{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T03:40:35Z","timestamp":1785901235651,"version":"3.56.0"},"reference-count":58,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,3,2]],"date-time":"2015-03-02T00:00:00Z","timestamp":1425254400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The support vector machine is used as a data mining technique to extract informative hydrologic data on the basis of a strong relationship between error tolerance and the number of support vectors. Hydrologic data of flash flood events in the Lan-Yang River basin in Taiwan were used for the case study. Various percentages (from 50% to 10%) of hydrologic data, including those for flood stage and rainfall data, were mined and used as informative data to characterize a flood hydrograph. Information on these mined hydrologic data sets was quantified using entropy indices, namely marginal entropy, joint entropy, transinformation, and conditional entropy. Analytical results obtained using the entropy indices proved that the mined informative data could be hydrologically interpreted and have a meaningful explanation based on information entropy. Estimates of marginal and joint entropies showed that, in view of flood forecasting, the flood stage was a more informative variable than rainfall. In addition, hydrologic models with variables containing more total information were preferable to variables containing less total information. Analysis results of transinformation explained that approximately 30% of information on the flood stage could be derived from the upstream flood stage and 10% to 20% from the rainfall. Elucidating the mined hydrologic data by applying information theory enabled using the entropy indices to interpret various hydrologic processes.<\/jats:p>","DOI":"10.3390\/e17031023","type":"journal-article","created":{"date-parts":[[2015,3,2]],"date-time":"2015-03-02T10:45:12Z","timestamp":1425293112000},"page":"1023-1041","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Mining Informative Hydrologic Data by Using Support Vector Machines and Elucidating Mined Data according to Information Entropy"],"prefix":"10.3390","volume":"17","author":[{"given":"Shien-Tsung","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Water Resources Engineering and Conservation, Feng Chia University, No. 100, Wenhua Road, Taichung City 40724, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Vapnik, V.N. (1995). The Nature of Statistical Learning Theory, Springer-Verlag.","DOI":"10.1007\/978-1-4757-2440-0"},{"key":"ref_2","unstructured":"Vapnik, V.N. (1998). Statistical Learning Theory, Wiley."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"209","DOI":"10.2166\/hydro.2004.0016","article-title":"EC-SVM approach for real-time hydrologic forecasting","volume":"6","author":"Yu","year":"2004","journal-title":"J. Hydroinform."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"265","DOI":"10.2166\/hydro.2004.0020","article-title":"Identification of support vector machines for runoff modeling","volume":"6","author":"Bray","year":"2004","journal-title":"J. Hydroinform."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"37","DOI":"10.2166\/nh.2005.0004","article-title":"Flow categorization model for improving forecasting","volume":"36","author":"Sivapragasam","year":"2005","journal-title":"Nord. Hydrol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"267","DOI":"10.2166\/hydro.2007.027","article-title":"Flood forecasting using support vector machines","volume":"9","author":"Han","year":"2007","journal-title":"J. Hydroinform."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.jhydrol.2009.03.032","article-title":"Support vector machine-based models for hourly reservoir inflow forecasting during typhoon-warning periods","volume":"372","author":"Lin","year":"2009","journal-title":"J. Hydrol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.jhydrol.2013.02.012","article-title":"Typhoon flood forecasting using integrated two-stage support vector machine approach","volume":"486","author":"Lin","year":"2013","journal-title":"J. Hydrol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1002\/hyp.9584","article-title":"Improving the forecasts of extreme streamflow by support vector regression with the data extracted by self-organizing map","volume":"28","author":"Wu","year":"2014","journal-title":"Hydrol. Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1111\/j.1752-1688.2002.tb01544.x","article-title":"Flood stage forecasting with support vector machines","volume":"38","author":"Liong","year":"2002","journal-title":"J. Am. Water Resour. Assoc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1016\/j.jhydrol.2006.01.021","article-title":"Support vector regression for real-time flood stage forecasting","volume":"328","author":"Yu","year":"2006","journal-title":"J. Hydrol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.jhydrol.2007.04.008","article-title":"Real-time probabilistic forecasting of flood stages","volume":"340","author":"Chen","year":"2007","journal-title":"J. Hydrol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.jhydrol.2007.08.029","article-title":"Pruning of support vector networks on flood forecasting","volume":"347","author":"Chen","year":"2007","journal-title":"J. Hydrol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3705","DOI":"10.1007\/s11269-012-0098-x","article-title":"Stage and discharge forecasting by SVM and ANN Techniques","volume":"26","author":"Aggarwal","year":"2012","journal-title":"Water Resour. Manag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5189","DOI":"10.1016\/j.eswa.2011.11.020","article-title":"Wavelet kernel support vector machines forecasting techniques: Case study on water-level predictions during typhoons","volume":"39","author":"Wei","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.2166\/hydro.2001.0014","article-title":"Rainfall and runoff forecasting with SSA-SVM approach","volume":"3","author":"Sivapragasam","year":"2001","journal-title":"J. Hydroinform."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"841","DOI":"10.2478\/v10006-012-0062-1","article-title":"A rainfall forecasting method using machine learning models and its application to the Fukuoka City case","volume":"22","author":"Sumi","year":"2012","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1061\/(ASCE)HE.1943-5584.0000875","article-title":"SVM-based model for short-term rainfall forecasts at a local scale in the Mumbai urban area, India","volume":"19","author":"Nikam","year":"2014","journal-title":"J. Hydrol. Eng."},{"key":"ref_19","first-page":"110","article-title":"Multiclass support vector classification to estimate typhoon rainfall distribution","volume":"6","author":"Chen","year":"2013","journal-title":"Disaster Adv."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.jhydrol.2013.04.050","article-title":"Development of an effective data-driven model for hourly typhoon rainfall forecasting","volume":"495","author":"Lin","year":"2013","journal-title":"J. Hydrol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.jhydrol.2014.12.009","article-title":"A real-time forecasting model for the spatial distribution of typhoon rainfall","volume":"521","author":"Lin","year":"2015","journal-title":"J. Hydrol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.jhydrol.2011.05.017","article-title":"Comparison of neural network architectures and inputs for radar rainfall adjustment for typhoon events","volume":"405","author":"Chen","year":"2011","journal-title":"J. Hydrol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2337","DOI":"10.1109\/TGRS.2012.2210429","article-title":"Modeling and prediction of rainfall using radar reflectivity data: A data-mining approach","volume":"51","author":"Kusiak","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1016\/j.jhydrol.2006.04.030","article-title":"Downscaling of precipitation for climate change scenarios: A support vector machine approach","volume":"330","author":"Tripathi","year":"2006","journal-title":"J. Hydrol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2692","DOI":"10.1109\/TGRS.2008.919819","article-title":"Downscaling and forecasting of evapotranspiration using a synthetic model of wavelets and support vector machines","volume":"46","author":"Kaheil","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.jhydrol.2010.01.021","article-title":"Statistical downscaling of daily precipitation using support vector machines and multivariate analysis","volume":"385","author":"Chen","year":"2010","journal-title":"J. Hydrol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1002\/hyp.7883","article-title":"Projection of climate change for daily precipitation: A case study in Shih-Men Reservoir catchment in Taiwan","volume":"25","author":"Yang","year":"2011","journal-title":"Hydrol. Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/TSMCB.2002.805808","article-title":"Feature subset selection for support vector machines through discriminative function pruning analysis","volume":"34","author":"Mao","year":"2004","journal-title":"IEEE Trans. Syst. Man Cybern. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1142\/S0129065706000688","article-title":"Pruning and model-selecting algorithms in the RBF frameworks constructed by support vector learning","volume":"16","author":"Hao","year":"2006","journal-title":"Int. J. Neural Syst."},{"key":"ref_30","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_31","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0022-1694(72)90003-0","article-title":"Principle of maximum entropy in hydrologic frequency analysis","volume":"17","author":"Sonuga","year":"1972","journal-title":"J. Hydrol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0022-1694(79)90004-0","article-title":"The extreme-value type-1 distribution and the principle of maximum entropy","volume":"42","author":"Jowitt","year":"1979","journal-title":"J. Hydrol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1029\/WR024i009p01519","article-title":"Maximum entropy spectral analysis of hydrologic data","volume":"24","author":"Padmanabhan","year":"1988","journal-title":"Water Resour. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1289\/ehp.0800089","article-title":"BME Estimation of Residential Exposure to Ambient PM10 and Ozone at Multiple Time-Scales","volume":"117","author":"Yu","year":"2009","journal-title":"Environ. Health Perspect."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.jhydrol.2009.11.046","article-title":"Understanding Space-time Patterns of Groundwater Systems by Empirical Orthogonal Functions: A case study in the Choshui River Alluvial Fan, Taiwan","volume":"381","author":"Yu","year":"2010","journal-title":"J. Hydrol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.3390\/ijerph8062153","article-title":"Estimation of fine particulate matter in Taipei using landuse regression and Bayesian maximum entropy methods","volume":"8","author":"Yu","year":"2011","journal-title":"Int. J. Environ. Res. Public Health."},{"key":"ref_37","first-page":"1416","article-title":"Quantile-based Bayesian maximum entropy approach for spatiotemporal modeling of ambient air quality levels","volume":"47","author":"Yu","year":"2013","journal-title":"Environ. Sci. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1029\/WR009i006p01511","article-title":"Entropy in the assessment of uncertainty in hydrologic systems and models","volume":"9","author":"Amorocho","year":"1973","journal-title":"Water Resour. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0022-1694(86)90079-X","article-title":"Entropy as a measure of hydrologic data uncertainty and model performance","volume":"85","author":"Chapman","year":"1986","journal-title":"J. Hydrol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1111\/j.1752-1688.1989.tb03088.x","article-title":"Hydrologic uncertainty measure and network design","volume":"25","author":"Husain","year":"1989","journal-title":"Water Resour. Bull."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/j.1752-1688.1992.tb03163.x","article-title":"Water quality monitoring network design: A problem of multi-objective decision making","volume":"28","author":"Harmancioglu","year":"1992","journal-title":"AWRA Water Resour. Bull."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/0022-1694(94)90111-2","article-title":"An entropy approach to data collection network design","volume":"157","author":"Yang","year":"1994","journal-title":"J. Hydrol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0022-1694(03)00244-0","article-title":"Entropy and generalized least square methods in assessment of the regional value of streamgages","volume":"283","author":"Markus","year":"2003","journal-title":"J. Hydrol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1016\/j.jhydrol.2009.11.015","article-title":"Hydrometric network evaluation for Canadian watersheds","volume":"380","author":"Mishra","year":"2010","journal-title":"J. Hydrol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1728","DOI":"10.3390\/e16031728","article-title":"Discharge estimation in a lined canal using information entropy","volume":"16","author":"Chen","year":"2014","journal-title":"Entropy"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"4626","DOI":"10.3390\/e16084626","article-title":"Spatiotemporal scaling effect on rainfall network design using entropy","volume":"16","author":"Wei","year":"2014","journal-title":"Entropy"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1002\/(SICI)1099-1085(199705)11:6<587::AID-HYP479>3.0.CO;2-P","article-title":"The use of entropy in hydrology and water resources","volume":"11","author":"Singh","year":"1997","journal-title":"Hydrol. Process."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Mishra, A.K., and Coulibaly, P. (2009). Development in hydrometric networks design: A review. Rev. Geophys., 47.","DOI":"10.1029\/2007RG000243"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"195","DOI":"10.3390\/e13010195","article-title":"Wavelet-based analysis on the complexity of hydrologic series data under multi-temporal scales","volume":"13","author":"Sang","year":"2011","journal-title":"Entropy"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.3390\/e14091784","article-title":"Bivariate rainfall and runoff analysis using entropy and copula theories","volume":"14","author":"Zhang","year":"2012","journal-title":"Entropy"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2754","DOI":"10.1002\/hyp.7372","article-title":"Input data selection for solar radiation estimation","volume":"23","author":"Ahmadi","year":"2009","journal-title":"Hydrol. Process."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"396","DOI":"10.2166\/hydro.2010.063","article-title":"Effect of data time interval on real-time flood forecasting","volume":"12","author":"Remesan","year":"2010","journal-title":"J. Hydroinform."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"114","DOI":"10.2166\/hydro.2014.138","article-title":"Input selection for long-lead precipitation prediction using large-scale climate variables: A case study","volume":"17","author":"Ahmadi","year":"2015","journal-title":"J. Hydroinform."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1061\/(ASCE)HE.1943-5584.0000332","article-title":"Hydrologic synthesis using entropy theory: Review","volume":"16","author":"Singh","year":"2011","journal-title":"J. Hydrol. Eng."},{"key":"ref_55","unstructured":"Hsu, C.W., Chang, C.C., and Lin, C.J. A Practical Guide to Support Vector Classification. Available online: http:\/\/www.csie.ntu.edu.tw\/~cjlin\/papers\/guide\/guide.pdf."},{"key":"ref_56","unstructured":"Wikipedia: Joint entropy. Available online: http:\/\/en.wikipedia.org\/wiki\/Joint_entropy."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1623\/hysj.48.3.399.45291","article-title":"Model trees as an alternative to neural networks in rainfall-runoff modelling","volume":"48","author":"Solomatine","year":"2003","journal-title":"Hydrol. Sci. J."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.jhydrol.2013.03.033","article-title":"Typhoon event-based evolutionary fuzzy inference model for flood stage forecasting","volume":"490","author":"Chen","year":"2013","journal-title":"J. Hydrol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/3\/1023\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:43:01Z","timestamp":1760215381000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/3\/1023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,2]]},"references-count":58,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,3]]}},"alternative-id":["e17031023"],"URL":"https:\/\/doi.org\/10.3390\/e17031023","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,2]]}}}