pvclust (version 2.2-0)

pvclust: Calculating P-values for Hierchical Clustering

Description

calculates \(p\)-values for hierarchical clustering via multiscale bootstrap resampling. Hierarchical clustering is done for given data and \(p\)-values are computed for each of the clusters.

Usage

pvclust(data, method.hclust="average",
        method.dist="correlation", use.cor="pairwise.complete.obs",
        nboot=1000, parallel=FALSE, r=seq(.5,1.4,by=.1),
        store=FALSE, weight=FALSE, iseed=NULL, quiet=FALSE)
parPvclust(cl=NULL, data, method.hclust="average",
           method.dist="correlation", use.cor="pairwise.complete.obs",
           nboot=1000, r=seq(.5,1.4,by=.1), store=FALSE, weight=FALSE,
           init.rand=NULL, iseed=NULL, quiet=FALSE)

Arguments

data

numeric data matrix or data frame.

method.hclust

the agglomerative method used in hierarchical clustering. This should be (an abbreviation of) one of "average", "ward.D", "ward.D2", "single", "complete", "mcquitty", "median" or "centroid". The default is "average". See method argument in hclust.

method.dist

the distance measure to be used. This should be a character string, or a function which returns a dist object. A character string should be (an abbreviation of) one of "correlation", "uncentered", "abscor" or those which are allowed for method argument in dist function. The default is "correlation". See details section in this help and method argument in dist.

use.cor

character string which specifies the method for computing correlation with data including missing values. This should be (an abbreviation of) one of "all.obs", "complete.obs" or "pairwise.complete.obs". See the use argument in cor function.

nboot

the number of bootstrap replications. The default is 1000.

parallel

switch for parallel computation. If FALSE the computation is done in non-parallel mode. If TRUE or a positive integer is supplied, parallel computation is done with automatically generated PSOCK cluster. Use TRUE for default cluster size (parallel::detectCores() - 1), or specify the size by an integer. If a cluster object is supplied the cluster is used for parallel computation. Note that NULL is currently not allowed for using the default cluster.

r

numeric vector which specifies the relative sample sizes of bootstrap replications. For original sample size \(n\) and bootstrap sample size \(n'\), this is defined as \(r=n'/n\).

store

locical. If store=TRUE, all bootstrap replications are stored in the output object. The default is FALSE.

cl

a cluster object created by package parallel or snow. If NULL, use the registered default cluster.

weight

logical. If weight=TRUE, resampling is made by weight vector instead of index vector. Useful for large r value (r>10). Currently, available only for distance "correlation" and "abscor".

init.rand

logical. If init.rand=TRUE, random number generators are initialized. Use iseed argument to achieve reproducible results. This argument is duplicated and will be unavailable in the future.

iseed

An integer. If non-NULL value is supplied random number generators are initialized. It is passed to set.seed or clusterSetRNGStream.

quiet

logical. If TRUE it does not report the progress.

Value

hclust

hierarchical clustering for original data generated by function hclust. See hclust for details.

edges

data frame object which contains \(p\)-values and supporting informations such as standard errors.

count

data frame object which contains primitive information about the result of multiscale bootstrap resampling.

msfit

list whose elements are results of curve fitting for multiscale bootstrap resampling, of class msfit. See msfit for details.

nboot

numeric vector of number of bootstrap replications.

r

numeric vector of the relative sample size for bootstrap replications.

store

list contains bootstrap replications if store=TRUE was given for function pvclust or parPvclust.

version

package_version of pvclust used to generate this object.

Details

Function pvclust conducts multiscale bootstrap resampling to calculate \(p\)-values for each cluster in the result of hierarchical clustering. parPvclust is the parallel version of this procedure which depends on package parallel for parallel computation.

For data expressed as \((n \times p)\) matrix or data frame, we assume that the data is \(n\) observations of \(p\) objects, which are to be clustered. The \(i\)'th row vector corresponds to the \(i\)'th observation of these objects and the \(j\)'th column vector corresponds to a sample of \(j\)'th object with size \(n\).

There are several methods to measure the dissimilarities between objects. For data matrix \(X=\{x_{ij}\}\), "correlation" method takes $$ 1 - \frac{ \sum_{i=1}^n (x_{ij} - \bar{x}_j) (x_{ik} - \bar{x}_k) } { \sqrt{\sum_{i=1}^n (x_{ij} - \bar{x}_j)^2} \sqrt{\sum_{i=1}^n (x_{ik} - \bar{x}_k)^2} } $$ for dissimilarity between \(j\)'th and \(k\)'th object, where \(\bar{x}_j = \frac{1}{n} \sum_{i=1}^n x_{ij} \mbox{and} \bar{x}_k = \frac{1}{n} \sum_{i=1}^n x_{ik}\).

"uncentered" takes uncentered sample correlation $$ 1 - \frac{ \sum_{i=1}^n x_{ij} x_{ik} } { \sqrt{\sum_{i=1}^n x_{ij}^2} \sqrt{\sum_{i=1}^n x_{ik}^2} } $$ and "abscor" takes the absolute value of sample correlation $$ 1 - \ \Biggl| \frac{ \sum_{i=1}^n (x_{ij} - \bar{x}_j) (x_{ik} - \bar{x}_k) } { \sqrt{\sum_{i=1}^n (x_{ij} - \bar{x}_j)^2} \sqrt{\sum_{i=1}^n (x_{ik} - \bar{x}_k)^2} } \Biggl|. $$

References

Suzuki, R. and Shimodaira, H. (2006) "Pvclust: an R package for assessing the uncertainty in hierarchical clustering", Bioinformatics, 22 (12): 1540-1542.

Shimodaira, H. (2004) "Approximately unbiased tests of regions using multistep-multiscale bootstrap resampling", Annals of Statistics, 32, 2616-2641.

Shimodaira, H. (2002) "An approximately unbiased test of phylogenetic tree selection", Systematic Biology, 51, 492-508.

Suzuki, R. and Shimodaira, H. (2004) "An application of multiscale bootstrap resampling to hierarchical clustering of microarray data: How accurate are these clusters?", The Fifteenth International Conference on Genome Informatics 2004, P034.

http://www.sigmath.es.osaka-u.ac.jp/shimo-lab/prog/pvclust/

See Also

lines.pvclust, print.pvclust, msfit, plot.pvclust, text.pvclust, pvrect and pvpick.

Examples

# NOT RUN {
### example using Boston data in package MASS
data(Boston, package = "MASS")

## multiscale bootstrap resampling (non-parallel)
boston.pv <- pvclust(Boston, nboot=100, parallel=FALSE)

## CAUTION: nboot=100 may be too small for actual use.
##          We suggest nboot=1000 or larger.
##          plot/print functions will be useful for diagnostics.

## plot dendrogram with p-values
plot(boston.pv)

ask.bak <- par()$ask
par(ask=TRUE)

## highlight clusters with high au p-values
pvrect(boston.pv)

## print the result of multiscale bootstrap resampling
print(boston.pv, digits=3)

## plot diagnostic for curve fitting
msplot(boston.pv, edges=c(2,4,6,7))

par(ask=ask.bak)

## print clusters with high p-values
boston.pp <- pvpick(boston.pv)
boston.pp

### Using a custom distance measure

## Define a distance function which returns an object of class "dist".
## The function must have only one argument "x" (data matrix or data.frame).
cosine <- function(x) {
    x <- as.matrix(x)
    y <- t(x) %*% x
    res <- 1 - y / (sqrt(diag(y)) %*% t(sqrt(diag(y))))
    res <- as.dist(res)
    attr(res, "method") <- "cosine"
    return(res)
}

result <- pvclust(Boston, method.dist=cosine, nboot=100)
plot(result)

# }
# NOT RUN {
### parallel computation
result.par <- pvclust(Boston, nboot=1000, parallel=TRUE)
plot(result.par)
# }
# NOT RUN {
# }