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Type: Package
Title: Taxicab Correspondence Analysis
Version: 0.1.1
Suggests: GA, testthat
Imports: grDevices, graphics, stats, utils
Author: Jacques Allard and Vartan Choulakian
Maintainer: Jacques Allard <jacques.allard@gmail.com>
Description: Computation and visualization of Taxicab Correspondence Analysis, Choulakian (2006) <doi:10.1007/s11336-004-1231-4>. Classical correspondence analysis (CA) is a statistical method to analyse 2-dimensional tables of positive numbers and is typically applied to contingency tables (Benzecri, J.-P. (1973). L'Analyse des Donnees. Volume II. L'Analyse des Correspondances. Paris, France: Dunod). Classical CA is based on the Euclidean distance. Taxicab CA is like classical CA but is based on the Taxicab or Manhattan distance. For some tables, Taxicab CA gives more informative results than classical CA.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
LazyData: true
RoxygenNote: 7.0.2
NeedsCompilation: no
Packaged: 2019-12-11 14:08:14 UTC; jacqu
Repository: CRAN
Date/Publication: 2019-12-11 14:30:03 UTC

Removes rows and columns of zeros and optionnally, row or column duplicates

Description

Removes rows and columns of zeros and optionnally, row or column duplicates

Usage

CombineCollinearRowsCols(Y, rows = F, cols = F)

Arguments

Y

A matrix or an object that can be coerced to a matrix

rows

Logical: Will duplicate rows be removed?

cols

Logical: Will duplicate columns be removed?

Details

Rows and columns of zeros will be removed.

A matrix of zeros will be returned as matrix with 0 row and 0 column.

If rows 1,2,3 are combined, the name of row 1 is kept. Similarly for columns.

Value

A matrix with rows and columns removed as requested

Examples

CombineCollinearRowsCols(matrix(1:3,nrow=3,ncol=2),cols=TRUE)

CombineCollinearRowsCols(cbind(matrix(1:3,nrow=3,ncol=2),rep(0,3)),cols=TRUE)

CombineCollinearRowsCols(cbind(matrix(1:3,nrow=3,ncol=2),rep(0,3)))

CombineCollinearRowsCols(matrix(0,nrow=3,ncol=3))

CombineCollinearRowsCols(rodent,TRUE,FALSE)

L1 norm of a projection

Description

L1 norm of a projection

Usage

ComputeLambda(uFT, pResidual)

Arguments

uFT

A vector of 0s and 1s of lenght nc: (-1)^uFT is a unit vector in Linf norm

pResidual

A matrix with nc columns

Details

This function is for internal usage only.

Value

L1 norm of the pResidual x (-1)^uFT

Examples

ComputeLambda(uFT=c(FALSE,TRUE,FALSE),pResidual=matrix(1:15,nr=5,nc=3))

Create all 2^n n-tuples of ab[1] and ab[2]

Description

Create all 2^n n-tuples of ab[1] and ab[2]

Usage

CreateAllBinaries(n = 1, ab = c(0, 1))

Arguments

n

An integer > 0

ab

A vector of length 2

Details

This function is for internal usage only.

Value

a n x 2^n matrix

Examples

 CreateAllBinaries(3,c(0,1))

Moves points that are close together

Description

Moves points that are close together

Usage

JitterPosition(x, y, jitterDefault = 0.01, Near = 0.045)

Arguments

x

The x-coordinates of the points

y

The y-coordinates of the points

jitterDefault

A positive number controlling the maximum jitter

Near

A positive number controlling the definition of "near"

Details

This function is for internal usage only.

Value

A list giving the new x and y coordinates, and, for each point, its number neighbours and a suggested relative size for the plotting symbol

Examples

JitterPosition(c(1:5,2,2,4,4,4),c(1:5,2,2,4,4,4))

Extract objects from a list

Description

Extract objects from a list to the global environment

Usage

ListToObjects(L, envir = .GlobalEnv)

Arguments

L

A list

envir

The environment into which variables are created

Details

This function is for internal usage only.

Value

No return

Examples

ListToObjects(list(x=5,A="Hello",M=matrix(1:8,nr=2)),envir=.GlobalEnv)

Removes rows and columns of zeros and optionnally, row or column duplicates

Description

Removes rows and columns of zeros and optionnally, row or column duplicates

Usage

RemoveRowsColumns0sAndDuplicates(Y, rows = F, cols = F, zeros = F)

Arguments

Y

A matrix

rows

Logical Will duplicate rows be removed?

cols

Logical Will duplicate columns be removed?

zeros

Logical Will rows and columns of zeros be removed?

Value

A matrix with rows and columns removed as requested

Examples

RemoveRowsColumns0sAndDuplicates(matrix(1:3,nrow=3,ncol=2),cols=TRUE)

RemoveRowsColumns0sAndDuplicates(cbind(matrix(1:3,nrow=3,ncol=2),rep(0,3)),cols=TRUE)

RemoveRowsColumns0sAndDuplicates(cbind(matrix(1:3,nrow=3,ncol=2),rep(0,3)),zeros=TRUE)

RemoveRowsColumns0sAndDuplicates(matrix(0,nrow=3,ncol=3),zeros=TRUE)

Search a taxicab principal component using the criss-cross algorithm

Description

Search a taxicab principal component using the criss-cross algorithm

Usage

SearchCrissCross(pResidual, iterationMax = 20)

Arguments

pResidual

A matrix of of non-negative numbers

iterationMax

Maximum number of iterations

Details

This function is for internal usage only.

The vector uMax is normalize to uMax[1] = 1

Value

A list: L1Max = maximum L1 norm; uMax = Linf unit vector giving the maximum L1 norm

Examples

SearchCrissCross(matrix(-3:8,nrow=4,ncol=3))

Search a taxicab principal component via exhaustive search

Description

Search a taxicab principal component via exhaustive search

Usage

SearchExhaustive(pResidual)

Arguments

pResidual

A matrix of of non-negative numbers

Details

This function is for internal usage only.

The vector uMax is normalize to uMax[1] = 1

Value

A list: L1Max = maximum L1 norm; uMax = Linf unit vector giving the maximum L1 norm

Examples

SearchExhaustive(matrix(-3:8,nrow=4,ncol=3))

Search a taxicab principal component using the genetic algorithm

Description

Search a taxicab principal component using the genetic algorithm

Usage

SearchGeneticAlgoritm(pResidual)

Arguments

pResidual

A matrix of of non-negative numbers

Details

This function is for internal usage only.

The vector uMax is normalize to uMax[1] = 1

Value

A list: L1Max = maximum L1 norm; uMax = Linf unit vector giving the maximum L1 norm

Examples

SearchGeneticAlgoritm(matrix(-3:8,nrow=4,ncol=3))

Counts of archeological objects

Description

Frequency of object types across the 19 huts of the P. Milazzese settlement in north-eastern Sicily.

Usage

data(milazzese)

Format

A data frame of frequencies with 31 rows and 19 columns

Source

Alberti, G., 2013, Making Sense of Contingency Tables in Archaeology: the Aid of Correspondence Analysis to Intra-Site Activity Areas Research, Journal of Data Science 11, 479-499

Examples

tca(milazzese,nAxes=6,algorithm = "criss-cross")

Creates a symmetric plot from a tca-class object

Description

Creates a symmetric plot from a tca-class object

Usage

## S3 method for class 'tca'
plot(
  x,
  y = NULL,
  axes = c(1, 2),
  labels.rc = c(0, 1),
  col.rc = c("blue", "red"),
  pch.rc = c(16, 21, 17, 24),
  mass.rc = c(F, F),
  cex.rc = c(NA, NA),
  jitter = c(T, F),
  ...
)

Arguments

x

A tca-class object created by tca

y

Unused

axes

The two axes to be plotted

labels.rc

Two numbers: 0 Symbol only; 1 Label only; 2 Symbol and label

col.rc

Colors for rows and columns contributions

pch.rc

Plotting characters for rows and columns contributions

mass.rc

Logical: Will the area of plotting characters be proportional to mass

cex.rc

An overall size factor

jitter

Logical: Will close points be moved slightly?

...

Unused.

Details

If the number of rows is very large, labels will not be printed.

In this version, jitter is coerced.

Value

None

Examples

plot(tca(rodent),labels=c(0,1))

Print result of Taxicab Analysis in easily readable format

Description

Print result of Taxicab Analysis in easily readable format

Usage

## S3 method for class 'tca'
print(x, ...)

Arguments

x

A tca tcaObject produced by the function tca

...

Unused

Value

An invisible list containing formated outputs

Examples

print(tca(rodent))

Rodent species abundance

Description

Counts of rodents by species and site

Usage

data(rodent)

Format

A data frame of counts with 28 rows and 9 columns

Source

Bolger et al. 1997, Response of rodents to habitat fragmentation in coastal Southern California, Ecological Applications 7, 552-563 (as modified and distributed in a University of British Columbia Zoology Department workshop)

Examples

tca(rodent,nAxes=4)

Save tca results to a folder

Description

Save tca results to a folder

Usage

saveTCA(
  tcaObject,
  path,
  folder = NULL,
  what = c("report", "csv", "plot", "dataMatrix", "tcaObject"),
  plotAxes = matrix((1:2), nrow = 1, ncol = 2, byrow = T),
  graphicDevice = c("pdf", "postscript", "xfig", "bitmap", "pictex", "cairo_pdf",
    "cairo_ps", "svg", "png", "jpeg", "bmp", "tiff"),
  csvFormat = c("csv", "csv2")
)

Arguments

tcaObject

a tca-class object created by tca

path

Location of the folder

folder

Name of the folder

what

What to save: all items specified will be saved

plotAxes

A k x 2 matrix giving pairs of axes to plot and save

graphicDevice

Format(s) of plots saved. Plots can be saved in more than one format

csvFormat

Format of csv files (North American or European)

Value

Figure

Examples

saveTCA(tca(rodent),path=tempdir())

Summary of the Taxicab analysis

Description

Summary of the Taxicab analysis

Usage

## S3 method for class 'tca'
summary(object, ...)

Arguments

object

A tca tcaObject produced by the function tca

...

Unused

Details

Shows the unstandardized dispersion values

Value

A list

Examples

summary(tca(rodent))

Taxicab Correspondance analysis

Description

Computes the Taxicab correspondance analysis of a matrix of non-negative numbers

Usage

tca(
  Y,
  nAxes = 2,
  dataName = NULL,
  combineCollinearRows = c(F, T),
  combineCollinearCols = c(F, T),
  algorithm = c("exhaustive", "criss-cross", "genetic"),
  returnInputMatrix = c(T, F),
  verbose = (nAxes > 2),
  exhaustiveAlgorithmMaxnCol = 20,
  L1MaxDeltaMax = 10^-10
)

Arguments

Y

A m x n matrix of non-negative numbers. If Y is not a matrix, the 'as.matrix' transformation will be attempted. Missing values are not allowed.

nAxes

Number of axes to compute

dataName

A name to be used to identify the outputs in 'plot' and 'saveTCA' ()

combineCollinearRows

Should collinear rows be combined?

combineCollinearCols

Should collinear columns be combined?

algorithm

Algorthim requested - may be abreviated to first two letters

returnInputMatrix

Will the input matrix be returned

verbose

Report progress (default) or not

exhaustiveAlgorithmMaxnCol

Maximum size for exhaustive search

L1MaxDeltaMax

Change of L1 norm acceptable for convergence in iterative searches

Details

Computations are carried out on the transposed matrix if nrow(Y) < ncol(Y). In the following, we assume that nrow(Y) >= ncol(Y)

Row and column names will be created if necessary.

Zeros rows and columns are removed.

If ncol(Y) <= exhaustiveAlgorithmMaxnCol the exhaustive algorithm used unless otherwise specified.

If ncol(Y) > exhaustiveAlgorithmMaxnCol the genetic algorithm used unless otherwise specified.

Algorithm = exhaustive is overridden if ncol(Y) > exhaustiveAlgorithmMaxnCol.

For ncol(Y) <= exhaustiveAlgorithmMaxnCol, the user may want to specify algorithm = genetic is nrow(Y) is very large, since exhaustive computation may be slow.

If ncol(Y) <= exhaustiveAlgorithmMaxnCol the genetic algorithm is used unless otherwise specified.

(ncol(Y) = 20 appears to be the maximum practical on 2017 vintage Intel-based desktops).

Value

A list with class 'tca' containing the following components:

dispersion

A nAxes-length vector of matrix of column contributions

rowScores

A m x nAxes matrix of column contributions

colScores

A nAxes x n matrix of row contributions

rowMass

Row weights: apply(Y,1,sum)/sum(Y)

colMass

Column weights: apply(Y,2,sum)/sum(Y)

dataName

A name to be used to identify the output in 'plot' and 'save'

algorithm

Algorithm used (may be different from the algorythm requested)

dataMatrixTotal

Sum of the input matrix entries

dataMatrix

The matrix used in the computation

rowColCombined

A list describing removed or combined rows and columns, if any

Examples

tca(rodent,nAxes=4)
tca(rodent,nAxes=4,combineCollinearRows=c(TRUE,FALSE))

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.