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We present Nubeam ( n ucleotide  b e  a  m atrix) 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 assigns numbers to reads based on the product matrix. Nubeam capitalizes on the noncommutative 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 includes the  k -mer method as a special case, but unlike the  k -mer method, it is convenient for Nubeam to account for GC bias and nucleotide quality. 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 data sets from metagenomics whole genome shotgun (WGS) sequencing, where the amount of unmapped reads is substantial. When applied to a WGS sequencing data set to quantify distances between metagenomics samples from various human body habitats, Nubeam recapitulates findings made by mapping-based methods and sheds light on contributions of unmapped reads. Nubeam is also useful in analyzing 16S rRNA sequencing data, which is a more prevalent type of data set in metagenomics studies. In our analysis, Nubeam recapitulated the findings that natural microbiota in mouse gut are resilient under challenges, and Nubeam detected differences in vaginal microbiota between cases of polycystic ovary syndrome and healthy controls.

The Nubeam reference-free approach to analyze metagenomic sequencing reads