Rank-R FNN: a tensor-based learning model for high-order data classificationRank-R FNN: a tensor-based learning model for high-order data classification Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2023-03-022021enThis work was supported in part by the Horizon 2020 Research Program through the European Union funded project HYPERION (Development of a Decision Support System for Improved Resilience & Sustainable Reconstruction of historic areas to cope with Climate Change & Extreme Events based on Novel Sensors and Modelling Tools) under Grant 821054, in part by the Horizon 2020 Research Program through the project Panoptis (Development of a Decision Support System for increasing the Resilience of Transportation Infrastructure Based on Combined Use of Terrestrial and Airborne Sensors and Advanced Modelling Tools) under Grant 769129, and in part by the European Union's Horizon 2020 Research and Innovation Programme through the TAMED project under Grant 101003397.An increasing number of emerging applications in data science and engineering are based on multidimensional and structurally rich data. The irregularities, however, of high-dimensional data often compromise the effectiveness of standard machine learning algorithms. We hereby propose the Rank- R Feedforward Neural Network (FNN), a tensor-based nonlinear learning model that imposes Canonical/Polyadic decomposition on its parameters, thereby offering two core advantages compared to typical machine learning methods. First, it handles inputs as multilinear arrays, bypassing the need for vectorization, and can thus fully exploit the structural information along every data dimension. Moreover, the number of the model's trainable parameters is substantially reduced, making it very efficient for small sample setting problems. We establish the universal approximation and learnability properties of Rank- R FNN, and we validate its performance on real-world hyperspectral datasets. Experimental evaluations show that Rank- R FNN is a computationally inexpensive alternative of ordinary FNN that achieves state-of-the-art performance on higher-order tensor data.http://creativecommons.org/licenses/by/4.0/IEEE Access958609–58620Makantasis_et_al_IEEE Access_9_2021.pdfChania [Greece]Library of TUC2023-03-02application/pdf2.2 MBfree Makantasis Konstantinos Μακαντασης Κωνσταντινος Georgogiannis Alexandros Γεωργογιαννης Αλεξανδρος Voulodimos, Athanasios Georgoulas Ioannis Doulamis, Anastasios Doulamis, Nikolaos Institute of Electrical and Electronics Engineers High-order data processing Hyperspectral data classifcation Rank-R FNN Tensor-based neural networks