FWOEOS1 - Structured Low-Rank matrix / tensor approximation: numerical optimization-based algorithms and applications


Today's information society is centered on the collection of large amounts of data, from which countless  applications  aim  at  extracting  information.  They  involve  the  manipulation of matrices and higher-order tensors, which can be viewed as large multi-way arrays containing numerical data. Key to their successful and efficient processing is the proper exploitation of available structure, and in particular  low rank. This project  aims to contribute innovative
structure-exploiting  methods  based  on  the  paradigm  of  low-rank matrix/tensor approximation, with a strong mathematical and algorithmic emphasis, and to apply them to large-scale  data  analysis,  information  retrieval  and  modelling. In WP 1, which supports and facilitates progress in the other WPs, we develop robust and computationally  efficient  algorithms  for  optimal  low-rank  approximation  w.r.t.  a  given criterion, including algorithms that estimate the rank when not specified by the user. In WP2 we use low-rank approaches to tackle the fundamental problem of computing matrix products
as cheaply as possible and to perform advanced curve fitting. In WP3 we develop large-scale structure-exploiting algorithms for nonnegative matrix factorization, a powerful tool to extract information  from  data, and  for large-scale pattern recognition, which is  at  the heart  of machine learning. Finally in WP 4 we exploit low-rank structure in the design of globally optimal  methods  for  system  identification,  model  reduction  and  signal  processin.


Ivan Markovsky
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