Subspace clustering groups a set of data into their underlying subspaces according to the low-dimensional subspace structure of data. The performance of spectral clustering-based approaches heavily depends on the learned block diagonal structure of the affinity matrix. However, this structure is fragile in the presence of noise within data. As such, the clustering performance is degraded significantly. On the other hand, in practice, we often do not have a prior knowledge of error distribution at all, which results in that we cannot model the error with suitable norms. To this end, in this paper, we propose a robust block diagonal representation learning for subspace clustering. Specifically, a non-convex regularizer is directly utilized to constrain the affinity matrix for exploiting the block diagonal structure. Furthermore, we use a penalty matrix to adaptively weight the reconstruction error so that we can handle noise without prior knowledge. We also devise an effective method to compute the parameters related to this matrix, reducing the complexity of the parameter trains. Experimental results show that our method outperformed the state-of-the-art methods on both synthetic data and real-world datasets.

子空间聚类根据数据的低维子空间结构将一组数据分组到其基础子空间中。基于频谱聚类的方法的性能在很大程度上取决于所学习的亲和矩阵的块对角线结构。但是，这种结构在数据中存在噪声的情况下是脆弱的。这样，群集性能会大大降低。另一方面，在实践中，我们通常往往根本不具备错误分布的先验知识，这导致我们无法使用合适的准则对错误进行建模。为此，在本文中，我们提出了一种用于子空间聚类的鲁棒块对角表示学习方法。具体地，非凸正则化器直接用于约束亲和度矩阵以利用块对角线结构。此外，我们使用惩罚矩阵自适应地加权重建误差，以便我们无需先验知识即可处理噪声。我们还设计了一种有效的方法来计算与此矩阵相关的参数，从而降低了参数序列的复杂性。实验结果表明，在合成数据和真实数据集上，我们的方法均优于最新方法。