arXiv subjects

Geert Roelof van der Ploeg

Publications and source records attributed to Geert Roelof van der Ploeg.

2 recordsLinked to original sources

arXiv2026

Nonlinear Tensor Decomposition for Pattern Discovery

The CANDECOMP/PARAFAC (CP) decomposition is widely used for revealing the underlying patterns from multiway data (also referred to as a higher-order tensor). When the data is clipped or saturated, however, the linear CP model becomes unreliable. Several remedies exist such as treating the clipped entries as missing or imputation; however, both fall short in different scenarios. We propose a nonlinear CP model (NCP) for pattern discovery in this setting, extending ideas from nonlinear matrix decompositions to tensors, and solve it using a flexible ADMM (Alternating Direction Method of Multipliers)-based framework that can accommodate a variety of nonlinearities. Using synthetic data with known factors and simulated metabolomics data where clipping arises from instrument detection limits, we demonstrate that NCP recovers the underlying factors more accurately than CP fitted to only the observed entries or threshold-imputed data.

eess.SP↗

arXiv2026

Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations

In order to understand complex systems such as the human metabolome or human brain, different sensing technologies are used, generating complex data. These datasets are often multiway, i.e., with more than two axes of variation such as a subjects by metabolites by time array. While tensor factorizations have successfully revealed interpretable patterns from such complex data, they have so far been mainly data-driven. On the other hand, there is more to data -- there are computational models (of these systems), which are rich sources of prior information. In this paper, we introduce a knowledge-guided approach that brings together data and computational models by jointly analyzing real data and simulated data (generated using a computational model) using coupled tensor factorizations with linear coupling. Our experiments on real metabolomics measurements demonstrate that guiding the analysis of such noisy data with simulated data improves the pattern discovery performance while also revealing potential discrepancies between data and computational models.

cs.LG↗