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.
Grading Philosophy
Continuous assessment
Course schedule
Course type
Lecture
Online Course Requirement
Instructor
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.
Please consider the following deadlines for inbound mobility to Grenoble:
- April 1st, 2020 for Full Year (September to June) and Fall Semester (September to January) intake ;
- September 1st, 2020 for Spring Semester intake (February – June).
Site for Inquiry
Please inquire about the courses at the address below.
Contact person: international.cic_tsukuba@grenoble-inp.fr