{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T11:09:49Z","timestamp":1771844989877,"version":"3.50.1"},"reference-count":69,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T00:00:00Z","timestamp":1619049600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04111\/2020, foRESTER PCIF\/SSI\/0102\/2017"],"award-info":[{"award-number":["UIDB\/04111\/2020, foRESTER PCIF\/SSI\/0102\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Instituto Lus\u00f3fono de Investiga\u00e7\u00e3o e Desenvolvimento","award":["COFAC\/ILIND\/COPELABS\/1\/2020"],"award-info":[{"award-number":["COFAC\/ILIND\/COPELABS\/1\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JSAN"],"abstract":"<jats:p>The localization of an acoustic source has attracted much attention in the scientific community, having been applied in several different real-life applications. At the same time, the use of neural networks in the acoustic source localization problem is not common; hence, this work aims to show their potential use for this field of application. As such, the present work proposes a deep feed-forward neural network for solving the acoustic source localization problem based on energy measurements. Several network typologies are trained with ideal noise-free conditions, which simplifies the usual heavy training process where a low mean squared error is obtained. The networks are implemented, simulated, and compared with conventional algorithms, namely, deterministic and metaheuristic methods, and our results indicate improved performance when noise is added to the measurements. Therefore, the current developed scheme opens up a new horizon for energy-based acoustic localization, a field where machine learning algorithms have not been applied in the past.<\/jats:p>","DOI":"10.3390\/jsan10020029","type":"journal-article","created":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T04:20:17Z","timestamp":1619065217000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Feed-Forward Neural Network Approach for Energy-Based Acoustic Source Localization"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1111-3513","authenticated-orcid":false,"given":"S\u00e9rgio D.","family":"Correia","sequence":"first","affiliation":[{"name":"COPELABS, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Campo Grande 376, 1749-024 Lisboa, Portugal"},{"name":"VALORIZA\u2014Research Centre for Endogenous Resource Valorization, Instituto Polit\u00e9cnico de Portalegre, Campus Polit\u00e9cnico n. 10, 7300-555 Portalegre, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5537-6716","authenticated-orcid":false,"given":"Slavisa","family":"Tomic","sequence":"additional","affiliation":[{"name":"COPELABS, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Campo Grande 376, 1749-024 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7315-8739","authenticated-orcid":false,"given":"Marko","family":"Beko","sequence":"additional","affiliation":[{"name":"Instituto de Telecominica\u00e7\u00f5es, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,22]]},"reference":[{"key":"ref_1","unstructured":"Uziel, S., Elste, T., Kattanek, W., Hollosi, D., Gerlach, S., and Goetze, S. (2013, January 8\u201310). Networked embedded acoustic processing system for smart building applications. Proceedings of the 2013 Conference on Design and Architectures for Signal and Image Processing, Cagliari, Italy."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Quintana-Su\u00e1rez, M., S\u00e1nchez-Rodr\u00edguez, D., Alonso-Gonz\u00e1lez, I., and Alonso-Hern\u00e1ndez, J. (2017). A Low Cost Wireless Acoustic Sensor for Ambient Assisted Living Systems. Appl. Sci., 7.","DOI":"10.3390\/app7090877"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"100241","DOI":"10.1016\/j.cosrev.2020.100241","article-title":"Localization schemes for Underwater Acoustic Sensor Networks\u2014A Review","volume":"37","author":"Toky","year":"2020","journal-title":"Comput. Sci. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1007\/s10015-016-0295-4","article-title":"Distributed sensor swarms for monitoring bird behavior: An integrated system using wildlife acoustics recorders","volume":"21","author":"Taylor","year":"2016","journal-title":"Artif. Life Robot."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"10407","DOI":"10.1007\/s11042-015-3105-4","article-title":"Detection, classification and localization of acoustic events in the presence of background noise for acoustic surveillance of hazardous situations","volume":"75","author":"Lopatka","year":"2015","journal-title":"Multimed. Tools Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/MC.2004.104","article-title":"Shooter localization in urban terrain","volume":"37","author":"Maroti","year":"2004","journal-title":"Computer"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Lammert-Siepmann, N., Bestgen, A.K., Edler, D., Kuchinke, L., and Dickmann, F. (2017). Audiovisual communication of object-names improves the spatial accuracy of recalled object-locations in topographic maps. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0186065"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.jenvp.2006.06.002","article-title":"Facilitating route memory with auditory route guidance systems","volume":"26","author":"Reagan","year":"2006","journal-title":"J. Environ. Psychol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2887","DOI":"10.1109\/TSP.2011.2116012","article-title":"Source Localization in Wireless Sensor Networks From Signal Time-of-Arrival Measurements","volume":"59","author":"Xu","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4598","DOI":"10.1109\/TSP.2009.2027765","article-title":"An Approximately Efficient TDOA Localization Algorithm in Closed-Form for Locating Multiple Disjoint Sources With Erroneous Sensor Positions","volume":"57","author":"Yang","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ali, A.M., Yao, K., Collier, T.C., Taylor, C.E., Blumstein, D.T., and Girod, L. (2007, January 25\u201327). An Empirical Study of Collaborative Acoustic Source Localization. Proceedings of the 2007 6th International Symposium on Information Processing in Sensor Networks, Cambridge, MA, USA.","DOI":"10.1109\/IPSN.2007.4379663"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1145\/1113830.1113837","article-title":"Range-Free Localization and Its Impact on Large Scale Sensor Networks","volume":"4","author":"He","year":"2005","journal-title":"ACM Trans. Embed. Comput. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.procs.2015.07.357","article-title":"Range Free Localization Techniques in Wireless Sensor Networks: A Review","volume":"57","author":"Singh","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_14","unstructured":"Hu, Y.H., and Li, D. (2002, January 9\u201311). Energy based collaborative source localization using acoustic micro-sensor array. Proceedings of the 2002 IEEE Workshop on Multimedia Signal Processing, St. Thomas, VI, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/TSP.2004.838930","article-title":"Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks","volume":"53","author":"Sheng","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Shareef, A., and Zhu, Y. (2009). Localization Using Extended Kalman Filters in Wireless Sensor Networks. Kalman Filter Recent Advances and Applications, I-Tech.","DOI":"10.5772\/6811"},{"key":"ref_17","first-page":"343","article-title":"Deep learning for indoor localization based on bimodal CSI data","volume":"17","author":"Wang","year":"2019","journal-title":"Appl. Mach. Learn. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Wang, Y., Gao, J., Li, Z., and Zhao, L. (2020). Robust and Accurate Wi-Fi Fingerprint Location Recognition Method Based on Deep Neural Network. Appl. Sci., 10.","DOI":"10.3390\/app10010321"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"20190616","DOI":"10.1098\/rsif.2019.0616","article-title":"Three-dimensional multi-source localization of underwater objects using convolutional neural networks for artificial lateral lines","volume":"17","author":"Wolf","year":"2020","journal-title":"J. R. Soc. Interface"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Livingstone, D.J. (2009). Artificial Neural Networks: Methods and Applications, Humana Press.","DOI":"10.1007\/978-1-60327-101-1"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Parathai, P., Tengtrairat, N., Woo, W.L., Abdullah, M.A.M., Rafiee, G., and Alshabrawy, O. (2020). Efficient Noisy Sound-Event Mixture Classification Using Adaptive-Sparse Complex-Valued Matrix Factorization and OvsO SVM. Sensors, 20.","DOI":"10.3390\/s20164368"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Meng, W., and Xiao, W. (2017). Energy-Based Acoustic Source Localization Methods: A Survey. Sensors, 17.","DOI":"10.3390\/s17020376"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1109\/TSP.2007.900757","article-title":"On Energy-Based Acoustic Source Localization for Sensor Networks","volume":"56","author":"Meesookho","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2542","DOI":"10.1109\/TASL.2007.903312","article-title":"An Accurate Algebraic Closed-Form Solution for Energy-Based Source Localization","volume":"15","author":"Ho","year":"2007","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1770","DOI":"10.1109\/TSP.2007.909342","article-title":"Exact and Approximate Solutions of Source Localization Problems","volume":"56","author":"Beck","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2293","DOI":"10.1109\/TVT.2011.2142204","article-title":"A Semidefinite Relaxation Method for Energy-Based Source Localization in Sensor Networks","volume":"60","author":"Wang","year":"2011","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Beko, M. (2011, January 28\u201331). Energy-based localization in wireless sensor networks using semidefinite relaxation. Proceedings of the 2011 IEEE Wireless Communications and Networking Conference, Cancun, Mexico.","DOI":"10.1109\/WCNC.2011.5779361"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1847","DOI":"10.1007\/s11277-014-1612-7","article-title":"Energy-Based Localization in Wireless Sensor Networks Using Second-Order Cone Programming Relaxation","volume":"77","author":"Beko","year":"2014","journal-title":"Wirel. Pers. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"8835","DOI":"10.1109\/JSEN.2018.2869000","article-title":"On the Semidefinite Programming Algorithm for Energy-Based Acoustic Source Localization in Sensor Networks","volume":"18","author":"Yan","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"163740","DOI":"10.1109\/ACCESS.2019.2952641","article-title":"Robust Semidefinite Relaxation Method for Energy-Based Source Localization: Known and Unknown Decay Factor Cases","volume":"7","author":"Shi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Deb, S., Fong, S., and Tian, Z. (2015, January 21\u201323). Elephant Search Algorithm for optimization problems. Proceedings of the 2015 Tenth International Conference on Digital Information Management (ICDIM), Jeju, Korea.","DOI":"10.1109\/ICDIM.2015.7381893"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1504\/IJBIC.2016.081335","article-title":"A new metaheuristic optimisation algorithm motivated by elephant herding behaviour","volume":"8","author":"Wang","year":"2016","journal-title":"Int. J. Bio Inspired Comput."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Correia, S.D., Beko, M., Cruz, L., and Tomic, S. (2018). Elephant Herding Optimization for Energy-Based Localization. Sensors, 18.","DOI":"10.20944\/preprints201807.0051.v1"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Correia, S.D., Beko, M., Da Silva Cruz, L.A., and Tomic, S. (2018, January 20\u201321). Implementation and Validation of Elephant Herding Optimization Algorithm for Acoustic Localization. Proceedings of the 2018 26th Telecommunications Forum (TELFOR), Belgrade, Serbia.","DOI":"10.1109\/TELFOR.2018.8611919"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"28548","DOI":"10.1109\/ACCESS.2020.2971787","article-title":"Energy-Based Acoustic Localization by Improved Elephant Herding Optimization","volume":"8","author":"Correia","year":"2020","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Correia, S.D., F\u00e9, J., Tomic, S., and Beko, M. (2020). Development of a Test-Bench for Evaluating the Embedded Implementation of the Improved Elephant Herding Optimization Algorithm Applied to Energy-Based Acoustic Localization. Computers, 9.","DOI":"10.3390\/computers9040087"},{"key":"ref_37","first-page":"3956282","article-title":"A Survey of Sound Source Localization Methods in Wireless Acoustic Sensor Networks","volume":"2017","author":"Cobos","year":"2017","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Sheng, X., and Hu, Y.H. (2003). Energy Based Acoustic Source Localization. Information Processing in Sensor Networks Lecture Notes in Computer Science, Springer.","DOI":"10.1007\/3-540-36978-3_19"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1109\/TIM.2010.2047035","article-title":"An Efficient EM Algorithm for Energy-Based Multisource Localization in Wireless Sensor Networks","volume":"60","author":"Meng","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Lu, L., and Wu, H.C. (2012, January 10\u201315). Novel energy-based localization technique for multiple sources. Proceedings of the 2012 IEEE International Conference on Communications (ICC), Ottawa, ON, Canada.","DOI":"10.1109\/ICC.2012.6364071"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Chang, S., Li, Y., He, Y., and Wang, H. (2018). Target Localization in Underwater Acoustic Sensor Networks Using RSS Measurements. Appl. Sci., 8.","DOI":"10.3390\/app8020225"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Morar, A., Moldoveanu, A., Mocanu, I., Moldoveanu, F., Radoi, I.E., Asavei, V., Gradinaru, A., and Butean, A. (2020). A Comprehensive Survey of Indoor Localization Methods Based on Computer Vision. Sensors, 20.","DOI":"10.3390\/s20092641"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Mao, G. (2009). Localization algorithms and strategies for wireless sensor networks monitoring and surveillance techniques for target tracking. Information Science Reference, IGI Global. Chapter 3.","DOI":"10.4018\/978-1-60566-396-8"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Bhatti, G. (2018). Machine Learning Based Localization in Large-Scale Wireless Sensor Networks. Sensors, 18.","DOI":"10.3390\/s18124179"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Ahmadi, H., and Bouallegue, R. (2015, January 24\u201328). Comparative study of learning-based localization algorithms for Wireless Sensor Networks: Support Vector regression, Neural Network and Na\u00efve Bayes. Proceedings of the 2015 International Wireless Communications and Mobile Computing Conference (IWCMC), Dubrovnik, Croatia.","DOI":"10.1109\/IWCMC.2015.7289314"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Alexandridis, A., and Mouchtaris, A. (2017). Multiple Sound Source Location Estimation in Wireless Acoustic Sensor Networks using DOA estimates: The Data-Association Problem. IEEE\/ACM Trans. Audio Speech Lang. Process.","DOI":"10.1109\/TASLP.2017.2772831"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"102853","DOI":"10.1016\/j.dsp.2020.102853","article-title":"Tracking multiple acoustic sources by adaptive fusion of TDOAs across microphone pairs","volume":"106","author":"Guo","year":"2020","journal-title":"Digit. Signal Process."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Evers, C., Dorfan, Y., Gannot, S., and Naylor, P.A. (2017, January 5\u20139). Source tracking using moving microphone arrays for robot audition. Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA.","DOI":"10.1109\/ICASSP.2017.7953337"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1109\/JOE.2019.2950954","article-title":"Underwater Acoustical Localization of the Black Box Utilizing Single Autonomous Underwater Vehicle Based on the Second-Order Time Difference of Arrival","volume":"45","author":"Sun","year":"2020","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.phycom.2017.10.005","article-title":"Bayesian methodology for target tracking using combined RSS and AoA measurements","volume":"25","author":"Tomic","year":"2017","journal-title":"Phys. Commun."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1023\/A:1012074215150","article-title":"Time Series Prediction and Neural Networks","volume":"31","author":"Frank","year":"2001","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Koh, B.H.D., Lim, C.L.P., Rahimi, H., Woo, W.L., and Gao, B. (2021). Deep Temporal Convolution Network for Time Series Classification. Sensors, 21.","DOI":"10.3390\/s21020603"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"110045","DOI":"10.1016\/j.chaos.2020.110045","article-title":"Robustness of LSTM neural networks for multi-step forecasting of chaotic time series","volume":"139","author":"Sangiorgio","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superpositions of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Math. Control Signals Syst."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","article-title":"Approximation capabilities of multilayer feedforward networks","volume":"4","author":"Hornik","year":"1991","journal-title":"Neural Netw."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.acha.2015.12.005","article-title":"Neural network with unbounded activation functions is universal approximator","volume":"43","author":"Sonoda","year":"2017","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_57","unstructured":"Kalman, B.L., and Kwasny, S.C. (1992, January 7\u201311). Why tanh: Choosing a sigmoidal function. Proceedings of the IJCNN International Joint Conference on Neural Networks, Baltimore, MD, USA."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Abdulkarim, M., Shafie, A., Ahmad, W.F.W., and Razali, R. (2014). Performance Comparison between MLP Neural Network and Exponential Curve Fitting on Airwaves Data. Lecture Notes in Electrical Engineering Advances in Computer Science and Its Applications, Springer.","DOI":"10.1007\/978-3-642-41674-3_150"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1162\/neco.1992.4.2.141","article-title":"First- and Second-Order Methods for Learning: Between Steepest Descent and Newton\u2019s Method","volume":"4","author":"Battiti","year":"1992","journal-title":"Neural Comput."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1109\/72.329697","article-title":"Training feedforward networks with the Marquardt algorithm","volume":"5","author":"Hagan","year":"1994","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1080\/01431160802549278","article-title":"How many hidden layers and nodes?","volume":"30","author":"Stathakis","year":"2009","journal-title":"Int. J. Remote Sens."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1109\/TNN.2003.809401","article-title":"Learning capability and storage capacity of two-hidden-layer feedforward networks","volume":"14","author":"Huang","year":"2003","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Tamura, S. (1991, January 18\u201321). Capabilities of a three layer feedforward neural network. Proceedings of the 1991 IEEE International Joint Conference on Neural Networks, Singapore.","DOI":"10.1109\/IJCNN.1991.170332"},{"key":"ref_65","unstructured":"Shin-ike, K. (2010, January 18\u201321). A two phase method for determining the number of neurons in the hidden layer of a 3-layer neural network. Proceedings of the SICE Annual Conference 2010, Taipei, Taiwan."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"425740","DOI":"10.1155\/2013\/425740","article-title":"Review on Methods to Fix Number of Hidden Neurons in Neural Networks","volume":"2013","author":"Sheela","year":"2013","journal-title":"Math. Probl. Eng."},{"key":"ref_67","first-page":"5875","article-title":"New Interpretations of Normalization Methods in Deep Learning","volume":"34","author":"Sun","year":"2020","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_68","unstructured":"Ioffe, S., and Szegedy, C. (2015, January 6\u201311). Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. Proceedings of the 32nd International Conference on International Conference on Machine Learning-ICML\u201915, Lille, France."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Beichelt, F. (2018). Functions of Random Variables. Appl. Probab. Stoch. Process., 155\u2013198.","DOI":"10.1201\/b21389-6"}],"container-title":["Journal of Sensor and Actuator Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2224-2708\/10\/2\/29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:51:05Z","timestamp":1760161865000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2224-2708\/10\/2\/29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,22]]},"references-count":69,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["jsan10020029"],"URL":"https:\/\/doi.org\/10.3390\/jsan10020029","relation":{},"ISSN":["2224-2708"],"issn-type":[{"value":"2224-2708","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,22]]}}}