Analyzing Data with Graphs: Metagenomic Data and the Phylogenetic Tree
In biological experiments, researchers often have information in the form of a graph that supplements observed numerical data. Incorporating the knowledge contained in these graphs into an analysis of the numerical data is an important and non trivial task. We look at the example of metagenomic data -- data from a genomic survey of the abundence of different species of bacteria in a sample. Here, the graph of interest is a phylogenetic tree depicting the interspecies relationships among the bacteria species. We demonstrate that analysis of the data in a non-standard inner-product space effectively uses this additional graphical information and produces more meaningful results.