Multi-view data can be generated from diverse sources, by different technologies, and in multiple modalities. In various fields, integrating information from multi-view data has pushed the frontier of discovery. In this paper, we develop a new approach for multi-view clustering, which overcomes the limitations of existing methods such as the need of pooling data across views, restrictions on the clustering algorithms allowed within each view, and the disregard for complementary information between views. Our new method, called CPS-merge analysis, merges clusters formed by the Cartesian product of single-view cluster labels, guided by the principle of maximizing clustering stability as evaluated by CPS analysis. In addition, we introduce measures to quantify the contribution of each view to the formation of any cluster. CPS-merge analysis can be easily incorporated into an existing clustering pipeline because it only requires single-view cluster labels instead of the original data. We can thus readily apply advanced single-view clustering algorithms. Importantly, our approach accounts for both consensus and complementary effects between different views, whereas existing ensemble methods focus on finding a consensus for multiple clustering results, implying that results from different views are variations of one clustering structure. Through experiments on single-cell datasets, we demonstrate that our approach frequently outperforms other state-of-the-art methods.

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