?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4068%2F&rft.title=Second+Order+Mathematical+Formulations+Programming+for+Discriminant+Analysis&rft.creator=Duarte+Silva%2C+A.P.&rft.creator=Stam%2C+A.&rft.description=This+paper+introduces+a+nonparametric+formulation-based+mathematical++programming+(MP)+for+solving+the+classification+problem+in+discriminant++analysis.+This+method+differs+from+previously+proposed+MP-based+models+in+that%2C+even+though+the+final+discriminant+function+is+linear+in+terms+of+the+parameters+to+be+estimated%2C+the+formulation+is+quadratic+in+terms+of+the+predictor+(attribute)+variables.+By+including+second+order+(i.e.%2C+quadratic+and+cross-product)+terms+of+the+attribute+variables%2C+the+model+is+similar+in+concept+to+the+usual+treatment+of+multiple+predictor+variables+in+statistical+methods+such+as+Fisher's+linear+discriminant+analysis%2C+and+allows+an+analysis+of+how+including+nonlinear+terms+and+interaction+affect+the+predictive+ability+of+the+estimated+classification+function.+Using+simulation+experiments+involving+data+conditions+for+which+nonlinear+classifiers+are+appropriate%2C+the+classificatory+performance+of+this+class+of+second+order+MP+models+is+compared+with+that+of+existing+statistical+(linear+and+quadratic)+and+first+order+MP-based+formulations.+The+results+of+these+experiments+show+that+the+proposed+formulation+appears+to+be+a+very+attractive+alternative+to+previously+introduced+linear+and+quadratic+statistical+and+linear+MP-based+classification+methods.&rft.publisher=RR-95-007.+Reprinted+from+European+Journal+of+Operational+Research%2C+72%3A4-22+%5B1994%5D.&rft.date=1994&rft.type=Monograph&rft.type=PeerReviewed&rft.format=text&rft.language=en&rft.rights=cc_by&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4068%2F1%2FRR-95-07.pdf&rft.identifier=++Duarte+Silva%2C+A.P.+%26+Stam%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1588.html%3E++(1994).++Second+Order+Mathematical+Formulations+Programming+for+Discriminant+Analysis.+++IIASA+Research+Report+(Reprint).+IIASA%2C+Laxenburg%2C+Austria%3A+RR-95-007.+Reprinted+from+European+Journal+of+Operational+Research%2C+72%3A4-22+%5B1994%5D.+++++