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300 2293 51 (3.) 51 SB375 2293 235 (Notation) 235 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font450 2371 1616 (This paper uses strange notation. The brief background information above uses a) 1616 SB450 2430 1607 (more standard notation normally found in decision theory, but of course, it is still) 1607 SB450 2489 1641 (not completely standard. Here are a few equivalencies. Notationally speaking, the) 1641 SB450 2548 1490 (section on Dempster-Shafer theory is much closer to other literature on the) 1490 SB450 2607 152 (subject.) 152 SB32 0 0 42 42 0 0 0 38 /Times-Italic /font31 ANSIFont font300 3069 912 (CPSC 599.14, Oct 18, 1993 A.D. Paul Schermerhorn) 912 SB1 #Cstatusdict begin /manualfeed false store endEJ RS%%PageTrailer%%PageResources: font Symbol%%+ font Times-Bold%%+ font Times-Italic%%+ font Times-Roman%%Page: 2 2%%PageResources: (atend)SS0 0 25 11 798 1100 300 SM32 0 0 50 50 1 0 0 45 /Times-Roman /font32 ANSIFont font0 0 0 fCgs 531 59 428 176 CB450 178 158 (Xu et al) 158 SBgrgs 375 59 960 176 CB983 178 218 ("Standard") 218 SBgr32 0 0 50 50 0 0 0 51 /Symbol fontgs 56 65 428 235 CB450 235 34 (L) 34 SBgr32 0 0 50 50 0 0 0 51 /Symbol fontgs 63 65 960 235 CB984 235 39 (W) 39 SBgrgs 63 65 960 235 CB983 235 39 (W) 39 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont fontgs 372 59 1336 235 CB1358 237 269 (Sample space) 269 SBgrgs 531 59 428 300 CB450 302 33 (C) 33 SBgr32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont fontgs 531 59 428 300 CB483 315 14 (i) 14 SBgr32 0 0 50 50 0 0 0 51 /Symbol fontgs 57 65 960 300 CB983 300 34 (w) 34 SBgr32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont fontgs 375 65 960 300 CB1017 319 14 (i) 14 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont fontgs 372 59 1336 300 CB1358 302 118 (Class ) 118 SBgr32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont fontgs 372 59 1336 300 CB1476 302 14 (i) 14 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont fontgs 531 78 428 365 CB450 371 33 (C) 33 SBgr32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont fontgs 531 78 428 365 CB483 384 14 (i) 14 SBgr32 0 0 50 50 0 0 0 51 /Symbol fontgs 137 78 428 365 CB497 378 36 (\316) 36 SBgr32 0 0 50 50 0 0 0 51 /Symbol fontgs 171 78 428 365 CB565 365 34 (L) 34 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont fontgs 531 78 428 365 CB599 371 163 (, i=M+1) 163 SBgr32 0 0 50 50 0 0 0 51 /Symbol fontgs 57 65 960 365 CB983 365 34 (w) 34 SBgr32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont fontgs 375 65 960 365 CB1017 384 25 (0) 25 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont fontgs 372 59 1336 365 CB1358 367 173 (Rejected) 173 SBgr32 0 0 67 67 0 0 0 60 /Times-Roman /font32 ANSIFont font300 564 51 (4.) 51 SB375 564 204 (Experts) 204 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font450 642 1554 (In this paper, an expert is a classifier. The focus is on combining the results of) 1554 SB450 701 1625 (multiple classifiers of possibly different types. It is assumed that we already know) 1625 SB450 760 979 (about these classifiers. A classifier is denoted by ) 979 SB32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font1429 760 22 (e) 22 SB1451 773 22 (k) 22 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font1473 760 551 (\(x\) where x is the input \(i.e.) 551 SB450 819 391 (feature vector\) and ) 391 SB32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font841 819 22 (k) 22 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font863 819 1132 ( is the specific classifier from a total of K classifiers. It is) 1132 SB450 878 1634 (further assumed that these classifiers have already been trained to the task at hand.) 1634 SB32 0 0 67 67 0 0 0 60 /Times-Roman /font32 ANSIFont font300 997 51 (5.) 51 SB375 997 413 (Classifier types) 413 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font300 1075 1798 (There are \(at least\) three types of output available depending on the type of classifier used.) 1798 SB32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font300 1193 88 (5.1.) 88 SB450 1193 142 (labels) 142 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font450 1262 1368 (The output is essentially the class the input represents, nothing more.) 1368 SB32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font300 1380 88 (5.2.) 88 SB450 1380 193 (ranking) 193 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font450 1449 1552 (Since we are selecting from a number of possible classes, a more sophisticated) 1552 SB450 1512 800 (classifier can rank the entire contents of ) 800 SB32 0 0 50 50 0 0 0 51 /Symbol fontgs 1290 3231 0 0 CB1251 1506 39 (W) 39 SBgrgs 1290 3231 0 0 CB1250 1506 39 (W) 39 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font1290 1512 737 ( in the order from most likely to least) 737 SB450 1573 119 (likely.) 119 SB32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font300 1691 88 (5.3.) 88 SB450 1691 165 (degree) 165 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font450 1760 1541 (In this case, not only can the output be ranked, but information about exactly ) 1541 SB32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font1991 1760 81 (how) 81 SB450 1819 100 (good) 100 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font550 1819 412 ( it is by some metric.) 412 SB450 1937 1645 (The focus of attention in this paper is the combination of classifiers of the first type) 1645 SB32 0 0 50 50 0 0 0 51 /Symbol fontgs 500 3231 0 0 CB450 1994 50 (\276) 50 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font500 2000 1597 (labels which are the lowest common denominator. Each one of the other classes) 1597 SB450 2061 564 (can be converted into labels.) 564 SB32 0 0 67 67 0 0 0 60 /Times-Roman /font32 ANSIFont font300 2180 51 (6.) 51 SB375 2180 856 (Combining Classifiers of type 3) 856 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font450 2258 1520 (This is the case where all classifiers are assumed to be Bayes classifiers. The) 1520 SB450 2317 1123 (method used to combine them is based on averaging the ) 1123 SB32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font1573 2317 234 (a posteriori) 234 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font1807 2317 255 ( probabilities) 255 SB450 2376 777 (outputs using either the mean or mode.) 777 SB32 0 0 58 58 1 0 0 54 /Times-Bold /font29 ANSIFont font300 2494 88 (6.1.) 88 SB32 0 0 58 58 1 0 0 54 /Times-Bold /font29 ANSIFont font388 2494 75 ( ) 75 SB450 2494 304 (Digression 1) 304 SB32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font754 2494 439 (: Bayes classifiers) 439 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 2566 19 (\267) 19 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font525 2563 533 (Optimal -- "Best" classifier) 533 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 2625 19 (\267) 19 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font525 2622 322 (For two classes:) 322 SB1 lc1 lj0 0 0 pC0 2 SP1157 2795 M 285 0 1 PPSn32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font957 2763 30 (P) 30 SB1009 2763 31 (B) 31 SB1057 2763 31 (A) 31 SB1164 2731 30 (P) 30 SB1219 2731 31 (A) 31 SB1263 2731 31 (B) 31 SB1340 2731 30 (P) 30 SB1391 2731 31 (B) 31 SB1251 2802 30 (P) 30 SB1306 2802 31 (A) 31 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font987 2763 17 (\() 17 SB1039 2763 10 (|) 10 SB1087 2763 17 (\)) 17 SB1194 2731 17 (\() 17 SB1247 2731 10 (|) 10 SB1294 2731 17 (\)) 17 SB1369 2731 17 (\() 17 SB1422 2731 17 (\)) 17 SB1281 2802 17 (\() 17 SB1336 2802 17 (\)) 17 SB32 0 0 50 50 0 0 0 51 /Symbol font1116 2757 27 (=) 27 SB1317 2725 13 (\327) 13 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 2867 19 (\267) 19 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font525 2864 387 (Or, more generally:) 387 SB32 0 0 42 42 0 0 0 38 /Times-Italic /font31 ANSIFont font300 3069 912 (CPSC 599.14, Oct 18, 1993 A.D. Paul Schermerhorn) 912 SB1 #Cstatusdict begin /manualfeed false store endEJ RS%%PageTrailer%%PageResources: font Symbol%%+ font Times-Bold%%+ font Times-Italic%%+ font Times-Roman%%Page: 3 3%%PageResources: (atend)SS0 0 25 11 798 1100 300 SM0 0 0 pC0 2 SP1120 279 M 369 0 1 PPSn32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font0 0 0 fC911 247 30 (P) 30 SB1020 247 31 (X) 31 SB1161 215 30 (P) 30 SB1215 215 31 (X) 31 SB1345 215 30 (P) 30 SB1208 286 30 (P) 30 SB1263 286 31 (X) 31 SB1383 286 30 (P) 30 SB32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font992 265 8 (i) 8 SB1288 233 8 (i) 8 SB1425 233 8 (i) 8 SB1332 304 7 (j) 7 SB1464 304 7 (j) 7 SB1129 352 7 (j) 7 SB1185 352 21 (m) 21 SB32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font941 247 17 (\() 17 SB1001 247 10 (|) 10 SB1050 247 17 (\)) 17 SB1190 215 17 (\() 17 SB1243 215 10 (|) 10 SB1299 215 17 (\)) 17 SB1374 215 17 (\() 17 SB1436 215 17 (\)) 17 SB1238 286 17 (\() 17 SB1338 286 17 (\)) 17 SB1413 286 17 (\() 17 SB1470 286 17 (\)) 17 SB32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font1149 353 14 ({) 14 SB1173 353 7 (.) 7 SB1179 353 7 (.) 7 SB1205 353 14 (}) 14 SB32 0 0 50 50 0 0 0 51 /Symbol font959 241 34 (w) 34 SB1255 209 34 (w) 34 SB1393 209 34 (w) 34 SB1300 280 34 (w) 34 SB1431 280 34 (w) 34 SB32 0 0 50 50 0 0 0 51 /Symbol font1079 241 27 (=) 27 SB1322 209 13 (\327) 13 SB1361 280 13 (\327) 13 SB32 0 0 29 29 0 0 0 29 /Symbol font1133 350 21 (\316) 21 SB32 0 0 75 75 0 0 0 76 /Symbol font1144 266 53 (\345) 53 SB32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font1161 353 14 (1) 14 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 397 19 (\267) 19 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font525 394 1533 (Evidence X must be independent. The assumption is that even it is not, good) 1533 SB525 453 548 (results can still be obtained.) 548 SB32 0 0 67 67 0 0 0 60 /Times-Roman /font32 ANSIFont font300 572 51 (7.) 51 SB375 572 985 (Combining Classifiers of other types) 985 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 653 19 (\267) 19 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font525 650 1446 (A kind of mathematical impedance matching is performed in order to use) 1446 SB525 709 1286 (classifiers \(e.g. type 2 rank\) with the Bayes combination method.) 1286 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 771 19 (\267) 19 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font525 768 1441 (In essence, we "fake" the Bayes posterior probabilities, and use the same) 1441 SB525 827 1518 (technique established above. The results from the k-NN classifier are simply) 1518 SB525 886 1109 (scaled to fit in the interval [0,1], the probability domain.) 1109 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 948 19 (\267) 19 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font525 945 1099 (An example classifier of this type is the k-NN classifier.) 1099 SB32 0 0 58 58 1 0 0 54 /Times-Bold /font29 ANSIFont font300 1063 88 (7.1.) 88 SB32 0 0 58 58 1 0 0 54 /Times-Bold /font29 ANSIFont font388 1063 75 ( ) 75 SB450 1063 304 (Digression 2) 304 SB32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font754 1063 427 (: k-NN classifiers) 427 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 1135 19 (\267) 19 SBgr32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font525 1132 929 (k-NN rule is a generalization of the 1-NN rule.) 929 SB32 0 0 42 42 0 0 0 42 /Symbol fontgs 469 3231 0 0 CB450 1194 19 (\267) 19 SBgr⌨️ 快捷键说明
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