{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T17:10:02Z","timestamp":1789751402134,"version":"4.0.1"},"reference-count":37,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,3,30]],"date-time":"2018-03-30T00:00:00Z","timestamp":1522368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In wireless sensor networks, the classification of incomplete data reported by sensor nodes is an open issue because it is difficult to accurately estimate the missing values. In many cases, the misclassification is unacceptable considering that it probably brings catastrophic damages to the data users. In this paper, a novel classification approach of incomplete data is proposed to reduce the misclassification errors. This method uses the regularized extreme learning machine to estimate the potential values of missing data at first, and then it converts the estimations into multiple classification results on the basis of the distance between interval numbers. Finally, an evidential reasoning rule is adopted to fuse these classification results. The final decision is made according to the combined basic belief assignment. The experimental results show that this method has better performance than other traditional classification methods of incomplete data.<\/jats:p>","DOI":"10.3390\/s18041046","type":"journal-article","created":{"date-parts":[[2018,3,30]],"date-time":"2018-03-30T12:43:48Z","timestamp":1522413828000},"page":"1046","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Classification of Incomplete Data Based on Evidence Theory and an Extreme Learning Machine in Wireless Sensor Networks"],"prefix":"10.3390","volume":"18","author":[{"given":"Yang","family":"Zhang","sequence":"first","affiliation":[{"name":"Key Laboratory of Communication and Information Systems, Beijing Municipal Commission of Education, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yun","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Communication and Information Systems, Beijing Municipal Commission of Education, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Han-Chieh","family":"Chao","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Fujian University of Technology, Fuzhou 350118, China"},{"name":"School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430024, China"},{"name":"Department of Electrical Engineering, National Dong Hwa University, Hualien 97401, Taiwan"},{"name":"Department of Computer Science and Information Engineering, National Ilan University, Yilan 26047, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenjiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Software Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Communication and Information Systems, Beijing Municipal Commission of Education, School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.inffus.2011.08.001","article-title":"Multisensor data fusion: A review of the state-of-the-art","volume":"14","author":"Khaleghi","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"20524","DOI":"10.3390\/s150820524","article-title":"Belief Function Based Decision Fusion for Decentralized Target Classification in Wireless Sensor Networks","volume":"15","author":"Zhang","year":"2015","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7049","DOI":"10.3390\/s140407049","article-title":"Novel Paradigm for Constructing Masses in Dempster-Shafer Evidence Theory for Wireless Sensor Network\u2019s Multisource Data Fusion","volume":"14","author":"Zhang","year":"2014","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/MWC.2014.6882291","article-title":"A Green Data Transmission Mechanism for Wireless Multimedia Sensor Networks Using Information Fusion","volume":"21","author":"Zhang","year":"2014","journal-title":"IEEE Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.adhoc.2015.05.014","article-title":"An efficient user authentication and key agreement scheme for heterogeneous wireless sensor network tailored for the Internet of Things environment","volume":"36","author":"Farash","year":"2016","journal-title":"Ad Hoc Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.patcog.2015.10.001","article-title":"Adaptive imputation of missing values for incomplete pattern classification","volume":"52","author":"Liu","year":"2016","journal-title":"Pattern Recognit."},{"key":"ref_7","unstructured":"Little, R.J., and Rubin, D.B. (2014). Statistical Analysis with Missing Data, John Wiley & Sons."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.neucom.2012.02.040","article-title":"Regularized extreme learning machine for regression with missing data","volume":"102","author":"Yu","year":"2013","journal-title":"Neurocomputing"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.knosys.2015.06.022","article-title":"Classification of incomplete data based on belief functions and K-nearest neighbors","volume":"89","author":"Liu","year":"2015","journal-title":"Knowl.-Based Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/TCYB.2014.2332037","article-title":"A new incomplete pattern classification method based on evidential reasoning","volume":"45","author":"Liu","year":"2015","journal-title":"IEEE Trans. Cybern."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. R. Statist. Soc. Ser. B (Methodol.), 1\u201338.","DOI":"10.1111\/j.2517-6161.1977.tb01600.x"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data, CRC Press.","DOI":"10.1201\/9781439821862"},{"key":"ref_13","unstructured":"Batista, G.E., and Monard, M.C. (2018, March 30). A Study of K-Nearest Neighbour as an Imputation Method. Available online: http:\/\/conteudo.icmc.usp.br\/pessoas\/gbatista\/files\/his2002.pdf."},{"key":"ref_14","unstructured":"Rubin, D.B. (2004). Multiple Imputation for Nonresponse in Surveys, John Wiley & Sons."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1002\/mpr.329","article-title":"Multiple imputation by chained equations: What is it and how does it work?","volume":"20","author":"Azur","year":"2011","journal-title":"Int. J. Methods Psychiatr. Res."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Koren, Y., Bell, R., and Volinsky, C. (2009). Matrix factorization techniques for recommender systems. Computer, 42.","DOI":"10.1109\/MC.2009.263"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, D., Deogun, J., Spaulding, W., and Shuart, B. (2004, January 1\u20135). Towards Missing Data Imputation: A Study of Fuzzy k-Means Clustering Method. Proceedings of the International Conference on Rough Sets and Current Trends in Computing, Uppsala, Sweden.","DOI":"10.1007\/978-3-540-25929-9_70"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ins.2013.01.021","article-title":"A hybrid method for imputation of missing values using optimized fuzzy c-means with support vector regression and a genetic algorithm","volume":"233","author":"Aydilek","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3716","DOI":"10.1016\/j.neucom.2011.06.013","article-title":"Regularized extreme learning machine for regression problems","volume":"74","year":"2011","journal-title":"Neurocomputing"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/TSMCB.2011.2168604","article-title":"Extreme learning machine for regression and multiclass classification","volume":"42","author":"Huang","year":"2012","journal-title":"IEEE Trans. Syst. Man Cybern. Part B (Cybern.)"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/TSMCB.2012.2212703","article-title":"Toward an Axiomatic Definition of Conflict between Belief Functions","volume":"43","author":"Destercke","year":"2013","journal-title":"IEEE Trans. Cybern."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press.","DOI":"10.1515\/9780691214696"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.inffus.2006.04.003","article-title":"Analyzing the combination of conflicting belief functions","volume":"8","author":"Smets","year":"2007","journal-title":"Inf. Fusion"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2115","DOI":"10.1109\/TII.2016.2558464","article-title":"Toward Belief Function-Based Cooperative Sensing for Interference Resistant Industrial Wireless Sensor Networks","volume":"12","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2783","DOI":"10.1109\/TSMC.2016.2622247","article-title":"Hybrid classification system for uncertain data","volume":"47","author":"Liu","year":"2017","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"19669","DOI":"10.3390\/s141019669","article-title":"An integrated model for robust multisensor data fusion","volume":"14","author":"Shen","year":"2014","journal-title":"Sensors"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.knosys.2016.11.001","article-title":"Data classification using evidence reasoning rule","volume":"116","author":"Xu","year":"2017","journal-title":"Knowl.-Based Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1109\/21.376493","article-title":"A k-nearest neighbor classification rule based on Dempster-Shafer theory","volume":"25","author":"Denoeux","year":"1995","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/3468.833094","article-title":"A neural network classifier based on Dempster-Shafer theory","volume":"30","author":"Denoeux","year":"2000","journal-title":"IEEE Trans. Syst. Man Cybern. Part A Syst. Hum."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2532","DOI":"10.1016\/j.patcog.2014.01.011","article-title":"Credal classification rule for uncertain data based on belief functions","volume":"47","author":"Liu","year":"2014","journal-title":"Pattern Recognit."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"396","DOI":"10.3724\/SP.J.1010.2011.00396","article-title":"Weighted evidence combination based on distance of evidence and uncertainty measure","volume":"30","author":"Han","year":"2011","journal-title":"J. Infrared Millim. Waves"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"9562","DOI":"10.3390\/s140609562","article-title":"Novel algorithm for identifying and fusing conflicting data in wireless sensor networks","volume":"14","author":"Zhang","year":"2014","journal-title":"Sensors"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.neucom.2005.12.126","article-title":"Extreme learning machine: Theory and applications","volume":"70","author":"Huang","year":"2006","journal-title":"Neurocomputing"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.neunet.2014.10.001","article-title":"Trends in extreme learning machines: A review","volume":"61","author":"Huang","year":"2015","journal-title":"Neural Netw."},{"key":"ref_35","unstructured":"Deng, W., Zheng, Q., and Chen, L. (April, January 30). Regularized Extreme Learning Machine. Proceedings of the IEEE Symposium on Computational Intelligence and Data Mining, Nashville, TN, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/S0165-0114(01)00195-6","article-title":"Comparison of fuzzy numbers using a fuzzy distance measure","volume":"130","author":"Tran","year":"2002","journal-title":"Fuzzy Sets Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1109\/JSEE.2014.000103","article-title":"Fast cross validation for regularized extreme learning machine","volume":"25","author":"Zhao","year":"2014","journal-title":"J. Syst. Eng. Electron."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1046\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:59:11Z","timestamp":1760194751000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,30]]},"references-count":37,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["s18041046"],"URL":"https:\/\/doi.org\/10.3390\/s18041046","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,30]]}}}