# Fusing Local and Global Information for One-Step Multi-View Subspace Clustering
## 2 Related Work
[28] propose to combine anchor learning and graph construction into a unified optimization framework, allowing the learned anchors to represent the actual latent data distribution more accurately, leading to a more discriminative clustering structure. Matrix factorization-based methods refer to obtaining consistent latent representations through matrix factorization. Specifically, a given data matrix can be represented by the product of two or more low-dimensional matrices. [PERSON] et al. [29] extended the traditional single-view non-negative matrix factorization algorithm to multi-view application scenarios and proposed a multi-view clustering algorithm based on non-negative matrix factorization. [PERSON] et al. [30] propose to exploit group sparsity inducing norm in a matrix factorization framework to learn shared sparse subspace representations. Recently, [PERSON] et al. [31] proposed a diversity non-negative matrix factorization multi-view clustering method by introducing a new diversity term to increase the diversity among multi-view representations and linearize the running time. [PERSON] et al. [32] propose a new joint clustering method named Fast Multi-view Matrix Tri-Factorization to reduce the information loss in the matrix factorization process, while reducing the computational complexity and improving the operational efficiency. [PERSON] et al. [33] propose a novel multi-view matrix factorization-based clustering method, which proposes to consider the higher-order relationships among features using an optimal graph regularization strategy and introduces the Hilbert-Schmidt independence criterion (HSIC) to fully explore the complementary information in different views. In addition, researchers have extended matrix factorization from the perspective of intact space learning [34]. For example, [PERSON] et al. [35] propose a latent multi-view subspace clustering that utilizes the latent representation for subspace clustering. [PERSON] et al. [36] propose a flexible multi-view representation learning that utilizes the kernel dependence measure to obtain a latent representation from different views for subspace clustering. [PERSON] et al. [37] propose a multi-view subspace clustering method that fuses graph learning, latent representation, and clustering into a unified optimization framework. Graph-based methods provides an effective way to solve the nonlinearly separated problems. For example, [PERSON] et al. [38] propose a fusion process using linked matrix factorization to fuse the graph matrices corresponding to all views with multiple sources of information. [PERSON] et al. [39] propose a multi-view graph clustering method based on the idea of manifold learning that can perform local structure learning and multi-view clustering at the same time and can also adaptively learn the weights corresponding to each view. Meanwhile, [PERSON] et al. [40] propose an automatic weighting method to fuse a series of view-specific low-quality graphs into a high-quality unified graph, while extending the Laplacian rank approach to multi-view learning. Similarly, [PERSON] et al. [41] further design a notable clustering method based on twostep multiple graph fusion strategy. Recently, [PERSON] et al. [42] proposed a method to learn a consensus graph matrix by all views by minimizing disagreement between different views and constraining the rank of the Laplacian matrix. [PERSON] et al. [43] propose another graph-based multi-view clustering method that automatically fuses multiple graph matrices to generate a unified graph matrix. The learned unified graph matrix can help the graph matrices of all views and gives the clustering indicator matrix. Recently, [PERSON] et al. [44] proposed to minimize the divergence between graphs using tensor Schatten \(p\)-norm regularization and integrate the tensor Schatten \(p\)-norm regularization and the manifold learning regularization into a unified framework to learn a shared common graph.