Low Rank Approximation (LRA) techniques, such as principal component analysis, are powerful tools for the representation and analysis of large data, and are used in many domains, including machine learning, signal processing, data analysis, and optimisation.

Without constraints, and using the lowest number of squares, LRA can be resolved by breaking data down into singular values. However, in practice, this model is often inadequate mainly because (i) some data is wrong or missing, or because of non-Gaussian noise, and (ii) the ways in which the data is broken down must satisfy certain constraints related to the application considered. The objective of this ERC project is to remove these issues, considering four different, but complementary, aspects: (1) algorithmic complexity, (2) algorithms with guaranteed success, (3) heuristics, and (4) applications.