Extended Graphical Lasso for Multiple Interaction Networks for High Dimensional Omics Data

Abstract

Compositional data are quantitative descriptions of the parts of some whole, conveying relative information, which are ubiquitous in many fields. There has been a spate of interest in association networks for such data in biological and medical research, for example, microbial interaction networks. In this paper, we propose a novel method, the extended joint hub graphical lasso (EDOHA), to estimate multiple related interaction networks for high dimensional compositional data across multiple distinct classes. To be specific, we construct a convex penalized log likelihood optimization problem using log ratios of compositional data and solve it with an alternating direction method of multipliers (ADMM) algorithm. The performance of the proposed method in the simulated studies shows that EDOHA has remarkable advantages in recognizing class-specific hubs than the existing comparable methods. We also present three applications of real datasets. Biological interpretations of our results confirm those of previous studies and offer a more comprehensive understanding of the underlying mechanism in disease.