Simultaneous clustering of multiview biomedical data using manifold optimization

Abstract

Motivation Multiview clustering has attracted much attention in recent years. Several models and algorithms have been proposed for finding the clusters. However, these methods are developed either to find the consistent/common clusters across different views, or to identify the differential clusters among different views. In reality, both consistent and differential clusters may exist in multiview datasets. Thus, development of simultaneous clustering methods such that both the consistent and the differential clusters can be identified is of great importance. Results In this paper, we proposed one method for simultaneous clustering of multiview data based on manifold optimization. The binary optimization model for finding the clusters is relaxed to a real value optimization problem on the Stiefel manifold, which is solved by the line-search algorithm on manifold. We applied the proposed method to both simulation data and four real datasets from TCGA. Both studies show that when the underlying clusters are consistent, our method performs competitive to the state-of-the-art algorithms. When there are differential clusters, our method performs much better. In the real data study, we performed experiments on cancer stratification and differential cluster (module) identification across multiple cancer subtypes. For the patients of different subtypes, both consistent clusters and differential clusters are identified at the same time. The proposed method identifies more clusters that are enriched by gene ontology and KEGG pathways. The differential clusters could be used to explain the different mechanisms for the cancer development in the patients of different subtypes. Availability and implementation Codes can be downloaded from: http://homepage.fudan.edu.cn/sqzhang/files/2018/12/MVCMOcode.zip. Supplementary information Supplementary data are available at Bioinformatics online.

Multiview learning for understanding functional multiomics

“…Most of the NMF-based methods are based on an alternating optimization technique, whereas spectral methods (e.g., spectral clustering) are based on solving a generalized eigenproblem. Spectral clustering can also be solved by an optimization procedure on a matrix manifold, such as Stiefel manifold [66]. Most deep learning approaches are solved by backpropagation and stochastic gradient descent methods, whereas many other solvers are based on a convex relaxation [64,97,98,76].…”

“…Yu and colleagues [66] proposed a method for simultaneous clustering of multiview cancer data using a multiview spectral clustering method. However, their computational method substantially differs from other spectral clustering approaches in that, rather than calculating eigenvectors, the optimization procedure therein involves of a line-search algorithm on Stiefel manifold.…”

Estimation of gender-specific connectional brain templates using joint multi-view cortical morphological network integration

“…Multi-view clustering using optimization manifolds (Step1) Unlike other methods (Dhifallah et al 2019) which generate CBTs by directly fusing heterogeneous connectional brain networks of a given population, first, we group subjects into more homogenous clusters by leveraging a multi-view clustering model developed by (Yu et al 2019), which returns the aligned clusters in each view. Thus, both the consistent clusters and the differential clusters are identified in each view.…”

“…Since we treat all views equally, we consider that networks are on the same level and we set β = 1. To solve the optimization problem (4), we implement the line search algorithm on Stiefel manifold (Yu et al 2019) to find the optimal solution of the objective function trace(U T LU) (Absil et al 2008). This approach includes three steps.…”

Clustering of Cancer Data Based on Stiefel Manifold for Multiple Views

“…However, the method (Kumar et al, 2011) tended to obtain the local optimal as described above, and the methods (Zhang et al, 2015;Chen et al, 2017) relax excessively the original multi-view point specific tangent condition, so that the information of each viewpoint may be lost. In the paper (Yu et al, 2019), the authors proposed the Multi-View Clustering using Manifold Optimization (MVCMO) method considering the diversity of the cluster. Consistent clusters and different clusters can be identified in each group.…”