Tensorized topological graph learning for generalized incomplete multi-view clustering

The success of the current multi-view clustering lies in the default assumption of completeness on each view, while it is hardly satisfied for real-world applications. Incomplete multi-view clustering (IMC) studies clustering multi-view instances that are partially observed due to data corruption or sensor failure. Although making some progress, the current research suffers from the following obstacles: (1) Existing works are always built on pairwise similarity measurement, which cannot fully capture the topological structure of incomplete multi-view samples for precise clustering; (2) Due to the absence of partially-observed samples across multiple views, how could we recover and enhance the high-order similarities across different views becomes one of the main bottlenecks of IMC; (3) Current research mainly aims to handle specific dual-view IMC, which greatly limits the deployment in real-world applications. In this paper, we propose a novel Tensorized Topological Graph Learning (TTGL) for the generalized incomplete multi-view clustering, which jointly considers the topological graph construction, missing feature completion, and high-order uncertain correlation enhancement. Specifically, instead of using pairwise similarity measurement, we formulate a consensus topological graph construction module, which can coalesce affinity matrices to analyze the topological structure of incomplete multi-view data. Moreover, we build an iterative missing similarity imputation scheme for feature completion, which ensures the intrinsic similarity preservation on observed instances as well as an imputation on unobserved ones. Furthermore, a low-rank tensor structure is imposed to capture the high-order similarities via both feature and similarity enhancement and completion across different views. Our method can cluster incomplete data with an arbitrary number of views and any missing statuses. Extensive experiments on several benchmark datasets validate the effectiveness of our method when compared with a series of state-of-the-art IMC clustering algorithms. The source code of our TTGL is available at: https://github.com/DarrenZZhang/TTGL.