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Nonlinear Eigenproblems for Data Analysis

Objective

In machine learning and exploratory data analysis, the major goal is the development
of solutions for the automatic and efficient extraction of knowledge from data. This
ability is key for further progress in science and engineering. A large class of
data analysis methods is based on linear eigenproblems. While linear eigenproblems are
well studied, and a large part of numerical linear algebra is dedicated to the efficient
calculation of eigenvectors of all kinds of structured matrices, they are limited in their
modeling capabilities. Important properties like robustness against outliers
and sparsity of the eigenvectors are impossible to realize. In turn, we have shown recently
that many problems in data analysis can be naturally formulated as nonlinear eigenproblems.

In order to use the rich structure of nonlinear eigenproblems with an ease
similar to that of linear eigenproblems, a major goal of this proposal is to develop a general
framework for the computation of nonlinear eigenvectors. Furthermore, the great potential of nonlinear eigenproblems will be explored in various application areas. As the scope of nonlinear eigenproblems goes far beyond data analysis, this project will have major impact not only in machine learning and its use in computer vision, bioinformatics, and information retrieval, but also in other areas of the natural sciences.

Field of science

  • /natural sciences/computer and information sciences/artificial intelligence/machine learning
  • /natural sciences/computer and information sciences/data science/data analysis

Call for proposal

ERC-2012-StG_20111012
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

UNIVERSITAT DES SAARLANDES
Address
Campus
66123 Saarbrucken
Germany
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 271 992
Principal investigator
Matthias Hein (Prof.)
Administrative Contact
Corinna Hahn (Mrs.)

Beneficiaries (1)

UNIVERSITAT DES SAARLANDES
Germany
EU contribution
€ 1 271 992
Address
Campus
66123 Saarbrucken
Activity type
Higher or Secondary Education Establishments
Principal investigator
Matthias Hein (Prof.)
Administrative Contact
Corinna Hahn (Mrs.)