Tensorized Parameter-free Multi-view Spectral Clustering based on Fair Representation Learning

The Multi-view clustering aims to cluster multi-view data into distinct clusters by exploring consistency and complementary information from different sources. However, most of the existing spectral clustering methods divide samples by similarity relationships, ignoring the higher-order information relationships of the underlying clusters in different views. Meanwhile, the performance of these methods involves the control of multiple hyperparameters, as multiple hyperparameters interact with each other, that tends to lead to uncontrollable performance of the methods, which further limits the practical application of the models. Existing methods treat the sample information of each view equally in the sample clustering process, which is not reasonable in real-world applications. The important information contained in each view is different, and treating each view equally will reduce the contribution of important information and increase the contribution of minor information, leading to a decrease in clustering performance. To solve these problems, this paper proposes a new spectral clustering model called Tensorized Parameter-free Multi-view Spectral Clustering based on Fair Representation Learning(TPSC). First, TPSC obtains spectral embedding matrices from different views and stacks them into tensors to mine the clustering relationships of the samples from different perspectives, as well as to explore the higher-order consistency information of each spectral embedding matrix. In addition, TPSC provides adaptive weights for the samples of each view to improve the robustness of the algorithm. The consistency relationships of different views can be mined using this strategy, and the intra-cluster relationships of sample points can be balanced from various perspectives. Finally, TPSC designs an efficient optimisation algorithm to solve the resulting optimisation problem. Extensive experiments are conducted on several baseline datasets to confirm the effectiveness of the approach.