Machine-learning Framework Aided By Stochastic

**Machine-learning framework aided by stochastic geometry and mathematical morphology for classifying RNA cell features**:

- Réf
- **ABG-110307**
- Stage master 2 / Ingénieur- Durée 6 mois- Salaire net mensuel 1200 euros brut par mois- 18/01/2023- Mines ParisTech- Lieu de travail- Fontainebleau Ile-de-France France- Champs scientifiques- Mathématiques
- Mots clés- Méthdoes d'apprentissage; Biologie; Analyse d'image**Établissement recruteur**:
The internship will be carried out at the Centre of Mathematical Morphology (CMM)
laboratory of Mines Paris, located in Fontainebleau, south of Paris. Regular meetings will be held in
Paris and Fontainebleau. Part-time remote working is possible.

**Description**:
Gene expression control strongly depends on the cells’ RNA abundance and localization. A team of
researchers from the CBIO laboratory of Mines Paris and Institut Curie [1] has developed
techniques based on image analysis of RNA fluorescence in-situ hybridization (FISH) that quantify
key features of cells, such as mRNA spots, sought to play an important role for the spatial control of
gene expression at the single cell level.
The dataset, obtained from a large number of experiments, provides information on populations of
cells, and may be described as a points patterns with various features attached to each point. The
main purpose of this internship is the development of original methods for describing and
classifying cell populations, based on a machine-learning framework. Here we propose to
investigate the newly-developed “morphological layers” deep-learning framework [2-3] developed
by Santiago Velasco-Forero. In contrast with classical machine-learning pipelines based on
convolutional layers, the morpho-layer networks use mathematical morphology transformations.
When trained, the method amounts to learn “structural elements” that are at the basis of
morphological operators (e.g. dilations, erosions). In doing so, the shape of these structural elements
discriminate between different types of point processes and their spatial dispersion, for instance
clusters and repulsion effects. From a theoretical point of view, these structural elements can be
regarded as “input values” of the so-called Choquet-capacity functional [4].
Rigorous reconstruction theorems from random sets theory state how such functional provides, in
theory, complete information on random sets, or in the present case, point processes. Although, in
practice, the functional can not generally be computed beyond elementary characteristics (typically
covariances) it has long been hypothesized that higher-order statistics could provide robust and
accurate descriptors. The internship therefore aims to explore whether one may use machine
- learning methods to provide, in practice, relevant shape-descriptors, that are able to describe the
spatial structure of random point processes with a good accuracy.

**Profil**:
We are seeking Master 2 students in machine learning, data science, image analysis
or biology with excellent mathematical background and a focus on research.

**Prise de fonction**:

- Dès que possible