uni.plot: Univariate Presentation of Multivariate Outliers
In mvoutlier: Multivariate Outlier Detection Based on Robust Methods
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
The function uni.plot plots each variable of x parallel in a one-dimensional
scatter plot and in addition marks multivariate outliers.
Usage
1
Arguments
x
matrix or data.frame containing the data.
symb
logical. if FALSE, only two colors and no special symbols are used. outliers are
marked red.
if TRUE different symbols (cross means big value, circle means little value) according to
the robust mahalanobis distance based on the mcd estimator and different colors (red means
big value, blue means little value) according to the euclidean distances of the observations
are used.
quan
amount of observations which are used for mcd estimations.
has to be between 0.5 and 1, default ist 0.5
alpha
amount of observations used for calculating the adjusted quantile (see function arw).
...
additional graphical parameters
Details
The function uni.plot shows the mutlivariate outliers in the single variables
by one-dimensional scatter plots.
If symb=FALSE (default), only two colors and no special symbols are used to
mark multivariate outliers (the outliers are marked red).
If symb=TRUE different symbols and colors are used.
The symbols (cross means big value, circle means little value) are selected according to
the robust mahalanobis distance based on the adjusted mcd estimator (see function symbol.plot)
Different colors (red means big value, blue means little value)
according to the euclidean distances of the observations (see function color.plot)
are used. For details see Filzmoser et al. (2005).
Value
outliers
boolean vector of outliers
md
robust multivariate mahalanobis distances of the data
euclidean
(only if symb=TRUE) multivariate euclidean distances of the observations
according to the minimum of the data.
Author(s)
Moritz Gschwandtner <e0125439@student.tuwien.ac.at>
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
http://cstat.tuwien.ac.at/filz/
References
P. Filzmoser, R.G. Garrett, and C. Reimann.
Multivariate outlier detection in exploration geochemistry.
Computers & Geosciences, 31:579-587, 2005.
See Also
map.plot, symbol.plot, color.plot, arw
Examples
1
2
3
4
5
6
Example output
Loading required package: sgeostat
sROC 0.1-2 loaded
$outliers
Courtelary Delemont Franches-Mnt Moutier Neuveville Porrentruy
FALSE TRUE TRUE TRUE FALSE TRUE
Broye Glane Gruyere Sarine Veveyse Aigle
TRUE TRUE TRUE TRUE TRUE FALSE
Aubonne Avenches Cossonay Echallens Grandson Lausanne
FALSE FALSE FALSE FALSE FALSE FALSE
La Vallee Lavaux Morges Moudon Nyone Orbe
FALSE FALSE FALSE FALSE FALSE FALSE
Oron Payerne Paysd'enhaut Rolle Vevey Yverdon
FALSE FALSE FALSE FALSE FALSE FALSE
Conthey Entremont Herens Martigwy Monthey St Maurice
TRUE TRUE TRUE TRUE TRUE TRUE
Sierre Sion Boudry La Chauxdfnd Le Locle Neuchatel
TRUE TRUE FALSE FALSE FALSE FALSE
Val de Ruz ValdeTravers V. De Geneve Rive Droite Rive Gauche
FALSE FALSE TRUE TRUE TRUE
$md
Courtelary Delemont Franches-Mnt Moutier Neuveville Porrentruy
1.9985581 12.9556569 15.0295900 5.4167605 1.7011647 12.8201054
Broye Glane Gruyere Sarine Veveyse Aigle
13.7895037 14.8434130 14.7679185 13.1923851 14.7050075 1.4597372
Aubonne Avenches Cossonay Echallens Grandson Lausanne
0.9997791 1.3753975 1.6817809 2.9931635 1.0476458 2.3516931
La Vallee Lavaux Morges Moudon Nyone Orbe
2.6536456 1.3807370 1.1220942 1.8760753 1.6125590 1.4855210
Oron Payerne Paysd'enhaut Rolle Vevey Yverdon
1.2005360 1.2969916 1.9646028 1.4332458 1.7930736 1.5510789
Conthey Entremont Herens Martigwy Monthey St Maurice
16.3809924 15.1964403 15.9003288 14.8661149 15.1076223 15.1013027
Sierre Sion Boudry La Chauxdfnd Le Locle Neuchatel
17.1280505 15.1105558 1.5201700 2.0850266 1.4719027 2.5909040
Val de Ruz ValdeTravers V. De Geneve Rive Droite Rive Gauche
1.3673747 1.8020833 6.6334650 7.7754565 8.0981202
$outliers
1 2 3 4 5 6 7 8 9 10 11 12 13
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
14 15 16 17 18 19 20 21 22 23 24 25 26
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
27 28 29 30 31 32 33 34 35 36 37 38 39
FALSE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE
40 41 42 43 44 45 46 47 48 49 50 51 52
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE TRUE FALSE
53 54 55 56 57 58 59 60 61 62 63 64 65
FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE
66 67 68 69 70 71 72 73 74 75 76 77 78
FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
79 80 81 82 83 84 85 86 87 88 89 90 91
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
92 93 94 95 96 97 98 99 100 101 102 103 104
FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
105 106 107 108 109 110 111 112 113 114 115 116 117
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE
118 119 120 121 122 123 124 125 126 127 128 129 130
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
131 132 133 134 135 136 137 138 139 140 141 142 143
FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
144 145 146 147 148 149 150 151 152 153 154 155 156
TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
157 158 159 160 161 162 163 164 165 166 167 168 169
FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
170 171 172 173 174 175 176 177 178 179 180 181 182
TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
183 184 185 186 187 188 189 190 191 192 193 194 195
FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
196 197 198 199 200 201 202 203 204 205 206 207 208
FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
209 210 211 212 213 214 215 216 217 218 219 220 221
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
222 223 224 225 226 227 228 229 230 231 232 233 234
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
235 236 237 238 239 240 241 242 243 244 245 246 247
FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
248 249 250 251 252 253 254 255 256 257 258 259 260
FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE TRUE FALSE FALSE
261 262 263 264 265 266 267 268 269 270 271 272 273
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
274 275 276 277 278 279 280 281 282 283 284 285 286
FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
287 288 289 290 291 292 293 294 295 296 297 298 299
FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
300 301 302 303 304 305 306 307 308 309 310 311 312
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
313 314 315 316 317 318 319 320 321 322 323 324 325
FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
326 327 328 329 330 331 332 333 334 335 336 337 338
TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE
339 340 341 342 343 344 345 346 347 348 349 350 351
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
352 353 354 355 356 357 358 359 360 361 362 363 364
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
365 366 367 368 369 370 371 372 373 374 375 376 377
TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
378 379 380 381 382 383 384 385 386 387 388 389 390
TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
391 392 393 394 395 396 397 398 399 400 401 402 403
FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
404 405 406 407 408 409 410 411 412 413 414 415 416
FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE FALSE
417 418 419 420 421 422 423 424 425 426 427 428 429
FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
430 431 432 433 434 435 436 437 438 439 440 441 442
FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
443 444 445 446 447 448 449 450 451 452 453 454 455
FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
456 457 458 459 460 461 462 463 464 465 466 467 468
FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
469 470 471 472 473 474 475 476 477 478 479 480 481
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
482 483 484 485 486 487 488 489 490 491 492 493 494
FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
495 496 497 498 499 500 501 502 503 504 505 506 507
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
508 509 510 511 512 513 514 515 516 517 518 519 520
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
521 522 523 524 525 526 527 528 529 530 531 532 533
TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
534 535 536 537 538 539 540 541 542 543 544 545 546
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
547 548 549 550 551 552 553 554 555 556 557 558 559
FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
560 561 562 563 564 565 566 567 568 569 570 571 572
FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
573 574 575 576 577 578 579 580 581 582 583 584 585
TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
586 587 588 589 590 591 592 593 594 595 596 597 598
TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
599 600 601 602 603 604 605 606 607 608 609 610 611
FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
612 613 614 615 616 617
FALSE TRUE TRUE TRUE TRUE FALSE
$md
1 2 3 4 5 6 7
1.5757134 3.6116303 1.7092686 2.2904406 3.8057979 2.4497456 2.8675959
8 9 10 11 12 13 14
3.8973142 9.6936944 1.7150253 1.5049389 2.5969813 1.7254002 3.7596509
15 16 17 18 19 20 21
3.3102669 1.6843433 1.3020299 1.8601825 2.5001771 1.4953379 2.5665269
22 23 24 25 26 27 28
2.1645011 2.3040605 1.8541297 2.8142078 1.6729697 3.7342336 14.3692541
29 30 31 32 33 34 35
4.4949767 1.1003395 4.0509112 3.0842667 2.3547104 6.4754572 10.1385008
36 37 38 39 40 41 42
3.3261920 2.0958377 1.5444070 3.1725132 3.0271198 2.6785740 2.6728036
43 44 45 46 47 48 49
2.4291286 1.7669720 2.7539742 1.6817061 2.6439830 4.6115499 4.5864963
50 51 52 53 54 55 56
2.8305758 6.0925398 2.8518317 3.2119566 2.2169515 1.5196099 2.1589968
57 58 59 60 61 62 63
1.4535782 1.7209971 1.5423435 4.0775485 2.9088693 2.3899682 4.4326831
64 65 66 67 68 69 70
3.0631110 3.7600566 2.4242584 10.5852813 1.7649591 1.1016048 3.8725877
71 72 73 74 75 76 77
1.5477023 2.5744786 2.7188116 2.4857178 12.3510647 1.7617825 2.7824822
78 79 80 81 82 83 84
1.0959276 2.0575341 1.9988729 2.4866963 2.3224352 3.3831239 2.7336114
85 86 87 88 89 90 91
2.0727760 3.0657160 10.4342803 2.6358014 2.6129116 5.0122160 2.4702634
92 93 94 95 96 97 98
3.5992970 1.5935193 1.5856749 3.1956772 2.9044888 4.1041973 1.8837426
99 100 101 102 103 104 105
1.9495807 2.3388201 2.7168256 2.6592398 1.9693866 2.2554258 2.2099506
106 107 108 109 110 111 112
2.9005176 3.0932787 2.0966247 1.7694370 2.3998116 2.4984212 2.3816668
113 114 115 116 117 118 119
2.2125080 2.6228486 6.8937338 10.4674296 2.5983601 1.6249174 1.7869580
120 121 122 123 124 125 126
2.9936791 2.1507436 2.0895731 1.3033208 2.2506152 2.4033362 4.2732730
127 128 129 130 131 132 133
2.2494758 1.8566022 1.5079949 3.6236788 1.8559736 3.0624956 8.5691826
134 135 136 137 138 139 140
2.5021698 12.8570927 1.9838991 2.6619854 2.0549043 2.1954311 2.2438385
141 142 143 144 145 146 147
1.7288414 1.9336391 3.8288519 5.5269778 4.7613066 1.0930596 2.2741350
148 149 150 151 152 153 154
2.8597697 2.3926908 2.4602200 3.0240598 3.1263183 1.5191415 2.3962763
155 156 157 158 159 160 161
2.1808853 4.5105972 1.7137116 2.7931210 1.6786067 3.3105992 6.2098507
162 163 164 165 166 167 168
2.8903639 1.7393683 6.4099290 2.9267992 2.6554230 3.0589177 3.9764869
169 170 171 172 173 174 175
3.3710361 4.4138374 2.3591433 1.6979091 9.6384527 1.1387770 2.5083317
176 177 178 179 180 181 182
3.0128132 1.3116645 3.4209370 1.3907018 2.1113668 3.1150990 1.8264820
183 184 185 186 187 188 189
1.4131402 2.6381538 2.1000781 2.1891016 3.3626291 4.9115849 1.9475856
190 191 192 193 194 195 196
2.4864523 3.0716605 3.9491839 3.0867067 4.7251836 3.2109527 1.4539071
197 198 199 200 201 202 203
5.3424377 2.0066360 2.0698341 2.2078349 4.7903269 2.9860835 1.4909352
204 205 206 207 208 209 210
1.9066554 3.2405818 1.9973804 1.7572396 2.8497571 2.5924217 3.0854658
211 212 213 214 215 216 217
2.5909420 2.6187829 2.1621126 2.7002444 2.6690953 3.2721787 2.2117532
218 219 220 221 222 223 224
2.5791671 2.5965432 1.8405651 2.8141238 1.5343889 1.3735626 3.0306980
225 226 227 228 229 230 231
1.8609899 1.9083351 3.3051309 3.2501141 2.6066015 2.8282841 1.6141405
232 233 234 235 236 237 238
5.3788846 1.9679456 2.4261985 3.6366290 2.1179800 2.7034917 4.2389467
239 240 241 242 243 244 245
1.9084004 4.0763557 3.1502348 2.8745379 1.9212592 3.5206458 2.0040114
246 247 248 249 250 251 252
2.2101917 1.9621363 3.0435903 4.3247858 3.8728521 1.4838800 2.3831422
253 254 255 256 257 258 259
4.1203162 2.2145849 1.7194846 3.4808939 4.8587688 11.7097170 2.9111995
260 261 262 263 264 265 266
2.5658439 2.7570456 3.8554544 3.5549933 1.4698605 2.3414152 2.5318302
267 268 269 270 271 272 273
1.9448631 2.1095619 1.8324651 2.8148640 1.8253149 2.4607291 1.9018523
274 275 276 277 278 279 280
2.1436556 4.1571497 4.3219907 3.9713726 2.4147763 2.0516914 1.5957765
281 282 283 284 285 286 287
2.4110145 2.9972308 2.0744132 2.4165383 1.8537693 0.9141890 3.4309029
288 289 290 291 292 293 294
2.5667122 3.4335103 8.3329807 1.4823493 1.3737738 1.2217789 3.8552818
295 296 297 298 299 300 301
1.4573975 1.5833919 3.7096280 2.0282107 5.2775531 1.9782443 3.5744667
302 303 304 305 306 307 308
2.2214675 1.8696454 3.5191021 2.2938265 1.6667680 1.5485073 2.0074772
309 310 311 312 313 314 315
2.1406282 2.3909036 6.5536922 1.5998957 1.5754702 2.1415399 2.4938331
316 317 318 319 320 321 322
4.0415303 2.5771368 2.0444254 1.9464491 1.8072520 2.2880106 1.7971862
323 324 325 326 327 328 329
1.4407115 1.6787051 1.8427856 4.5993068 4.2407071 1.4790853 3.2528022
330 331 332 333 334 335 336
1.7446704 1.3904575 5.7456142 4.2539264 5.9224176 3.4151762 0.7361370
337 338 339 340 341 342 343
2.7891575 1.4896807 1.4892884 1.4366595 2.2467197 2.4097180 2.4765360
344 345 346 347 348 349 350
2.8536265 3.4467065 2.1072180 1.5261578 1.9431411 1.6695894 1.5005219
351 352 353 354 355 356 357
1.4376830 3.6841292 2.0082544 2.1108021 3.1937281 1.4488334 2.4967738
358 359 360 361 362 363 364
3.1431951 3.6971833 1.5996282 0.9241339 3.7750861 2.6596160 1.5117958
365 366 367 368 369 370 371
4.0203713 1.1375494 1.5979768 0.6383187 2.7761859 2.0364195 1.7330732
372 373 374 375 376 377 378
2.9742991 3.2000022 2.2042528 3.0873122 3.1668688 1.5706642 5.7573549
379 380 381 382 383 384 385
1.3129157 3.8454250 3.6374951 1.8834701 6.5645360 1.5142057 3.4874598
386 387 388 389 390 391 392
2.4368387 2.0714778 2.7610503 2.7040846 5.2973412 0.9372919 1.7507086
393 394 395 396 397 398 399
2.8606203 2.0980102 5.4694482 2.1044255 2.5712697 2.0626024 3.9175064
400 401 402 403 404 405 406
2.3225761 3.0494559 3.0070604 2.9205406 2.5115209 1.3678511 3.1959269
407 408 409 410 411 412 413
1.7545648 4.0746871 5.3731116 4.1660239 2.2596195 3.3427058 2.9594568
414 415 416 417 418 419 420
2.4546249 5.1661737 1.4991169 2.2317469 2.9249862 4.4412289 3.0773373
421 422 423 424 425 426 427
1.6762850 2.2053337 4.7317722 1.7586374 3.8057492 2.3892683 2.5972214
428 429 430 431 432 433 434
2.5059840 1.4631444 3.3815659 5.0604631 3.2324948 1.8455384 2.4950007
435 436 437 438 439 440 441
3.9386194 2.3578320 4.0118697 2.4321359 2.2523641 1.8337878 1.5462765
442 443 444 445 446 447 448
2.2410003 2.9544891 3.7333784 3.2663602 3.0936882 4.8993342 4.5824475
449 450 451 452 453 454 455
6.1399912 1.7728841 4.1938829 1.1766179 2.6561550 2.4304340 2.2997071
456 457 458 459 460 461 462
1.7950447 1.9195677 3.0810876 1.4986270 4.1526012 2.1715808 2.9087472
463 464 465 466 467 468 469
2.1494186 1.4732558 1.8525470 1.5280989 2.0187257 4.4103542 1.6237197
470 471 472 473 474 475 476
3.5390497 1.5635561 3.9923740 3.9641846 1.8736389 2.6329885 3.2380466
477 478 479 480 481 482 483
2.3801189 19.2562058 3.3630814 3.1052243 3.4551309 2.3644328 3.3118196
484 485 486 487 488 489 490
2.1683514 1.2842702 2.7737493 6.8397800 2.3449381 2.7971718 2.2859782
491 492 493 494 495 496 497
2.9461988 2.5981425 2.1218729 2.4587049 2.9754919 1.4472053 1.9826996
498 499 500 501 502 503 504
1.5851962 2.0836878 2.5462241 2.2700374 1.9236056 3.1904344 2.5585178
505 506 507 508 509 510 511
1.9451812 2.7002822 2.1262802 1.6853377 3.8314809 2.6925135 1.4583519
512 513 514 515 516 517 518
2.8448026 1.0122740 2.3734066 3.5031461 3.4770628 1.9398710 2.0025170
519 520 521 522 523 524 525
2.1021482 2.4091317 5.3285854 0.8968741 2.9480644 3.3091902 2.7149596
526 527 528 529 530 531 532
3.1313441 1.6375541 1.9363123 2.4947093 2.0332412 2.7446802 1.0854833
533 534 535 536 537 538 539
3.1437129 2.8732844 3.6395426 2.2837745 1.8744025 2.0854400 1.3874864
540 541 542 543 544 545 546
1.8510846 2.2741116 2.5108424 3.9283866 3.6689858 2.9416619 2.2430771
547 548 549 550 551 552 553
1.3075366 6.7088698 1.1131010 2.6673467 1.9563132 3.7982948 2.1316790
554 555 556 557 558 559 560
2.1715092 3.4349771 3.9364403 5.1269695 2.8613661 3.2614356 2.8438394
561 562 563 564 565 566 567
2.6976080 2.1225267 1.0335762 3.6745971 2.9328517 1.9210472 9.1283316
568 569 570 571 572 573 574
3.1346276 5.2522292 1.9092378 1.5983306 2.5429802 4.0846208 2.4158790
575 576 577 578 579 580 581
1.8228094 2.4626838 2.9425665 1.1440927 1.2025453 4.8054854 2.0262992
582 583 584 585 586 587 588
1.6622656 2.1486954 3.4686612 1.5853844 4.8547864 1.6672603 2.7537023
589 590 591 592 593 594 595
6.2301028 2.5261177 1.8638496 2.6062682 2.2547019 2.0974885 2.1783027
596 597 598 599 600 601 602
2.4240175 3.5409230 2.3931881 1.6204219 1.3601869 2.4320030 2.3556523
603 604 605 606 607 608 609
1.5500537 2.8647348 4.0655967 1.5967935 2.3732907 1.4948108 1.4576303
610 611 612 613 614 615 616
2.9936636 2.1893528 2.5094612 8.8270825 4.0200840 7.0462588 4.5469319
617
2.6410765
$euclidean
1 2 3 4 5 6 7 8
9.404639 9.088475 9.583875 10.367520 8.751696 11.019380 9.811020 8.050946
9 10 11 12 13 14 15 16
12.623733 8.554799 9.185788 10.130167 10.239847 10.061580 10.818222 10.614834
17 18 19 20 21 22 23 24
9.623012 10.126215 7.246763 9.778468 10.784067 8.698959 9.068921 9.655385
25 26 27 28 29 30 31 32
10.250240 8.839417 12.011043 18.143632 11.833872 9.604975 11.935036 9.525595
33 34 35 36 37 38 39 40
9.458963 12.689146 17.898240 8.621565 9.704603 9.312188 11.375020 7.689387
41 42 43 44 45 46 47 48
9.843533 9.496908 8.091136 9.412124 10.391329 9.563052 10.784598 11.012079
49 50 51 52 53 54 55 56
13.591462 9.152581 12.968993 8.657816 9.284863 10.683996 8.362001 9.083075
57 58 59 60 61 62 63 64
9.078784 10.718654 10.013723 10.991467 11.031389 9.740551 11.529222 10.136415
65 66 67 68 69 70 71 72
9.631703 9.733935 17.575530 9.115547 9.241602 10.298724 9.851977 9.516839
73 74 75 76 77 78 79 80
9.109481 8.943530 16.913797 10.612802 10.010214 9.679835 9.146033 8.145849
81 82 83 84 85 86 87 88
8.695277 11.557946 11.435186 11.459108 9.393971 8.452163 16.456330 9.359204
89 90 91 92 93 94 95 96
9.833925 10.535260 10.550612 12.678844 9.176534 9.656772 11.035576 8.291568
97 98 99 100 101 102 103 104
7.955829 9.492259 8.362651 7.660762 7.748433 7.676321 9.090285 10.717633
105 106 107 108 109 110 111 112
9.379137 10.442693 8.177787 9.750660 9.774150 9.624679 10.055584 9.953159
113 114 115 116 117 118 119 120
10.378434 9.727161 15.392742 17.235441 10.459396 9.476073 8.422110 11.651049
121 122 123 124 125 126 127 128
10.453569 8.999913 9.733854 8.289584 9.338012 11.140213 10.327017 9.464273
129 130 131 132 133 134 135 136
9.499619 8.906149 8.883073 8.860021 11.545946 10.012983 11.763498 8.829584
137 138 139 140 141 142 143 144
8.374159 9.303480 10.063427 8.994381 10.101894 9.222062 7.734942 14.444524
145 146 147 148 149 150 151 152
12.079850 9.561756 9.030975 10.155711 10.180155 9.814763 11.144681 10.010680
153 154 155 156 157 158 159 160
9.508693 10.257771 10.384825 13.562123 9.230846 9.716283 8.608414 8.118788
161 162 163 164 165 166 167 168
14.685214 8.353048 10.836758 14.085088 11.781931 10.440722 7.757507 8.464961
169 170 171 172 173 174 175 176
10.592515 13.210574 9.041275 9.938824 17.498534 9.580067 9.841413 11.083619
177 178 179 180 181 182 183 184
9.992249 8.681716 8.809767 9.072364 9.085630 8.125150 8.688002 10.118312
185 186 187 188 189 190 191 192
9.069301 9.560094 11.614765 8.446626 9.673631 10.805872 8.441277 9.995260
193 194 195 196 197 198 199 200
10.322136 10.519675 9.884466 9.156855 12.867115 11.502604 10.229574 9.209038
201 202 203 204 205 206 207 208
9.191908 8.770834 10.524097 9.585763 10.032351 9.295929 9.529226 11.228752
209 210 211 212 213 214 215 216
9.010811 9.094886 10.662332 9.447884 11.008403 8.918383 8.330969 8.868431
217 218 219 220 221 222 223 224
9.112306 8.809752 10.092755 9.999378 9.898142 9.311904 9.998219 8.403557
225 226 227 228 229 230 231 232
10.522170 10.758523 8.069814 10.575217 9.617165 10.755347 8.357400 13.100213
233 234 235 236 237 238 239 240
9.876940 10.386237 9.741589 10.002587 9.629356 9.494341 10.392422 8.392678
241 242 243 244 245 246 247 248
10.307772 10.634010 10.463381 8.580648 10.375208 10.134784 9.540585 10.233982
249 250 251 252 253 254 255 256
12.182824 10.507772 9.981141 8.523725 6.502860 10.402461 9.375972 7.764010
257 258 259 260 261 262 263 264
13.372247 15.937607 9.258238 8.639672 7.931906 11.242332 12.078039 9.833400
265 266 267 268 269 270 271 272
11.526817 8.964593 9.944203 10.302180 10.640665 8.245674 9.418305 7.957885
273 274 275 276 277 278 279 280
9.103333 10.212548 9.954289 11.743445 8.412483 9.776165 10.480724 9.135826
281 282 283 284 285 286 287 288
10.030089 12.234567 9.484869 7.880974 9.678918 9.369002 8.186470 9.088456
289 290 291 292 293 294 295 296
9.292393 13.066528 8.531553 9.593225 10.312316 8.360296 10.347248 10.022308
297 298 299 300 301 302 303 304
7.847614 9.956934 12.995432 10.071291 8.279636 8.841071 10.727860 12.086325
305 306 307 308 309 310 311 312
10.352295 9.789434 9.829749 9.245851 9.891218 8.085560 12.915338 10.142699
313 314 315 316 317 318 319 320
9.967488 9.672914 9.888846 9.187606 7.823892 9.718736 8.872779 9.731573
321 322 323 324 325 326 327 328
9.543830 8.811359 9.637847 9.706421 10.487461 13.439352 9.499244 8.425397
329 330 331 332 333 334 335 336
12.053532 9.520843 9.289363 10.015075 11.312059 13.962850 12.010710 9.472793
337 338 339 340 341 342 343 344
9.876861 10.113548 8.731088 8.607421 10.255252 8.272175 10.726437 11.475119
345 346 347 348 349 350 351 352
8.514562 10.667060 9.436280 9.421886 9.274055 9.518190 9.896841 11.692789
353 354 355 356 357 358 359 360
9.232871 9.880201 9.173639 9.760427 10.048612 9.723624 9.670891 8.821742
361 362 363 364 365 366 367 368
10.037138 9.989948 8.307890 10.345148 12.165392 9.132490 9.320342 9.291806
369 370 371 372 373 374 375 376
11.419443 8.309176 9.363744 11.066178 11.136954 8.462049 6.997555 9.514284
377 378 379 380 381 382 383 384
9.219597 12.063630 9.569994 11.349344 10.487804 10.720549 14.907969 8.713729
385 386 387 388 389 390 391 392
6.568434 8.808238 8.958281 9.076488 7.870674 7.681569 9.585709 10.322696
393 394 395 396 397 398 399 400
10.272060 9.149415 12.446883 8.116054 8.708550 9.125569 9.667199 8.715771
401 402 403 404 405 406 407 408
9.238867 11.129903 10.988165 8.733910 8.455725 10.094964 9.966046 13.179326
409 410 411 412 413 414 415 416
13.266956 8.291169 10.476079 8.498654 11.779233 8.086795 11.967009 9.416062
417 418 419 420 421 422 423 424
10.197397 8.221195 9.546181 8.823084 8.841904 10.086634 12.731998 9.615956
425 426 427 428 429 430 431 432
11.423634 9.504752 10.076083 9.412030 8.914769 11.370723 13.214284 10.992242
433 434 435 436 437 438 439 440
8.672811 10.222030 7.672615 9.910474 11.497865 8.422907 8.618263 8.681887
441 442 443 444 445 446 447 448
9.487939 8.594034 8.033557 11.041947 9.505147 9.495566 10.856663 8.225097
449 450 451 452 453 454 455 456
9.546612 9.778059 7.023882 8.377621 9.817270 10.095311 9.912201 10.351467
457 458 459 460 461 462 463 464
10.629035 12.457239 9.635520 9.883385 8.582244 12.062817 10.980256 9.970576
465 466 467 468 469 470 471 472
9.890318 9.802856 9.119183 12.671429 9.157794 8.190350 9.248347 9.369834
473 474 475 476 477 478 479 480
11.526747 10.481917 10.590737 8.425195 9.553719 14.435996 10.386534 9.256864
481 482 483 484 485 486 487 488
7.514432 7.753905 11.671322 8.781905 8.823457 9.626449 14.015791 9.836393
489 490 491 492 493 494 495 496
7.189506 9.410297 8.192368 10.639448 9.721296 7.876234 10.915427 10.615271
497 498 499 500 501 502 503 504
10.082684 8.917262 8.645095 10.590350 10.192127 8.873319 11.523864 10.164510
505 506 507 508 509 510 511 512
9.506917 8.658132 8.445638 8.391029 11.048740 9.869563 9.214057 8.484569
513 514 515 516 517 518 519 520
9.090972 10.287975 9.922871 8.373349 10.311314 8.814409 9.053837 7.937971
521 522 523 524 525 526 527 528
8.960872 8.826065 9.991778 10.718160 8.105568 9.455205 9.238003 9.058048
529 530 531 532 533 534 535 536
9.651025 8.795601 8.745416 9.751880 8.512548 7.925609 10.953879 9.404072
537 538 539 540 541 542 543 544
9.608768 10.329487 8.717701 10.141494 10.734629 8.344896 12.430417 9.746952
545 546 547 548 549 550 551 552
10.929991 8.441131 9.679103 12.641752 8.850487 8.076786 10.328368 9.844767
553 554 555 556 557 558 559 560
9.135937 10.397829 11.024895 8.038567 10.192996 12.182481 9.190358 12.152018
561 562 563 564 565 566 567 568
9.341504 10.609429 9.934406 7.638116 7.676991 9.624544 15.846881 10.626814
569 570 571 572 573 574 575 576
8.856966 10.987633 9.000799 10.128749 11.926897 11.293005 9.953820 9.787224
577 578 579 580 581 582 583 584
10.828214 9.932138 9.445964 12.603132 10.433033 10.621477 8.157944 11.322254
585 586 587 588 589 590 591 592
9.475193 12.815248 9.939320 10.793786 13.029898 9.700654 10.469621 10.796760
593 594 595 596 597 598 599 600
10.889065 9.298005 9.427583 8.462440 8.029292 8.931948 9.363467 8.556474
601 602 603 604 605 606 607 608
10.651265 9.349132 9.007963 8.713379 8.118796 10.280407 9.722678 9.187471
609 610 611 612 613 614 615 616
9.451008 9.343130 9.014660 10.221517 15.917047 11.878402 10.618598 12.569171
617
11.022221
mvoutlier documentation built on July 30, 2021, 9:09 a.m.
R Package Documentation
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
The function uni.plot plots each variable of x parallel in a one-dimensional scatter plot and in addition marks multivariate outliers.
Usage
1 |
Arguments
x |
matrix or data.frame containing the data. |
symb |
logical. if FALSE, only two colors and no special symbols are used. outliers are marked red. if TRUE different symbols (cross means big value, circle means little value) according to the robust mahalanobis distance based on the mcd estimator and different colors (red means big value, blue means little value) according to the euclidean distances of the observations are used. |
quan |
amount of observations which are used for mcd estimations. has to be between 0.5 and 1, default ist 0.5 |
alpha |
amount of observations used for calculating the adjusted quantile (see function arw). |
... |
additional graphical parameters |
Details
The function uni.plot shows the mutlivariate outliers in the single variables by one-dimensional scatter plots. If symb=FALSE (default), only two colors and no special symbols are used to mark multivariate outliers (the outliers are marked red). If symb=TRUE different symbols and colors are used. The symbols (cross means big value, circle means little value) are selected according to the robust mahalanobis distance based on the adjusted mcd estimator (see function symbol.plot) Different colors (red means big value, blue means little value) according to the euclidean distances of the observations (see function color.plot) are used. For details see Filzmoser et al. (2005).
Value
outliers |
boolean vector of outliers |
md |
robust multivariate mahalanobis distances of the data |
euclidean |
(only if symb=TRUE) multivariate euclidean distances of the observations according to the minimum of the data. |
Author(s)
Moritz Gschwandtner <e0125439@student.tuwien.ac.at>
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
http://cstat.tuwien.ac.at/filz/
References
P. Filzmoser, R.G. Garrett, and C. Reimann. Multivariate outlier detection in exploration geochemistry. Computers & Geosciences, 31:579-587, 2005.
See Also
map.plot, symbol.plot, color.plot, arw
Examples
1 2 3 4 5 6 |
Example output
Loading required package: sgeostat
sROC 0.1-2 loaded
$outliers
Courtelary Delemont Franches-Mnt Moutier Neuveville Porrentruy
FALSE TRUE TRUE TRUE FALSE TRUE
Broye Glane Gruyere Sarine Veveyse Aigle
TRUE TRUE TRUE TRUE TRUE FALSE
Aubonne Avenches Cossonay Echallens Grandson Lausanne
FALSE FALSE FALSE FALSE FALSE FALSE
La Vallee Lavaux Morges Moudon Nyone Orbe
FALSE FALSE FALSE FALSE FALSE FALSE
Oron Payerne Paysd'enhaut Rolle Vevey Yverdon
FALSE FALSE FALSE FALSE FALSE FALSE
Conthey Entremont Herens Martigwy Monthey St Maurice
TRUE TRUE TRUE TRUE TRUE TRUE
Sierre Sion Boudry La Chauxdfnd Le Locle Neuchatel
TRUE TRUE FALSE FALSE FALSE FALSE
Val de Ruz ValdeTravers V. De Geneve Rive Droite Rive Gauche
FALSE FALSE TRUE TRUE TRUE
$md
Courtelary Delemont Franches-Mnt Moutier Neuveville Porrentruy
1.9985581 12.9556569 15.0295900 5.4167605 1.7011647 12.8201054
Broye Glane Gruyere Sarine Veveyse Aigle
13.7895037 14.8434130 14.7679185 13.1923851 14.7050075 1.4597372
Aubonne Avenches Cossonay Echallens Grandson Lausanne
0.9997791 1.3753975 1.6817809 2.9931635 1.0476458 2.3516931
La Vallee Lavaux Morges Moudon Nyone Orbe
2.6536456 1.3807370 1.1220942 1.8760753 1.6125590 1.4855210
Oron Payerne Paysd'enhaut Rolle Vevey Yverdon
1.2005360 1.2969916 1.9646028 1.4332458 1.7930736 1.5510789
Conthey Entremont Herens Martigwy Monthey St Maurice
16.3809924 15.1964403 15.9003288 14.8661149 15.1076223 15.1013027
Sierre Sion Boudry La Chauxdfnd Le Locle Neuchatel
17.1280505 15.1105558 1.5201700 2.0850266 1.4719027 2.5909040
Val de Ruz ValdeTravers V. De Geneve Rive Droite Rive Gauche
1.3673747 1.8020833 6.6334650 7.7754565 8.0981202
$outliers
1 2 3 4 5 6 7 8 9 10 11 12 13
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
14 15 16 17 18 19 20 21 22 23 24 25 26
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
27 28 29 30 31 32 33 34 35 36 37 38 39
FALSE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE
40 41 42 43 44 45 46 47 48 49 50 51 52
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE TRUE FALSE
53 54 55 56 57 58 59 60 61 62 63 64 65
FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE
66 67 68 69 70 71 72 73 74 75 76 77 78
FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
79 80 81 82 83 84 85 86 87 88 89 90 91
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
92 93 94 95 96 97 98 99 100 101 102 103 104
FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
105 106 107 108 109 110 111 112 113 114 115 116 117
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE
118 119 120 121 122 123 124 125 126 127 128 129 130
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
131 132 133 134 135 136 137 138 139 140 141 142 143
FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
144 145 146 147 148 149 150 151 152 153 154 155 156
TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
157 158 159 160 161 162 163 164 165 166 167 168 169
FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
170 171 172 173 174 175 176 177 178 179 180 181 182
TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
183 184 185 186 187 188 189 190 191 192 193 194 195
FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
196 197 198 199 200 201 202 203 204 205 206 207 208
FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
209 210 211 212 213 214 215 216 217 218 219 220 221
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
222 223 224 225 226 227 228 229 230 231 232 233 234
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
235 236 237 238 239 240 241 242 243 244 245 246 247
FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
248 249 250 251 252 253 254 255 256 257 258 259 260
FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE TRUE FALSE FALSE
261 262 263 264 265 266 267 268 269 270 271 272 273
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
274 275 276 277 278 279 280 281 282 283 284 285 286
FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
287 288 289 290 291 292 293 294 295 296 297 298 299
FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
300 301 302 303 304 305 306 307 308 309 310 311 312
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
313 314 315 316 317 318 319 320 321 322 323 324 325
FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
326 327 328 329 330 331 332 333 334 335 336 337 338
TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE
339 340 341 342 343 344 345 346 347 348 349 350 351
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
352 353 354 355 356 357 358 359 360 361 362 363 364
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
365 366 367 368 369 370 371 372 373 374 375 376 377
TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
378 379 380 381 382 383 384 385 386 387 388 389 390
TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
391 392 393 394 395 396 397 398 399 400 401 402 403
FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
404 405 406 407 408 409 410 411 412 413 414 415 416
FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE FALSE
417 418 419 420 421 422 423 424 425 426 427 428 429
FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
430 431 432 433 434 435 436 437 438 439 440 441 442
FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
443 444 445 446 447 448 449 450 451 452 453 454 455
FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE
456 457 458 459 460 461 462 463 464 465 466 467 468
FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
469 470 471 472 473 474 475 476 477 478 479 480 481
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
482 483 484 485 486 487 488 489 490 491 492 493 494
FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
495 496 497 498 499 500 501 502 503 504 505 506 507
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
508 509 510 511 512 513 514 515 516 517 518 519 520
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
521 522 523 524 525 526 527 528 529 530 531 532 533
TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
534 535 536 537 538 539 540 541 542 543 544 545 546
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
547 548 549 550 551 552 553 554 555 556 557 558 559
FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
560 561 562 563 564 565 566 567 568 569 570 571 572
FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
573 574 575 576 577 578 579 580 581 582 583 584 585
TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
586 587 588 589 590 591 592 593 594 595 596 597 598
TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
599 600 601 602 603 604 605 606 607 608 609 610 611
FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
612 613 614 615 616 617
FALSE TRUE TRUE TRUE TRUE FALSE
$md
1 2 3 4 5 6 7
1.5757134 3.6116303 1.7092686 2.2904406 3.8057979 2.4497456 2.8675959
8 9 10 11 12 13 14
3.8973142 9.6936944 1.7150253 1.5049389 2.5969813 1.7254002 3.7596509
15 16 17 18 19 20 21
3.3102669 1.6843433 1.3020299 1.8601825 2.5001771 1.4953379 2.5665269
22 23 24 25 26 27 28
2.1645011 2.3040605 1.8541297 2.8142078 1.6729697 3.7342336 14.3692541
29 30 31 32 33 34 35
4.4949767 1.1003395 4.0509112 3.0842667 2.3547104 6.4754572 10.1385008
36 37 38 39 40 41 42
3.3261920 2.0958377 1.5444070 3.1725132 3.0271198 2.6785740 2.6728036
43 44 45 46 47 48 49
2.4291286 1.7669720 2.7539742 1.6817061 2.6439830 4.6115499 4.5864963
50 51 52 53 54 55 56
2.8305758 6.0925398 2.8518317 3.2119566 2.2169515 1.5196099 2.1589968
57 58 59 60 61 62 63
1.4535782 1.7209971 1.5423435 4.0775485 2.9088693 2.3899682 4.4326831
64 65 66 67 68 69 70
3.0631110 3.7600566 2.4242584 10.5852813 1.7649591 1.1016048 3.8725877
71 72 73 74 75 76 77
1.5477023 2.5744786 2.7188116 2.4857178 12.3510647 1.7617825 2.7824822
78 79 80 81 82 83 84
1.0959276 2.0575341 1.9988729 2.4866963 2.3224352 3.3831239 2.7336114
85 86 87 88 89 90 91
2.0727760 3.0657160 10.4342803 2.6358014 2.6129116 5.0122160 2.4702634
92 93 94 95 96 97 98
3.5992970 1.5935193 1.5856749 3.1956772 2.9044888 4.1041973 1.8837426
99 100 101 102 103 104 105
1.9495807 2.3388201 2.7168256 2.6592398 1.9693866 2.2554258 2.2099506
106 107 108 109 110 111 112
2.9005176 3.0932787 2.0966247 1.7694370 2.3998116 2.4984212 2.3816668
113 114 115 116 117 118 119
2.2125080 2.6228486 6.8937338 10.4674296 2.5983601 1.6249174 1.7869580
120 121 122 123 124 125 126
2.9936791 2.1507436 2.0895731 1.3033208 2.2506152 2.4033362 4.2732730
127 128 129 130 131 132 133
2.2494758 1.8566022 1.5079949 3.6236788 1.8559736 3.0624956 8.5691826
134 135 136 137 138 139 140
2.5021698 12.8570927 1.9838991 2.6619854 2.0549043 2.1954311 2.2438385
141 142 143 144 145 146 147
1.7288414 1.9336391 3.8288519 5.5269778 4.7613066 1.0930596 2.2741350
148 149 150 151 152 153 154
2.8597697 2.3926908 2.4602200 3.0240598 3.1263183 1.5191415 2.3962763
155 156 157 158 159 160 161
2.1808853 4.5105972 1.7137116 2.7931210 1.6786067 3.3105992 6.2098507
162 163 164 165 166 167 168
2.8903639 1.7393683 6.4099290 2.9267992 2.6554230 3.0589177 3.9764869
169 170 171 172 173 174 175
3.3710361 4.4138374 2.3591433 1.6979091 9.6384527 1.1387770 2.5083317
176 177 178 179 180 181 182
3.0128132 1.3116645 3.4209370 1.3907018 2.1113668 3.1150990 1.8264820
183 184 185 186 187 188 189
1.4131402 2.6381538 2.1000781 2.1891016 3.3626291 4.9115849 1.9475856
190 191 192 193 194 195 196
2.4864523 3.0716605 3.9491839 3.0867067 4.7251836 3.2109527 1.4539071
197 198 199 200 201 202 203
5.3424377 2.0066360 2.0698341 2.2078349 4.7903269 2.9860835 1.4909352
204 205 206 207 208 209 210
1.9066554 3.2405818 1.9973804 1.7572396 2.8497571 2.5924217 3.0854658
211 212 213 214 215 216 217
2.5909420 2.6187829 2.1621126 2.7002444 2.6690953 3.2721787 2.2117532
218 219 220 221 222 223 224
2.5791671 2.5965432 1.8405651 2.8141238 1.5343889 1.3735626 3.0306980
225 226 227 228 229 230 231
1.8609899 1.9083351 3.3051309 3.2501141 2.6066015 2.8282841 1.6141405
232 233 234 235 236 237 238
5.3788846 1.9679456 2.4261985 3.6366290 2.1179800 2.7034917 4.2389467
239 240 241 242 243 244 245
1.9084004 4.0763557 3.1502348 2.8745379 1.9212592 3.5206458 2.0040114
246 247 248 249 250 251 252
2.2101917 1.9621363 3.0435903 4.3247858 3.8728521 1.4838800 2.3831422
253 254 255 256 257 258 259
4.1203162 2.2145849 1.7194846 3.4808939 4.8587688 11.7097170 2.9111995
260 261 262 263 264 265 266
2.5658439 2.7570456 3.8554544 3.5549933 1.4698605 2.3414152 2.5318302
267 268 269 270 271 272 273
1.9448631 2.1095619 1.8324651 2.8148640 1.8253149 2.4607291 1.9018523
274 275 276 277 278 279 280
2.1436556 4.1571497 4.3219907 3.9713726 2.4147763 2.0516914 1.5957765
281 282 283 284 285 286 287
2.4110145 2.9972308 2.0744132 2.4165383 1.8537693 0.9141890 3.4309029
288 289 290 291 292 293 294
2.5667122 3.4335103 8.3329807 1.4823493 1.3737738 1.2217789 3.8552818
295 296 297 298 299 300 301
1.4573975 1.5833919 3.7096280 2.0282107 5.2775531 1.9782443 3.5744667
302 303 304 305 306 307 308
2.2214675 1.8696454 3.5191021 2.2938265 1.6667680 1.5485073 2.0074772
309 310 311 312 313 314 315
2.1406282 2.3909036 6.5536922 1.5998957 1.5754702 2.1415399 2.4938331
316 317 318 319 320 321 322
4.0415303 2.5771368 2.0444254 1.9464491 1.8072520 2.2880106 1.7971862
323 324 325 326 327 328 329
1.4407115 1.6787051 1.8427856 4.5993068 4.2407071 1.4790853 3.2528022
330 331 332 333 334 335 336
1.7446704 1.3904575 5.7456142 4.2539264 5.9224176 3.4151762 0.7361370
337 338 339 340 341 342 343
2.7891575 1.4896807 1.4892884 1.4366595 2.2467197 2.4097180 2.4765360
344 345 346 347 348 349 350
2.8536265 3.4467065 2.1072180 1.5261578 1.9431411 1.6695894 1.5005219
351 352 353 354 355 356 357
1.4376830 3.6841292 2.0082544 2.1108021 3.1937281 1.4488334 2.4967738
358 359 360 361 362 363 364
3.1431951 3.6971833 1.5996282 0.9241339 3.7750861 2.6596160 1.5117958
365 366 367 368 369 370 371
4.0203713 1.1375494 1.5979768 0.6383187 2.7761859 2.0364195 1.7330732
372 373 374 375 376 377 378
2.9742991 3.2000022 2.2042528 3.0873122 3.1668688 1.5706642 5.7573549
379 380 381 382 383 384 385
1.3129157 3.8454250 3.6374951 1.8834701 6.5645360 1.5142057 3.4874598
386 387 388 389 390 391 392
2.4368387 2.0714778 2.7610503 2.7040846 5.2973412 0.9372919 1.7507086
393 394 395 396 397 398 399
2.8606203 2.0980102 5.4694482 2.1044255 2.5712697 2.0626024 3.9175064
400 401 402 403 404 405 406
2.3225761 3.0494559 3.0070604 2.9205406 2.5115209 1.3678511 3.1959269
407 408 409 410 411 412 413
1.7545648 4.0746871 5.3731116 4.1660239 2.2596195 3.3427058 2.9594568
414 415 416 417 418 419 420
2.4546249 5.1661737 1.4991169 2.2317469 2.9249862 4.4412289 3.0773373
421 422 423 424 425 426 427
1.6762850 2.2053337 4.7317722 1.7586374 3.8057492 2.3892683 2.5972214
428 429 430 431 432 433 434
2.5059840 1.4631444 3.3815659 5.0604631 3.2324948 1.8455384 2.4950007
435 436 437 438 439 440 441
3.9386194 2.3578320 4.0118697 2.4321359 2.2523641 1.8337878 1.5462765
442 443 444 445 446 447 448
2.2410003 2.9544891 3.7333784 3.2663602 3.0936882 4.8993342 4.5824475
449 450 451 452 453 454 455
6.1399912 1.7728841 4.1938829 1.1766179 2.6561550 2.4304340 2.2997071
456 457 458 459 460 461 462
1.7950447 1.9195677 3.0810876 1.4986270 4.1526012 2.1715808 2.9087472
463 464 465 466 467 468 469
2.1494186 1.4732558 1.8525470 1.5280989 2.0187257 4.4103542 1.6237197
470 471 472 473 474 475 476
3.5390497 1.5635561 3.9923740 3.9641846 1.8736389 2.6329885 3.2380466
477 478 479 480 481 482 483
2.3801189 19.2562058 3.3630814 3.1052243 3.4551309 2.3644328 3.3118196
484 485 486 487 488 489 490
2.1683514 1.2842702 2.7737493 6.8397800 2.3449381 2.7971718 2.2859782
491 492 493 494 495 496 497
2.9461988 2.5981425 2.1218729 2.4587049 2.9754919 1.4472053 1.9826996
498 499 500 501 502 503 504
1.5851962 2.0836878 2.5462241 2.2700374 1.9236056 3.1904344 2.5585178
505 506 507 508 509 510 511
1.9451812 2.7002822 2.1262802 1.6853377 3.8314809 2.6925135 1.4583519
512 513 514 515 516 517 518
2.8448026 1.0122740 2.3734066 3.5031461 3.4770628 1.9398710 2.0025170
519 520 521 522 523 524 525
2.1021482 2.4091317 5.3285854 0.8968741 2.9480644 3.3091902 2.7149596
526 527 528 529 530 531 532
3.1313441 1.6375541 1.9363123 2.4947093 2.0332412 2.7446802 1.0854833
533 534 535 536 537 538 539
3.1437129 2.8732844 3.6395426 2.2837745 1.8744025 2.0854400 1.3874864
540 541 542 543 544 545 546
1.8510846 2.2741116 2.5108424 3.9283866 3.6689858 2.9416619 2.2430771
547 548 549 550 551 552 553
1.3075366 6.7088698 1.1131010 2.6673467 1.9563132 3.7982948 2.1316790
554 555 556 557 558 559 560
2.1715092 3.4349771 3.9364403 5.1269695 2.8613661 3.2614356 2.8438394
561 562 563 564 565 566 567
2.6976080 2.1225267 1.0335762 3.6745971 2.9328517 1.9210472 9.1283316
568 569 570 571 572 573 574
3.1346276 5.2522292 1.9092378 1.5983306 2.5429802 4.0846208 2.4158790
575 576 577 578 579 580 581
1.8228094 2.4626838 2.9425665 1.1440927 1.2025453 4.8054854 2.0262992
582 583 584 585 586 587 588
1.6622656 2.1486954 3.4686612 1.5853844 4.8547864 1.6672603 2.7537023
589 590 591 592 593 594 595
6.2301028 2.5261177 1.8638496 2.6062682 2.2547019 2.0974885 2.1783027
596 597 598 599 600 601 602
2.4240175 3.5409230 2.3931881 1.6204219 1.3601869 2.4320030 2.3556523
603 604 605 606 607 608 609
1.5500537 2.8647348 4.0655967 1.5967935 2.3732907 1.4948108 1.4576303
610 611 612 613 614 615 616
2.9936636 2.1893528 2.5094612 8.8270825 4.0200840 7.0462588 4.5469319
617
2.6410765
$euclidean
1 2 3 4 5 6 7 8
9.404639 9.088475 9.583875 10.367520 8.751696 11.019380 9.811020 8.050946
9 10 11 12 13 14 15 16
12.623733 8.554799 9.185788 10.130167 10.239847 10.061580 10.818222 10.614834
17 18 19 20 21 22 23 24
9.623012 10.126215 7.246763 9.778468 10.784067 8.698959 9.068921 9.655385
25 26 27 28 29 30 31 32
10.250240 8.839417 12.011043 18.143632 11.833872 9.604975 11.935036 9.525595
33 34 35 36 37 38 39 40
9.458963 12.689146 17.898240 8.621565 9.704603 9.312188 11.375020 7.689387
41 42 43 44 45 46 47 48
9.843533 9.496908 8.091136 9.412124 10.391329 9.563052 10.784598 11.012079
49 50 51 52 53 54 55 56
13.591462 9.152581 12.968993 8.657816 9.284863 10.683996 8.362001 9.083075
57 58 59 60 61 62 63 64
9.078784 10.718654 10.013723 10.991467 11.031389 9.740551 11.529222 10.136415
65 66 67 68 69 70 71 72
9.631703 9.733935 17.575530 9.115547 9.241602 10.298724 9.851977 9.516839
73 74 75 76 77 78 79 80
9.109481 8.943530 16.913797 10.612802 10.010214 9.679835 9.146033 8.145849
81 82 83 84 85 86 87 88
8.695277 11.557946 11.435186 11.459108 9.393971 8.452163 16.456330 9.359204
89 90 91 92 93 94 95 96
9.833925 10.535260 10.550612 12.678844 9.176534 9.656772 11.035576 8.291568
97 98 99 100 101 102 103 104
7.955829 9.492259 8.362651 7.660762 7.748433 7.676321 9.090285 10.717633
105 106 107 108 109 110 111 112
9.379137 10.442693 8.177787 9.750660 9.774150 9.624679 10.055584 9.953159
113 114 115 116 117 118 119 120
10.378434 9.727161 15.392742 17.235441 10.459396 9.476073 8.422110 11.651049
121 122 123 124 125 126 127 128
10.453569 8.999913 9.733854 8.289584 9.338012 11.140213 10.327017 9.464273
129 130 131 132 133 134 135 136
9.499619 8.906149 8.883073 8.860021 11.545946 10.012983 11.763498 8.829584
137 138 139 140 141 142 143 144
8.374159 9.303480 10.063427 8.994381 10.101894 9.222062 7.734942 14.444524
145 146 147 148 149 150 151 152
12.079850 9.561756 9.030975 10.155711 10.180155 9.814763 11.144681 10.010680
153 154 155 156 157 158 159 160
9.508693 10.257771 10.384825 13.562123 9.230846 9.716283 8.608414 8.118788
161 162 163 164 165 166 167 168
14.685214 8.353048 10.836758 14.085088 11.781931 10.440722 7.757507 8.464961
169 170 171 172 173 174 175 176
10.592515 13.210574 9.041275 9.938824 17.498534 9.580067 9.841413 11.083619
177 178 179 180 181 182 183 184
9.992249 8.681716 8.809767 9.072364 9.085630 8.125150 8.688002 10.118312
185 186 187 188 189 190 191 192
9.069301 9.560094 11.614765 8.446626 9.673631 10.805872 8.441277 9.995260
193 194 195 196 197 198 199 200
10.322136 10.519675 9.884466 9.156855 12.867115 11.502604 10.229574 9.209038
201 202 203 204 205 206 207 208
9.191908 8.770834 10.524097 9.585763 10.032351 9.295929 9.529226 11.228752
209 210 211 212 213 214 215 216
9.010811 9.094886 10.662332 9.447884 11.008403 8.918383 8.330969 8.868431
217 218 219 220 221 222 223 224
9.112306 8.809752 10.092755 9.999378 9.898142 9.311904 9.998219 8.403557
225 226 227 228 229 230 231 232
10.522170 10.758523 8.069814 10.575217 9.617165 10.755347 8.357400 13.100213
233 234 235 236 237 238 239 240
9.876940 10.386237 9.741589 10.002587 9.629356 9.494341 10.392422 8.392678
241 242 243 244 245 246 247 248
10.307772 10.634010 10.463381 8.580648 10.375208 10.134784 9.540585 10.233982
249 250 251 252 253 254 255 256
12.182824 10.507772 9.981141 8.523725 6.502860 10.402461 9.375972 7.764010
257 258 259 260 261 262 263 264
13.372247 15.937607 9.258238 8.639672 7.931906 11.242332 12.078039 9.833400
265 266 267 268 269 270 271 272
11.526817 8.964593 9.944203 10.302180 10.640665 8.245674 9.418305 7.957885
273 274 275 276 277 278 279 280
9.103333 10.212548 9.954289 11.743445 8.412483 9.776165 10.480724 9.135826
281 282 283 284 285 286 287 288
10.030089 12.234567 9.484869 7.880974 9.678918 9.369002 8.186470 9.088456
289 290 291 292 293 294 295 296
9.292393 13.066528 8.531553 9.593225 10.312316 8.360296 10.347248 10.022308
297 298 299 300 301 302 303 304
7.847614 9.956934 12.995432 10.071291 8.279636 8.841071 10.727860 12.086325
305 306 307 308 309 310 311 312
10.352295 9.789434 9.829749 9.245851 9.891218 8.085560 12.915338 10.142699
313 314 315 316 317 318 319 320
9.967488 9.672914 9.888846 9.187606 7.823892 9.718736 8.872779 9.731573
321 322 323 324 325 326 327 328
9.543830 8.811359 9.637847 9.706421 10.487461 13.439352 9.499244 8.425397
329 330 331 332 333 334 335 336
12.053532 9.520843 9.289363 10.015075 11.312059 13.962850 12.010710 9.472793
337 338 339 340 341 342 343 344
9.876861 10.113548 8.731088 8.607421 10.255252 8.272175 10.726437 11.475119
345 346 347 348 349 350 351 352
8.514562 10.667060 9.436280 9.421886 9.274055 9.518190 9.896841 11.692789
353 354 355 356 357 358 359 360
9.232871 9.880201 9.173639 9.760427 10.048612 9.723624 9.670891 8.821742
361 362 363 364 365 366 367 368
10.037138 9.989948 8.307890 10.345148 12.165392 9.132490 9.320342 9.291806
369 370 371 372 373 374 375 376
11.419443 8.309176 9.363744 11.066178 11.136954 8.462049 6.997555 9.514284
377 378 379 380 381 382 383 384
9.219597 12.063630 9.569994 11.349344 10.487804 10.720549 14.907969 8.713729
385 386 387 388 389 390 391 392
6.568434 8.808238 8.958281 9.076488 7.870674 7.681569 9.585709 10.322696
393 394 395 396 397 398 399 400
10.272060 9.149415 12.446883 8.116054 8.708550 9.125569 9.667199 8.715771
401 402 403 404 405 406 407 408
9.238867 11.129903 10.988165 8.733910 8.455725 10.094964 9.966046 13.179326
409 410 411 412 413 414 415 416
13.266956 8.291169 10.476079 8.498654 11.779233 8.086795 11.967009 9.416062
417 418 419 420 421 422 423 424
10.197397 8.221195 9.546181 8.823084 8.841904 10.086634 12.731998 9.615956
425 426 427 428 429 430 431 432
11.423634 9.504752 10.076083 9.412030 8.914769 11.370723 13.214284 10.992242
433 434 435 436 437 438 439 440
8.672811 10.222030 7.672615 9.910474 11.497865 8.422907 8.618263 8.681887
441 442 443 444 445 446 447 448
9.487939 8.594034 8.033557 11.041947 9.505147 9.495566 10.856663 8.225097
449 450 451 452 453 454 455 456
9.546612 9.778059 7.023882 8.377621 9.817270 10.095311 9.912201 10.351467
457 458 459 460 461 462 463 464
10.629035 12.457239 9.635520 9.883385 8.582244 12.062817 10.980256 9.970576
465 466 467 468 469 470 471 472
9.890318 9.802856 9.119183 12.671429 9.157794 8.190350 9.248347 9.369834
473 474 475 476 477 478 479 480
11.526747 10.481917 10.590737 8.425195 9.553719 14.435996 10.386534 9.256864
481 482 483 484 485 486 487 488
7.514432 7.753905 11.671322 8.781905 8.823457 9.626449 14.015791 9.836393
489 490 491 492 493 494 495 496
7.189506 9.410297 8.192368 10.639448 9.721296 7.876234 10.915427 10.615271
497 498 499 500 501 502 503 504
10.082684 8.917262 8.645095 10.590350 10.192127 8.873319 11.523864 10.164510
505 506 507 508 509 510 511 512
9.506917 8.658132 8.445638 8.391029 11.048740 9.869563 9.214057 8.484569
513 514 515 516 517 518 519 520
9.090972 10.287975 9.922871 8.373349 10.311314 8.814409 9.053837 7.937971
521 522 523 524 525 526 527 528
8.960872 8.826065 9.991778 10.718160 8.105568 9.455205 9.238003 9.058048
529 530 531 532 533 534 535 536
9.651025 8.795601 8.745416 9.751880 8.512548 7.925609 10.953879 9.404072
537 538 539 540 541 542 543 544
9.608768 10.329487 8.717701 10.141494 10.734629 8.344896 12.430417 9.746952
545 546 547 548 549 550 551 552
10.929991 8.441131 9.679103 12.641752 8.850487 8.076786 10.328368 9.844767
553 554 555 556 557 558 559 560
9.135937 10.397829 11.024895 8.038567 10.192996 12.182481 9.190358 12.152018
561 562 563 564 565 566 567 568
9.341504 10.609429 9.934406 7.638116 7.676991 9.624544 15.846881 10.626814
569 570 571 572 573 574 575 576
8.856966 10.987633 9.000799 10.128749 11.926897 11.293005 9.953820 9.787224
577 578 579 580 581 582 583 584
10.828214 9.932138 9.445964 12.603132 10.433033 10.621477 8.157944 11.322254
585 586 587 588 589 590 591 592
9.475193 12.815248 9.939320 10.793786 13.029898 9.700654 10.469621 10.796760
593 594 595 596 597 598 599 600
10.889065 9.298005 9.427583 8.462440 8.029292 8.931948 9.363467 8.556474
601 602 603 604 605 606 607 608
10.651265 9.349132 9.007963 8.713379 8.118796 10.280407 9.722678 9.187471
609 610 611 612 613 614 615 616
9.451008 9.343130 9.014660 10.221517 15.917047 11.878402 10.618598 12.569171
617
11.022221
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