Citation: Tzortzis, I.N.; Davradou, A.; Rallis, I.; Kaselimi, M.; Makantasis, K.; Doulamis, A.; Doulamis, N. Tensor-Based Learning for Detecting Abnormalities on Digital Mammograms. Diagnostics 2022, 12, 2389. https://doi.org/10.3390/ diagnostics12102389 Academic Editors: Karen Drukker, Lubomir Hadjiiski, Despina Kontos, Marco Caballo and Shandong Wu Received: 5 September 2022 Accepted: 29 September 2022 Published: 1 October 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). diagnostics Article Tensor-Based Learning for Detecting Abnormalities on Digital Mammograms Ioannis N. Tzortzis 1,* , Agapi Davradou 1 , Ioannis Rallis 1 , Maria Kaselimi 1 , Konstantinos Makantasis 2 , Anastasios Doulamis 1 and Nikolaos Doulamis 1 1 Department of Rural Surveying Engineering and Geoinformatics Engineering, National Technical University of Athens, 157 80 Athens, Greece 2 Department of Artificial Intelligence, University of Malta, MSD2080 Msida, Malta * Correspondence: itzortzis@mail.ntua.gr Abstract: In this study, we propose a tensor-based learning model to efficiently detect abnormalities on digital mammograms. Due to the fact that the availability of medical data is limited and often restricted by GDPR (general data protection regulation) compliance, the need for more sophisti- cated and less data-hungry approaches is urgent. Accordingly, our proposed artificial intelligence framework utilizes the canonical polyadic decomposition to decrease the trainable parameters of the wrapped Rank-R FNN model, leading to efficient learning using small amounts of data. Our model was evaluated on the open source digital mammographic database INBreast and compared with state-of-the-art models in this domain. The experimental results show that the proposed solution performs well in comparison with the other deep learning models, such as AlexNet and SqueezeNet, achieving 90% ± 4% accuracy and an F1 score of 84% ± 5%. Additionally, our framework tends to attain more robust performance with small numbers of data and is computationally lighter for inference purposes, due to the small number of trainable parameters. Keywords: mammography; deep learning; machine learning; tensor-based learning; CP decomposition; breast cancer; computer-aided detection; screening 1. Introduction Breast cancer is the leading cause of death in women worldwide, accounting for more than 685,000 deaths in 2020, and it is the most commonly diagnosed type of cancer, with more than 2.26 million new cases [1]. It is a variation of malignant growth expanding from breast tissue, often in the interior area of the breast, metastasizing to other body areas (i.e., lymph nodes). It commonly affects women above 40 years old, with the main risk factors being the patient’s age, family history, and level of obesity [2,3]. Fortunately, observational studies have shown that the early-stage detection of breast nodules leads to a very high 5-year survival rate, exceeding 90%, while on the contrary, the survival rate drops by 27% in cases of late diagnosis [4]. This emphasizes the need for better prognosis and the development of improved screening strategies. The assessment of breast cancer detection in a non-invasive manner is very important for identifying abnormal regions of interest (ROIs) on medical imaging modalities. One of the most effective non-invasive screening techniques for the early detection of breast cancer is digital mammography. It is the most commonly used diagnostic test; it uses low-energy X-rays to identify lumps in dense tissue and has been proven to assist in the decrease in mortality rates [5,6]. However, despite its advantages, mammography presents many limitations. More specifically, it is associated with (a) high risk of false positives [7–9], where in many cases the biopsy detects no cancer, as well as (b) a high risk of false negatives [10–12], where the breast cancer remains underdiagnosed. Therefore, in recent decades, many methods have been adopted in order to help radiologists reduce Diagnostics 2022, 12, 2389. https://doi.org/10.3390/diagnostics12102389 https://www.mdpi.com/journal/diagnostics