An ensemble learning method for joint kernel association testing and principal component analysis on multiple kernels

In high-dimensional omics studies, researchers often conduct kernel association testing to power-fully detect the relationship of the genetic or microbial composition with human health or disease. Especially, in human microbiome studies, its dimension reduction analysis follows to visually represent complex microbiome data in a simple two- or three-dimensional coordinate space. However, various kernels exist, and they produce all different outcomes; hence, it is hard to interpret them all consistently. Then, omnibus testing has recently been a subject of intense investigation for a unified and powerful statistical inference. However, current omnibus tests are purely a test for significance producing only a P-value as their outcome with no related dimension reduction and visualization approach; hence, their utility is still limited. In this paper, I introduce an ensemble learning method, named as enKern, for joint kernel associating testing and principal component analysis on multiple kernels. enKern is based on a weight learning scheme that leverages complementary contributions from multiple kernels for powerful performance for various association patterns. I show that applying the weights to individual test statistics or individual kernels is equivalent, which in turn enables a visualization in a reduced dimensional coordinate space based on the weighted kernel to be matched with its original significance testing scheme. I demonstrate its use for human microbiome {beta}-diversity analysis. I also demonstrate its outperformance in validity and power through simulation experiments. enKern is freely available in R computing environment at https://github.com/hk1785/enkern.