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# Factorization of multidimensional observation - WPMTFMO7

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• #### Number of hours

• Lectures : 12.0
• Tutorials : 6.0
• Laboratory works : 0
• Projects : 0
• Internship : 0
• Written tests : 0
ECTS : 2.0

### Goals

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

Contact Christian JUTTEN

Content

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.

Tests

Semester 9 - The exam is given in english only

Average of quick tests made at the beginning of each course

Semester 9 - This course is given in english only

Curriculum->Master TSI SIGMA->Semester 9
Curriculum->Double-Diploma SICOM-TSI SIGMA->Semester 9
Curriculum->Master->Semester 9
Curriculum->Double-Diploma Engineer/Master->Semester 9

Bibliography

P. COMON, C. JUTTEN, eds., Handbook of Blind Source Separation, Independent Component Analysis and Applications, Academic Press, 2010.
http://www.gipsa-lab.grenoble-inp.fr/~pierre.comon/FichiersPdf/HandBook.pdf
http://www.elsevier.com/wps/find/bookdescription.cws_home/717222/description

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Date of update January 9, 2017

## Version française

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