Session Chair: Giorgio Tomasi, University of Copenhagen
08:30–09:20
Federico Marini, University of Rome "La Sapienza"
Abstract: TBD
Coffee Break 09:30–09:50
09:50–10:40
Paul-Albert Schneide, University of Copenhagen
Abstract: The extraction of chemical information from instrumental analytical raw data is one of the core objectives within chemometrics. For extracting chemical information from three-way data, tri-linear factor decomposition models are widely established, especially, when they are good models of underlying physical principles such as the Beer-Lambert Law. In these situations, the factors estimated from analytical raw data can be interpreted in a chemically meaningful way.
However, due to imperfections in the measurement process or non-linear signal responses, the assumption of a tri-linear, rank-one structure of the chemical signal is often violated in real data. More flexible, bi-linear models can accommodate these deviations from tri-linear behaviour but the factors are only under certain conditions uniquely identifiable. Hence, the ambiguity in the factorization can make the chemical interpretation of the factors difficult.
Block-term decompositions in (L_r, L_r, 1)-form are promising in that they allow factors to have more flexible structures while providing unique solutions under conditions that are often fulfilled with chemometric data. Conceptually, block-term decompositions bridge the “modelling gap” between (strictly) tri-linear data and bi-linear data in chemometric applications where the chemical signal has a non-tri-linear, low-rank approximable structure.
The talk will introduce an extension of the MCR-tri-linearity framework to approximate block-term decompositions in (L_r, L_r, 1)-form. Applications to kinetic and chromatographic data are shown, and limitations of the proposed method are discussed.
This is joint work with Rasmus Bro, Neal Gallagher and Roma Tauler.
10.50–11:40
Jesper L. Hinrich, Technical University of Denmark
Abstract: Nuclear Magnetic Resonance (NMR) spectroscopy is a highly used technique for quantification of chemicals in various chemical and biological samples. However, signal overlap and compound specific shifts violates the assumptions of bi- or multi-linearity. To get around this issue, I will present shift-invariant decompositions focusing on where one or more modes is allowed to shift linearly and independently for each component and for each sample. I will focus on shifts in one mode in the context of NMF and Candecomp/PARAFAC but also elaborate on shifts in shifts in multiple modes and for joint matrix-tensor factorization. I will present how the optimization problem can be cast in a Bayesian framework to aid automatic model order selection and enforcing sparsity on the learned components to aid in unique recovery. I will present some results on NMR data (1H, TOCSY, HSQC) and discuss the implications for other analytical chemical techniques.
Lunch/ Lunch to go 12:00