Help for package andrews

Type:

Package

Title:

Various Andrews Curves

Version:

1.1.2

Maintainer:

Sigbert Klinke <sigbert@hu-berlin.de>

Depends:

R (≥ 2.10)

Description:

Visualisation of multidimensional data through different Andrews curves: Andrews, D. F. (1972) Plots of High-Dimensional Data. Biometrics, 28(1), 125-136. <doi:10.2307/2528964>.

License:

GPL-3

URL:

https://github.com/sigbertklinke/andrews (development version)

Encoding:

UTF-8

LazyData:

true

Imports:

grDevices, graphics, gmp

Suggests:

knitr, rmarkdown, robustbase, mclust

VignetteBuilder:

knitr

RoxygenNote:

7.2.3

NeedsCompilation:

Packaged:

2023-10-23 09:45:57 UTC; sk

Author:

Jaroslav Myslivec [aut], Sigbert Klinke [cre, ctb]

Repository:

CRAN

Date/Publication:

2023-10-23 10:20:05 UTC

Andrews curves

Description

Andrews curves for visualization of multidimensional data. For colouring the curves see the details. For differences between andrews and andrews0 see the vignette("andrews"). With the same parameters called both functions should create the same plot. type==5 is a modification of type==3 and type==6 is a modification of type==4.

Usage

andrews(
  df,
  type = 1,
  clr = NULL,
  step = 100,
  ymax = 10,
  alpha = NULL,
  palcol = NULL,
  lwd = 1,
  lty = "solid",
  ...
)

Arguments

df

data frame or an R object that can be converted into a data frame with as.data.frame

type

type of curve

1: f(t)=x_1/\sqrt{2}+x_2\sin(t)+x_3\cos(t)+x_4\sin(2t)+x_5\cos(2t)+...
2: f(t)=x_1\sin(t)+x_2\cos(t)+x_3\sin(2t)+x_4\cos(2t)+...
3: f(t)=x_1\cos(t)+x_2\cos(\sqrt{2t})+x_3\cos(\sqrt{3t})+...
4: f(t)=0.5^{p/2}x_1+0.5^{(p-1)/2} x_2(\sin(t)+\cos(t))+0.5^{(p-2)/2} x_3(\sin(t)-\cos(t))+0.5^{(p-3)/2} x_4(\sin(2t)+\cos(2t))+0.5^{(p-4)/2}x_5(\sin(2t)-\cos(2t))+...) with p the number of variables
5: f(t)=x_1\cos(\sqrt{p_0} t)+x_2\cos(\sqrt{p_1}t)+x_3\cos(\sqrt{p_2}t)+... with p_0=1 and p_i the i-th prime number
6: f(t)=1/\sqrt{2}(x_1+x_2(\sin(t)+\cos(t))+x_3(\sin(t)-\cos(t))+x_4(\sin(2t)+\cos(2t))+x_5(\sin(2t)-\cos(2t))+...)

clr

number/name of column in the data frame for color of curves

step

smoothness of curves

ymax

maximum of y coordinate

alpha

semi-transparent color (0 < alpha < 1) which are supported only on some devices

palcol

a function which generates a set of colors, see details

lwd

line width, a positive number, defaulting to 1.

lty

line type, can either be specified as an integer (0=blank, 1=solid (default), 2=dashed, 3=dotted, 4=dotdash, 5=longdash, 6=twodash) or as one of the character strings "blank", "solid", "dashed", "dotted", "dotdash", "longdash", or "twodash", where "blank" uses ‘invisible lines’ (i.e., does not draw them).

...

further named parameters given to graphics::plot.default() except x, y, and type.

Details

If clr has length one then it is used as column number or column name for coloring the curves:

If df[,clr] is numeric then palcol must be function which returns colors for values in the range ⁠\[0, 1\]⁠ using normalized variable. The default is function function(v) { hsv(0,1,v) }.
Otherwise df[,clr] is converted to a factor and palcol must be a function which returns for each level a color. The parameter for palcol is the numbe of levels and the default is grDevices::rainbow(). If the length of clr is the number of rows of df then clr is interpreted as colors.

Andrews curves transform multidimensional data into curves. This package presents four types of curves.

Value

nothing

Author(s)

Sigbert Klinke sigbert@hu-berlin.de, Jaroslav Myslivec jaroslav.myslivec@upce.cz

References

Andrews, D. F. (1972) Plots of High-Dimensional Data. Biometrics, vol. 28, no. 1, pp. 125-136.
Khattree, R., Naik, D. N. (2002) Andrews Plots for Multivariate Data: Some New Suggestions and Applications. Journal of Statistical Planning and Inference, vol. 100, no. 2, pp. 411-425.

Examples

data(iris)
op <- par(mfrow=c(1,2))
andrews0(iris,clr=5,ymax=3)
andrews(iris,clr=5,ymax=3)
par(op)
andrews(iris,type=4,clr=5,ymax=NA)

Andrews curves

Description

Andrews curves for visualization of multidimensional data. For differences between andrews and andrews2 see the 'vignette("andrews"). For colouring the curves see the details.

Usage

andrews0(
  df,
  type = 1,
  clr = NULL,
  step = 100,
  ymax = 10,
  main = NULL,
  sub = NULL
)

Arguments

df

data frame

type

type of curve

1: f(t)=x_1/\sqrt{2}+x_2\sin(t)+x_3\cos(t)+x_4\sin(2t)+x_5\cos(2t)+...
2: f(t)=x_1\sin(t)+x_2\cos(t)+x_3\sin(2t)+x_4\cos(2t)+...
3: f(t)=0.5^{p/2}x_1+0.5^{(p-1)/2} x_2(\sin(t)+\cos(t))+0.5^{(p-2)/2} x_3(\sin(t)-\cos(t))+0.5^{(p-3)/2} x_4(\sin(2t)+\cos(2t))+0.5^{(p-6)/2}x_5(\sin(2t)-\cos(2t))+...) with $p$ the number of variables
4: f(t)=1/\sqrt{2}(x_1+x_2(\sin(t)+\cos(t))+x_3(\sin(t)-\cos(t))+x_4(\sin(2t)+\cos(2t))+x_5(\sin(2t)-\cos(2t))+...)

clr

number/name of column in the date frame for color of curves

step

smoothness of curves

ymax

maximum of y coordinate.

main

main title for the plot

sub

sub title for the plot

Details

Andrews curves transform multidimensional data into curves. This package presents four types of curves

If df[,clr] is numeric then hsv(1,1,v) with the normalized values (on ⁠\[0, 1\]⁠) of df[,clr] is used. Otherwise the number of unique values in nuv <- unique(df[,clr]) is used in connection with rainbow(nuv).

Value

nothing

Author(s)

Jaroslav Myslivec jaroslav.myslivec@upce.cz

References

Andrews, D. F. (1972) Plots of High-Dimensional Data. Biometrics, vol. 28, no. 1, pp. 125-136.
Khattree, R., Naik, D. N. (2002) Andrews Plots for Multivariate Data: Some New Suggestions and Applications. Journal of Statistical Planning and Inference, vol. 100, no. 2, pp. 411-425.

Examples

data(iris)
andrews0(iris,clr=5,ymax=3)
andrews0(iris,type=4,clr=5,ymax=2)

Swiss banknotes data

Description

The data set contains six measurements made on 100 genuine and 100 counterfeit old-Swiss 1000-franc bank notes. The data frame and the documentation is a copy of mclust::banknote.

Usage

banknote

Format

A data frame with 200 rows and 7 columns:

Status: the status of the banknote: genuine or counterfeit
Length: Length of bill (mm)
Left: Width of left edge (mm)
Right: Width of right edge (mm)
Bottom: Bottom margin width (mm)
Top: Top margin width (mm)
Diagonal: Length of diagonal (mm)

Source

Flury, B. and Riedwyl, H. (1988). Multivariate Statistics: A practical approach. London: Chapman & Hall, Tables 1.1 and 1.2, pp. 5-8.

deftype

Description

Defines a function which can be used as basis for Andrews curves f_t(t) = \sum_{j=1}^p x_{ij} f_i(t).

Usage

deftype(index = NULL, FUN = NULL, xlim = c(-pi, pi))

Arguments

index

index/name of the function

FUN

function of the form function(n, t) {...}

xlim

default range for displaying curves (default: c(-pi,pi))

Value

either a list of all functions or a single function

Examples

# define a new andrews curve, just with sine curves
deftype("sine", function(n, t) {
          n <- as.integer(if (n<1) 1 else n)
          m <- matrix(NA, nrow=length(t), ncol=n)
          for (i in 1:n) m[,i] <- sin(i*t)
          m
         })
andrews(iris, "sine")
# query
deftype()
deftype("sine")

Generate a Sequence of Prime Numbers

Description

Generates a vector of the first n primes using gmp::nextprime().

Usage

generate_n_primes(n, one = FALSE)

Arguments

n

the number of primes to generate.

one

should 1 included in the sequence (default: FALSE)

Value

an integer vector of prime numbers

Examples

generate_n_primes(5)
generate_n_primes(5, TRUE)

Normalization

Description

Normalization of a variable:

type==1: ar normalized into [0,1],
type==2: ar is standardized,
otherwise no normalization is done.

Usage

normalize(ar, type = 1)

Arguments

ar

numeric variable.

type

integer: type of normalization (default: 1)

Details

Normalization of variable: ar<-(ar-min(ar))/(max(ar)-min(ar))

Value

Returns normalized variable.

Author(s)

Jaroslav Myslivec jaroslav.myslivec@upce.cz, Sigbert Klinke sigbert@hu-berlin.de

Examples

normalize(iris[,1])

Numeric array

Description

Extracts numeric array from data frame.

Usage

numarray(df)

Arguments

df

data frame.

Details

Extracts numeric array from data frame.

Value

Returns numeric array.

Author(s)

Jaroslav Myslivec jaroslav.myslivec@upce.cz, Sigbert Klinke sigbert@hu-berlin.de

Examples

numarray(iris)

outlyingness

Description

Computes the Stahel-Donoho outlyingness. If type is any of the available types by andrews() then the projection vectors are generated along the andrews curves. Otherwise step random directions will be used. Note that the projection vectors are always normalized to length one.

Usage

outlyingness(x, type = 1, step = 100, xlim = NULL, normalize = 1)

Arguments

x

data frame

type

type of curve, see andrews()

step

step smoothness of curves

xlim

the x limits (x1, x2)

normalize

type of normalization, see normalize()

Value

the Stahel-Donoho outlyingness

References

Stahel, W. (1981), Robuste Schätzungen: infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen, PhD thesis, ETH Z¨urich.
Donoho, D. (1982), Breakdown properties of multivariate location estimators, Ph.D. Qualifying paper, Dept. Statistics, Harvard University, Boston.

Examples

# use projection vectors from the Andrews curve
sdo <- outlyingness(iris)
col <- gray(1-sdo/max(sdo))
andrews(iris, clr=col, ymax=NA)
# use 1000 random projection vectors
sdo <- outlyingness(iris, type=0, step=1000)
col <- gray(1-sdo/max(sdo))
andrews(iris, clr=col, ymax=NA)
# use 1000 random projection vectors with adjusted outlyingness
library("robustbase")
x   <- numarray(iris)
x   <- scale(x, center=apply(x, 2, min), scale=apply(x, 2, max)-apply(x, 2, min))
sdo <- adjOutlyingness(x, ndir=1000, only.outlyingness=TRUE)
col <- gray(1-sdo/max(sdo))
andrews(as.data.frame(x), clr=col, ymax=NA)

Selecting in Andrews curves

Description

Selecting object utility in Andrews curves

Usage

selectand(df, type = 1, step = 100, ncol = 0, from = 0, to = 1, col = 2)

Arguments

df

data frame.

type

type of curve.

step

smoothness of curves.

ncol

number of column in data frame for selection.

from

from value.

to

to value.

col

color of selected objects.

Details

Define which objects will be selected (colored) in Andrews curves.

Value

Nothing

Author(s)

Jaroslav Myslivec jaroslav.myslivec@upce.cz

Examples

data(iris)
andrews(iris,clr=5,ymax=3)
selectand(iris,ncol=1,from=5,to=5.5,col=1)

Comparison

Description

Creates and displays a temporary PDF file with different diagrams comparing andrews and andrews0 plots.

Usage

zzz()

Value

nothing

Examples

if (interactive()) zzz()