| Title: | Multivariate Projection Methods |
|---|---|
| Description: | Exploratory graphical analysis of multivariate data, specifically gene expression data with different projection methods: principal component analysis, correspondence analysis, spectral map analysis. |
| Authors: | Luc Wouters <[email protected]> |
| Maintainer: | Tobias Verbeke <[email protected]> |
| License: | GPL (>=2) |
| Version: | 1.0-20 |
| Built: | 2024-08-24 03:43:59 UTC |
| Source: | https://github.com/r-forge/mpm |
Generic Function to Export Output to Files
export(x, filename, ...)export(x, filename, ...)
x |
object to export to a file |
filename |
name of the file to which the output should be exported |
... |
further arguments for the method |
Tobias Verbeke
Export the summary output for an mpm object to a text file Output the mpm summary to a tab-demimited file for processing by other programs (Excel, Spotfire...) If the filename is empty, return the data instead of writing to file (useful for web services).
## S3 method for class 'summary.mpm' export(x, filename="", ...)## S3 method for class 'summary.mpm' export(x, filename="", ...)
x |
object of class |
filename |
prefix used to name the output file following <filename>_xyz.txt |
... |
further arguments; currently none are used |
Polar (spherical) coordinates are added if the summary.spm object
contains 2 (3) dimensions.
the output is returned invisibly
Rudi Verbeeck, Tobias Verbeke
Famin81A Data Data with demographic indicators by region of the world
Friday, L. and Laskey, R. (1989). The Fragile Environment, The Darwin College Lecture. Cambridge University Press, UK.
Golub (1999) Data Golub et al. (1999) data on gene expression profiles of 38 patients suffering from acute leukemia and a validation sample of 34 patients.
The original data of Golub et al. (1999) were preprocessed as follows: genes that were called 'absent' in all samples were removed from the data sets, since these measurements are considered unreliable by the manufacturer of the technology. Negative measurements in the data were set to 1.
The resulting data frame contains 5327 genes of the 6817 originally reported by Golub et al. (1999).
Luc Wouters et al. (2003), p. 1134 contains a typo concerning the sample sizes of AML- and ALL-type and erroneously reported
Luc Wouters et al. (2003). Graphical Exploration of Gene Expression Data: A Comparative Study of Three Multivariate Methods, Biometrics, 59, 1131-1139.
Spectral Map Analysis
Produces an object of class mpm that allows for exploratory
multivariate analysis of large data matrices, such as gene expression data
from microarray experiments.
mpm(data, logtrans=TRUE, logrepl=1e-09, center=c("double", "row", "column", "global", "none"), normal=c("global", "row", "column", "none"), closure=c("none", "row", "column", "global", "double"), row.weight=c("constant", "mean", "median", "max", "logmean", "RW"), col.weight=c("constant", "mean", "median", "max", "logmean", "CW"), CW=rep(1, ncol(data) - 1), RW=rep(1, nrow(data)), pos.row=rep(FALSE, nrow(data)), pos.column=rep(FALSE, ncol(data) - 1))mpm(data, logtrans=TRUE, logrepl=1e-09, center=c("double", "row", "column", "global", "none"), normal=c("global", "row", "column", "none"), closure=c("none", "row", "column", "global", "double"), row.weight=c("constant", "mean", "median", "max", "logmean", "RW"), col.weight=c("constant", "mean", "median", "max", "logmean", "CW"), CW=rep(1, ncol(data) - 1), RW=rep(1, nrow(data)), pos.row=rep(FALSE, nrow(data)), pos.column=rep(FALSE, ncol(data) - 1))
data |
a data frame with the row descriptors in the first column. For microarray data rows indicate genes and columns biological samples. |
logtrans |
an optional logical value. If |
logrepl |
an optional numeric value that replaces non-positive numbers
in log-transformations. Defaults to |
closure |
optional character string specifying the closure operation that is carried out on the optionally log-transformed data matrix. If "double", data are divided by row- and column-totals. If "row" data are divided by row-totals. If "column" data are divided by column-totals. If "none" no closure is carried out. Defaults to "none". |
center |
optional character string specifying the centering operation that is carried out on the optionally log-transformed, closed data matrix. If "double" both row- and column-means are subtracted. If "row" row-means are subtracted. If "column" column-means are subtracted. If "none" the data are left uncentered. Defaults to "double". |
normal |
optional character string specifying the normalization operation that is carried out on the optionally log-transformed, closed, and centered data matrix. If "global" the data are normalized using the global standard deviation. If "row" data are divided by the standard deviations of the respective row. If "column" data are divided by their respective column standard deviation. If "none" no normalization is carried out. Defaults to "global". |
row.weight |
optional character string specifying the weights of the different rows in the analysis. This can be "constant", "mean", "median", "max", "logmean", or "RW". If "RW" is specified, weights must be supplied in the vector RW. In other cases weights are computed from the data. Defaults to "constant", i.e. constant weighting. |
col.weight |
optional character string specifying the weights of the
different columns in the analysis. This can be "constant",
"mean", "median", "max", "logmean", or "CW".
If "CW" is specified, weights must be supplied in the vector
|
CW |
optional numeric vector with external column weights. Defaults to 1 (constant weights). |
RW |
optional numeric vector with external row weights. Defaults to 1 (constant weights). |
pos.row |
logical vector indicating rows that are not to be included in
the analysis but must be positioned on the projection obtained with the
remaining rows. Defaults to |
pos.column |
logical vector indicating columns that are not to be
included in the analysis but must be positioned on the projection obtained
with the remaining columns. Defaults to |
The function mpm presents a unified approach to exploratory
multivariate analysis encompassing principal component analysis,
correspondence factor analysis, and spectral map analysis. The algorithm
computes projections of high dimensional data in an orthogonal space. The
resulting object can subsequently be used in the construction of biplots
(i.e. plot.mpm).
The projection of the pre-processed data matrix in the orthogonal space is
calculated using the La.svd function.
An object of class mpm representing the projection of data
after the different operations of transformation, closure, centering, and
normalization in an orthogonal space. Generic functions plot and
summary have methods to show the results of the analysis in more
detail. The object consists of the following components:
TData |
matrix with the data after optional log-transformation, closure, centering and normalization. |
row.names |
character vector with names of the row elements as supplied in the first column of the original data matrix |
col.names |
character vector with the names of columns obtained from the column names from the original data matrix |
closure |
closure operation as specified in the function call |
center |
centering operation as specified in the function call |
normal |
normalization operation as specified in the function call |
row.weight |
type of weighting used for rows as specified in the function call |
col.weight |
type of weighting used for columns as specified in the function call |
Wn |
vector with calculated weights for rows |
Wp |
vector with calculated weights for columns |
RM |
vector with row means of original data |
CM |
vector with column means of original data |
pos.row |
logical vector indicating positioned rows as specified in the function call |
pos.column |
logical vector indicating positioned columns as specified in the function call |
SVD |
list with components returned
by |
eigen |
eigenvalues for each orthogonal factor from obtained from the weighted singular value decomposition |
contrib |
contributions of each factor to the total variance of the pre-processed data, i.e. the eigenvalues as a fraction of the total eigenvalue. |
call |
the matched call. |
Principal component analysis is defined as the projection onto an orthogonal space of the column-centered and column-normalized data. In correspondence factor analysis the data are pre-processed by double closure, double centering, and global normalization. Orthogonal projection is carried out using the weighted singular value decomposition. Spectral map analysis is in essence a principal component analysis on the log-transformed, double centered and global normalized data. Weighted spectral map analysis has been proven to be successful in the detection of patterns in gene expression data (Wouters et al., 2003).
Luc Wouters, Rudi Verbeeck, Tobias Verbeke
Wouters, L., Goehlmann, H., Bijnens, L., Kass, S.U., Molenberghs, G., Lewi, P.J. (2003). Graphical exploration of gene expression data: a comparative study of three multivariate methods. Biometrics 59, 1131-1140.
data(Golub) # Principal component analysis r.pca <- mpm(Golub[,1:39], center = "column", normal = "column") # Correspondence factor analysis r.cfa <- mpm(Golub[,1:39],logtrans = FALSE, row.weight = "mean", col.weight = "mean", closure = "double") # Weighted spectral map analysis r.sma <- mpm(Golub[,1:39], row.weight = "mean", col.weight = "mean")data(Golub) # Principal component analysis r.pca <- mpm(Golub[,1:39], center = "column", normal = "column") # Correspondence factor analysis r.cfa <- mpm(Golub[,1:39],logtrans = FALSE, row.weight = "mean", col.weight = "mean", closure = "double") # Weighted spectral map analysis r.sma <- mpm(Golub[,1:39], row.weight = "mean", col.weight = "mean")
Spectral Map Plot of Multivariate Data
Produces a spectral map plot (biplot) of an object of class mpm
## S3 method for class 'mpm' plot(x, scale=c("singul", "eigen", "uvr", "uvc"), dim=c(1, 2), zoom=rep(1, 2), show.row=c("all", "position"), show.col=c("all", "position"), col.group=rep(1, length(x$col.names)), colors=c("orange1", "red", rainbow(length(unique(col.group)), start = 2/6, end = 4/6)), col.areas=TRUE, col.symbols=c(1, rep(2, length(unique(col.group)))), sampleNames=TRUE, rot=rep(-1, length(dim)), labels, label.tol=1, label.col.tol=1, lab.size=0.725, col.size=10, row.size=10, do.smoothScatter=FALSE, do.plot=TRUE, ...)## S3 method for class 'mpm' plot(x, scale=c("singul", "eigen", "uvr", "uvc"), dim=c(1, 2), zoom=rep(1, 2), show.row=c("all", "position"), show.col=c("all", "position"), col.group=rep(1, length(x$col.names)), colors=c("orange1", "red", rainbow(length(unique(col.group)), start = 2/6, end = 4/6)), col.areas=TRUE, col.symbols=c(1, rep(2, length(unique(col.group)))), sampleNames=TRUE, rot=rep(-1, length(dim)), labels, label.tol=1, label.col.tol=1, lab.size=0.725, col.size=10, row.size=10, do.smoothScatter=FALSE, do.plot=TRUE, ...)
x |
object of class |
scale |
optional character string specifying the type of factor scaling of the biplot. This can be either "singul" (singular value scaling), "eigen" (eigenvalue scaling), "uvr" (unit row-variance scaling), "uvc" (unit column-variance scaling). The latter is of particular value when analyzing large matrices, such as gene expression data. Singular value scaling "singul" is customary in spectral map analysis. Defaults to "singul". |
dim |
optional principal factors that are plotted along the horizontal
and vertical axis. Defaults to |
zoom |
optional zoom factor for row and column items. Defaults to
|
show.row |
optional character string indicating whether all rows ("all") are to be plotted or just the positioned rows "position". |
show.col |
optional character string indicating whether all columns ("all") are to be plotted or just the positioned columns "position". |
col.group |
optional vector (character or numeric) indicating the
different groupings of the columns, e.g. |
colors |
vector specifying the colors for the annotation of the plot; the first two elements concern the rows; the third till the last element concern the columns; the first element will be used to color the unlabeled rows; the second element for the labeled rows and the remaining elements to give different colors to different groups of columns. |
col.areas |
logical value indicating whether columns should be plotted
as squares with areas proportional to their marginal mean and colors
representing the different groups ( |
col.symbols |
vector of symbols when |
sampleNames |
Either a logical vector of length one or a character
vector of length equal to the number of samples in the dataset. If a
logical is provided, sample names will be displayed on the plot
( |
rot |
rotation of plot. Defaults to |
labels |
character vector to be used for labeling points on the graph;
if |
label.tol |
numerical value specifying either the percentile
( |
label.col.tol |
numerical value specifying either the percentile
( |
lab.size |
size of identifying labels for row- and column-items as
|
col.size |
size in mm of the column symbols |
row.size |
size in mm of the row symbols |
do.smoothScatter |
use smoothScatter or not instead of plotting individual points |
do.plot |
produce a plot or not |
... |
further arguments to |
Spectral maps are special types of biplots with the area of the symbols
proportional to some measure, usually the row or column mean value and an
identification of row- and column-items. For large matrices, such as gene
expression data, where there is an abundance of rows, this can obscure the
plot. In this case, the argument label.tol can be used to select the
most informative rows, i.e. rows that are most distant from the center of
the plot. Only these row-items are then labeled and represented as circles
with their areas proportional to the marginal mean value. For the
column-items it can be useful to apply some grouping specified by
col.group. Examples of groupings are different pathologies, such as
specified in Golub.grp
An object of class plot.mpm that has the following
components:
Rows |
a data frame with the X and Y coordinates of the
rows and an indication |
Columns |
a data frame with the X and Y coordinates of the columns |
value is returned invisibly, but is available for further use
when an explicit assignment is made
Luc Wouters
Wouters, L., Goehlmann, H., Bijnens, L., Kass, S.U., Molenberghs, G., Lewi, P.J. (2003). Graphical exploration of gene expression data: a comparative study of three multivariate methods. Biometrics 59, 1131-1140.
# Weighted spectral map analysis data(Golub) # Gene expression data of leukemia patients data(Golub.grp) # Pathological classes coded as 1, 2, 3 r.sma <- mpm(Golub[,1:39], row.weight = "mean", col.weight = "mean") # Spectral map biplot with result r <- plot(r.sma, label.tol = 20, scale = "uvc", col.group = (Golub.grp)[1:38], zoom = c(1,1.2), col.size = 5) Golub[r$Rows$Select, 1] # 20 most extreme genes# Weighted spectral map analysis data(Golub) # Gene expression data of leukemia patients data(Golub.grp) # Pathological classes coded as 1, 2, 3 r.sma <- mpm(Golub[,1:39], row.weight = "mean", col.weight = "mean") # Spectral map biplot with result r <- plot(r.sma, label.tol = 20, scale = "uvc", col.group = (Golub.grp)[1:38], zoom = c(1,1.2), col.size = 5) Golub[r$Rows$Select, 1] # 20 most extreme genes
Print Method for mpm Objects
## S3 method for class 'mpm' print(x, digits=3, ...)## S3 method for class 'mpm' print(x, digits=3, ...)
x |
object of class mpm |
digits |
minimum number of significant digits to be printed |
... |
further arguments for the print method (for printing the contributions) |
x is returned invisibly
Print Method for summary.mpm Objects
## S3 method for class 'summary.mpm' print(x, digits=2, what=c("columns", "rows", "all"), ...)## S3 method for class 'summary.mpm' print(x, digits=2, what=c("columns", "rows", "all"), ...)
x |
object of class summary.mpm |
digits |
minimum number of significant digits to print, defaults to 2 |
what |
one of |
... |
further arguments for the print method |
x is returned invisibly
Summary Statistics for Spectral Map Analysis
Summary method for object of class mpm.
## S3 method for class 'mpm' summary(object, maxdim=4, ...)## S3 method for class 'mpm' summary(object, maxdim=4, ...)
object |
an object of class |
maxdim |
maximum number of principal factors to be reported. Defaults
to |
... |
further arguments; currently none are used |
The function summary.mpm computes and returns a list of summary
statistics of the spectral map analysis given in x.
An object of class summary.mpm with the following components:
call |
the call to |
Vxy |
sum of eigenvalues |
VPF |
a matrix with on the first line the eigenvalues and on the
second line the cumulative eigenvalues of each of the principal factors
( |
Rows |
a data frame with summary statistics for the row-items, as described below. |
Columns |
a data frame with with summary statistics for the
column-items, as described below. |
Posit |
binary
indication of whether the row or column was positioned ( |
Weight |
weight applied to the row or column in the
function |
PRF1-PRFmaxdim |
factor scores or loadings for
the first |
Resid |
residual score or loading not accounted for by the first
|
Norm |
length of the vector representing the row or column in factor space. |
Contrib |
contribution of row or column to the sum of eigenvalues. |
Accuracy |
accuracy of the
representation of the row or column by means of the first |
Luc Wouters
Wouters, L., Goehlmann, H., Bijnens, L., Kass, S.U., Molenberghs, G., Lewi, P.J. (2003). Graphical exploration of gene expression data: a comparative study of three multivariate methods. Biometrics 59, 1131-1140.
# Example 1 weighted spectral map analysis Golub data data(Golub) r.sma <- mpm(Golub[,1:39], row.weight = "mean", col.weight = "mean") # summary report summary(r.sma) # Example 2 using print function data(Famin81A) r.fam <- mpm(Famin81A, row.weight = "mean", col.weight = "mean") r.sum <- summary(r.fam) print(r.sum, what = "all")# Example 1 weighted spectral map analysis Golub data data(Golub) r.sma <- mpm(Golub[,1:39], row.weight = "mean", col.weight = "mean") # summary report summary(r.sma) # Example 2 using print function data(Famin81A) r.fam <- mpm(Famin81A, row.weight = "mean", col.weight = "mean") r.sum <- summary(r.fam) print(r.sum, what = "all")