?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%2F4934%2F&rft.title=An+Efficient+Mixed+Integer+Programming+Algorithm+for+Minimizing+the+Training+Sample+Misclassification+Cost+in+Two-group+Classification&rft.creator=Duarte+Silva%2C+A.P.&rft.creator=Stam%2C+A.&rft.description=In+this+paper%2C+we+introduce+the+Divide+and+Conquer+(D%26C)+algorithm%2C+a+computationally+efficient+algorithm+for+determining+classification+rules+which+minimize+the+training+sample+misclassification+cost+in+two-group+classification.+This+classification+rule+can+be+derived+using+mixed+integer+programming+(MIP)+techniques.+However%2C+it+is+well-documented+that+the+complexity+of+MIP-based+classification+problems+grows+exponentially+as+a+function+of+the+size+of+the+training+sample+and+the+number+of+attributes+describing+the+observations%2C+requiring+special-purpose+algorithms+to+solve+even+small+size+problems+within+a+reasonable+computational+time.+The+D%26C+algorithm+derives+its+name+from+the+fact+that+it+relies%2C+a.o.%2C+on+partitioning+the+problem+in+smaller%2C+more+easily+handled+subproblems%2C+rendering+it+substantially+faster+than+previously+proposed+algorithms.+%0D%0A%0D%0AThe+D%26C+algorithm+solves+the+problem+to+the+exact+optimal+solution+(i.e.%2C+it+is+not+a+heuristic+that+approximates+the+solution)%2C+and+allows+for+the+analysis+of+much+larger+training+samples+than+previous+methods.+For+instance%2C+our+computational+experiments+indicate+that%2C+on+average%2C+the+D%26C+algorithm+solves+problems+with+2+attributes+and+500+observations+more+than+3+times+faster%2C+and+problems+with+5+attributes+and+100+observations+over+50+times+faster+than+Soltysik+and+Yarnold's+software%2C+which+may+be+the+fastest+existing+algorithm.+We+believe+that+the+D%26C+algorithm+contributes+significantly+to+the+field+of+classification+analysis%2C+because+it+substantially+widens+the+array+of+data+sets+that+can+be+analyzed+meaningfully+using+methods+which+require+MIP+techniques%2C+in+particular+methods+which+seek+to+minimize+the+misclassification+cost+in+the+training+sample.+The+programs+implementing+the+D%26C+algorithm+are+available+from+the+authors+upon+request.&rft.publisher=WP-96-093&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%2F4934%2F1%2FWP-96-093.pdf&rft.identifier=++Duarte+Silva%2C+A.P.+%26+Stam%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1588.html%3E++(1996).++An+Efficient+Mixed+Integer+Programming+Algorithm+for+Minimizing+the+Training+Sample+Misclassification+Cost+in+Two-group+Classification.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-96-093+++++