{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:07:38Z","timestamp":1760058458890,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T00:00:00Z","timestamp":1744243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Instituto Politecnico Nacional research projects","award":["20241511","20241721","20250424","20253411"],"award-info":[{"award-number":["20241511","20241721","20250424","20253411"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This work establishes a simple algorithm to recover an information vector from a predefined database available every time. It is considered that the information analyzed may be incomplete, damaged, or corrupted. This algorithm is inspired by Hopfield Neural Networks (HNN), which allows the recursive reconstruction of an information vector through an energy-minimizing optimal process, but this paper presents a procedure that generates results in a single iteration. Images have been chosen for the information recovery application to build the vector information. In addition, a filter is added to the algorithm to focus on the most important information when reconstructing data, allowing it to work with damaged or incomplete vectors, even without losing the ability to be a non-iterative process. A brief theoretical introduction and a numerical validation for recovery information are shown with an example of a database containing 40 images.<\/jats:p>","DOI":"10.3390\/computation13040095","type":"journal-article","created":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T11:26:41Z","timestamp":1744284401000},"page":"95","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Non-Iterative Recovery Information Procedure with Database Inspired in Hopfield Neural Networks"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1011-8005","authenticated-orcid":false,"given":"Cesar U.","family":"Solis","sequence":"first","affiliation":[{"name":"Automatic Control Department, CINVESTAV-IPN, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico City 07360, Mexico"},{"name":"Unidad Profesional Adolfo L\u00f3pez Mateos, Department of Control and Automation Engineering, Instituto Polit\u00e9cnico Nacional, Zacatenco, Mexico City 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0928-9907","authenticated-orcid":false,"given":"Jorge","family":"Morales","sequence":"additional","affiliation":[{"name":"Unidad Profesional Adolfo L\u00f3pez Mateos, Department of Control and Automation Engineering, Instituto Polit\u00e9cnico Nacional, Zacatenco, Mexico City 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5137-1093","authenticated-orcid":false,"given":"Carlos M.","family":"Montelongo","sequence":"additional","affiliation":[{"name":"Unidad Profesional Adolfo L\u00f3pez Mateos, Department of Control and Automation Engineering, Instituto Polit\u00e9cnico Nacional, Zacatenco, Mexico City 07738, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,10]]},"reference":[{"key":"ref_1","unstructured":"Rojas, R. (2013). Neural Networks: A Systematic Introdution, Springer Science and Business Media."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","article-title":"\u201cNeural\u201d computation of decisions in optimization problems","volume":"52","author":"Hopfield","year":"1985","journal-title":"Biol. Cybern."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4869","DOI":"10.1109\/TNNLS.2019.2958556","article-title":"Hopfield Neural Network Flow: A Geometric Viewpoint","volume":"31","author":"Halder","year":"2020","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"ref_4","first-page":"1","article-title":"The application of artificial intelligence in project management research: A review","volume":"6","author":"Gil","year":"2021","journal-title":"Int. J. Interact. Multimed. Artif. Intell."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Neshat, M., and Zadeh, A.E. (2010, January 7\u20139). Hopfield neural network and fuzzy Hopfield neural network for diagnosis of liver disorders. Proceedings of the 2010 5th IEEE International Conference Intelligent Systems, London, UK.","DOI":"10.1109\/IS.2010.5548321"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhong, C., Luo, C., Chu, Z., and Gan, W. (2017, January 14\u201319). A continuous hopfield neural network based on dynamic step for the traveling salesman problem. Proceedings of the 2017 International Joint Conference on Neural Networks (IJCNN), Anchorage, AK, USA.","DOI":"10.1109\/IJCNN.2017.7966272"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ma, X., Zhong, L., and Chen, X. (2023, January 8\u20139). Application of Hopfield Neural Network Algorithm in Mathematical Modeling. Proceedings of the 2023 IEEE 12th International Conference on Communication Systems and Network Technologies (CSNT), Bhopal, India.","DOI":"10.1109\/CSNT57126.2023.10134711"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1016\/S0031-3203(00)00041-8","article-title":"Segmentation of FLIR images by Hopfield neural network with edge constraint","volume":"34","author":"Sang","year":"2001","journal-title":"Pattern Recognit."},{"key":"ref_9","first-page":"56","article-title":"Solving the Weighted Constraint Satisfaction Problems Via the Neural Network Approach","volume":"4","author":"Haddouch","year":"2016","journal-title":"Int. J. Interact. Multimed. Artif. Intell."},{"key":"ref_10","first-page":"63","article-title":"Robust artificial immune system in the Hopfield network for maximum k-satisfiability","volume":"4","author":"Sathasivam","year":"2017","journal-title":"Int. J. Interact. Multimed. Artif. Intell."},{"key":"ref_11","first-page":"52","article-title":"Genetic algorithm for restricted maximum k-satisfiability in the Hopfield network","volume":"4","author":"Kasihmuddin","year":"2016","journal-title":"Int. J. Interact. Multimed. Artif. Intell."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.neunet.2020.06.013","article-title":"A new Lyapunov functional for stability analysis of neutral-type Hopfield neural networks with multiple delays","volume":"129","author":"Faydasicok","year":"2020","journal-title":"Neural Netw."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1016\/S0031-3203(97)00089-7","article-title":"Multi-modal image segmentation using a modified Hopfield neural network","volume":"31","author":"Rout","year":"1998","journal-title":"Pattern Recognit."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0893-6080(88)90262-6","article-title":"Extended hopfield neural network: A complementary approach","volume":"1","author":"Cursino","year":"1988","journal-title":"Neural Netw."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jim\u00e9nez, M., Avedillo, M.J., Linares-Barranco, B., and N\u00fa\u00f1ez, J. (2023). Learning algorithms for oscillatory neural networks as associative memory for pattern recognition. Front. Neurosci., 17.","DOI":"10.3389\/fnins.2023.1257611"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"427878","DOI":"10.1155\/2010\/427878","article-title":"Appling a Novel Cost Function to Hopfield Neural Network for Defects Boundaries Detection of Wood Image","volume":"2010","author":"Dawei","year":"2010","journal-title":"Eurasip J. Adv. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2274","DOI":"10.1109\/TNNLS.2020.2995413","article-title":"Two-Level Complex-Valued Hopfield Neural Networks","volume":"32","author":"Kobayashi","year":"2021","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"109954","DOI":"10.1016\/j.patcog.2023.109954","article-title":"Training feedforward neural nets in Hopfield-energy-based configuration: A two-step approach","volume":"145","author":"Wang","year":"2024","journal-title":"Pattern Recognit."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1080\/00207161003653459","article-title":"Noise removal using hysteretic Hopfield tunnelling network in message transmission systems","volume":"88","author":"Gladis","year":"2011","journal-title":"Int. J. Comput. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2222","DOI":"10.1016\/j.matpr.2017.09.222","article-title":"Singular value decomposition applied to associative memory of Hopfield neural network","volume":"5","author":"Deb","year":"2018","journal-title":"Mater. Today Proc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"189368","DOI":"10.1155\/2011\/189368","article-title":"An optimal implementation on FPGA of a hopfield neural network","volume":"2011","author":"Mansour","year":"2011","journal-title":"Adv. Artif. Neural Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"8175","DOI":"10.1007\/s00521-019-04305-7","article-title":"Memristive continuous Hopfield neural network circuit for image restoration","volume":"32","author":"Hong","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_23","unstructured":"Krotov, D., and Hopfield, J. (2020). Large associative memory problem in neurobiology and machine learning. arXiv."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1162\/08997660360581958","article-title":"The Concave-Convex Procedure","volume":"15","author":"Yuille","year":"2003","journal-title":"Neural Comput."},{"key":"ref_25","unstructured":"Googleapis.com (2024, September 10). Open Images V7- Download. Available online: https:\/\/storage.googleapis.com\/openimages\/web\/download_v7.html."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/4\/95\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:12:28Z","timestamp":1760029948000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/4\/95"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,10]]},"references-count":25,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["computation13040095"],"URL":"https:\/\/doi.org\/10.3390\/computation13040095","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2025,4,10]]}}}