Most Constrained Laplacian Rank methods rely on first-order similarity graphs, which capture only direct neighbor relations and constrain the discovery of latent high-order structures, such as indirect connections, particularly in single-view settings. Furthermore, fusing simply multi-order proximity matrices without structural alignment results in redundancy and inconsistency. As the proximity order increases, it tends to introduce irrelevant high-order information, degrading clustering performance and stability. To address these issues, we propose a high-order clustering method that constructs anchor-sample high-order bipartite graphs using recursively computed SVD-based similarity matrices, effectively capturing indirect neighborhood relations and enhancing global structural representation. A unified feature embedding space is designed to enable cross-order knowledge transfer via co-clustering, where low-order embeddings guide high-order representations, improving structural consistency and feature discriminability while filtering irrelevant links. Additionally, nuclear norm and sparsity regularization are applied to suppress redundancy and enhance robustness. Experiments on five public datasets show that our method consistently outperforms state-of-the-art approaches across four clustering metrics, validating its effectiveness and resilience.