The Latent Block Model (LBM) is a prominent model-based co-clustering method, returning parametric representations of each block cluster and allowing the use of well-grounded model selection methods. The LBM, while adapted in literature to handle different feature types, cannot be applied to datasets consisting of multiple disjoint sets of features, termed views, for a common set of observations. In this work, we introduce the multi-view LBM, extending the LBM method to multi-view data, where each view marginally follows an LBM. In the case of two views, the dependence between them is captured by a cluster membership matrix, and we aim to learn the structure of this matrix. We develop a likelihood-based approach in which parameter estimation uses a stochastic EM algorithm integrating a Gibbs sampler, and an ICL criterion is derived to determine the number of row and column clusters in each view. To motivate the application of multi-view methods, we extend recent work developing hypothesis tests for the null hypothesis that clusters of observations in each view are independent of each other. The testing procedure is integrated into the model estimation strategy. Furthermore, we introduce a penalty scheme to generate sparse row clusterings. We verify the performance of the developed algorithm using synthetic datasets, and provide guidance for optimal parameter selection. Finally, the multi-view co-clustering method is applied to a complex genomics dataset, and is shown to provide new insights for high-dimension multi-view problems.

翻译：潜在块模型（LBM）是一种重要的基于模型的协同聚类方法，可返回每个块簇的参数化表示，并允许使用基于充分理论依据的模型选择方法。尽管文献中已对LBM进行改进以处理不同特征类型，但该方法无法应用于由多个互斥特征集（称为视图）构成的共享一组观测值的数据集。本文提出多视图LBM，将LBM方法扩展到多视图数据，其中每个视图边缘服从LBM分布。对于两个视图的情况，视图间的依赖关系通过簇成员矩阵捕捉，我们的目标是学习该矩阵的结构。我们开发了一种基于似然的方法，其中参数估计采用集成吉布斯采样的随机EM算法，并推导出ICL准则以确定每个视图中行簇和列簇的数量。为促进多视图方法的应用，我们扩展了近期工作，开发了针对各视图中观测簇相互独立这一零假设的假设检验。测试过程被整合到模型估计策略中。此外，我们引入惩罚机制以生成稀疏的行聚类。我们使用合成数据集验证所开发算法的性能，并提供最优参数选择的指导。最后，将多视图协同聚类方法应用于复杂基因组学数据集，结果表明该方法可为高维多视图问题提供新见解。