Section: New Results

Topological Data Analysis

Leyla Mirvakhabova has defended and obtained her BSc memoir on "Distance geometry and biodiversity patterns" at the Department of Mathematics of the National Research University - Higher School of Economics, Moscow. Here is the abstract: In this work, we study the biodiversity of the tree species in French Guiana. We consider the matrix of the pairwise genetic distances between the 1501 species. The distances are measured by using the Smith-Waterman algorithm applied to the trnH regions - the chloroplasts of trees. The aim of the project is to analyze the shape of a point cloud in a Euclidean space built from the pairwise distances. To study the structure of the point cloud built from the given distances, we have considered the following methods: Hierarchical Clustering, Multidimensional Scaling (MDS), Nonlinear Mapping (NLM), t-Distributed Stochastic Neighbor Embedding (t-SNE), and Topological Data Analysis (TDA). For the first four methods, we used the Python package scikit-learn 0.17.1 implementations and have written the program for the TDA algorithm. All of these methods were tested on the given dataset. This work has been performed as part of a collaborative research project of the PLEIADE team in the Inria Bordeaux – Sud-Ouest (supervisor Alain Franc) with the Laboratory of System Biology and Computational Genetics in the Vavilov Institute of General Genetics (supervisor Ivan Kulakovskiy).