Perform principal components analysis on the samples (columns) from a microarray or proteomics experiment.
1 2 3 
data 
Either a data frame or matrix with numeric values or an

splitter 
If 
center 
A logical value; should the rows of the data matrix be centered first? 
usecor 
A logical value; should the rows of the data matrix be scaled to have standard deviation 1? 
x 
A 
col 
A list of colors to represent each level of the

main 
A character string; the plot title 
which 
A numeric vector of length two specifying which two principal components should be included in the plot. 
... 
Additional graphical parameters for 
.
The main reason for developing the SamplePCA
class is that the
princomp
function is very inefficient when the number of
variables (in the microarray setting, genes) far exceeds the number of
observations (in the microarray setting, biological samples). The
princomp
function begins by computing the full covariance
matrix, which gets rather large in a study involving tens of thousands
of genes. The SamplePCA
class, by contrast, uses singular
value decomposition (svd
) on the original data matrix to
compute the principal components.
The base functions screeplot
, which produces a barplot of the
percentage of variance explained by each component, and plot
,
which produces a scatter plot comparing two selected components
(defaulting to the first two), have been generalized as methods for
the SamplePCA
class. You can add sample labels to the scatter
plot using either the text
or identify
methods. One
should, however, note that the current implementaiton of these methods
only works when plotting the first two components.
The SamplePCA
function constructs and returns an object of the
SamplePCA
class. We assume that the input data matrix has N
columns (of biological samples) and P rows (of genes).
The predict
method returns a matrix whose size is the number of
columns in the input by the number of principal components.
Objects should be created using the SamplePCA
function. In the
simplest case, you simply pass in a data matrix and a logical vector,
splitter
, assigning classes to the columns, and the constructor
performs principal components analysis on the column. The
splitter
is ignored by the constructor and is simply saved to
be used by the plotting routines. If you omit the splitter
,
then no grouping structure is used in the plots.
If you pass splitter
as a factor instead of a logical vector,
then the plotting routine will distinguish all levels of the factor.
The code is likely to fail, however, if one of the levels of the
factor has zero representatives among the data columns.
As with the class comparison functions (see, for example,
MultiTtest
) that are part of OOMPA,
we can also perform PCA on
ExpressionSet
objects
from the BioConductor libraries. In this case, we pass in an
ExpressionSet
object along with a character string containing the
name of a factor to use for splitting the data.
scores
:A matrix
of size NxN, where N is the
number of columns in the input, representing the projections of
the input columns onto the first N principal components.
variances
:A numeric
vector of length N; the
amount of the total variance explained by each principal component.
components
:A matrix
of size PxN (the same size
as the input matrix) containing each of the first P principal
components as columns.
splitter
:A logical vector or factor of length N classifying the columns into known groups.
usecor
:A logical
value; was the data standardized?
shift
:A numeric
vector of length P; the mean
vector of the input data, which is used for centering by the
predict
method.
scale
:A numeric
vector of length P; the
standard deviation of the input data, which is used for scaling by
the predict
method.
call
:An object of class call
that records
how the object was created.
signature(x = SamplePCA, y = missing)
: Plot the
samples in a twodimensional principal component space.
signature(object = SamplePCA)
: Project new
data into the principal component space.
signature(x = SamplePCA)
: Produce a bar
chart of the variances explained by each principal component.
signature(object = SamplePCA)
: Write out a
summary of the object.
signature(object = SamplePCA)
: interactively
identify points in the plot of a SamplePCA
object.
signature(object = SamplePCA)
: Add sample
identifiers to the scatter plot of a SamplePCA
object,
using the base text
function.
Kevin R. Coombes krc@silicovore.com
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  showClass("SamplePCA")
## simulate data from three different groups
d1 < matrix(rnorm(100*10, rnorm(100, 0.5)), nrow=100, ncol=10, byrow=FALSE)
d2 < matrix(rnorm(100*10, rnorm(100, 0.5)), nrow=100, ncol=10, byrow=FALSE)
d3 < matrix(rnorm(100*10, rnorm(100, 0.5)), nrow=100, ncol=10, byrow=FALSE)
dd < cbind(d1, d2, d3)
kind < factor(rep(c('red', 'green', 'blue'), each=10))
colnames(dd) < paste(kind, rep(1:10, 3), sep='')
## perform PCA
spc < SamplePCA(dd, splitter=kind)
## plot the results
plot(spc, col=levels(kind))
## mark the group centers
x1 < predict(spc, matrix(apply(d1, 1, mean), ncol=1))
points(x1[1], x1[2], col='red', cex=2)
x2 < predict(spc, matrix(apply(d2, 1, mean), ncol=1))
points(x2[1], x2[2], col='green', cex=2)
x3 < predict(spc, matrix(apply(d3, 1, mean), ncol=1))
points(x3[1], x3[2], col='blue', cex=2)
## check out the variances
screeplot(spc)
## cleanup
rm(d1, d2, d3, dd,kind, spc, x1, x2, x3)

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