Matrix-based clustering methods have drawn much attention due to their express two-dimensional (2D) data directly. However, most of the existing methods magnify the influence of outliers and noise, since the construction of objective function is based on squared Frobenius norm. In this paper, we propose a novel approach called capped \(l_{2,1}\) -norm two-dimensional k-subspace clustering (C2DkSC). Our method employs a capped \(l_{2,1}\) -norm to minimize the matrix-based within-cluster distance and meanwhile maximize the matrix-based between-cluster distance, enabling direct clustering of data samples into k-subspaces directly. In this way, on the premise of preserving the original matrix data structure, the capped \(l_{2,1}\) -norm used in C2DkSC makes it robust to outliers and noise. A regularization term is also considered in the between-cluster scatter matrix, which makes C2DkSC to avoid the small sample size (SSS) problem. C2DkSC is solved through a series of generalized eigenvalue problems. The experimental results on several image datasets demonstrate the superiority of the proposed method, especially for noise data.
