A geometric view of Biodiversity: scaling to metagenomics

We have designed a new efficient dimensionality reduction algorithm in order to investigate new ways of accurately characterizing the biodiversity, namely from a geometric point of view, scaling with large environmental sets produced by NGS ($\sim 10^5$ sequences). The approach is based on Multidimensional Scaling (MDS) that allows for mapping items on a set of $n$ points into a low dimensional euclidean space given the set of pairwise distances. We compute all pairwise distances between reads in a given sample, run MDS on the distance matrix, and analyze the projection on first axis, by visualization tools. We have circumvented the quadratic complexity of computing pairwise distances by implementing it on a hyperparallel computer (Turing, a Blue Gene Q), and the cubic complexity of the spectral decomposition by implementing a dense random projection based algorithm. We have applied this data analysis scheme on a set of $10^5$ reads, which are amplicons of a diatom environmental sample from Lake Geneva. Analyzing the shape of the point cloud paves the way for a geometric analysis of biodiversity, and for accurately building OTUs (Operational Taxonomic Units), when the data set is too large for implementing unsupervised, hierarchical, high-dimensional clustering.

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