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Essential Simplices in Persistent Homology and Subtle Admixture Detection

Authors Saugata Basu , Filippo Utro , Laxmi Parida



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Author Details

Saugata Basu
  • Department of Mathematics, Purdue University, West Lafayette, IN 47906, USA
Filippo Utro
  • Computational Biology Center, IBM T. J. Watson Research, Yorktown Heights, NY 10598, USA
Laxmi Parida
  • Computational Biology Center, IBM T. J. Watson Research, Yorktown Heights, NY 10598, USA

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Saugata Basu, Filippo Utro, and Laxmi Parida. Essential Simplices in Persistent Homology and Subtle Admixture Detection. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 14:1-14:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.WABI.2018.14

Abstract

We introduce a robust mathematical definition of the notion of essential elements in a basis of the homology space and prove that these elements are unique. Next we give a novel visualization of the essential elements of the basis of the homology space through a rainfall-like plot (RFL). This plot is data-centric, i.e., is associated with the individual samples of the data, as opposed to the structure-centric barcodes of persistent homology. The proof-of-concept was tested on data generated by SimRA that simulates different admixture scenarios. We show that the barcode analysis can be used not just to detect the presence of admixture but also estimate the number of admixed populations. We also demonstrate that data-centric RFL plots have the potential to further disentangle the common history into admixture events and relative timing of the events, even in very complex scenarios.

Subject Classification

ACM Subject Classification
  • Applied computing → Life and medical sciences
Keywords
  • population admixture
  • topological data analysis
  • persistent homology
  • population evolution

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References

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