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We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to…
We propose data thinning, an approach for splitting an observation into two or more independent parts that sum to the original observation, and that follow the same distribution as the original observation, up to a (known) scaling of a…
We propose a novel framework for combining datasets via alignment of their intrinsic geometry. This alignment can be used to fuse data originating from disparate modalities, or to correct batch effects while preserving intrinsic data…
With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…
Canonical Correlation Analysis (CCA) has been widely applied to jointly embed multiple views of data in a maximally correlated latent space. However, the alignment between various data perspectives, which is required by traditional…
A recently proposed mutual information based algorithm for decomposing data into least dependent components (MILCA) is applied to spectral analysis, namely to blind recovery of concentrations and pure spectra from their linear mixtures. The…
A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…
Complex computer codes are widely used in science to model physical systems. Sensitivity analysis aims to measure the contributions of the inputs on the code output variability. An efficient tool to perform such analysis are the…
Compositional data, also referred to as simplicial data, naturally arise in many scientific domains such as geochemistry, microbiology, and economics. In such domains, obtaining sensible lower-dimensional representations and modes of…
A fundamental challenge in science and engineering is the simulation-to-experiment gap. While we often possess prior knowledge of physical laws, these physical laws can be too difficult to solve exactly for complex systems. Such systems are…
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the…
We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our…
To analyze dynamic positron emission tomography (PET) images, various generic multivariate data analysis techniques have been considered in the literature, such as principal component analysis (PCA), independent component analysis (ICA),…
Component separation is one of the key stages of any modern, cosmic microwave background (CMB) data analysis pipeline. It is an inherently non-linear procedure and typically involves a series of sequential solutions of linear systems with…
Independent component analysis (ICA) is a cornerstone of modern data analysis. Its goal is to recover a latent random vector S with independent components from samples of X=AS where A is an unknown mixing matrix. Critically, all existing…
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…
Many processes of scientific and technological interest are characterized by time scales that render their simulation impossible if one uses present day simulation capabilities. To overcome this challenge a variety of enhanced simulation…
We applied two methods of "blind" spectral decomposition (MILCA and SNICA) to quantitative and qualitative analysis of UV absorption spectra of several non-trivial mixture types. Both methods use the concept of statistical independence and…
A major challenge in nuclear fusion research is the coherent combination of data from heterogeneous diagnostics and modelling codes for machine control and safety as well as physics studies. Measured data from different diagnostics often…