Ensemble Partial Least Squares for Outlier Detection

Outlier detection with ensemble partial least squares.

Usage

enpls.od(
  x,
  y,
  maxcomp = NULL,
  cvfolds = 5L,
  reptimes = 500L,
  method = c("mc", "boot"),
  ratio = 0.8,
  parallel = 1L
)

Arguments

x: Predictor matrix.
y: Response vector.
maxcomp: Maximum number of components included within each model. If not specified, will use the maximum number possible (considering cross-validation and special cases where n is smaller than p).
cvfolds: Number of cross-validation folds used in each model for automatic parameter selection, default is 5.
reptimes: Number of models to build with Monte-Carlo resampling or bootstrapping.
method: Resampling method. "mc" (Monte-Carlo resampling) or "boot" (bootstrapping). Default is "mc".
ratio: Sampling ratio used when method = "mc".
parallel: Integer. Number of CPU cores to use. Default is 1 (not parallelized).

Value

A list containing four components:

error.mean - error mean for all samples (absolute value)
error.median - error median for all samples
error.sd - error sd for all samples
predict.error.matrix - the original prediction error matrix

Note

To maximize the probablity that each observation can be selected in the test set (thus the prediction uncertainty can be measured), please try setting a large reptimes.

Author

Nan Xiao <https://nanx.me>

Examples

data("alkanes")
x <- alkanes$x
y <- alkanes$y

set.seed(42)
od <- enpls.od(x, y, reptimes = 50)
print(od)
#> Outlier Detection by Ensemble Partial Least Squares
#> ---
#> Mean residual for each sample:
#>   [1]  2.75921773 11.36519417  2.86997847  3.72358683  2.58864423  0.69950317
#>   [7]  2.47046080  0.04090356  0.72374081  0.67761648  0.60657038  0.05203462
#>  [13]  4.81214619  0.48047678  0.31426341  4.45439789  1.81680825  0.00486926
#>  [19]  1.40762012  2.76733128  0.25816473  0.11014460  2.76375525  0.24664065
#>  [25]  0.18795164  2.89461883  0.60293011  0.54016143  3.69778413  0.84421368
#>  [31]  2.40482744  0.08033139  0.65464173  0.28846939  0.96347563  1.16604993
#>  [37]  2.42467651  1.80624634  2.08209599  0.64821359  0.06219722  2.36510870
#>  [43]  1.08902416  2.09141868  2.06910689  1.38871463  1.16310209  2.07153015
#>  [49]  2.41222206  1.99819780  1.02797377  1.09358743  6.44005724  2.66972544
#>  [55]  1.18031132  0.96520499  2.91887428  3.88938152  0.93689004  0.04277856
#>  [61]  0.09383582  3.13664578 17.11229300  6.53632442  0.44617481  2.72369291
#>  [67]  2.83683060  0.41927300  1.57410904  1.62112809  0.11859181  1.41609908
#>  [73]  0.66340508  1.53271330  0.20100807  3.47461828  1.36388771  1.47275628
#>  [79]  2.03870349  1.42598923  0.21947290  0.25046323  6.82282300  0.91802223
#>  [85]  2.63298282  1.68299675  1.67646979  1.56930079  0.77600240  0.57822702
#>  [91]  1.03364347  4.42455671  1.06359453  3.14333266  7.53801734  1.87522128
#>  [97]  3.14718740  1.28679073  1.55473026  0.81210377  1.62480053  1.55781168
#> [103]  1.07627481  0.48852462  0.52741604  1.70822777  0.11695013  0.32088398
#> [109]  3.10218596  2.17914452  2.19815151  3.41522772  3.09238815  2.52872181
#> [115]  0.69580966  0.01307271  3.61323553  0.50675263  2.09524681  4.06314768
#> [121]  1.50053126  3.56251067  0.02603732  2.52175184  0.46881633  1.17158669
#> [127]  0.35500780  0.14109849  0.02583630  4.39330939  5.83211202  3.93926189
#> [133]  1.70661275  0.73174502  3.67211046  0.15568680  1.01687679  4.73752709
#> [139]  4.75850118  6.28985938  3.00910912  0.55664806  2.53554817  3.77837005
#> [145]  0.81599912  1.00770488  4.21709646  3.29187061  0.02806380  3.95040415
#> [151]  2.81500647  2.24470051  0.16533690  1.69112925 11.12871713  2.64622693
#> [157]  2.36619343  0.80239235  3.13253142  3.73983802  1.05180495  0.75120889
#> [163]  5.55274842  0.93965402  5.44634050  0.91052763 12.86047051  8.16501444
#> [169]  5.28568842  1.94774611  1.42523305  3.51056559  3.55810920  9.05314678
#> [175]  5.73253024  3.79497529  5.01317052  0.64924425  0.77081874  2.24917960
#> [181]  2.97614143  1.73162082  4.05394871  0.78070127  4.54159467  1.20684823
#> [187]  3.03099951  2.65903955  1.45986082  0.83727406  4.74072104  0.75646839
#> [193]  4.69534977  1.36865729  3.20102779  0.18763266 10.61033130  4.46728417
#> [199]  8.16220823  3.61534939  4.17841145  2.49200986  1.05991605  5.30421423
#> [205]  2.08243043  2.47518723  5.36082689
#> ---
#> Residual SD for each sample:
#>   [1] 2.77082522 3.18518150 0.74165858 2.23594825 1.23169974 0.42687633
#>   [7] 1.50625099 0.79975392 1.41280667 0.46584217 1.17084856 0.93096232
#>  [13] 0.88984994 0.75917079 0.57559100 0.64465715 0.47396718 0.56017441
#>  [19] 0.68267751 0.65140968 0.41747884 0.56358621 0.67966904 0.43427716
#>  [25] 0.37536436 0.64008708 0.44791500 0.59112318 0.88170164 0.41258090
#>  [31] 0.63087919 0.43212128 0.50448177 0.26486222 0.71583384 0.42491843
#>  [37] 2.11640004 0.40073941 0.88944036 0.32170138 0.48828519 0.41031319
#>  [43] 0.50217099 1.59534185 0.33617303 0.50260003 0.94105157 0.63972291
#>  [49] 0.50587685 0.37551763 0.41497134 0.42771863 0.46207727 1.40571227
#>  [55] 0.51642660 0.42393378 0.43527285 0.08752688 0.45192162 0.51780544
#>  [61] 0.61052739 0.43776137 0.31398455 0.32995059 2.00011552 0.87425403
#>  [67] 0.31162653 0.63105402 0.24649488 0.31711494 0.49936385 0.59978816
#>  [73] 0.59653589 0.50852740 2.53110721 0.41851982 1.10184218 0.21710200
#>  [79] 0.43937877 0.35242335 0.33627934 0.34095574 0.33341472 0.69920856
#>  [85] 0.48311083 0.23781167 0.32765431 0.70053129 0.40945258 0.08585720
#>  [91] 0.24244975 0.36514882 0.79025058 0.44402145 0.46959851 0.47803736
#>  [97] 0.66037588 0.69332640 0.29156760 0.42604792 0.47781693 0.32571532
#> [103] 0.31530154 0.43322187 0.64879644 0.67484355 0.40328109 0.51379190
#> [109] 0.25584801 0.78167536 0.46379337 1.02646245 0.48038341 0.42723380
#> [115] 0.71363249 0.69063925 0.59453418 0.65063662 0.86515782 1.17342811
#> [121] 0.78617936 0.47367019 0.24439560 0.70316651 0.73449508 1.79527777
#> [127] 0.44260783 0.33808668 0.81899089 0.32662542 0.73804730 2.75960043
#> [133] 0.64233354 0.47841244 0.75136350 0.32979985 0.94649800 0.24178213
#> [139] 1.11533236 2.49301466 0.35001294 0.80453705 0.35011625 0.83446145
#> [145] 0.58759196 0.40320473 0.29256353 0.77961214 0.39795562 1.01770854
#> [151] 0.45468083 0.62303222 0.40692023 0.44973569 1.25950083 0.53901537
#> [157] 0.34171577 1.08900598 0.71282202 1.29978898 0.82451430 0.44599800
#> [163] 0.77330806 0.51100098 0.51146626 0.53756880 1.01862539 0.84995332
#> [169] 1.18180361 3.93102487 1.04156903 1.13106025 0.52150688 1.24405827
#> [175] 0.67447926 1.17640208 0.64074369 0.28467185 0.33626125 1.94356528
#> [181] 0.62001275 0.44932588 0.16634723 0.40215221 0.40529902 0.45155131
#> [187] 0.23942115 1.16054612 0.39605799 0.47297038 0.33345301 0.27533596
#> [193] 0.36658302 0.80698643 0.73877079 0.55089330 1.40387322 0.73798595
#> [199] 0.38540824 0.26297673 0.58085243 0.64409232 0.52326994 0.87634496
#> [205] 0.53404341 0.62252334 0.45961173
plot(od)

plot(od, criterion = "sd")