DPM: Distance Precision Matrix

Installation

First, install the necessary R packages from CRAN:

install.packages(c("corpcor", "devtools"))

Then install DPM using the install_github function in the devtools package.

library(devtools)
devtools::install_github("ghanbari/DPM",host="github.molgen.mpg.de/api/v3")
library(DPM)

Format of input data

The (reg.)DPM function takes as input argument a matrix DataMat where each column of the matrix corresponds to a variable and each row corresponds to a sample. The column names of the DataMat specify the names of the variables. You can also specify the name of samples as rownames but this is not necessary. For example, the following code generate a fake data matrix:

DataMat <- matrix(sample(1:10, 200, replace=TRUE), ncol=10, nrow=20)
colnames(DataMat) <- paste("variable", 1:10, sep="")
rownames(DataMat) <- paste("Sample", 1:20, sep="")
head(DataMat)

In the context of gene networks variables correspond to genes. The input is gene expression data as a matrix in which columns correspond to genes and rows correspond to samples. As an example, we have one data from DREAM4 challenge (insilico_size10_1_knockouts):

library(DPM)
data(dream4)
head(dream4)

Computing DPM and reg-DPM

The following example computes DPM and reg-DPM scores for dream4 data. As previously discussed, you can use your own data as a matrix containing samples in rows and variables in columns.

library(DPM)
data(dream4)
dpmres <- dpm(dream4)
regdpmres <- reg.dpm(dream4)

Visualization of the network

You can visualize the constructed network using qgraph package. First you need to install it:

install.packages("qgraph")

Then you can visualize the network with different options using following parameters (for more details check the documentation of qgraph package):

layout: this argument controls the layout of the graph. "circle" places all nodes in a single circle and "spring" gives a force embedded layout. Defaults to "circular" in weighted graphs and "spring" in unweighted graphs.

minimum: edges with absolute weights under this value are not shown (but not omitted). Defaults to 0.

threshold: a numeric value that defaults to 0. Edges with absolute weight that are not above this value are REMOVED from the network. This differs from minimum which simply changes the scaling of width and color so that edges with absolute weight under minimum are not plotted/invisible. Setting a threshold influences the spring layout and centrality measures obtained with the graph whereas setting a minimum does not.

cut: in weighted graphs, this argument can be used to cut the scaling of edges in width and color saturation. Edges with absolute weights over this value will have the strongest color intensity and become wider the stronger they are, and edges with absolute weights under this value will have the smallest width and become vaguer the weaker the weight. If this is set to NULL, no cutoff is used and all edges vary in width and color. Defaults to NULL for graphs with less then 20 nodes. For larger graphs the cut value is automatically chosen to be equal to the maximum of the 75th quantile of absolute edge strengths or the edge strength corresponding to 2n-th edge strength (n being the number of nodes.)

library(qgraph)
qgraph(dpmres, layout = "spring" , minimum=0.25, cut=0.55, filename="dpm-network", filetype="png")
qgraph(regdpmres, layout = "spring" , minimum=0.25, cut=0.55, filename="regdpm-network", filetype="png")

Threshold selection

We recommend you to look at the distribution of the scores and based on that decide for a threshold. You can plot the distribution of DPM and reg-DPM scores using:

library("ggplot2")
dpmdat <- data.frame(score = abs(dpmres[lower.tri(dpmres)]),name ='DPM')
regdpmdat <-data.frame(score = abs( regdpmres[lower.tri(regdpmres)]), name='reg-DPM')
dat <- rbind(dpmdat,regdpmdat)

ggplot(dat, aes(x=score,color=name))+ theme_bw()  + geom_density(size=1.5)+scale_color_manual(values=c("DPM"="SteelBlue3","reg-DPM"="dodgerblue4"))
ggsave(“ScoreDistribution.png”, plot = last_plot(), device = “png”)

When you decide for the threshold you can visualize the resulted network (see section Visualization of the network ) and get all the links with a score higher than the threshold (see subsection Get only the links with a score higher than a threshold )

However, we provide a threshold selection method based on k-means clustering. You can compute the threshold for the DREAM4 data with the following command where:

• score_matrix is the score matrix obtained from DPM or reg.DPM.

dpmtr <- kmeans_links(dpmres)$threshold
regdpmtr <- kmeans_links(regdpmres)$threshold

You can visualize the position of the threshold on the distribution of the scores:

library("ggplot2")
dpmdat <- data.frame(score = abs(dpmres[lower.tri(dpmres)]),name ='DPM')
regdpmdat <-data.frame(score = abs( regdpmres[lower.tri(regdpmres)]), name='reg-DPM')
dat <- rbind(dpmdat,regdpmdat)

ggplot(dat, aes(x=score,color=name))+ theme_bw()  + geom_density(size=1.5)+scale_color_manual(values=c("DPM"="SteelBlue3","reg-DPM"="dodgerblue4"))+ geom_vline(xintercept=dpmtr, size=1, color="SteelBlue3") + geom_vline(xintercept=regdpmtr, size=1,color="dodgerblue4")

ggsave(“ScoreDistribution.png”, plot = last_plot(), device = “png”)

You can also get all the links considered as true links based on k-means clustering:

dpm_links <- kmeans_links(dpmres)$Listlink
regdpm_links <- kmeans_links(regdpmres)$Listlink

As an alternative, you can select the top-ranked links based on (reg.)DPM score which are most likely to be true links. See section Get only the top ranked links

Get the list of the links

You need to first install the necessary R packages from CRAN:

install.packages("reshape2")

Get all the links

You can get the list of all links (from the highest to the lowest score) with the following command, where the resulting dpm/reddpm_list contains the ranking of links. Each row corresponds to a link. The first and second columns show the corresponding nodes and the third column indicates the score of the link.

library(reshape2)
dpm_links <- get_link(dpmres)
dim(dpm_links)
head(dpm_links)

regdpm_links <- get_link(regdpmres)
dim(regdpm_links)
head(regdpm_links)

Get only the links with a score higher than a threshold

If you are interested in extracting the links with scores higher than a threshold use the parameter threshold and specify your threshold:

dpm_links <- get_link(dpmres,threshold = 0.2)
dim(dpm_links)
head(dpm_links)

regdpm_links <- get_link(regdpmres,threshold = 0.2)
dim(regdpm_links)
head(regdpm_links)

Get only the top ranked links

If you are interested in extracting the top links with the highest scores, use the parameter top_ranked and specify the number of top-ranked links to report:

dpm_links <- get_link(dpmres,top_ranked = 10)
dim(dpm_links)
head(dpm_links)

regdpm_links <- get_link(regdpmres,top_ranked = 10)
dim(regdpm_links)
head(regdpm_links)

Simulation of data

linear data

To simulate linear data you need to first install the necessary R packages from CRAN:

install.packages(c("pcalg","mvtnorm","qpgraph"))

Then you can simulate linear data by specifying your desired number of nodes (nnodes) and number of samples (nsamp).

library(DPM)
data <- rdata(nnodes=10,nsamp=100)[["data"]]
dpmres <- dpm(data)
regdpmres <- reg.dpm(data)

non-linear data

To simulate non-linear data from the network mentioned in the paper with your desired number of samples (nsamp) and the standard deviation of the noise added to the generated data (sigma) use:

library(DPM)
data <- nldata(nsamp=100,sigma=0.2)[["data"]]
dpmres <- dpm(data)
regdpmres <- reg.dpm(data)