## CourseDetail

Degree
Master
2nd year of master
Course delivery methods
face-to-face
Subject
Engineering & technology
Program
School
Grenoble INP Institute of Engineering Univ. Grenoble Alpes
Department
Campus
Grenoble - Polygone scientifique
Classroom
Course Offering Year
Course Offering Month
-
Weekday and Period
Capacity
Credits
2
Language
English
Course Number

### Factorization of multidimensional observation Université Grenoble Alpes

#### Course Overview

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.

http://phelma.grenoble-inp.fr/en/studies/factorization-of-multidimensional-observation-wpmtfmo7

#### Learning Achievement

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

#### Competence

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.

#### Course prerequisites

Elementary linear algebra. Basic probability.

Continuous assessment

Lecture

Christian Jutten

#### Other information

Course content can evolve at any time before the start of the course. It is strongly recommended to discuss with the course contact about the detailed program.