
Introduction to Patterns: a modeling tool dedicated to biological network modeling
Frédéric Bertrand and Myriam Maumy-Bertrand
Université de Strasbourg et CNRS,IRMA, labex IRMIAfrederic.bertrand@lecnam.net
2025-09-15
Source:vignettes/IntroPatterns.Rmd
IntroPatterns.Rmd
Patterns: a modeling tool dedicated to biological network modeling
It allows for single or joint modeling of, for instance, genes and proteins. It is design to work with patterned data. Famous examples of problems related to patterned data are: * recovering signals in networks after a stimulation (cascade network reverse engineering), * analysing periodic signals.
- It starts with the selection of the actors that will be the used in the reverse engineering upcoming step. An actor can be included in that selection based on its differential effects (for instance gene expression or protein abundance) or on its time course profile.
- Wrappers for actors clustering functions and cluster analysis are provided.
- It also allows reverse engineering of biological networks taking into account the observed time course patterns of the actors. Interactions between clusters of actors can be set by the user. Any number of clusters can be activated at a single time.
- Many inference functions are provided with the
Patterns
package and dedicated to get specific features for the inferred network such as sparsity, robust links, high confidence links or stable through resampling links.-
lasso, from the
lars
package -
lasso, from the
glmnet
package. An unweighted and a weighted version of the algorithm are available -
spls, from the
spls
package -
elasticnet, from the
elasticnet
package -
stability selection, from the
c060
package implementation of stability selection -
weighted stability selection, a new weighted
version of the
c060
package implementation of stability selection that I created for the package -
robust, lasso from the
lars
package with light random Gaussian noise added to the explanatory variables -
selectboost, from the
selectboost
package. The selectboost algorithm looks for the more stable links against resampling that takes into account the correlated structure of the predictors -
weighted selectboost, a new weighted version of the
selectboost
.
-
lasso, from the
- Some simulation and prediction tools are also available for cascade networks.
- Examples of use with microarray or RNA-Seq data are provided.
The weights are viewed as a penalty factors in the penalized regression model: it is a number that multiplies the lambda value in the minimization problem to allow differential shrinkage, Friedman et al. 2010, equation 1 page 3. If equal to 0, it implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables. Infinity means that the variable is excluded from the model. Note that the weights are rescaled to sum to the number of variables.
Due to maximum size requirement for CRAN packages, most of the graphics of the vignette will be created when the code is run.
A word for those that have been using our seminal work, the
Cascade
package that we created several years ago and that
was a very efficient network reverse engineering tool for cascade
networks (Jung, N., Bertrand, F., Bahram, S., Vallat, L., and
Maumy-Bertrand, M. (2014), https://doi.org/10.1093/bioinformatics/btt705, https://cran.r-project.org/package=Cascade, https://github.com/fbertran/Cascade and https://fbertran.github.io/Cascade/).
The Patterns
package is more than (at least) a threeway
major extension of the Cascade
package :
-
any number of groups can be used whereas in the
Cascade
package only 1 group for each timepoint could be created, which prevented the users to create homogeneous clusters of genes in datasets that featured more than a few dozens of genes. -
custom
matrices shapes whereas in the
Cascade
package only 1 shape was provided:- interaction between groups
- custom design of inner cells of the matrix
- the custom matrices allow to deal with heteregeneous networks with several kinds of actors such as mixing genes and proteins in a single network to perform joint inference.
- about nine inference algorithms are provided,
whereas 1 (lasso) in
Cascade
.
Hence the Patterns
package should be viewed more as a
completely new modelling tools than as an extension of the
Cascade
package.
This website and these examples were created by F. Bertrand and M. Maumy-Bertrand.
Installation
You can install the released version of Patterns from CRAN with:
install.packages("Patterns")
You can install the development version of Patterns from github with:
devtools::install_github("fbertran/Patterns")
Examples
Data management
Import Cascade Data (repeated measurements on several subjects) from the CascadeData package and turn them into a omics array object. The second line makes sure the CascadeData package is installed.
library(Patterns)
if(!require(CascadeData)){install.packages("CascadeData")}
data(micro_US)
micro_US<-as.omics_array(micro_US[1:100,],time=c(60,90,210,390),subject=6)
str(micro_US)
Get a summay and plots of the data:
Gene selection
There are several functions to carry out gene selection before the inference. They are detailed in the vignette of the package.
Data simulation
Let’s simulate some cascade data and then do some reverse engineering.
We first design the F matrix for
times and
groups. The Fmat
object is an array of sizes
.
Ti<-4
Ngrp<-4
Fmat=array(0,dim=c(Ti,Ti,Ngrp^2))
for(i in 1:(Ti^2)){
if(((i-1) %% Ti) > (i-1) %/% Ti){
Fmat[,,i][outer(1:Ti,1:Ti,function(x,y){0<(x-y) & (x-y)<2})]<-1
}
}
The Patterns
function CascadeFinit
is an
utility function to easily define such an F matrix.
Fbis=Patterns::CascadeFinit(Ti,Ngrp,low.trig=FALSE)
str(Fbis)
Check if the two matrices Fmat
and Fbis
are
identical.
End of F matrix definition.
Fmat[,,3]<-Fmat[,,3]*0.2
Fmat[3,1,3]<-1
Fmat[4,2,3]<-1
Fmat[,,4]<-Fmat[,,3]*0.3
Fmat[4,1,4]<-1
Fmat[,,8]<-Fmat[,,3]
We set the seed to make the results reproducible and draw a scale free random network.
set.seed(1)
Net<-Patterns::network_random(
nb=100,
time_label=rep(1:4,each=25),
exp=1,
init=1,
regul=round(rexp(100,1))+1,
min_expr=0.1,
max_expr=2,
casc.level=0.4
)
Net@F<-Fmat
str(Net)
Plot the simulated network.
Patterns::plot(Net, choice="network")
If a gene clustering is known, it can be used as a coloring scheme.
Plot the F matrix, for low dimensional F matrices.
plot(Net, choice="F")
Plot the F matrix using the pixmap
package, for high
dimensional F matrices.
plot(Net, choice="Fpixmap")
We simulate gene expression according to the network that was previously drawn
set.seed(1)
M <- Patterns::gene_expr_simulation(
omics_network=Net,
time_label=rep(1:4,each=25),
subject=5,
peak_level=200,
act_time_group=1:4)
str(M)
Get a summay and plots of the simulated data:
summary(M)
plot(M)
Network inferrence
We infer the new network using subjectwise leave one out cross-validation (default setting): all measurements from the same subject are removed from the dataset). The inference is carried out with a general Fshape.
Net_inf_P <- Patterns::inference(M, cv.subjects=TRUE)
Plot of the inferred F matrix
plot(Net_inf_P, choice="F")
Heatmap of the inferred coefficients of the Omega matrix
stats::heatmap(Net_inf_P@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
Default values fot the
matrices. The Finit
matrix (starting values for the
algorithm). In our case, the Finit
object is an array of
sizes
.
Ti<-4;
ngrp<-4
nF<-ngrp^2
Finit<-array(0,c(Ti,Ti,nF))
for(ii in 1:nF){
if((ii%%(ngrp+1))==1){
Finit[,,ii]<-0
} else {
Finit[,,ii]<-cbind(rbind(rep(0,Ti-1),diag(1,Ti-1)),rep(0,Ti))+rbind(cbind(rep(0,Ti-1),diag(1,Ti-1)),rep(0,Ti))
}
}
The Fshape
matrix (default shape for F
matrix the algorithm). Any interaction between groups and times are
permitted except the retro-actions (a group on itself, or an action at
the same time for an actor on another one).
Fshape<-array("0",c(Ti,Ti,nF))
for(ii in 1:nF){
if((ii%%(ngrp+1))==1){
Fshape[,,ii]<-"0"
} else {
lchars <- paste("a",1:(2*Ti-1),sep="")
tempFshape<-matrix("0",Ti,Ti)
for(bb in (-Ti+1):(Ti-1)){
tempFshape<-replaceUp(tempFshape,matrix(lchars[bb+Ti],Ti,Ti),-bb)
}
tempFshape <- replaceBand(tempFshape,matrix("0",Ti,Ti),0)
Fshape[,,ii]<-tempFshape
}
}
Any other form can be used. A “0” coefficient is missing from the model. It allows testing the best structure of an “F” matrix and even performing some significance tests of hypothses on the structure of the matrix.
The IndicFshape
function allows to design custom F
matrix for cascade networks with equally spaced measurements by
specifying the zero and non zero
cells of the
matrix. It is useful for models featuring several clusters of actors
that are activated at the time. Let’s define the following indicatrix
matrix (action of all groups on each other, which is not a possible real
modeling setting and is only used as an example):
For that choice, we get those init and shape matrices.
IndicFinit(Ti,ngrp,TestIndic)
IndicFshape(Ti,ngrp,TestIndic)
Those matrices are lower diagonal ones to enforce that an observed value at a given time can only be predicted by a value that was observed in the past only (i.e. neither at the same moment or in the future).
The plotF
is convenient to display F matrices. Here are
the the displays of the three
matrices we have just introduced.
plotF(Fshape,choice="Fshape")
plotF(CascadeFshape(4,4),choice="Fshape")
plotF(IndicFshape(Ti,ngrp,TestIndic),choice="Fshape")
We now fit the model with an matrix that is designed for cascade networks.
Specific Fshape
Net_inf_P_S <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4))
Plot of the inferred F matrix
plot(Net_inf_P_S, choice="F")
Heatmap of the coefficients of the Omega matrix of the network. They reflect the use of a special matrix. It is an example of an F matrix specifically designed to deal with cascade networks.
stats::heatmap(Net_inf_P_S@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
There are many fitting functions provided with the
Patterns
package in order to search for specific
features for the inferred network such as
sparsity, robust links, high
confidence links or stable through resampling
links. :
-
LASSO, from the
lars
package -
LASSO2, from the
glmnet
package. An unweighted and a weighted version of the algorithm are available -
SPLS, from the
spls
package -
ELASTICNET, from the
elasticnet
package -
stability.c060, from the
c060
package implementation of stability selection -
stability.c060.weighted, a new weighted version of
the
c060
package implementation of stability selection -
robust, lasso from the
lars
package with light random Gaussian noise added to the explanatory variables -
selectboost.weighted, a new weighted version of the
selectboost
package implementation of the selectboost algorithm to look for the more stable links against resampling that takes into account the correlated structure of the predictors. If no weights are provided, equal weigths are for all the variables (=non weighted case).
Net_inf_P_Lasso2 <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="LASSO2")
Plot of the inferred F matrix
plot(Net_inf_P_Lasso2, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_Lasso2@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
We create a weighting vector to perform weighted lasso inference.
Weights_Net=slot(Net,"omics_network")
Weights_Net[Net@omics_network!=0]=.1
Weights_Net[Net@omics_network==0]=1000
Net_inf_P_Lasso2_Weighted <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="LASSO2", priors=Weights_Net)
Plot of the inferred F matrix
plot(Net_inf_P_Lasso2_Weighted, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_Lasso2_Weighted@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
Net_inf_P_SPLS <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="SPLS")
Plot of the inferred F matrix
plot(Net_inf_P_SPLS, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_SPLS@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
Net_inf_P_ELASTICNET <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="ELASTICNET")
Plot of the inferred F matrix
plot(Net_inf_P_ELASTICNET, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_ELASTICNET@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
Net_inf_P_stability <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="stability.c060")
Plot of the inferred F matrix
plot(Net_inf_P_stability, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_stability@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
Net_inf_P_StabWeight <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="stability.c060.weighted", priors=Weights_Net)
Plot of the inferred F matrix
plot(Net_inf_P_StabWeight, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_StabWeight@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
Net_inf_P_Robust <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="robust")
Plot of the inferred F matrix
plot(Net_inf_P_Robust, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_Robust@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
Weights_Net_1 <- Weights_Net
Weights_Net_1[,] <- 1
Net_inf_P_SelectBoost <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="selectboost.weighted",priors=Weights_Net_1)
Plot of the inferred F matrix
plot(Net_inf_P_SelectBoost, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_SelectBoost@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
Net_inf_P_SelectBoostWeighted <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="selectboost.weighted",priors=Weights_Net)
Plot of the inferred F matrix
plot(Net_inf_P_SelectBoostWeighted, choice="F")
Heatmap of the coefficients of the Omega matrix of the network
stats::heatmap(Net_inf_P_SelectBoostWeighted@omics_network, Rowv = NA, Colv = NA, scale="none", revC=TRUE)
###Post inference network analysis Such an analysis is only required if the model was not fitted using the stability selection or the selectboost algorithm.
Create an animation of the network with increasing cutoffs with an
animated .gif format or a html webpage. See the the webpage of the
Patterns
package for the animation results at the .gif
and .html formats.
data(network)
sequence<-seq(0,0.2,length.out=20)
evolution(network,sequence,type.ani = "gif")
evolution(network,sequence,type.ani = "html")
Evolution of some properties of a reverse-engineered network with increasing cut-off values.
data(Net)
data(Net_inf_PL)
#Comparing true and inferred networks
Crit_values=NULL
#Here are the cutoff level tested
test.seq<-seq(0,max(abs(Net_inf_PL@omics_network*0.9)),length.out=200)
for(u in test.seq){
Crit_values<-rbind(Crit_values,Patterns::compare(Net,Net_inf_PL,u))
}
matplot(test.seq,Crit_values,type="l",ylab="Criterion value",xlab="Cutoff level",lwd=2)
legend(x="topleft", legend=colnames(Crit_values), lty=1:5,col=1:5,ncol=2,cex=.9)
We switch to data that were derived from the inferrence of a real
biological network and try to detect the optimal cutoff value: the best
cutoff value for a network to fit a scale free network. The
cutoff
was validated only single group cascade networks
(number of actors groups = number of timepoints) and for genes dataset.
Instead of the cutoff
function, manual curation or the
stability selection or the selectboost algorithm should be used.
Analyze the network with a cutoff set to the previouly found 0.133 optimal value.
analyze_network(networkCascade,nv=0.133)
Perform gene selection
Import data.
library(Patterns)
library(CascadeData)
data(micro_S)
micro_S<-as.omics_array(micro_S,time=c(60,90,210,390),subject=6,gene_ID=rownames(micro_S))
data(micro_US)
micro_US<-as.omics_array(micro_US,time=c(60,90,210,390),subject=6,gene_ID=rownames(micro_US))
Select early genes (t1 or t2):
Selection1<-Patterns::geneSelection(x=micro_S,y=micro_US,20,wanted.patterns=rbind(c(0,1,0,0),c(1,0,0,0),c(1,1,0,0)))
Section genes with first significant differential expression at t1:
Selection2<-geneSelection(x=micro_S,y=micro_US,20,peak=1)
Section genes with first significant differential expression at t2:
Selection3<-geneSelection(x=micro_S,y=micro_US,20,peak=2)
Select later genes (t3 or t4)
Selection4<-geneSelection(x=micro_S,y=micro_US,50,
wanted.patterns=rbind(c(0,0,1,0),c(0,0,0,1),c(1,1,0,0)))
Merge those selections:
Selection<-unionOmics(Selection1,Selection2)
Selection<-unionOmics(Selection,Selection3)
Selection<-unionOmics(Selection,Selection4)
head(Selection)
Summarize the final selection:
summary(Selection)
Plot the final selection:
plot(Selection)
This process could be improved by retrieve a real gene_ID using the
bitr
function of the ClusterProfiler
package
or by performing independent filtering using jetset
package
to only keep at most only probeset (the best one, if there is one good
enough) per gene_ID.