Package 'jvcoords'

Package overview

Description

The jvcoords package provides functions to standardize and whiten data, and an implementation of Principal Component Analysis (PCA). All three transformations are implemented using a common class ⁠coords⁠ which allows to easily convert data from and to the new coordinate systems.

See the documentation for standardize, whiten, and PCA for information on how to use this package.

Author(s)

Jochen Voss <[email protected]>

See Also

standardize, whiten, PCA, coords

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An S3 class to represent affine coordinate transforms

Description

Perform affine coordinate transformations.

Usage

coords(p, name = NULL, shift = 0)
  appendTrfm(trfm, op = c("diag", "orth"), val)
  toCoords(trfm, x)
  fromCoords(trfm, y, apply.shift = TRUE)

Arguments

p	The number of variables in the original data.
name	A short name for the coordinate transformation (optional).
shift	A value subtracted from the data as the first step of the coordinate transformation. Usually, this will be the mean of the data (optional).
trfm	An object of class coords.
op	The type of transformation to append.
val	Data for the transformation to append.
x	Data matrix, rows are observations, columns are variables.
y	Transformed data matrix, rows are observations, columns are variables.
apply.shift	Whether to apply the final shift of coordinates. Set this to FALSE in order to only apply the linear part of the transformation.

Details

The function coords() creates a new object representing an affine coordinate transformation. Initially, the object represents a shift by the amount shift, mapping p-dimensional vectors x to x-shift. The function appendTrfm() can then be used to modify the transformation. The optional argument name, if set, is used when printing objects of class coords.

The function toCoords() applies the affine transformation trfm to the data x. The data x must either be a vector of length trfm$p, in which case the result is a vector of length trfm$q, or a matrix with trfm$p columns, in which case the transformation is applied to each row of the matrix separately.

The function fromCoords() implements the inverse transform to toCoords(). The output always satisfies toCoords(trfm, fromCoords(trfm, y)) == y. If trfm$p == trfm$q, i.e. if the transformation is bijective, the fromCoords(trfm, toCoords(trfm, x)) == x also holds. The argument apply.shift can be set to false to apply only the linear part of the (inverse) transformation, leaving out the final shift.

The function appendTrfm() concatenates trfm with an additional, linear transformation and returns the result. The arguments op and val specify which kind of linear transformation to append. There are two choices for op:

• diag denotes multiplication with a diagonal matrix: an input vector x is mapped to the output x * val. The scaling factor val can either be a vector of length trfm$q (for element-wise scaling), or a number.

• orth denotes multiplication with an orthogonal matrix. val must be a matrix with orthogonal columns (not necessarily square) and trfm$q rows. An input vector x is mapped to the output x %*% orth.

The new transformation is applied after any other transformations already associated with trfm.

Value

An object of class coords, as a list with the following components:

p	the number of variables in the original data set
q	the number of variables in the transformed data set
shift	the affine part of the transformation
name	the name of the transformation
cmds	a representation of the transformation (internal use only)

Author(s)

Jochen Voss <[email protected]>

See Also

standardize, whiten, PCA

Examples

pc <- PCA(iris[, 1:4], n.comp = 3)
  toCoords(pc, c(5, 3, 4, 1))
  fromCoords(pc, c(1, 0, 0))

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Perform Principal Component Analysis (PCA)

Description

Perform principal components analysis on a data matrix and return the results as an object of class coords.

Usage

PCA(x, n.comp, scale = FALSE, compute.scores = TRUE)

Arguments

x	A data matrix, rows are observations, columns are variables.
n.comp	How many principal components to compute.
scale	Whether to standardize the columns before doing PCA.
compute.scores	Whether to compute the scores (i.e. x in the new basis).

Details

This function performs Principal Component Analysis (PCA) on the data. Variables are always centred before the PCA is performed and, if scale is set, the variables will also be rescaled to unit variance.

If compute.scores is set to FALSE, only the information required for the toPC() and fromPC() to work is stored in the returned coords object; otherwise the scores will be stored in the $y field of the coords object.

The PCA() function is an alternative to the prcomp() command from the standard library. The main advantage of PCA() is that the coords class provides functions to convert between the original basis and the principal component basis.

Value

An object of class coords, with the following additional components added:

loadings	the loadings, each column is one of the new basis vectors
y	if compute.scores==TRUE, this is x expressed in the new basis
var	the variance of the data along each of the new basis vectors
total.var	the total variance of the data

Author(s)

Jochen Voss <[email protected]>

See Also

coords; alternative implementations: prcomp, princomp

Examples

pc <- PCA(iris[, 1:4], scale = TRUE, n.comp = 2)
  pc
  plot(pc$y, col=iris$Species)

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Standardize data

Description

Standardize each column of a data matrix and return the results as an object of class coords.

Usage

standardize(x, compute.scores = TRUE)

Arguments

x	A data matrix, rows are observations, columns are variables.
compute.scores	Whether to compute the scores (i.e. x in the new basis).

Details

This function standardizes the columns of x by subtracting the mean of each column and then dividing by the standard deviation. The transformed data is stored in the $y field of the returned coords object.

If compute.scores is set to FALSE, only the information required for the toCoords() and fromCoords() to work is stored in the returned coords object; otherwise the scores (transformed data) will be stored in the $y field of the coords object.

Value

An object of class coords, with the following additional components added:

y	if compute.scores==TRUE, this is x expressed in the new basis

Author(s)

Jochen Voss <[email protected]>

See Also

coords; alternative implementation scale

Examples

w <- standardize(iris[, 1:4])
  colMeans(w$y)
  apply(w$y, 2, sd)

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Whiten data

Description

Whiten data and return the results as an object of class coords.

Usage

whiten(x, compute.scores = TRUE)

Arguments

x	A data matrix, rows are observations, columns are variables.
compute.scores	Whether to compute the scores (i.e. x in the new basis).

Details

This function whitens the data by finding an affine transformation such that the transformed data has mean 0 and identity covariance matrix.

If compute.scores is set to FALSE, only the information required for the toCoords() and fromCoords() to work is stored in the returned coords object; otherwise the scores (transformed data) will be stored in the $y field of the coords object.

Value

An object of class coords, with the following additional components added:

loadings	the loadings, each column is one of the new basis vectors
y	if compute.scores==TRUE, this is x expressed in the new basis

Author(s)

Jochen Voss <[email protected]>

See Also

coords

Examples

w <- whiten(iris[, 1:4])
  colMeans(w$y)
  round(cov(w$y), 3)

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