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lung, data, been, data(lung), original, Description, genes, cluster, Ryota, each, Resampling, Bootstrap, Multiscale, Suzuki, Microarray, 2015-10-23, License, analysis., topics, provides, 16:23:16, Date/Publication, (approximately, CRAN, unbiased), Repository, p-value, well, (bootstrap, probability)

October 23, 2015

Version 2.0-0

Date 2015-10-23

Title Hierarchical Clustering with P-Values via Multiscale Bootstrap

Resampling

Author Ryota Suzuki

Maintainer Ryota Suzuki

Depends R (>= 2.10.0)

Suggests MASS, parallel

Description An implementation of multiscale bootstrap resampling for

assessing the uncertainty in hierarchical cluster analysis.

It provides AU (approximately unbiased) p-value as well as

BP (bootstrap probability) value for each cluster in a dendrogram.

License GPL (>= 2)

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

NeedsCompilation no

Repository CRAN

Date/Publication 2015-10-23 16:23:16

R topics documented:

plot.pvclust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

print.pvclust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Index 14

2 lung

lung DNA Microarray Data of Lung Tumors

Description

DNA Microarray data of 73 lung tissues including 67 lung tumors. There are 916 observations of

genes for each lung tissue.

Usage

data(lung)

Format

data frame of size 916× 73.

Details

This dataset has been modified from original data. Each one observation of duplicate genes has

been removed. See source section in this help for original data source.

Source

http://genome-www.stanford.edu/lung_cancer/adeno/

References

Garber, M. E. et al. (2001) "Diversity of gene expression in adenocarcinoma of the lung", Proceedings of the National Academy of Sciences, 98, 13784-13789.

Examples

## Reading the data

data(lung)

## Multiscale Bootstrap Resampling

lung.pv <- pvclust(lung, nboot=100)

## 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 the result

plot(lung.pv, cex=0.8, cex.pv=0.7)

ask.bak <- par()$ask

par(ask=TRUE)

msfit 3

pvrect(lung.pv, alpha=0.9)

msplot(lung.pv, edges=c(51,62,68,71))

par(ask=ask.bak)

## Print a cluster with high p-value

lung.pp <- pvpick(lung.pv, alpha=0.9)

lung.pp$clusters[[2]]

## Print its edge number

lung.pp$edges[2]

## We recommend parallel computing for large dataset as this one

## Not run:

library(snow)

cl <- makeCluster(10, type="MPI")

lung.pv <- parPvclust(cl, lung, nboot=1000)

## End(Not run)

msfit Curve Fitting for Multiscale Bootstrap Resampling

Description

msfit performs curve fitting for multiscale bootstrap resampling. It generates an object of class

msfit. Several generic methods are available.

Usage

msfit(bp, r, nboot)

## S3 method for class 'msfit'

plot(x, curve=TRUE, main=NULL, sub=NULL, xlab=NULL, ylab=NULL, ...)

## S3 method for class 'msfit'

lines(x, col=2, lty=1, ...)

## S3 method for class 'msfit'

summary(object, digits=3, ...)

Arguments

bp numeric vector of bootstrap probability values.

r numeric vector of relative sample size of bootstrap samples defined as r = n′/n

for original sample size n and bootstrap sample size n′.

nboot numeric value (vector) of the number of bootstrap replications.

4 msfit

x object of class msfit.

curve logical. If TRUE, the fitted curve is drawn.

main, sub, xlab, ylab, col, lty

generic graphic parameters.

object object of class msfit.

digits integer indicating the precision to be used in rounding.

... other parameters to be used in the functions.

Details

function msfit performs the curve fitting for multiscale bootstrap resampling. In package pvclust

this function is only called from the function pvclust (or parPvclust), and may never be called

from users. However one can access a list of msfit objects by x$msfit, where x is an object of

class pvclust.

Value

msfit returns an object of class msfit. It contains the following objects:

p numeric vector of p-values. au is AU (Approximately Unbiased) p-value computed by multiscale bootstrap resampling, which is more accurate than BP value

(explained below) as unbiased p-value. bp is BP (Bootstrap Probability) value,

which is simple but tends to be unbiased when the absolute value of c (a value

in coef vector, explained below) is large.

se numeric vector of estimated standard errors of p-values.

coef numeric vector related to geometric aspects of hypotheses. v is signed distance

and c is curvature of the boundary.

df numeric value of the degree of freedom in curve fitting.

rss residual sum of squares.

pchi p-value of chi-square test based on asymptotic theory.

Author(s)

Ryota Suzuki

References

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.

msplot 5

msplot Drawing the Results of Curve Fitting for Pvclust Object

Description

draws the results of curve fitting for pvclust object.

Usage

msplot(x, edges=NULL, ...)

Arguments

x object of class pvclust.

edges numeric vector of edge numbers to be plotted.

... other parameters to be used in the function.

Author(s)

Ryota Suzuki

See Also

plot.msfit

plot.pvclust Draws Dendrogram with P-values for Pvclust Object

Description

plot dendrogram for a pvclust object and add p-values for clusters.

Usage

## S3 method for class 'pvclust'

plot(x, print.pv=TRUE, print.num=TRUE, float=0.01,

col.pv=c(2,3,8), cex.pv=0.8, font.pv=NULL, col=NULL, cex=NULL,

font=NULL, lty=NULL, lwd=NULL, main=NULL, sub=NULL, xlab=NULL, ...)

## S3 method for class 'pvclust'

text(x, col=c(2,3,8), print.num=TRUE, float=0.01, cex=NULL, font=NULL, ...)

6 plot.pvclust

Arguments

x object of class pvclust, which is generated by function pvclust. See pvclust

for details.

print.pv logical flag to specify whether print p-values above the edges (clusters).

print.num logical flag to specify whether print edge numbers below clusters.

float numeric value to adjust the height of p-values from edges.

col.pv numeric vector of length three to specify the colors for p-values and edge numbers. From the beginning each value corresponds to the color of AU values, BP

values and edge numbers, respectively.

cex.pv numeric value which specifies the size of characters for p-values and edge numbers. See cex argument for par.

font.pv numeric value which specifies the font of characters for p-values and edge numbers. See font argument for par.

col, cex, font in text function, they correspond to col.pv, cex.pv and font.pv in plot function, respectively. In plot function they are used as generic graphic parameters.

lty, lwd, main, sub, xlab, ...

generic graphic parameters. See par for details.

Details

This function plots a dendrogram with p-values for given object of class pvclust. AU p-value

(printed in red color in default) is the abbreviation of "approximately unbiased" p-value, which

is calculated by multiscale bootstrap resampling. BP value (printed in green color in default) is

"bootstrap probability" value, which is less accurate than AU value as p-value. One can consider

that clusters (edges) with high AU values (e.g. 95%) are strongly supported by data.

Author(s)

Ryota Suzuki

References

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.

See Also

text.pvclust

print.pvclust 7

print.pvclust Print Function for Pvclust Object

Description

print clustering method and distance measure used in hierarchical clustering, p-values and related

statistics for a pvclust object.

Usage

## S3 method for class 'pvclust'

print(x, which=NULL, digits=3, ...)

Arguments

x object of class pvclust.

which numeric vector which specifies the numbers of edges (clusters) of which the

values are printed. If NULL is given, it prints the values of all edges. The default

is NULL.

digits integer indicating the precision to be used in rounding.

... other parameters used in the function.

Value

this function prints p-values and some related statistics.

au AU (Approximately Unbiased) p-value, which is more accurate than BP value

as unbiased p-value. It is computed by multiscale bootstrap resampling.

bp BP (Bootstrap Probability) value, which is a simple statistic computed by bootstrap resampling. This value tends to be biased as p-value when the absolute

value of c (explained below) is large.

se.au, se.bp estimated standard errors for au and bp, respectively.

v, c values related to geometric aspects of hypotheses. v is signed distance and c is

curvature of the boundary.

pchi p-values of chi-square test based on asymptotic theory.

Author(s)

Ryota Suzuki

8 pvclust

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 nonparallel 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.

pvclust 9

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.

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× 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 =

{xij}, "correlation" method takes

i=1(xij − x̄j)(xik − x̄k)√∑n

i=1(xij − x̄j)2

i=1(xik − x̄k)2

for dissimilarity between j’th and k’th object, where x̄j = 1n

i=1 xijandx̄k =

n

i=1 xik.

"uncentered" takes uncentered sample correlation

i=1 xijxik√∑n

i=1 x

ij

i=1 x

ik and "abscor" takes the absolute value of sample correlation

i=1(xij − x̄j)(xik − x̄k)√∑n

i=1(xij − x̄j)2

i=1(xik − x̄k)2

Value

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

hclust for details.

10 pvclust

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.

Author(s)

Ryota Suzuki

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

### 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

pvpick 11

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)

## End(Not run)

pvpick Find Clusters with High/Low P-values

Description

find clusters with relatively high/low p-values. pvrect and lines (S3 method for class pvclust)

highlight such clusters in existing plot, and pvpick returns a list of such clusters.

12 pvpick

Usage

pvpick(x, alpha=0.95, pv="au", type="geq", max.only=TRUE)

pvrect(x, alpha=0.95, pv="au", type="geq", max.only=TRUE, border=2, ...)

## S3 method for class 'pvclust'

lines(x, alpha=0.95, pv="au", type="geq", col=2, lwd=2, ...)

Arguments

x object of class pvclust.

alpha threshold value for p-values.

pv character string which specifies the p-value to be used. It should be either of

"au" or "bp", corresponding to AU p-value or BP value, respectively. See

plot.pvclust for details.

type one of "geq", "leq", "gt" or "lt". If "geq" is specified, clusters with p-value

greater than or equals the threshold given by "alpha" are returned or displayed.

Likewise "leq" stands for lower than or equals, "gt" for greater than and "lt"

for lower than the threshold value. The default is "geq".

max.only logical. If some of clusters with high/low p-values have inclusion relation, only

the largest cluster is returned (or displayed) when max.only=TRUE.

border numeric value which specifies the color of borders of rectangles.

col numeric value which specifies the color of lines.

lwd numeric value which specifies the width of lines.

... other graphic parameters to be used.

Value

pvpick returns a list which contains the following values.

clusters a list of character string vectors. Each vector corresponds to the names of objects

in each cluster.

edges numeric vector of edge numbers. The i’th element (number) corresponds to the

i’th name vector in clusters.

Author(s)

Ryota Suzuki

seplot 13

seplot Diagnostic Plot for Standard Error of p-value

Description

draws diagnostic plot for standard error of p-value for pvclust object.

Usage

seplot(object, type=c("au", "bp"), identify=FALSE, main=NULL,

xlab=NULL, ylab=NULL, ...)

Arguments

object object of class pvclust.

type the type of p-value to be plotted, one of "au" or "bp".

identify logical. If TRUE, edge numbers can be identified interactively. See identify for

basic usage.

main, xlab, ylab

generic graphic parameters. See par for details.

... other graphical parameters to be passed to generic plot or identify function.

Author(s)

Ryota Suzuki

Index

∗Topic aplot

pvpick, 11

∗Topic cluster

pvclust, 8

∗Topic datasets

lung, 2

∗Topic hplot

msplot, 5

plot.pvclust, 5

seplot, 13

∗Topic htest

msfit, 3

∗Topic print

print.pvclust, 7

cor, 8

dist, 8

hclust, 8, 9

identify, 13

lines.msfit (msfit), 3

lines.pvclust, 10

lines.pvclust (pvpick), 11

lung, 2

msfit, 3, 10

msplot, 5

par, 6, 13

parPvclust (pvclust), 8

plot.msfit, 5

plot.msfit (msfit), 3

plot.pvclust, 5, 10

print.pvclust, 7, 10

pvclust, 6, 8

pvpick, 10, 11

pvrect, 10

pvrect (pvpick), 11

seplot, 13

summary.msfit (msfit), 3

text.pvclust, 6, 10

text.pvclust (plot.pvclust), 5

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