FCM) and collaborative fuzzy C-means (CoFKM). Then, an improved mathematical model for the multi-view collaborative fuzzy clustering problem with variable weights is established. This model incorporates a view-weight based on the state of each view, taking into account the importance of clustering for each perspective, and constructs a view-weight adjuster from the standpoint of the separability of each view’s clustering. Additionally, a regularization term based on Shannon entropy is integrated into the objective function to prevent over-fitting of training data. Subsequently, a necessary condition for the optimal solution of this model is presented after transforming it into an unconstrained optimization problem using the Lagrange multiplier method. Based on this conclusion, a heuristic variable-weighted multi-view collaborative fuzzy clustering algorithm is constructed. Finally, the effectiveness of this algorithm is validated through simulation experiments on University of California Irvine (UCI) public datasets and electric power load datasets. The simulation results demonstrate that, compared with state-of-the-art clustering methods such as FCM, CoFKM, and WCoFKM, the proposed algorithm exhibits distinct advantages.