Robust Dual Clustering with Adaptive Manifold Regularization

In recent years, various data clustering algorithms have been proposed in the data mining and engineering communities. However, there are still drawbacks in traditional clustering methods which are worth to be further investigated, such as clustering for the high dimensional data, learning an ideal affinity matrix which optimally reveals the global data structure, discovering the intrinsic geometrical and discriminative properties of the data space, and reducing the noises influence brings by the complex data input. In this paper, we propose a novel clustering algorithm called robust dual clustering with adaptive manifold regularization (RDC), which simultaneously performs dual matrix factorization tasks with the target of an identical cluster indicator in both of the original and projected feature spaces, respectively. Among which, the l2,1-norm is used instead of the conventional l2-norm to measure the loss, which helps to improve the model robustness by relieving the influences by the noises and outliers. In order to better consider the intrinsic geometrical and discriminative data structure, we incorporate the manifold regularization term on the cluster indicator by using a particularly learned affinity matrix which is more suitable for the clustering task. Moreover, a novel augmented lagrangian method (ALM) based procedure is designed to effectively and efficiently seek the optimal solution of the proposed RDC optimization. Numerous experiments on the representative data sets demonstrate the superior performance of the proposed method compares to the existing clustering algorithms.