Real-me Classfcao of Large Daa Ses usg Bary Kapsack Reao Bru bru@ds.uroma. Uversy of Roma La Sapeza AIRO 004-35h ANNUAL CONFERENCE OF THE ITALIAN OPERATIONS RESEARCH Sepember 7-0, 004, Lecce, Ialy
Oule The Daa Classfcao Problem Barzao of Daa Records Evaluao of Alerave Barzaos Seleco of Bary Arbues Compuaoal Resuls
Daa Classfcao Fdg models ha descrbe ad dsgush classes or coceps for fuure predco More specfcally: gve a rag se S of daa already paroed classes S ad S -, predc whch class each ew daa belogs o A supervsed learg problem Wh he feld of daa mg : exraco of eresg o-rval, mplc, prevously ukow ad poeally useful formao or paers from daa large daabases We deal wh massve daa ses wh real me requremes
Daa Records Daa are srucured o records. A record scheme s a se of felds R = { f f m } A record sace s a se of values r = { v v m } Each feld f has s doma D : he se of every possble value v, cludg errors. Example: for records represeg persos, feld ca be age, maral saus, correspodg values ca be 8, sgle, correspodg domas ca be Z U {blak}, {sgle, marred, separae, dvorced, wdow, blak}.
Felds ad Arbues Felds ca be: umercal or quaave caegorcal or qualave couous: real-valued dscree: eger or bary ordered o ordered Geerally, classfcao procedures requre a coverso of all felds f o bary oes. They wll here be called arbues a {0,} f {a a } R b = {a a a m a m m }
Barzao A basc ad maly used barzao procedure s he dervao of cu-pos e.g. LAD [Boros-Hammer-Ibarak-Koga]: gve r r such ha her values o feld f are separaed by o oher record, D r r - derve a cu-po α = [v r v r - ] / Cu-po are used o geerae arbues: above or below α May cupos are obaable. For each group of hem, we have a barzao. May alerave barzaos are possble Selecg he bes oe s a combaoral opmzao problem
Example S S - Wegh 90 00 75 05 70 Hegh 95 05 80 90 75 Class yes yes yes o o Classfcao baskeball players ad o baskeball players Wegh 70 75 90 00 05 - - 7.5 0.5 Hegh 75 80 90 95 05 - - 77.5 85 9.5 Possble Barzaos: usg all cu pos bad 7.5, 0.5 ad 77.5 3 7.5 ad 0.5 4
Evaluao of Cu-pos We vesgae a crero for evaluag he qualy of a barzao wh a fas procedure. We evaluae each sgle cupo usg he rag se. They ca be dffere suaos: dsrbuo of dsrbuo of - a - - - α a α a 3 α a 4 α a 5 α a 6 α a dsrbuo of dsrbuo of - b - - - α b α b 3 α b 4 α b 5 α b dsrbuo of dsrbuo of - c - - - α c
Probably Issues The odds of gvg correc posve [egave] classfcao usg α q = l Pr class α Pr class α. Pr class α Pr class α [0, We wa a evaluao of each cu-po ha ca be summed The probably of a couco of eves s a produc Therefore, we cosder he logarhm obag a sum Le N N- be he real ukow classfcao ad A A- be he supposed classfcao kow By defo of probably, N A Pr class α = N Therefore, = l N N A q. A N N A A
Felds wh Normal Dsrbuo We do o kow N N-, bu for felds wh a Normal Gaussa dsrbuo we guess were hey are by usg S ad S- as follows: We hypohesze hs for all couous felds ad dscree felds wh large umber of values hypohess s esable We compue mea value m m - ad devao σ σ - from S S- ad for a raso from o we have: = d e d e d e d e q m m m m α σ α σ α σ α σ σ π σ π σ π σ π. l
Felds wh Bomal Dsrbuo We do o kow N N-, bu for felds wh a Bomal Beroull dsrbuo we guess were hey are by usg S ad S- as follows: We hypohesze hs for all dscree felds ad ordered caegorcal felds hypohess s esable We compue umber of values - ad probably of success p p - from S S- ad for a raso from o we have: = = = = = 0 0!!!!!!.!!!!!! l m m m m p p p p p p p p q α α α α
Felds wh Ukow Dsrbuo For felds havg ukow dsrbuo: caegorcal felds, or felds where oher hypohess are o verfed, we smply replace N N- wh S S-, ad compue he qualy as follows = l S A q. S A S S A A Whe o dsrbuo hypohess ca be doe, we are fac uable o guess were he posve ad egave pos o he rag se should be
The Kapsack Model Now we eed o choose he bes barzao We assocae o cu-pos bary varables x = f α s used 0 oherwse I early real-me applcao, we ca compue he umber b of arbues we ca deal wh reasoable me max, p, x q x b x {0,} If all p are, hs kapsack becomes a easy problem: a greedy heursc fds he opmal soluo
Classfcao Oce daa are barzed, he acual classfcao sep s performed usg he followg weghed sum, where P s he se of arbues gvg a posve classfcao N s he se of arbues gvg a egave classfcao r =, P w a r, N w a r 0 r s classfed < 0 r s classfed - weghs w for he arbues are posve [egave] values proporoal o he cardaly of he par of S [ S-] coaed such arbues
Compuaoal Resuls The algorhm s mplemeed C ad esed o he larges daases wh bary classfcao of he UCI reposory: hp://www.cs.uc.edu/mlear/mlreposory.hml spam e-mal, adul, germa cred, musk, pma das Tess usg 0%, 5% ad 30% of daase as rag se Each resul s average o 5 rals wh radom seleco of he rag se
Spam E-mal Daase Classfy emal spam or o: 460 records each havg 58 umercal felds 55 real dscree 0% 5% 30% Accuracy 96.74 97.3 96.53 Tme sec. 0.78 0.8 0.85 Bes leraure: comparable 97 98% wh much larger rag se 50% ad more me ~0x
Adul Daase Decde wheher aual come > 50,000 $ : 45 mssg removed records each havg 5 felds 6 real 8 caegorcal 0% 5% 30% Accuracy 76.73 75.96 76.78 Tme sec. 3.4 3.53 3.7 Bes leraure: moderaely beer 85 86% wh much larger rag se 75% ad more me ~0x
Salog - Germa Cred Daase Classfy good ad bad credors: 000 records each havg 0 felds 7 umercal 3 caegorcal 0% 5% 30% Accuracy 63.88 68.89 65.7 Tme sec. 0.7 0.7 0.7 Bes leraure: moderaely beer 75% wh much larger rag se 60% ad much more me ~50x
Musk clea Daase Classfy molecules musk or o: 6598 records each havg 67 real felds 0% 5% 30% Accuracy 86.00 86.47 88.94 me.75.76.96 Bes leraure: slghly beer 9% wh much larger rag se 50% ad more me ~0x
Pma Idas Daase Classfy paes dabec or o: 768 records each havg 8 umercal felds real 6 dscree 0% 5% 30% Accuracy 65.9 65.9 66.30 Tme sec. 0.05 0.03 0.04 Bes leraure: moderaely beer 70 75% wh much larger rag se 50% ad much more me ~00x
Coclusos The proposed approach classfes exremely shor mes large daases, obag a good accuracy ad usg very reduced rag ses Compuaoal me may be decded advace, hece he procedure s suable for dealg wh real-me requremes Accuracy creases wh he dmeso of he rag se ul a cera dmeso. Whe furher creasg he rag se, hece he graulary of he barzao, logcal combaos of arbues become useful e.g. LAD