{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:52Z","timestamp":1760242252280,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,8]],"date-time":"2017-03-08T00:00:00Z","timestamp":1488931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["61371189"],"award-info":[{"award-number":["61371189"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Artificial neural networks are widely applied for prediction, function simulation, and data classification. Among these applications, the wavelet neural network is widely used in image classification problems due to its advantages of high approximation capabilities, fault-tolerant capabilities, learning capacity, its ability to effectively overcome local minimization issues, and so on. The error function of a network is critical to determine the convergence, stability, and classification accuracy of a neural network. The selection of the error function directly determines the network\u2019s performance. Different error functions will correspond with different minimum error values in training samples. With the decrease of network errors, the accuracy of the image classification is increased. However, if the image classification accuracy is difficult to improve upon, or is even decreased with the decreasing of the errors, then this indicates that the network has an \u201cover-learning\u201d phenomenon, which is closely related to the selection of the function errors. With regards to remote sensing data, it has not yet been reported whether there have been studies conducted regarding the \u201cover-learning\u201d phenomenon, as well as the relationship between the \u201cover-learning\u201d phenomenon and error functions. This study takes SAR, hyper-spectral, high-resolution, and multi-spectral images as data sources, in order to comprehensively and systematically analyze the possibility of an \u201cover-learning\u201d phenomenon in the remote sensing images from the aspects of image characteristics and neural network. Then, this study discusses the impact of three typical entropy error functions (NB, CE, and SH) on the \u201cover-learning\u201d phenomenon of a network. The experimental results show that the \u201cover-learning\u201d phenomenon may be caused only when there is a strong separability between the ground features, a low image complexity, a small image size, and a large number of hidden nodes. The SH entropy error function in that case will show a good \u201cover-learning\u201d resistance ability. However, for remote sensing image classification, the \u201cover-learning\u201d phenomenon will not be easily caused in most cases, due to the complexity of the image itself, and the diversity of the ground features. In that case, the NB and CE entropy error network mainly show a good stability. Therefore, a blind selection of a SH entropy error function with a high \u201cover-learning\u201d resistance ability from the wavelet neural network classification of the remote sensing image will only decrease the classification accuracy of the remote sensing image. It is therefore recommended to use an NB or CE entropy error function with a stable learning effect.<\/jats:p>","DOI":"10.3390\/e19030101","type":"journal-article","created":{"date-parts":[[2017,3,8]],"date-time":"2017-03-08T07:42:58Z","timestamp":1488958978000},"page":"101","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["\u201cOver-Learning\u201d Phenomenon of Wavelet Neural Networks in Remote Sensing Image Classifications with Different Entropy Error Functions"],"prefix":"10.3390","volume":"19","author":[{"given":"Dongmei","family":"Song","sequence":"first","affiliation":[{"name":"School of Geosciences, China University of Petroleum, Qingdao 266580, China"},{"name":"Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yajie","family":"Zhang","sequence":"additional","affiliation":[{"name":"The First Institute of Geodetic Surveying, NASG, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinjian","family":"Shan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianyong","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Geosciences, China University of Petroleum, Qingdao 266580, China"},{"name":"Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huisheng","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Geosciences, China University of Petroleum, Qingdao 266580, China"},{"name":"Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,8]]},"reference":[{"key":"ref_1","first-page":"5630","article-title":"Detection and classification of oil spill and look-alike spots from SAR imagery using an artificial neural network","volume":"53","author":"Singha","year":"2012","journal-title":"Int. Geosci. Remote Sens. Symp."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2134","DOI":"10.3390\/rs6032134","article-title":"Artificial neural network modeling of high arctic phytomass using synthetic aperture radar and multispectral data","volume":"6","author":"Collingwood","year":"2014","journal-title":"Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.3390\/rs70201529","article-title":"Multilayer Perceptron Neural Networks Model for Meteosat Second Generation SEVIRI Daytime Cloud Masking","volume":"7","author":"Taravat","year":"2015","journal-title":"Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1109\/TGRS.2014.2335751","article-title":"Compressed-domain ship detection on spaceborne optical image using deep neural network and extreme learning machine","volume":"53","author":"Tang","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1109\/LGRS.2016.2595108","article-title":"A Self-Improving Convolution Neural Network for the Classification of Hyperspectral Data","volume":"13","author":"Ghamisi","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4753","DOI":"10.1007\/s00500-015-1739-9","article-title":"An efficient radial basis function neural network for hyperspectral remote sensing image classification","volume":"20","author":"Li","year":"2016","journal-title":"Soft Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1109\/TGRS.2016.2612821","article-title":"Convolutional Neural Networks for Large-Scale Remote-Sensing Image Classification","volume":"55","author":"Maggiori","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.patcog.2016.10.019","article-title":"Hyperspectral image reconstruction by deep convolutional neural network for classification","volume":"63","author":"Li","year":"2017","journal-title":"Pattern Recognit."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/j.patcog.2016.07.001","article-title":"Towards better exploiting convolutional neural networks for remote sensing scene classification","volume":"61","author":"Nogueira","year":"2017","journal-title":"Pattern Recognit."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1080\/2150704X.2016.1235299","article-title":"SatCNN: Satellite image dataset classification using agile convolutional neural networks","volume":"8","author":"Zhong","year":"2017","journal-title":"Remote Sens. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/36.124218","article-title":"Classification of multispectral remote sensing data using a back-propagation neural network","volume":"30","author":"Heermann","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","first-page":"153","article-title":"Supervised classification of multispectral remote sensing image using a BP neural network","volume":"17","author":"Li","year":"1998","journal-title":"J. Infrared Millim. Waves"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.13031\/2013.2971","article-title":"Backpropagation neural network design and evaluation for classifying weed species using color image texture","volume":"43","author":"Burks","year":"2000","journal-title":"Trans. ASAE"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1109\/TGRS.2013.2251888","article-title":"Using partial least squares-artificial neural network for inversion of inland water Chlorophyll-a","volume":"52","author":"Song","year":"2014","journal-title":"IEEE Trans. Geosci Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagation errors","volume":"323","author":"Rumerhart","year":"1986","journal-title":"Nature"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1109\/72.165591","article-title":"Wavelet networks","volume":"3","author":"Zhang","year":"1992","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7878","DOI":"10.1080\/01431161.2014.978037","article-title":"Impact of different saturation encoding modes on object classification using a BP wavelet neural network","volume":"35","author":"Song","year":"2014","journal-title":"Int. J. Remote Sens."},{"key":"ref_18","first-page":"64","article-title":"Fault Diagnosis of Analog Circuit Based on BP Wavelet Neural Network","volume":"26","author":"Jin","year":"2007","journal-title":"Meas. Control Technol."},{"key":"ref_19","unstructured":"Hsu, P.H., and Yang, H.H. (2007, January 23\u201328). Hyperspectral image classification using wavelet networks. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2007, Barcelona, Spain."},{"key":"ref_20","first-page":"913","article-title":"Structure Modality of the Error Function for Feedforward Neural Networks","volume":"40","author":"Jin","year":"2003","journal-title":"J. Comput. Res. Dev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1109\/TNN.2002.1031939","article-title":"Two highly efficient second-order algorithms for training feedforward networks","volume":"13","author":"Ampazis","year":"2002","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2883","DOI":"10.1080\/01431169308904316","article-title":"Conjugate-gradient neural networks in classification of multisource and very-high-dimensional remote sensing data","volume":"14","author":"Benediktsson","year":"1993","journal-title":"Int. J. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1109\/72.788640","article-title":"The Nature of Statistical Learning Theory","volume":"10","author":"Vapnik","year":"1995","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1109\/82.160170","article-title":"Fast learning algorithms for neural networks","volume":"39","author":"Karayiannis","year":"1992","journal-title":"IEEE Trans. Circuits Syst. II Analog Digit. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/0893-6080(92)90008-7","article-title":"Improving the Convergence of the Back-Propagation Algorithm","volume":"5","author":"Van","year":"1992","journal-title":"Neural Netw."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"11","DOI":"10.4218\/etrij.95.0195.0012","article-title":"A modified error function to improve the error back-propagation algorithm for multi-layer perceptrons","volume":"17","author":"Oh","year":"1995","journal-title":"ETRI J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1109\/72.572117","article-title":"Improving the Error Back Propagation Algorithm with a Modified Error Function","volume":"8","author":"Oh","year":"1997","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_28","first-page":"260","article-title":"Neural Network Learning Algorithm of Over-learning and Solving Method","volume":"22","author":"Li","year":"2002","journal-title":"J. Vib. Meas. Diagn."},{"key":"ref_29","unstructured":"Sun, J. (2009). Principles and Applications of Remote Sensing, Wuhan University Press."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/01431169608949000","article-title":"The influence of relative sample size in training artificial neural networks","volume":"17","author":"Blamire","year":"1996","journal-title":"Int. J. Remote Sens."},{"key":"ref_31","first-page":"391","article-title":"Classification of remotely sensed data by an artificial neural network: Issues related to training data characteristics","volume":"61","author":"Foody","year":"1995","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/j.1538-7305.1948.tb00917.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell. Syst. Tech. J."},{"key":"ref_33","first-page":"256","article-title":"Modified Linear-Prediction Based Band Selection for Hyperspectral Image","volume":"33","author":"Zhou","year":"2013","journal-title":"Acta Opt. Sin."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1175\/BAMS-D-12-00154.1","article-title":"Heihe Watershed Allied Telemetry Experimental Research (Hiwater): Scientific Objectives and Experimental Design","volume":"94","author":"Li","year":"2013","journal-title":"Bull. Am. Meteorol. Soc."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/3\/101\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:30:01Z","timestamp":1760207401000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/3\/101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,8]]},"references-count":34,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["e19030101"],"URL":"https:\/\/doi.org\/10.3390\/e19030101","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,3,8]]}}}