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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. 

The architectures of many neural networks rely heavily on the underlying grid associated with the variables, for instance, the lattice of pixels in an image. For general biomedical data without a grid structure, the multi‐layer perceptron (MLP) and deep belief network (DBN) are often used. However, in these networks, variables are treated homogeneously in the sense of network structure; and it is difficult to assess their individual importance. In this paper, we propose a novel neural network called Variable‐block tree Net (VtNet) whose architecture is determined by an underlying tree with each node corresponding to a subset of variables. The tree is learned from the data to best capture the causal relationships among the variables. VtNet contains a long short‐term memory (LSTM)‐like cell for every tree node. The input and forget gates of each cell control the information flow through the node, and they are used to define a significance score for the variables. To validate the defined significance score, VtNet is trained using smaller trees with variables of low scores removed. Hypothesis tests are conducted to show that variables of higher scores influence classification more strongly. Comparison is made with the variable importance score defined in Random Forest from the aspect of variable selection. Our experiments demonstrate that VtNet is highly competitive in classification accuracy and can often improve accuracy by removing variables with low significance scores.