Abstract The key point of anomaly detection on attributed networks lies in the seamless integration of network structure information and attribute information. A vast majority of existing works are mainly based on the Homophily assumption that implies the nodal attribute similarity of connected nodes. Nonetheless, this assumption is untenable in practice as the existence of noisy and structurally irrelevant attributes may adversely affect the anomaly detection performance. Despite the fact that recent attempts perform subspace selection to address this issue, these algorithms treat subspace selection and anomaly detection as two separate steps which often leads to suboptimal solutions. In this paper, we investigate how to fuse attribute and network structure information more synergistically to avoid the adverse effects brought by noisy and structurally irrelevant attributes. Methodologically, we propose a novel joint framework to conduct attribute selection and anomaly detection as a whole based on CUR decomposition and residual analysis. By filtering out noisy and irrelevant node attributes, we perform anomaly detection with the remaining representative attributes. Experimental results on both synthetic and real-world datasets corroborate the effectiveness of the proposed framework.