NOLEPRO · Nonlinear Eigenproblems for Data Analysis

In machine learning and exploratory data analysis, the major goal is the developmentof solutions for the automatic and efficient extraction of knowledge from data. Thisability is key for further progress in science and engineering. A large class ofdata analysis methods is based on linear eigenproblems. While linear eigenproblems arewell studied, and a large part of numerical linear algebra is dedicated to the efficientcalculation of eigenvectors of all kinds of structured matrices, they are limited in theirmodeling capabilities. Important properties like robustness against outliersand sparsity of the eigenvectors are impossible to realize. In turn, we have shown recentlythat many problems in data analysis can be naturally formulated as nonlinear eigenproblems.In order to use the rich structure of nonlinear eigenproblems with an easesimilar to that of linear eigenproblems, a major goal of this proposal is to develop a generalframework 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.