A unifying framework for modelling non-negative bi-linear, tri-linear and “in-between” data in chemometrics. Part I: Theoretical framework and concepts [Dataset]
In chemometrics, extracting chemically meaningful information from multi-way analytical data is often challenged by deviations from ideal tri-linear structure of the chemical information. This work introduces a novel modeling approach based on (1, L<inf>r</inf>, L<inf>r</inf>...
| Autores: | , , , , |
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| Tipo de recurso: | conjunto de datos |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/417164 |
| Acceso en línea: | http://hdl.handle.net/10261/417164 https://doi.org/10.20350/digitalCSIC/17935 https://digital.csic.es/handle/10261/417159 |
| Access Level: | acceso abierto |
| Palabra clave: | Chemometrics Chemometric applications http://metadata.un.org/sdg/3 http://metadata.un.org/sdg/11 http://metadata.un.org/sdg/9 Ensure healthy lives and promote well-being for all at all ages Build resilient infrastructure, promote inclusive and sustainable industrialization and foster innovation Make cities and human settlements inclusive, safe, resilient and sustainable |
| Sumario: | In chemometrics, extracting chemically meaningful information from multi-way analytical data is often challenged by deviations from ideal tri-linear structure of the chemical information. This work introduces a novel modeling approach based on (1, L<inf>r</inf>, L<inf>r</inf>) block term decompositions, which flexibly bridges the gap between bi-linear and tri-linear models. The method builds upon the MCR-tri-linearity framework and leverages uniqueness conditions established by De Lathauwer to ensure interpretable factor solutions under practical conditions. A rank-constrained alternating optimization algorithm is proposed to adaptively determine the number of principal components needed for reconstructing varying-mode factors, based on a user-defined reconstruction error tolerance. This adaptive decomposition balances the essential uniqueness of tri-linear models with the flexibility of bi-linear approaches, addressing limitations in both. Simulated data with controlled component ranks demonstrate the method's ability to recover ground-truth factors more accurately than classical tri-linear models, while reducing ambiguity compared to bi-linear models. The results confirm that the proposed approach provides an effective framework for analyzing multi-way chemical data with partial or full deviations from tri-linearity, making it a promising tool for a wide range of chemometric applications. |
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