?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%2F4935%2F&rft.title=Mathematical+Programming+Formulations+for+Two-group+Classification+with+Binary+Variables&rft.creator=Asparoukhov%2C+O.K.&rft.creator=Stam%2C+A.&rft.description=In+this+paper%2C+we+introduce+a+nonparametric+mathematical+programming+(MP)+approach+for+solving+the+binary+variable+classification+problem.+In+practice%2C+there+exists+a+substantial+interest+in+the+binary+variable+classification+problem.+For+instance%2C+medical+diagnoses+are+often+based+on+the+presence+or+absence+of+relevant+symptoms%2C+and+binary+variable+classification+has+long+been+used+as+a+means+to+predict+(diagnose)+the+nature+of+the+medical+condition+of+patients.+Our+research+is+motivated+by+the+fact+that+none+of+the+existing+statistical+methods+for+binary+variable+classification+--+parametric+and+nonparametric+alike+--+are+fully+satisfactory.+%0D%0A%0D%0AThe+general+class+of+MP+classification+methods+facilitates+a+geometric+interpretation%2C+and+MP-based+classification+rules+have+intuitive+appeal+because+of+their+potentially+robust+properties.+These+intuitive+arguments+appear+to+have+merit%2C+and+a+number+of+research+studies+have+confirmed+that+MP+methods+can+indeed+yield+effective+classification+rules+under+certain+non-normal+data+conditions%2C+for+instance+if+the+data+set+is+outlier-contaminated+or+highly+skewed.+However%2C+the+MP-based+approach+in+general+lacks+a+probabilistic+foundation%2C+an+ad+hoc+assessment+of+its+classification+performance.+%0D%0A%0D%0AOur+proposed+nonparametric+mixed+integer+programming+(MIP)+formulation+for+the+binary+variable+classification+problem+not+only+has+a+geometric+interpretation%2C+but+also+is+consistent+with+the+Bayes+decision+theoretic+approach.+Therefore%2C+our+proposed+formulation+possesses+a+strong+probabilistic+foundation.+We+also+introduce+a+linear+programming+(LP)+formulation+which+parallels+the+concepts+underlying+the+MIP+formulation%2C+but+does+not+possess+the+decision+theoretic+justification.+%0D%0A%0D%0AAn+additional+advantage+of+both+our+LP+and+MIP+formulations+is+that%2C+due+to+the+fact+that+the+attribute+variables+are+binary%2C+the+training+sample+observations+can+be+partitioned+into+multinomial+cells%2C+allowing+for+a+substantial+reduction+in+the+number+of+binary+and+deviational+variables%2C+so+that+our+formulation+can+be+used+to+analyze+training+samples+of+almost+any+size.+%0D%0A%0D%0AWe+illustrate+our+formulations+using+an+example+problem%2C+and+use+three+real+data+sets+to+compare+its+classification+performance+with+a+variety+of+parametric+and+nonparametric+statistical+methods.+For+each+of+these+data+sets%2C+our+proposed+formulation+yields+the+minimum+possible+number+of+misclassifications%2C+both+using+the+resubstitution+and+the+leave-one-out+method.&rft.publisher=WP-96-092&rft.date=1996-08&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4935%2F1%2FWP-96-092.pdf&rft.identifier=++Asparoukhov%2C+O.K.+%26+Stam%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1588.html%3E++(1996).++Mathematical+Programming+Formulations+for+Two-group+Classification+with+Binary+Variables.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-96-092+++++