# PoissonDistance: Given a n-by-p data matrix, compute the corresponding n-by-n... In PoiClaClu: Classification and Clustering of Sequencing Data Based on a Poisson Model

## 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

 ```1 2``` ```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

## 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.

Daniela Witten

## References

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

`FindBestTransform`

## Examples

 ```1 2 3 4 5``` ```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) ```

### Example output

```Value of alpha used to transform data:  0.3938776
This type of normalization was performed: mle
Dissimilarity computed for  20  observations.
```

PoiClaClu documentation built on May 2, 2019, 8:29 a.m.