PoissonDistance {PoiClaClu}

Given a n-by-p data matrix, compute the corresponding n-by-n Poisson dissimilarity matrix.

Description

This function computes a Poisson dissimilarity matrix as described in the paper referenced below, and is intended to be applied to a data matrix of counts resulting from a sequencing experiment. The (i,k) element of the Poisson dissimilarity matrix is the dissimilarity between observations i and k of the data matrix x: that is, the log likelihood ratio statistic under a simple Poisson model.

Usage

PoissonDistance(x, beta = 1, type=c("mle","deseq","quantile"),
transform=TRUE, alpha=NULL, perfeature=FALSE)

Arguments

x

A n-by-p data matrix with observations on the rows, and p features on the columns. The (i,j) element of x is the number of reads in observation i that mapped to feature (e.g. gene or exon) j.

beta

A smoothing term; essentially the parameter beta in a Gamma(beta,beta) prior used to estimate the log likelihood ratio statistic for computing the dissimilarity between a pair of observations. Recommended to leave it at 1, the default value.

type

How should the observations be normalized within the Poisson model, i.e. how should the size factors be estimated? Options are "quantile" or "deseq" (more robust) or "mle" (less robust).

In greater detail: "quantile" is quantile normalization approach of Bullard et al 2010 BMC Bioinformatics, "deseq" is median of the ratio of an observation to a pseudoreference obtained by taking the geometric mean, described in Anders and Huber 2010 Genome Biology and implemented in Bioconductor package "DESeq", and "mle" is the sum of counts for each sample; this is the maximum likelihood estimate under a simple Poisson model.

transform

Should data matrix x first be power transformed so that it more closely fits the Poisson model? TRUE or FALSE. Power transformation is especially useful if the data are overdispersed relative to the Poisson model.

alpha

If transform=TRUE, this determines the power to which the data matrix x is transformed. If alpha=NULL then the transformation that makes the Poisson model best fit the data is computed. Or a value of alpha, 0<alpha<=1, can be entered by the user.

perfeature

If perfeature=TRUE, then in addition to the nxn dissimilarity matrix, a nxnxp array will be returned. Its elements will be the contributions of each of the p features to the nxn dissimilarity matrix; summing over the 3rd index will simply give back the nxn dissimilarity matrix.

Details

More details can be found in the paper referenced below.

Value

dd

A nxn Poisson dissimilarity matrix, containing pairwise dissimilarities between observations based on the original nxp data matrix x input by the user.

alpha

Power to which data was transformed before computing dissimilarity matrix, if transform was TRUE. This was either input by the user, or computed automatically if not specified.

x

Data used to compute dissimilarity matrix, this will be x raised to the power alpha.

ddd

If perfeature=TRUE, then this is the nxnxp array containing the contribution of each feature to the nxn dissimilarity matrix.

Author(s)

Daniela Witten

References

D Witten (2011) Classification and clustering of sequencing data using a Poisson model. To appear in Annals of Applied Statistics.

See Also

FindBestTransform

Examples

set.seed(1)
dat <- CountDataSet(n=20,p=100,sdsignal=2,K=4,param=10)
dd <- PoissonDistance(dat$x,type="mle")
print(dd)
ColorDendrogram(hclust(dd$dd), y=dat$y, branchlength=10)