Human microbiome sequences in the light of the Nubeam

We present Nubeam (nucleotide be a matrix) as a novel reference-free approach to analyze short sequencing reads. Nubeam represents nucleotides by matrices, transforms a read into a product of matrices, and based on which assigns numbers to reads. Nubeam capitalizes on the non-commutative property of matrix multiplication, such that different reads are assigned different numbers, and similar reads similar numbers. A sample, which is a collection of reads, becomes a collection of numbers that form an empirical distribution. We demonstrate that the genetic difference between samples can be quantified by the distance between empirical distributions. Nubeam can account for GC bias and nucleotide quality, and is computationally efficient; the K-mer method is a special case of Nubeam, but without those benefits. As a reference-free approach, Nubeam avoids reference bias and mapping bias and can work with organisms without reference genomes. Thus, Nubeam is ideal to analyze datasets from metagenomic whole-genome sequencing, where the amount of unmapped reads is substantial. When applied to human microbiome sequencing, Nubeam recapitulated findings made by mapping-based methods, and shed lights on contributions of unmapped reads. In particular, body habitats dominate clustering of unmapped pseudo-samples; there are more outliers in skin whole samples than the skin mapped pseudo-samples; and analysis of unmapped reads suggested that the sequencing depth is far from sufficient for urogenital samples.