Single phase multi-view clustering using unified graph learning and spectral representation

The most widely used multi-view clustering approaches can be classified into different groups: Subspace multi-view clustering algorithms, multi-view kernel approaches, matrix factorization approaches, and spectral clustering algorithms. Most approaches rely on combining predefined individual similarity matrices from multiple views, and then estimate the common similarity matrix. Therefore, their performance can be severely affected by noisy original similarity matrices. Moreover, most of these methods integrate different spectral projection matrices of each view together, which can also affect the clustering results.To address these shortcomings, we propose a single-phase multiview clustering method with Consensus Graph Learning and Spectral Representation (MCGLSR) in this paper. Instead of directly integrating the similarity matrices of the different views, which could introduce noise, our proposed method jointly generates similarity graphs of the views and their common similarity matrix (graph matrix) using a unified global objective function. At this stage, the similarity matrices of the different views are enforced to be sufficiently similar, which eliminates the problem of noise and promotes a clearer unified data structure. Moreover, our proposed objective function is able to recover the common spectral projection and soft cluster assignments based on the common graph structure. The proposed method takes as input a kernelized representation of the views features and directly provides the individual graphs, the common graph, the common spectral representation, and the cluster assignments. Our technique allows us to obtain the final cluster assignments without requiring an external clustering algorithm. Several real-world datasets are used to evaluate our technique and demonstrate its efficacy. The code of the proposed method will be available at the following link: https://github .com /SallyHajjar /MCGLSR .git.