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Last data update: 2014.03.03

R: Principal Components Analysis

pcomp

R Documentation

Principal Components Analysis

Description

Perform a principal components analysis on a matrix or data frame and return a pcomp object.

Usage

pcomp(x, ...)
## S3 method for class 'formula'
pcomp(formula, data = NULL, subset, na.action,
    method = c("svd", "eigen"), ...)
## Default S3 method:
pcomp(x, method = c("svd", "eigen"), scores = TRUE,
    center = TRUE, scale = TRUE, tol = NULL, covmat = NULL,
	subset = rep(TRUE, nrow(as.matrix(x))), ...)

## S3 method for class 'pcomp'
print(x, ...)
## S3 method for class 'pcomp'
summary(object, loadings = TRUE, cutoff = 0.1, ...)
## S3 method for class 'summary.pcomp'
print(x, digits = 3, loadings = x$print.loadings,
    cutoff = x$cutoff, ...)

## S3 method for class 'pcomp'
plot(x, which = c("screeplot", "loadings", "correlations", "scores"),
    choices = 1L:2L, col = par("col"), bar.col = "gray", circle.col = "gray",
    ar.length = 0.1, pos = NULL, labels = NULL, cex = par("cex"),
    main = paste(deparse(substitute(x)), which, sep = " - "), xlab, ylab, ...)
## S3 method for class 'pcomp'
screeplot(x, npcs = min(10, length(x$sdev)), type = c("barplot", "lines"),
    col = "cornsilk", main = deparse(substitute(x)), ...)
## S3 method for class 'pcomp'
points(x, choices = 1L:2L, type = "p", pch = par("pch"),
    col = par("col"), bg = par("bg"), cex = par("cex"), ...)
## S3 method for class 'pcomp'
lines(x, choices = 1L:2L, groups, type = c("p", "e"),
    col = par("col"), border = par("fg"), level = 0.9, ...)
## S3 method for class 'pcomp'
text(x, choices = 1L:2L, labels = NULL, col = par("col"),
    cex = par("cex"), pos = NULL, ...)
## S3 method for class 'pcomp'
biplot(x, choices = 1L:2L, scale = 1, pc.biplot = FALSE, ...)

## S3 method for class 'pcomp'
pairs(x, choices = 1L:3L, type = c("loadings", "correlations"),
    col = par("col"), circle.col = "gray", ar.col = par("col"), ar.length = 0.05,
    pos = NULL, ar.cex = par("cex"), cex = par("cex"), ...)

## S3 method for class 'pcomp'
predict(object, newdata, dim = length(object$sdev), ...) 
## S3 method for class 'pcomp'
correlation(x, newvars, dim = length(x$sdev), ...)
scores(x, ...)
## S3 method for class 'pcomp'
scores(x, labels = NULL, dim = length(x$sdev), ...)

Arguments

`x`	a matrix or data frame with numeric data.
`formula`	a formula with no response variable, referring only to numeric variables.
`data`	an optional data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`subset`	an optional vector used to select rows (observations) of the data matrix `x`.
`na.action`	a function which indicates what should happen when the data contain `NA`s. The default is set by the `na.action` setting of `options`, and is `na.fail` if that is unset. The 'factory-fresh' default is `na.omit`.
`method`	either `"svd"` (the function uses `prcomp`), or `"eigen"` (the function uses `princomp`), or an abbreviation.
`...`	arguments passed to or from other methods. If `x` is a formula one might specify `scale`, `tol` or `covmat`.
`scores`	a logical value indicating whether the score on each principal component should be calculated.
`center`	a logical value indicating whether the variables should be shifted to be zero centered. Alternately, a vector of length equal the number of columns of `x` can be supplied. The value is passed to `scale`. Note that this argument is ignored for `method = "eigen"` and the dataset is always centered in this case.
`scale`	a logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place. The default is `TRUE`, which in general, is advisable. Alternatively, a vector of length equal the number of columns of `x` can be supplied. The value is passed to `scale`.
`tol`	only when `method = "svd"`. A value indicating the magnitude below which components should be omitted. (Components are omitted if their standard deviations are less than or equal to `tol` times the standard deviation of the first component.) With the default null setting, no components are omitted. Other settings for tol could be `tol = 0` or `tol = sqrt(.Machine$double.eps)`, which would omit essentially constant components.
`covmat`	a covariance matrix, or a covariance list as returned by `cov.wt` (and `cov.mve` or `cov.mcd` from package MASS). If supplied, this is used rather than the covariance matrix of `x`.
`object`	a 'pcomp' object.
`loadings`	do we also summarize the loadings?
`cutoff`	the cutoff value below which loadings are replaced by white spaces in the table. That way, larger values are easier to spot and to read in large tables.
`digits`	the number of digits to print.
`which`	the graph to plot.
`choices`	which principal axes to plot. For 2D graphs, specify two integers.
`col`	the color to use in graphs.
`bar.col`	the color of bars in the screeplot.
`circle.col`	the color for the circle in the loadings or correlations plots.
`ar.length`	the length of the arrows in the loadings and correlations plots.
`pos`	the position of text relative to arrows in loadings and correlations plots.
`labels`	the labels to write. If `NULL` default values are computed.
`cex`	the factor of expansion for text (labels) in the graphs.
`main`	the title of the graph.
`xlab`	the label of X-axis.
`ylab`	the label of Y-axis.
`pch`	type of symbol to use.
`bg`	background color for symbols.
`groups`	a grouping factor.
`border`	the color of the border.
`level`	the probability level to use to draw the ellipse.
`pc.biplot`	do we create a Gabriel's biplot (see `biplot()` documentation)?
`npcs`	the number of principal components to represent in the screeplot.
`type`	the type of screeplot (`"barplot"` or `"lines"`) or pairs plot (`"loadings"` or `"correlations"`).
`ar.col`	color of arrows.
`ar.cex`	expansion factor for terxt on arrows.
`newdata`	new individuals with observations for the same variables as those used for making the PCA. You can then plot these additional individuals in the scores graph.
`newvars`	new variables with observations for same individuals as those used for making the PCA. Correlation with PCs is calculated. You can then plot these additional variables in the correlation graph.
`dim`	The number of principal components to keep.

Details

pcomp() is a generic function with "formula" and "default" methods. It is essentially a wrapper around prcomp() and princomp() to provide a coherent interface and object for both methods.

A 'pcomp' object is created. It inherits from 'pca' (as in labdsv package, but not compatible with the 'pca' object of package ade4!) and of 'princomp'.

For more information on calculation done, refer to prcomp for method = "svd" or princomp for method = "eigen".

Value

A c("pcomp", "pca", "princomp") object containing list components:

comp_i

Description of comp_i.

TODO: complete this (also speak about the various methods)!

Note

The signs of the columns of the loadings and scores are arbitrary, and so may differ between different programs for PCA, and even between different builds of R.

Author(s)

Philippe Grosjean <phgrosjean@sciviews.org>, but the core code is indeed in package stats.

Examples

## We will analyze mtcars without the Mercedes data (rows 8:14)
data(mtcars)
cars.pca <- pcomp(~mpg+cyl+disp+hp+drat+wt+qsec, data = mtcars, subset = -(8:14))
cars.pca
summary(cars.pca)
screeplot(cars.pca)

## Loadings are extracted and plotted like this
(cars.ldg <- loadings(cars.pca))
plot(cars.pca, which = "loadings") # Equivalent to vectorplot(cars.ldg)

## Similarly, correlations of variables with PCs are extracted and plotted
(cars.cor <- correlation(cars.pca))
plot(cars.pca, which = "correlations") # Equivalent to vectorplot(cars.cor)
## One can add supplementary variables on this graph
lines(correlation(cars.pca,
    newvars = mtcars[-(8:14), c("vs", "am", "gear", "carb")]))

## Plot the scores
plot(cars.pca, which = "scores", cex = 0.8) # Similar to plot(scores(x)[, 1:2])
## Add supplementary individuals to this plot (labels), use also points() or lines()
text(predict(cars.pca, newdata = mtcars[8:14, ]), col = "gray", cex = 0.8)

## More scores plot
## TODO...

## Pairs plot for 3 PCs
iris.pca <- pcomp(iris[, -5])
pairs(iris.pca, col = (2:4)[iris$Species])

## rgl plot for 3 PCs
## TODO...

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(SciViews)
Loading required package: MASS
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/SciViews/pcomp.Rd_%03d_medium.png", width=480, height=480)
> ### Name: pcomp
> ### Title: Principal Components Analysis
> ### Aliases: pcomp pcomp.default pcomp.formula print.pcomp summary.pcomp
> ###   print.summary.pcomp plot.pcomp screeplot.pcomp points.pcomp
> ###   lines.pcomp text.pcomp biplot.pcomp pairs.pcomp predict.pcomp
> ###   correlation.pcomp scores scores.pcomp
> ### Keywords: models
> 
> ### ** Examples
> 
> ## We will analyze mtcars without the Mercedes data (rows 8:14)
> data(mtcars)
> cars.pca <- pcomp(~mpg+cyl+disp+hp+drat+wt+qsec, data = mtcars, subset = -(8:14))
> cars.pca
Call:
pcomp(formula = ~mpg + cyl + disp + hp + drat + wt + qsec, data = mtcars, 
    subset = -(8:14))

Variances:
       PC1        PC2        PC3        PC4        PC5        PC6        PC7 
5.13759552 1.21698212 0.28325478 0.15620899 0.12409321 0.05604916 0.02581622 

 7  variables and  25 observations.
> summary(cars.pca)
Importance of components (eigenvalues):
                         PC1   PC2    PC3    PC4    PC5     PC6     PC7
Variance               5.138 1.217 0.2833 0.1562 0.1241 0.05605 0.02582
Proportion of Variance 0.734 0.174 0.0405 0.0223 0.0177 0.00801 0.00369
Cumulative Proportion  0.734 0.908 0.9483 0.9706 0.9883 0.99631 1.00000

Loadings (eigenvectors, rotation matrix):
     PC1    PC2    PC3    PC4    PC5    PC6    PC7   
mpg  -0.415        -0.107  0.754 -0.353  0.318  0.144
cyl   0.425        -0.165  0.447  0.289 -0.485  0.521
disp  0.423 -0.110  0.234  0.465  0.103        -0.726
hp    0.385  0.349  0.106        -0.817 -0.203       
drat -0.320  0.505  0.736         0.208 -0.222       
wt    0.400 -0.262  0.499                0.590  0.416
qsec -0.240 -0.733  0.323        -0.267 -0.475       
> screeplot(cars.pca)
> 
> ## Loadings are extracted and plotted like this
> (cars.ldg <- loadings(cars.pca))

Loadings:
     PC1    PC2    PC3    PC4    PC5    PC6    PC7   
mpg  -0.415        -0.107  0.754 -0.353  0.318  0.144
cyl   0.425        -0.165  0.447  0.289 -0.485  0.521
disp  0.423 -0.110  0.234  0.465  0.103        -0.726
hp    0.385  0.349  0.106        -0.817 -0.203       
drat -0.320  0.505  0.736         0.208 -0.222       
wt    0.400 -0.262  0.499                0.590  0.416
qsec -0.240 -0.733  0.323        -0.267 -0.475       

                 PC1   PC2   PC3   PC4   PC5   PC6   PC7
SS loadings    1.000 1.000 1.000 1.000 1.000 1.000 1.000
Proportion Var 0.143 0.143 0.143 0.143 0.143 0.143 0.143
Cumulative Var 0.143 0.286 0.429 0.571 0.714 0.857 1.000
> plot(cars.pca, which = "loadings") # Equivalent to vectorplot(cars.ldg)
> 
> ## Similarly, correlations of variables with PCs are extracted and plotted
> (cars.cor <- correlation(cars.pca))
Matrix of PCA variables and components correlation:
     PC1    PC2    PC3    PC4    PC5    PC6    PC7   
mpg  -0.940  0.055 -0.057  0.298 -0.124  0.075  0.023
cyl   0.963  0.062 -0.088  0.177  0.102 -0.115  0.084
disp  0.960 -0.122  0.124  0.184  0.036 -0.003 -0.117
hp    0.873  0.385  0.056 -0.039 -0.288 -0.048  0.005
drat -0.726  0.557  0.392  0.030  0.073 -0.053  0.009
wt    0.906 -0.289  0.266 -0.006  0.004  0.140  0.067
qsec -0.544 -0.808  0.172  0.010 -0.094 -0.112  0.010
> plot(cars.pca, which = "correlations") # Equivalent to vectorplot(cars.cor)
> ## One can add supplementary variables on this graph
> lines(correlation(cars.pca,
+     newvars = mtcars[-(8:14), c("vs", "am", "gear", "carb")]))
> 
> ## Plot the scores
> plot(cars.pca, which = "scores", cex = 0.8) # Similar to plot(scores(x)[, 1:2])
Warning message:
In isTRUE(!as.numeric(labels)) : NAs introduced by coercion
> ## Add supplementary individuals to this plot (labels), use also points() or lines()
> text(predict(cars.pca, newdata = mtcars[8:14, ]), col = "gray", cex = 0.8)
> 
> ## More scores plot
> ## TODO...
> 
> ## Pairs plot for 3 PCs
> iris.pca <- pcomp(iris[, -5])
> pairs(iris.pca, col = (2:4)[iris$Species])
> 
> ## rgl plot for 3 PCs
> ## TODO...
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>