Description Usage Arguments Details Value Author(s) References See Also Examples
In a multivariate framework outlier(s) are detected using ICS. The function works on an object of class ics2
and decides automatically about the number of invariant components to use to search for the outliers and the number of outliers
detected on these components. Currently the function is restricted to the case of searching outliers only on the first components.
1 2 3 4 
object 
object of class 
method 
name of the method used to select the ICS components involved to compute ICS distances. Options are

test 
name of the marginal normality test to use if 
mEig 
number of simulations performed to derive the cutoff values for selecting the ICS components. Only if 
level.test 

adjust 
logical. For selecting the invariant coordinates, the level of the test can be adjusted for each component to deal with multiple testing. See 
level.dist 

mDist 
number of simulations performed to derive the cutoff value for the ICS distances.
See 
type 
currently the only option is 
ncores 
number of cores to be used in 
iseed 
If parallel computation is used the seed passed on to 
pkg 
When using parallel computing, a character vector listing all the packages which need to be loaded on the different cores via 
qtype 
specifies the quantile algorithm used in 
... 
passed on to other methods. 
The ICS method has attractive properties for outlier detection in the case of a small proportion of outliers. As for PCA three steps have to be performed: (i) select the components most useful for the detection, (ii) compute distances as outlierness measures for all observation and finally (iii) label outliers using some cutoff value.
This function performs these three steps automatically:
For choosing the components of interest two methods are proposed: "norm.test"
based on some marginal normality tests (see details in comp.norm.test
)
or "simulation"
based on a parallel analysis (see details in comp.simu.test
). These two approaches lie on the intrinsic property of ICS in case of a small proportion
of outliers with the choice of S1 "more robust" than S2, which ensures to find outliers on the first components. Indeed when using S1 = MeanCov
and S2 = Mean3Cov4
,
the Invariant Coordinates are ordered according to their classical Pearson kurtosis values in decreasing order. The information to find the outliers should be then contained in the first
k nonnormal directions.
Then the ICS distances are computed as the Euclidian distances on the selected k centered components Z_k.
Finally the outliers are identified based on a cutoff derived from simulations. If the distance of an observation exceeds the expectation under the normal model,
this observation is labeled as outlier (see details in dist.simu.test
).
As a rule of thumb, the percentage of contamination should be limited to 10% in case of a mixture of gaussian distributions and using the default combination of locations and scatters for ICS.
an object of class icsOut
Aurore Archimbaud and Klaus Nordhausen
Archimbaud, A., Nordhausen, K. and RuizGazen, A. (2016), Multivariate Outlier Detection With ICS, <https://arxiv.org/abs/1612.06118>.
ics2
, comp.norm.test
, comp.simu.test
, dist.simu.test
,
icsOutclass
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  # ReliabilityData example: the observations 414 and 512 are suspected to be outliers
library(REPPlab)
data(ReliabilityData)
icsReliabilityData < ics2(ReliabilityData, S1 = tM, S2 = MeanCov)
# For demo purpose only small mDist value, but as extreme quantiles
# are of interest mDist should be much larger. Also number of cores used
# should be larger if available
icsOutlierDA < ics.outlier(icsReliabilityData, level.dist = 0.01, mDist = 50, ncores = 1)
icsOutlierDA
summary(icsOutlierDA)
plot(icsOutlierDA)
## Not run:
# For using several cores and for using a scatter function from a different package
# Using the parallel package to detect automatically the number of cores
library(parallel)
# ICS with MCD estimates and the usual estimates
# Need to create a wrapper for the CovMcd function to return first the location estimate
# and the scatter estimate secondly.
data(HTP)
library(rrcov)
myMCD < function(x,...){
mcd < CovMcd(x,...)
return(list(location = mcd@center, scatter = mcd@cov))
}
icsHTP < ics2(HTP, S1 = myMCD, S2 = MeanCov, S1args = list(alpha = 0.75))
# For demo purpose only small m value, should select the first seven components
icsOutlier < ics.outlier(icsHTP, mEig = 50, level.test = 0.05, adjust = TRUE,
level.dist = 0.025, mDist = 50,
ncores = detectCores()1, iseed = 123,
pkg = c("ICSOutlier", "rrcov"))
icsOutlier
## End(Not run)
# Exemple of no direction and hence also no outlier
set.seed(123)
X = rmvnorm(500, rep(0, 2), diag(rep(0.1,2)))
icsX < ics2(X)
icsOutlierJB < ics.outlier(icsX, test = "jarque", level.dist = 0.01,
level.test = 0.01, mDist = 100, ncores = 1)
summary(icsOutlierJB)
plot(icsOutlierJB)
rm(.Random.seed)
# Example of no outlier
set.seed(123)
X = matrix(rweibull(1000, 4, 4), 500, 2)
X = apply(X,2, function(x){ifelse(x<5 & x>2, x, runif(sum(!(x<5 & x>2)), 5, 5.5))})
icsX < ics2(X)
icsOutlierAG < ics.outlier(icsX, test = "anscombe", level.dist = 0.01,
level.test = 0.05, mDist = 100, ncores = 1)
summary(icsOutlierAG)
plot(icsOutlierAG)
rm(.Random.seed)

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