Séminaire de Mathématique-Biologie
# Detecting and Exploiting Non-Trivial Geometrical Data Structures for Obtaining Insights Into Biology

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Europe/Paris

Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

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

Description

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

presented.

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