Package 'mvoutlier' reference manual

Title:	Multivariate Outlier Detection Based on Robust Methods
Description:	Various methods for multivariate outlier detection: arw, a Mahalanobis-type method with an adaptive outlier cutoff value; locout, a method incorporating local neighborhood; pcout, a method for high-dimensional data; mvoutlier.CoDa, a method for compositional data. References are provided in the corresponding help files.
Authors:	Peter Filzmoser <[email protected]> and Moritz Gschwandtner <[email protected]>
Maintainer:	P. Filzmoser <[email protected]>
License:	GPL (>= 3)
Version:	2.1.1
Built:	2024-05-07 08:15:56 UTC
Source:	CRAN

Title:

Multivariate Outlier Detection Based on Robust Methods

Description:

Various methods for multivariate outlier detection: arw, a Mahalanobis-type method with an adaptive outlier cutoff value; locout, a method incorporating local neighborhood; pcout, a method for high-dimensional data; mvoutlier.CoDa, a method for compositional data. References are provided in the corresponding help files.

Authors:

Peter Filzmoser <[email protected]> and Moritz Gschwandtner <[email protected]>

Maintainer:

P. Filzmoser <[email protected]>

License:

GPL (>= 3)

Version:

2.1.1

Built:

2024-05-07 08:15:56 UTC

Source:

CRAN

B-horizon of the Kola Data

Description

The Kola data were collected in the Kola Project (1993-1998, Geological Surveys of Finland (GTK) and Norway (NGU) and Central Kola Expedition (CKE), Russia). More than 600 samples in five different layers were analysed, this dataset contains the B-horizon.

Usage

data(bhorizon)

Format

A data frame with 609 observations on the following 48 variables.

ID: a numeric vector
XCOO: a numeric vector
YCOO: a numeric vector
Ag: a numeric vector
Al: a numeric vector
Al_XRF: a numeric vector
As: a numeric vector
Ba: a numeric vector
Be: a numeric vector
Bi: a numeric vector
Ca: a numeric vector
Ca_XRF: a numeric vector
Cd: a numeric vector
Co: a numeric vector
Cr: a numeric vector
Cu: a numeric vector
EC: a numeric vector
Fe: a numeric vector
Fe_XRF: a numeric vector
K: a numeric vector
K_XRF: a numeric vector
LOI: a numeric vector
La: a numeric vector
Li: a numeric vector
Mg: a numeric vector
Mg_XRF: a numeric vector
Mn: a numeric vector
Mn_XRF: a numeric vector
Mo: a numeric vector
Na: a numeric vector
Na_XRF: a numeric vector
Ni: a numeric vector
P: a numeric vector
P_XRF: a numeric vector
Pb: a numeric vector
S: a numeric vector
Sc: a numeric vector
Se: a numeric vector
Si: a numeric vector
Si_XRF: a numeric vector
Sr: a numeric vector
Te: a numeric vector
Th: a numeric vector
Ti: a numeric vector
Ti_XRF: a numeric vector
V: a numeric vector
Y: a numeric vector
Zn: a numeric vector

Source

Kola Project (1993-1998)

References

Reimann C, Äyräs M, Chekushin V, Bogatyrev I, Boyd R, Caritat P de, Dutter R, Finne TE, Halleraker JH, Jæger Ø, Kashulina G, Lehto O, Niskavaara H, Pavlov V, Räisänen ML, Strand T, Volden T. Environmental Geochemical Atlas of the Central Barents Region. NGU-GTK-CKE Special Publication, Geological Survey of Norway, Trondheim, Norway, 1998.

Examples

data(bhorizon)
# classical versus robust correlation
corr.plot(log(bhorizon[,"Al"]), log(bhorizon[,"Na"]))

C-horizon of the Kola Data

Description

The Kola Data were collected in the Kola Project (1993-1998, Geological Surveys of Finland (GTK) and Norway (NGU) and Central Kola Expedition (CKE), Russia). More than 600 samples in five different layers were analysed, this dataset contains the C-horizon.

Usage

data(chorizon)

Format

A data frame with 606 observations on the following 110 variables.

ID: a numeric vector
XCOO: a numeric vector
YCOO: a numeric vector
Ag: a numeric vector
Ag_INAA: a numeric vector
Al: a numeric vector
Al2O3: a numeric vector
As: a numeric vector
As_INAA: a numeric vector
Au_INAA: a numeric vector
B: a numeric vector
Ba: a numeric vector
Ba_INAA: a numeric vector
Be: a numeric vector
Bi: a numeric vector
Br_IC: a numeric vector
Br_INAA: a numeric vector
Ca: a numeric vector
Ca_INAA: a numeric vector
CaO: a numeric vector
Cd: a numeric vector
Ce_INAA: a numeric vector
Cl_IC: a numeric vector
Co: a numeric vector
Co_INAA: a numeric vector
EC: a numeric vector
Cr: a numeric vector
Cr_INAA: a numeric vector
Cs_INAA: a numeric vector
Cu: a numeric vector
Eu_INAA: a numeric vector
F_IC: a numeric vector
Fe: a numeric vector
Fe_INAA: a numeric vector
Fe2O3: a numeric vector
Hf_INAA: a numeric vector
Hg: a numeric vector
Hg_INAA: a numeric vector
Ir_INAA: a numeric vector
K: a numeric vector
K2O: a numeric vector
La: a numeric vector
La_INAA: a numeric vector
Li: a numeric vector
LOI: a numeric vector
Lu_INAA: a numeric vector
wt_INAA: a numeric vector
Mg: a numeric vector
MgO: a numeric vector
Mn: a numeric vector
MnO: a numeric vector
Mo: a numeric vector
Mo_INAA: a numeric vector
Na: a numeric vector
Na_INAA: a numeric vector
Na2O: a numeric vector
Nd_INAA: a numeric vector
Ni: a numeric vector
Ni_INAA: a numeric vector
NO3_IC: a numeric vector
P: a numeric vector
P2O5: a numeric vector
Pb: a numeric vector
pH: a numeric vector
PO4_IC: a numeric vector
Rb: a numeric vector
S: a numeric vector
Sb: a numeric vector
Sb_INAA: a numeric vector
Sc: a numeric vector
Sc_INAA: a numeric vector
Se: a numeric vector
Se_INAA: a numeric vector
Si: a numeric vector
SiO2: a numeric vector
Sm_INAA: a numeric vector
Sn_INAA: a numeric vector
SO4_IC: a numeric vector
Sr: a numeric vector
Sr_INAA: a numeric vector
SUM_XRF: a numeric vector
Ta_INAA: a numeric vector
Tb_INAA: a numeric vector
Te: a numeric vector
Th: a numeric vector
Th_INAA: a numeric vector
Ti: a numeric vector
TiO2: a numeric vector
U_INAA: a numeric vector
V: a numeric vector
W_INAA: a numeric vector
Y: a numeric vector
Yb_INAA: a numeric vector
Zn: a numeric vector
Zn_INAA: a numeric vector
ELEV: a numeric vector
COUN: a numeric vector
ASP: a numeric vector
TOPC: a numeric vector
LITO: a numeric vector
Al_XRF: a numeric vector
Ca_XRF: a numeric vector
Fe_XRF: a numeric vector
K_XRF: a numeric vector
Mg_XRF: a numeric vector
Mn_XRF: a numeric vector
Na_XRF: a numeric vector
P_XRF: a numeric vector
Si_XRF: a numeric vector
Ti_XRF: a numeric vector

Source

Kola Project (1993-1998)

References

Examples

data(chorizon)
# classical versus robust correlation
corr.plot(log(chorizon[,"Al"]), log(chorizon[,"Na"]))

# create data: x <- cbind(rnorm(100), rnorm(100)) y <- cbind(rnorm(10, 3, 1), rnorm(10, 3, 1)) z <- rbind(x,y) # execute: dd.plot(z) # # Identify multivariate outliers for Co-Cu-Ni in humus layer of Kola data: data(humus) dd.plot(log(humus[,c("Co","Cu","Ni")]))

locoutNeighbor(dat, X, Y, propneighb = 0.1, variant = c("dist", "knn"), usemax = 1/3, npoints = 50, chisqqu = 0.975, indices = NULL, xlab = NULL, ylab = NULL, colall = gray(0.7), colsel = 1, ...)

# use data from illustrative example in paper: data(X) data(Y) data(dat) res <- locoutNeighbor(dat,X,Y,variant="knn",usemax=1,chisqqu=0.975,indices=c(1,11,24,36), propneighb=0.1,npoints=100)

locoutPercent(dat, X, Y, dist = NULL, k = 10, chisqqu = 0.975, sortup = 10, sortlow = 90, nlinesup = 10, nlineslow = 10, indices = NULL, xlab = "(Sorted) Index", ylab = "Distance to neighbor", col = gray(0.7), ...)

# geochemical data from northern Europe data(bsstop) x=bsstop[,5:14] # identify multivariate outliers x.out=pcout(x,makeplot=FALSE) # visualize multivariate outliers in the map op <- par(mfrow=c(1,2)) data(bss.background) pbb(asp=1) points(bsstop$XCOO,bsstop$YCOO,pch=16,col=x.out$wfinal01+2) title("Outlier detection based on pcout") legend("topleft",legend=c("potential outliers","regular observations"),pch=16,col=c(2,3)) # compare with outlier detection based on MCD: x.mcd <- robustbase::covMcd(x) pbb(asp=1) points(bsstop$XCOO,bsstop$YCOO,pch=16,col=x.mcd$mcd.wt+2) title("Outlier detection based on MCD") legend("topleft",legend=c("potential outliers","regular observations"),pch=16,col=c(2,3)) par(op)

## S3 method for class 'mvoutlierCoDa' plot(x, ..., which = c("biplot", "map", "uni", "parallel"), choice = 1:2, coord = NULL, map = NULL, onlyout = TRUE, bw = FALSE, symb = TRUE, symbtxt = FALSE, col = NULL, pch = NULL, obj.cex = NULL, transp = 1)

data(humus) el=c("As","Cd","Co","Cu","Mg","Pb","Zn") dsel <- humus[,el] data(kola.background) # contains different information (coast, borders, etc.) coo <- rbind(kola.background$coast,kola.background$boundary,kola.background$borders) XY <- humus[,c("XCOO","YCOO")] set.seed(123) res <- mvoutlier.CoDa(dsel) par(ask=TRUE) ### Parallel coordinate plot: ## show for all obvervations (transp is only useful when generating e.g. a pdf): # plot(res,onlyout=FALSE,bw=TRUE,which="parallel",symb=FALSE,symbtxt=FALSE,transp=0.3) ## show only outliers with special colors and labels in the margins: plot(res,onlyout=TRUE,bw=FALSE,which="parallel",symb=TRUE,symbtxt=TRUE,transp=0.3) ### Biplot: ## show all data points, outliers are in different color and have different symbol: # plot(res,onlyout=FALSE,which="biplot",bw=FALSE,symb=FALSE,symbtxt=FALSE) ## show only the outliers with special symbols and colors: plot(res,onlyout=TRUE,which="biplot",bw=FALSE,symb=TRUE,symbtxt=TRUE) ### Map: ## show all data points, outliers are in different color and have different symbol: # plot(res,coord=XY,map=coo,onlyout=FALSE,which="map",bw=FALSE,symb=FALSE,symbtxt=FALSE) ## show only the outliers with special symbols and colors: plot(res,coord=XY,map=coo,onlyout=TRUE,which="map",bw=FALSE,symb=TRUE,symbtxt=TRUE) ### Univariate scatterplot: ## show all data points, outliers are in different color and have different symbol: # plot(res,onlyout=FALSE,which="uni",symb=FALSE,symbtxt=FALSE) ## show only the outliers with special symbols and colors: plot(res,onlyout=TRUE,which="uni",symb=TRUE,symbtxt=TRUE)

# geochemical data from northern Europe data(bsstop) x=bsstop[,5:14] # identify multivariate outliers x.out=sign1(x,makeplot=FALSE) # visualize multivariate outliers in the map op <- par(mfrow=c(1,2)) data(bss.background) pbb(asp=1) points(bsstop$XCOO,bsstop$YCOO,pch=16,col=x.out$wfinal01+2) title("Outlier detection based on signout") legend("topleft",legend=c("potential outliers","regular observations"),pch=16,col=c(2,3)) # compare with outlier detection based on MCD: x.mcd <- robustbase::covMcd(x) pbb(asp=1) points(bsstop$XCOO,bsstop$YCOO,pch=16,col=x.mcd$mcd.wt+2) title("Outlier detection based on MCD") legend("topleft",legend=c("potential outliers","regular observations"),pch=16,col=c(2,3)) par(op)

# geochemical data from northern Europe data(bsstop) x=bsstop[,5:14] # identify multivariate outliers x.out=sign2(x,makeplot=FALSE) # visualize multivariate outliers in the map op <- par(mfrow=c(1,2)) data(bss.background) pbb(asp=1) points(bsstop$XCOO,bsstop$YCOO,pch=16,col=x.out$wfinal01+2) title("Outlier detection based on signout") legend("topleft",legend=c("potential outliers","regular observations"),pch=16,col=c(2,3)) # compare with outlier detection based on MCD: x.mcd <- robustbase::covMcd(x) pbb(asp=1) points(bsstop$XCOO,bsstop$YCOO,pch=16,col=x.mcd$mcd.wt+2) title("Outlier detection based on MCD") legend("topleft",legend=c("potential outliers","regular observations"),pch=16,col=c(2,3)) par(op)

`x`	matrix or data.frame containing the data; has to be at least two-dimensional
`delta`	quantile of the chi-squared distribution with ncol(x) degrees of freedom. This quantile appears as cyan-colored vertical line in the plot.
`quan`	proportion of observations which are used for mcd estimations; has to be between 0.5 and 1, default ist 0.5
`alpha`	Maximum thresholding proportion (optional scalar, default: alpha = 0.05)

`x`	Dataset (n x p)
`m0`	Initial location estimator (1 x p)
`c0`	Initial scatter estimator (p x p)
`alpha`	Maximum thresholding proportion (optional scalar, default: alpha = 0.025)
`pcrit`	Critical value obtained by simulations (optional scalar, default value obtained from simulations)

`m`	Adaptive location estimator (p x 1)
`c`	Adaptive scatter estimator (p x p)
`cn`	Adaptive threshold ("adjusted quantile")
`w`	Weight vector (n x 1)

`x`	matrix or data.frame containing the data
`quan`	amount of observations which are used for mcd estimations. has to be between 0.5 and 1, default ist 0.5
`ask`	logical. specifies whether user interacton is allowed or not. default is TRUE
`...`	additional graphical parameters

`x`	two dimensional matrix or data.frame containing the data.
`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

`outliers`	boolean vector of outliers
`md`	robust mahalanobis distances of the data
`euclidean`	euclidean distances of the observations according to the minimum of the data.

`x`	vector to be plotted against y and of which the correlation with y is calculated.
`y`	vector to be plotted against x and of which the correlation with x is calculated.
`quan`	amount of observations which are used for mcd estimations. has to be between 0.5 and 1, default ist 0.5
`alpha`	Determines the size of the ellipsoids. An observation will be outside of the ellipsoid if its mahalanobis distance exceeds the 1-alpha quantile of the chi-squared distribution.
`...`	additional graphical parameters

`cor.cla`	correlation between x and y based on classical estimation of location and scatter
`cor.rob`	correlation between x and y based on robust estimation of location and scatter

`x`	matrix or data frame containing the data
`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

`outliers`	boolean vector of outliers
`md.cla`	mahalanobis distances of the observations based on classical estimators of location and scatter.
`md.rob`	mahalanobis distances of the observations based on robust estimators of location and scatter (mcd).

`dat`	multivariate data set (without coordinates)
`X`	X coordinates of the data points
`Y`	Y coordinates of the data points
`propneighb`	proportion of neighbors to be included in tolerance ellipse
`variant`	either search for neighbors according to the Eucl.Distance, or according to kNN
`usemax`	for either variant: give fraction of points (max Dist) that is used for the plot
`npoints`	computation is done at most at npoints points
`chisqqu`	quantile of the chisquare distribution for splitting the plot
`indices`	if this is not NULL, these should be indices of observations to be highlighted
`xlab`	x-axis label for plot
`ylab`	y-axis label for plot
`colall`	color for lines if indices is NULL
`colsel`	color for lines if indices are selected
`...`	additional parameters for plotting

`indices.reg`	indices of the (selected) observations being regular observations
`indices.out`	indices of the (selected) observations being golbal outliers

`sel`	plot coordinates of the selected region
`indices.reg`	indices of the bservations being regular observations
`indices.out`	indices of the observations being golbal outliers

`coord`	(x,y)-coordinates of the data
`data`	matrix or data.frame containing the data.
`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).
`symb`	logical for plotting special symbols (see details).
`plotmap`	logical for plotting the background map.
`map`	see plot.kola.background()
`which.map`	see plot.kola.background()
`map.col`	see plot.kola.background()
`map.lwd`	see plot.kola.background()
`...`	additional graphical parameters

`x`	data set (matrix or data frame) containing the raw untransformed compositional data
`quan`	quantity of data used for robust estimation; between 0.5 and 1
`alpha`	maximum threshold for adaptive outlier detection
`col.quantile`	quantiles of an average concentration defining the colors
`symb.pch`	plotting character for symbols
`symb.cex`	plotting size for symbols
`adaptive`	if TRUE then the adaptive method for the outlier threshold is used

`map`	List of coordinates. For the correct format see also help(kola.background)
`add.plot`	logical. If true background is added to an existing plot
`...`	additional plot parameters, see help(par)

`wfinal01`	0/1 vector with final weights for each observation; weight 0 indicates potential multivariate outliers.
`wfinal`	numeric vector with final weights for each observation; small values indicate potential multivariate outliers.
`wloc`	numeric vector with weights for each observation; small values indicate potential location outliers.
`wscat`	numeric vector with weights for each observation; small values indicate potential scatter outliers.
`x.dist1`	numeric vector with distances for location outlier detection.
`x.dist2`	numeric vector with distances for scatter outlier detection.
`M1`	upper boundary for assigning weight 1 in location outlier detection.
`const1`	lower boundary for assigning weight 0 in location outlier detection.
`M2`	upper boundary for assigning weight 1 in scatter outlier detection.
`const2`	lower boundary for assigning weight 0 in scatter outlier detection.

`map`	List of coordinates. For the correct format see also help(kola.background)
`which.map`	which==1 ... plot project boundary \# which==2 ... plot coast line \# which==3 ... plot country borders \# which==4 ... plot lakes and rivers
`map.col`	Map colors to be used
`map.lwd`	Defines linestyle of the background
`add.plot`	logical. if true background is added to an existing plot
`...`	additional plot parameters, see help(par)

`wfinal01`	0/1 vector with final weights for each observation; weight 0 indicates potential multivariate outliers.
`x.dist`	numeric vector with distances used for outlier detection.
`const`	outlier cutoff value.

`ilrvariables`	the ilr transformed data matrix
`outliers`	TRUE/FALSE vector; TRUE refers to outlier
`pcaobj`	object from PCA
`colcol`	vector with the colors
`colbw`	vector with the grey scales
`pchvec`	vector with plotting symbols
`cexvec`	vector with sizes of plot symbols

`x`	a numeric matrix or data frame which provides the data for outlier detection
`makeplot`	a logical value indicating whether a diagnostic plot should be generated (default to FALSE)
`explvar`	a numeric value between 0 and 1 indicating how much variance should be covered by the robust PCs (default to 0.99)
`crit.M1`	a numeric value between 0 and 1 indicating the quantile to be used as lower boundary for location outlier detection (default to 1/3)
`crit.c1`	a positive numeric value used for determining the upper boundary for location outlier detection (default to 2.5)
`crit.M2`	a numeric value between 0 and 1 indicating the quantile to be used as lower boundary for scatter outlier detection (default to 1/4)
`crit.c2`	a numeric value between 0 and 1 indicating the quantile to be used as upper boundary for scatter outlier detection (default to 0.99)
`cs`	a numeric value indicating the scaling constant for combined location and scatter weights (default to 0.25)
`outbound`	a numeric value between 0 and 1 indicating the outlier boundary for defining values as final outliers (default to 0.25)
`...`	additional plot parameters, see help(par)

`x`	resulting object from function `mvoutlier.CoDa`
`...`	further plotting arguments
`which`	type of plot that should be made
`choice`	select the pair of PCs used for the biplot
`coord`	coordinates for the presentation in a map
`map`	coordinates for the background map; see details below
`onlyout`	if TRUE only the outliers are shown in the plot
`bw`	if TRUE symbold will be in grey scale rather than in color
`symb`	if TRUE special symbols are used according to outlyingness
`symbtxt`	if TRUE text labels are used for plotting
`col`	define colors to be used for outliers and non-outliers
`pch`	define plotting symbols to be used for outliers and non-outliers
`obj.cex`	define symbol size for outliers and non-outliers
`transp`	define transparancy for parallel coordinate plot

`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

Package 'mvoutlier'

Help Index

Adjusted Quantile Plot

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Adaptive reweighted estimator for multivariate location and scatter

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

B-horizon of the Kola Data

Description

Usage

Format

Source

References

Examples

Background map for the BSS project

Description

Usage

Format

Details

Source

References

Examples

Bottom Layer of the BSS Data

Description

Usage

Format

Source

References

Examples

Top Layer of the BSS Data

Description

Usage

Format

Source

References

Examples

Chi-Square Plot

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

C-horizon of the Kola Data

Description

Usage

Format

Source

References

Examples

Color Plot

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Correlation Plot: robust versus classical bivariate correlation

Description

Usage

Arguments

Value