Tensorized diversity and consistency with Laplacian manifold for multi-view clustering

The advantage of multi-view clustering lies in its ability to leverage the diversity and consistency among multiple views to better capture the intrinsic structure of the data. However, existing multi-view methods treat diversity and consistency as a set of opposing attributes, overlooking their inherent connections. Meanwhile, the complete information across multiple views is not fully utilized. To address these issues, this paper proposes the tensorized diversity and consistency with Laplacian manifold for multi-view clustering method (TDCLM). Specifically, starting from the self-expressive property of the original data, we obtain the diversity graphs and the consistency graph, and for the first time, we combined Laplacian manifold constraints to strengthen the relationship between diversity and consistency while jointly optimizing the diversity graphs and the consistency graph. Additionally, we innovatively combine the diversity graphs and the consistency graph into a tensor and subject it to the constraint of tensor nuclear norm. By doing so, we not only obtain the complete information between multiple views but also enable the mutual learning and mutual enhancement of the diversity graphs and the consistency graph. Finally, by adopting the augmented Lagrange multiplier method, we integrate the two steps into a comprehensive framework. The TDCLM shows a performance enhancement of up to 25.85%, with experimental results across diverse datasets demonstrating that the TDCLM algorithm surpasses the state-of-the-art algorithms. In other words, these experimental results validate the importance of obtaining complete information from multiple views and effectively leveraging the diversity and consistency inherent in this complete information. The code is publicly available at https://github.com/TongWuahpu/TDCLM.