Reweighted Subspace Clustering Guided by Local and Global Structure Preservation

Subspace clustering has attracted significant interest for its capacity to partition high-dimensional data into multiple subspaces. The current approaches to subspace clustering predominantly revolve around two key aspects: 1) the construction of an effective similarity matrix and 2) the pursuit of sparsity within the projection matrix. However, assessing whether the dimensionality of the projected subspace is the true dimensionality of the data is challenging. Therefore, the clustering performance may decrease when dealing with scenarios such as subspace overlap, insufficient projected dimensions, data noise, etc., since the defined dimensionality of the projected lower-dimensional space may deviate significantly from its true value. In this research, we introduce a novel reweighting strategy, which is applied to projected coordinates for the first time and propose a reweighted subspace clustering model guided by the preservation of the both local and global structural characteristics (RWSC). The projected subspaces are reweighted to augment or suppress the importance of different coordinates, so that data with overlapping subspaces can be better distinguished and the redundant coordinates produced by the predefined number of projected dimensions can be further removed. By introducing reweighting strategies, the bias caused by imprecise dimensionalities in subspace clustering can be alleviated. Moreover, global scatter structure preservation and adaptive local structure learning are integrated into the proposed model, which helps RWSC capture more intrinsic structures and its robustness and applicability can then be improved. Through rigorous experiments on both synthetic and real-world datasets, the effectiveness and superiority of RWSC are empirically verified.