Spectral-type subspace clustering algorithms have shown excellent performance in many subspace clustering applications. The existing spectral-type subspace clustering algorithms either focus on designing constraints for the reconstruction coefficient matrix or feature extraction methods for finding latent features of original data samples. In this paper, inspired by graph convolutional networks, we use the graph convolution technique to develop a feature extraction method and a coefficient matrix constraint simultaneously. And the graph-convolutional operator is updated iteratively and adaptively in our proposed algorithm. Hence, we call the proposed method adaptive graph convolutional subspace clustering (AGCSC). We claim that by using AGCSC, the aggregated feature representation of original data samples is suitable for subspace clustering, and the coefficient matrix could reveal the subspace structure of the original data set more faithfully. Finally, plenty of subspace clustering experiments prove our conclusions and show that AGCSC outperforms some related methods as well as some deep models.

翻译：谱型子空间聚类算法在许多子空间聚类应用中表现出色。现有谱型子空间聚类算法要么专注于设计重建系数矩阵的约束条件，要么致力于寻找原始数据样本潜在特征的特征提取方法。受图卷积网络启发，本文同时利用图卷积技术开发了一种特征提取方法和一种系数矩阵约束。此外，图卷积算子在我们提出的算法中进行迭代自适应更新。因此，我们将所提方法称为自适应图卷积子空间聚类（AGCSC）。我们声称，通过使用AGCSC，原始数据样本的聚合特征表示适用于子空间聚类，且系数矩阵能更忠实地揭示原始数据集的子空间结构。最后，大量子空间聚类实验验证了我们的结论，并表明AGCSC优于某些相关方法及部分深度模型。