There is a growing recognition that the human microbiome - microbes living in intimate association with us - forms a vital part of our biology, and plays an important role in both health and sickness. A huge amount of data are being generated about these communities, much through metagenomics methods, which sequence DNA without directly identifying which organisms they come from. These data pose a tremendous opportunity for understanding, and a tremendous computational and theoretical challenge. In this paper, we compare several linear and nonlinear methods to explore human microbiome. There i...