Ensemble clustering with low-rank optimal Laplacian matrix learning

Abstract

The co-association (CA) matrix that describes connection relationship between instances is of importance for ensemble clustering. Existing ensemble clustering methods demonstrate that Laplacian matrix can help to improve the quality of CA matrix and finally produce better clustering results. However, they usually consider the first-order information only and ignore the higher-order information that exists among base clustering results. To address this issue, this paper introduces the theory of higher-order connectivity in ensemble clustering for the first time and further proposes a low-rank optimal Laplacian matrix learning (LROLML) approach for ensemble clustering. Specifically, the proposed LROLML first constructs a set of multi-order Laplacian matrices and then learns the optimal Laplacian matrix from the Laplacian matrix set with different orders. The optimal Laplacian matrix mines more higher-order link information, thereby improving the ensemble performance. We use alternating direction method of multipliers (ADMM) to solve the optimization problem and then apply the average-link hierarchical agglomerative clustering to get the final result. We conducted extensive experiments on 20 popular datasets to validate the proposed LROLML, which is compared with two types of results of basic k-means clustering and seven state-of-the-art ensemble clustering models. The results demonstrate the LROLML is superior to the compared models, showing that the LROLML is promising for ensemble clustering.