Nonlinear Joint Latent Variable Models and Integrative Tumor Subtype Discovery

Integrative analysis has been used to identify clusters by integrating data of disparate types, such as deoxyribonucleic acid (DNA) copy number alterations and DNA methylation changes for discovering novel subtypes of tumors. Most existing integrative analysis methods are based on joint latent variable models, which are generally divided into two classes: joint factor analysis and joint mixture modeling, with continuous and discrete parameterizations of the latent variables respectively. Despite recent progresses, many issues remain. In particular, existing integration methods based on joint factor analysis may be inadequate to model multiple clusters due to the unimodality of the assumed Gaussian distribution, while those based on joint mixture modeling may not have the ability for dimension reduction and/or feature selection. In this paper, we employ a nonlinear joint latent variable model to allow for flexible modeling that can account for multiple clusters as well as conduct dimension reduction and feature selection. We propose a method, called integrative and regularized generative topographic mapping (irGTM), to perform simultaneous dimension reduction across multiple types of data while achieving feature selection separately for each data type. Simulations are performed to examine the operating characteristics of the methods, in which the proposed method compares favorably against the popular iCluster that is based on a linear joint latent variable model. Finally, a glioblastoma multiforme (GBM) dataset is examined.