Factorization of multidimensional observation - WPMTFMO7

• Number of hours

• Lectures 10.0
• Projects 0
• Tutorials 0
• Internship 0
• Laboratory works 8.0
• Written tests 0

ECTS 2.0

Goal(s)

Introduction of methods for the analysis and representation of multivariate, multidimensional data.

Contact Bertrand RIVET

Content(s)

Observations of a physical system depending on D variables (also called diversities) naturally provide a D-way hypercube of data. A simple data model is based on the decomposition of the observations into a sum of R products between simpler terms, each simple term being related to a unique diversity. In most cases, the factorization is not unique and the search for a solution must be regularized by resorting to constraints. In fact, the goal is to explain observations by R latent variables in a unique way, with a physical meaning. In this context, we present factorization methods, either on matrices (D = 2 diversities) or on tensors (D > 2), exploiting complementary features that are known beforehand, such as: source statistical independence, source nonnegativity, source sparsity, etc... In addition, theoretical principles and algorithms are illustrated by actual unmixing applications in brain and hyperspectral imaging, chemical engineering, communications, internet recommendation systems, etc.

Prerequisites

Elementary linear algebra. Basic probability.

Test

Semester 9 - The exam is given in english only

Session 1 = 100% Based on reports
Session 2 = a new project to do => mark = 100% report on the new project

Session 1 = 100% Based on reports
Session 2 = un sujet de BE à travailler => note = 100% rapport sur ce nouveau BE