CGC: A Flexible and Robust Approach to Integrating Co-Regularized Multi-Domain Graph for Clustering

Bayesian Multi-View Clustering given complex inter-view structure

Multi-view datasets are becoming increasingly prevalent. These datasets consist of different modalities that provide complementary characterizations of the same underlying system. They can include heterogeneous types of information with complex relationships, varying degrees of missingness, and assorted sample sizes, as is often the case in multi-omic biological studies. Clustering multi-view data allows us to leverage different modalities to infer underlying systematic structure, but most existing approaches are limited to contexts in which entities are the same across views or have clear one-to-one relationships across data types with a common sample size. Many methods also make strong assumptions about the similarities of clusterings across views. We propose a Bayesian multi-view clustering approach (BMVC) which can handle the realities of multi-view datasets that often have complex relationships and diverse structure. BMVC incorporates known and complex many-to-many relationships between entities via a probabilistic graphical model that enables the joint inference of clusterings specific to each view, but where each view informs the others. Additionally, BMVC estimates the strength of the relationships between each pair of views, thus moderating the degree to which it imposes dependence constraints. We benchmarked BMVC on simulated data to show that it accurately estimates varying degrees of inter-view dependence when inter-view relationships are not limited to one-to-one correspondence. Next, we demonstrated its ability to capture visually interpretable inter-view structure in a public health survey of individuals and households in Puerto Rico following Hurricane Maria. Finally, we showed that BMVC clusters integrate the complex relationships between multi-omic profiles of breast cancer patient data, improving the biological homogeneity of clusters and elucidating hypotheses for functional biological mechanisms. We found that BMVC leverages complex inter-view structure to produce higher quality clusters than those generated by standard approaches. We also showed that BMVC is a valuable tool for real-world discovery and hypothesis generation.

Semi-Supervised Non-Negative Matrix Factorization With Dissimilarity and Similarity Regularization

In this article, we propose a semi-supervised non-negative matrix factorization (NMF) model by means of elegantly modeling the label information. The proposed model is capable of generating discriminable low-dimensional representations to improve clustering performance. Specifically, a pair of complementary regularizers, i.e., similarity and dissimilarity regularizers, is incorporated into the conventional NMF to guide the factorization. And, they impose restrictions on both the similarity and dissimilarity of the low-dimensional representations of data samples with labels as well as a small number of unlabeled ones. The proposed model is formulated as a well-posed constrained optimization problem and further solved with an efficient alternating iterative algorithm. Moreover, we theoretically prove that the proposed algorithm can converge to a limiting point that meets the Karush-Kuhn-Tucker conditions. Extensive experiments as well as comprehensive analysis demonstrate that the proposed model outperforms the state-of-the-art NMF methods to a large extent over five benchmark data sets, i.e., the clustering accuracy increases to 82.2% from 57.0%.

Multi-Domain Networks Association for Biological Data Using Block Signed Graph Clustering

Multi-domain biological network association and clustering have attracted a lot of attention in biological data integration and understanding, which can provide a more global and accurate understanding of biological phenomenon. In many problems, different domains may have different cluster structures. Due to rapid growth of data collection from different sources, some domains may be strongly or weakly associated with the other domains. A key challenge is how to determine the degree of association among different domains, and to achieve accurate clustering results by data integration. In this paper, we propose an unsupervised learning approach for multi-domain network association by using block signed graph clustering. In particular, with consistency weights calculation, the proposed algorithm automatically identify domains relevant to each other strongly (or weakly) by assigning them larger (or smaller) weights. This approach not only significantly improve clustering accuracy but also understand multi-domain networks association. In each iteration of the proposed algorithm, we update consistency weights based on cluster structure of each domain, and then make use of different sets of eigenvectors to obtain different cluster structures in each domain. Experimental results on both synthetic data sets and real data sets (including neuron activity data and gene expression data) empirically demonstrate the effectiveness of the proposed algorithm in clustering performance and in domain association capability.