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]  2.961290487 10.705505984  2.695084840  3.311091685  2.805275319
#>   [6]  0.653303940  2.406471830  0.060138450  1.085301918  0.681639253
#>  [11]  0.602668291  0.051825623  5.074258601  0.401223791  0.200469288
#>  [16]  4.510123865  1.691529502  0.145738484  1.525737814  2.765037846
#>  [21]  0.166203922  0.139797229  2.696201419  0.193069694  0.183589250
#>  [26]  2.914078924  0.416333768  0.521945702  3.580281229  0.818709605
#>  [31]  2.373884289  0.046727036  0.619399010  0.256234952  0.939652083
#>  [36]  1.173721209  2.024661441  1.809535161  2.154042307  0.644501989
#>  [41]  0.061133489  2.444588094  1.098370439  1.603545811  2.163023752
#>  [46]  1.402565514  1.451659515  2.139296149  2.443892391  1.997895711
#>  [51]  1.029372888  1.136841149  6.421380060  2.649873372  1.224674598
#>  [56]  0.964921264  2.919868131  3.793601358  1.120247119  0.042588935
#>  [61]  0.363153216  3.165008537 17.162269124  6.528451648  0.520605496
#>  [66]  2.687075808  2.837691454  0.396424034  1.586470400  1.549832092
#>  [71]  0.122850422  1.412340751  0.697607289  1.569135383  0.123461109
#>  [76]  3.449456659  1.446110833  1.469166518  1.951656184  1.363008306
#>  [81]  0.100632290  0.214244858  6.822557951  0.781231958  2.558088525
#>  [86]  1.693194231  1.705163184  1.594881212  0.618256405  0.481129274
#>  [91]  1.022913007  4.341302506  1.110030176  3.176739370  7.516301621
#>  [96]  1.862482389  3.146321553  1.282671387  1.549270795  0.543544329
#> [101]  1.609953582  1.539486441  1.097285036  0.463297596  0.363243731
#> [106]  1.711660532  0.109005089  0.383383442  3.109554290  2.025583099
#> [111]  2.201838698  3.600461547  3.105103207  2.633412696  0.729670194
#> [116]  0.008296581  3.552415058  0.578271953  2.078384037  3.902482546
#> [121]  1.727881731  3.650065811  0.051772790  2.497201225  0.467536756
#> [126]  1.489009588  0.340541361  0.132148886  0.045135994  4.427647349
#> [131]  5.731789181  3.981627154  1.716354159  0.601427917  3.652150258
#> [136]  0.133532207  1.154975295  4.738600731  4.734765402  6.532606222
#> [141]  3.127767647  0.576464339  2.530101636  3.654622902  0.818384270
#> [146]  0.951243454  4.200623693  3.203804245  0.045774602  3.965457304
#> [151]  2.838265623  2.248011967  0.231138969  1.688400253 11.172263932
#> [156]  2.510655273  2.348956100  0.744693282  3.031595000  3.711339945
#> [161]  1.056457714  0.760364230  5.608100327  0.935520150  5.458962465
#> [166]  0.927523129 12.972029443  8.165533524  5.328551168  2.484859013
#> [171]  1.426435908  3.418963109  3.510966949  9.082680058  5.707308495
#> [176]  3.787580722  4.998185217  0.787402138  0.843890420  1.977324388
#> [181]  2.970935803  1.865369664  4.064825229  0.754344632  4.640244745
#> [186]  1.208198413  3.029808379  2.870715190  1.474642147  0.794823265
#> [191]  4.756522825  0.808924951  4.646357523  1.529725624  3.158674232
#> [196]  0.126320735 10.757378072  4.493208107  8.261099389  3.629763251
#> [201]  4.294356510  2.396207505  1.086055946  5.281273194  2.343797603
#> [206]  2.393339996  5.608819248
#> ---
#> Residual SD for each sample:
#>   [1] 2.0295383 3.4591717 0.7499505 2.3497525 1.3438661 0.3988746 1.3521295
#>   [8] 0.6652582 1.4428361 0.4479827 1.1262145 0.8221188 0.9776006 0.6809018
#>  [15] 0.6082052 0.8580075 0.4563067 0.5095403 0.7951279 0.6467609 0.2721467
#>  [22] 0.6421179 0.6828399 0.4560934 0.4037567 0.6743393 0.3928832 0.6132695
#>  [29] 0.8256517 0.4056097 0.6128104 0.4178502 0.4754206 0.1959964 0.7369961
#>  [36] 0.4117097 1.7630091 0.3959147 0.8356341 0.3178605 0.4366360 0.3783586
#>  [43] 0.4867093 1.3986540 0.4482564 0.4912262 1.1030168 0.5667523 0.5239153
#>  [50] 0.3305965 0.4215010 0.5583729 0.4475138 1.3956538 0.5452551 0.4287959
#>  [57] 0.4345434 0.2303998 0.3009805 0.5306827 0.3846033 0.4022502 0.4005202
#>  [64] 0.3321732 1.9126931 0.8840468 0.2943275 0.6316034 0.2845289 0.2691855
#>  [71] 0.5016976 0.6198970 0.5633499 0.5270424 2.3760941 0.4301166 1.1617749
#>  [78] 0.2173916 0.4655769 0.3940509 0.3757747 0.3497275 0.3408768 0.5654717
#>  [85] 0.5408820 0.2431220 0.3395991 0.5735671 0.4370117 0.2435098 0.2388147
#>  [92] 0.3611832 0.7032879 0.3711193 0.4676772 0.4741993 0.6589015 0.6691025
#>  [99] 0.2896359 0.4720292 0.4810888 0.3346725 0.2942896 0.4406352 0.6772854
#> [106] 0.6753430 0.4242848 0.5187864 0.2329660 0.6413186 0.4552588 0.8210198
#> [113] 0.5212761 0.5316555 0.6732566 0.6948988 0.5722847 0.7572715 0.8682066
#> [120] 1.1984446 0.9276504 0.3272545 0.3763540 0.6842576 0.7662407 1.5708247
#> [127] 0.4425074 0.5372279 0.8630043 0.3355082 0.7097854 2.8301358 0.6207378
#> [134] 0.5604660 0.7827631 0.3548840 0.8135893 0.2485782 1.0185353 2.7216649
#> [141] 0.3765149 0.7282017 0.3539299 0.7998218 0.6350542 0.3872337 0.3196118
#> [148] 0.7272254 0.3906945 0.9074750 0.4313804 0.6164112 0.3909732 0.4712198
#> [155] 0.9828852 0.4958444 0.3522701 1.0701713 0.7098826 1.2925881 0.8318430
#> [162] 0.4494351 0.7327667 0.5391705 0.5821006 0.5230504 1.0236914 0.8394606
#> [169] 1.1569645 4.2022268 1.0436467 1.0621529 0.5589578 1.2767804 0.6687279
#> [176] 1.1668815 0.6607189 0.4421853 0.2008011 1.5162833 0.6090324 0.5296534
#> [183] 0.1686241 0.4156801 0.4007409 0.4526070 0.2362218 1.3948848 0.3850594
#> [190] 0.3991635 0.3768532 0.2678034 0.3900775 0.7123945 0.7198617 0.5281178
#> [197] 1.2265782 0.7673352 0.4887232 0.2826173 0.4897703 0.8893651 0.4974242
#> [204] 0.8264030 0.6131327 0.7606467 0.2861122
plot(od)

plot(od, criterion = "sd")