My main fields of interest are geometric data analysis, numerical differential geometry (optimization on smooth manifolds), and dimensionality reduction; with applications to pattern recognition, computer vision, statistical signal processing, and hyperspectral image analysis. A common theme of these topics is in describing similarities between data, where different observations of objects with the same identity can be approximated by linear combinations of a low-dimensional basis. Often times the low-rank model is inspired domain-specific knowledge, so the rank of the solution is predetermined and enforced through constraints. In other situations the goal is to identify the natural, unknown dimension of the data, and thus a low-rank representation is uncovered as the result of the optimization or analysis.
I currently work under the Excellence of Science grant: Structured Low-Rank Matrix/Tensor Approximation (SeLMA), which is a collaboration of four Belgian universities that 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.