Séminaire de Mathématique-Biologie

Detecting and Exploiting Non-Trivial Geometrical Data Structures for Obtaining Insights Into Biology

by Prof. Andrei ZINOVYEV (Institut Curie, Paris)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette

Thanks to recent progress in biotechnologies, the high-throughput data
in molecular biology are getting more
 and more interesting from the point of view of application of advanced
methods for data analysis, aimed
 at finding non-trivial topological characteristics in the data such as
branching points and holes. Existence
 of such non-trivial structures in the data can have direct biological
interpretations such as the process
 of cell fate decisions during cell differentiation or existence of
cyclic processes in a cell (e.g., cell cycle).

 I will present examples of application of such methods in studying
various biological systems and explain their general
 principles. I will focus on the universal method of elatic principal
graphs for topological data analysis developed by us.
 The method is based on application of the notion of harmonic graph
embedding into a multi-dimensional space,
 minimization of graph elastic energy and using graph grammars defining
a family of possible graph structures (such as trees).
 Simplest implementations of the approach already give very usefull
data approximators such as principal curves,
 principal closed curves, principal manifolds and principal trees.
Several ideas for making these data approximators
 robust to the noise and outliers in the biological data will be