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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.
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.
lars
packageglmnet
package. An
unweighted and a weighted version of the algorithm are availablespls
packageelasticnet
packagec060
package implementation of stability selectionc060
package implementation of stability
selection that I created for the packagelars
package
with light random Gaussian noise added to the explanatory variablesselectboost
package. The selectboost algorithm looks for the more stable links
against resampling that takes into account the correlated structure of
the predictorsselectboost
.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 :
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.Cascade
package only 1 shape
was provided:
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.
You can install the released version of Patterns from CRAN with:
You can install the development version of Patterns from github with:
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)
#> Formal class 'omics_array' [package "Patterns"] with 7 slots
#> ..@ omicsarray: num [1:100, 1:24] 103.2 26 70.7 213.7 13.7 ...
#> .. ..- attr(*, "dimnames")=List of 2
#> .. .. ..$ : chr [1:100] "1007_s_at" "1053_at" "117_at" "121_at" ...
#> .. .. ..$ : chr [1:24] "N1_US_T60" "N1_US_T90" "N1_US_T210" "N1_US_T390" ...
#> ..@ name : chr [1:100] "1007_s_at" "1053_at" "117_at" "121_at" ...
#> ..@ gene_ID : num 0
#> ..@ group : num 0
#> ..@ start_time: num 0
#> ..@ time : num [1:4] 60 90 210 390
#> ..@ subject : num 6
Get a summay and plots of the data:
summary(micro_US)
#> N1_US_T60 N1_US_T90 N1_US_T210 N1_US_T390
#> Min. : 12.2 Min. : 12.9 Min. : 1.5 Min. : 10.1
#> 1st Qu.: 177.7 1st Qu.: 198.7 1st Qu.: 189.0 1st Qu.: 196.7
#> Median : 513.0 Median : 499.4 Median : 608.5 Median : 541.2
#> Mean :1386.6 Mean :1357.7 Mean :1450.4 Mean :1331.2
#> 3rd Qu.:1912.3 3rd Qu.:1883.4 3rd Qu.:2050.2 3rd Qu.:1646.2
#> Max. :6348.4 Max. :6507.3 Max. :6438.5 Max. :6351.4
#> N2_US_T60 N2_US_T90 N2_US_T210 N2_US_T390
#> Min. : 16.7 Min. : 3.4 Min. : 5.5 Min. : 6.1
#> 1st Qu.: 212.4 1st Qu.: 185.7 1st Qu.: 214.7 1st Qu.: 230.1
#> Median : 584.1 Median : 501.5 Median : 596.0 Median : 601.8
#> Mean :1381.9 Mean :1345.4 Mean :1410.5 Mean :1403.7
#> 3rd Qu.:1616.2 3rd Qu.:1830.5 3rd Qu.:2005.8 3rd Qu.:1901.7
#> Max. :6149.3 Max. :6090.8 Max. :6160.6 Max. :6143.1
#> N3_US_T60 N3_US_T90 N3_US_T210 N3_US_T390
#> Min. : 1.9 Min. : 10.3 Min. : 3.3 Min. : 6.6
#> 1st Qu.: 187.4 1st Qu.: 194.6 1st Qu.: 177.8 1st Qu.: 222.6
#> Median : 611.4 Median : 576.2 Median : 552.2 Median : 593.7
#> Mean :1365.4 Mean :1381.2 Mean :1310.1 Mean :1427.1
#> 3rd Qu.:1855.2 3rd Qu.:2040.2 3rd Qu.:1784.5 3rd Qu.:2131.7
#> Max. :6636.6 Max. :6515.5 Max. :6530.4 Max. :6177.2
#> N4_US_T60 N4_US_T90 N4_US_T210 N4_US_T390
#> Min. : 20.2 Min. : 15.6 Min. : 19.8 Min. : 9.3
#> 1st Qu.: 199.3 1st Qu.: 215.4 1st Qu.: 207.0 1st Qu.: 197.8
#> Median : 610.8 Median : 614.0 Median : 544.9 Median : 590.7
#> Mean :1505.1 Mean :1526.7 Mean :1401.6 Mean :1458.8
#> 3rd Qu.:2198.1 3rd Qu.:2168.9 3rd Qu.:1831.2 3rd Qu.:1984.8
#> Max. :6986.2 Max. :7148.0 Max. :6820.0 Max. :6762.3
#> N5_US_T60 N5_US_T90 N5_US_T210 N5_US_T390
#> Min. : 3.4 Min. : 10.0 Min. : 10.7 Min. : 16.5
#> 1st Qu.: 213.2 1st Qu.: 209.8 1st Qu.: 202.0 1st Qu.: 208.2
#> Median : 609.4 Median : 561.3 Median : 555.6 Median : 570.5
#> Mean :1498.2 Mean :1424.8 Mean :1394.1 Mean :1435.3
#> 3rd Qu.:2008.7 3rd Qu.:1906.5 3rd Qu.:1923.9 3rd Qu.:1867.8
#> Max. :7268.2 Max. :6857.8 Max. :6574.0 Max. :6896.6
#> N6_US_T60 N6_US_T90 N6_US_T210 N6_US_T390
#> Min. : 13.0 Min. : 6.6 Min. : 3.8 Min. : 14.4
#> 1st Qu.: 207.5 1st Qu.: 198.6 1st Qu.: 203.9 1st Qu.: 195.8
#> Median : 516.2 Median : 530.6 Median : 578.0 Median : 580.0
#> Mean :1412.9 Mean :1388.3 Mean :1416.5 Mean :1360.8
#> 3rd Qu.:2037.4 3rd Qu.:1889.8 3rd Qu.:2030.8 3rd Qu.:1872.6
#> Max. :6898.1 Max. :6749.4 Max. :6490.0 Max. :6780.2
There are several functions to carry out gene selection before the inference. They are detailed in the vignette of the package.
Let’s simulate some cascade data and then do some reverse engineering.
We first design the F matrix for \(T_i=4\) times and \(Ngrp=4\) groups. The
Fmat
object is an array of sizes \((T_i,T-i,Ngrp^2)=(4,4,16)\).
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)
#> num [1:4, 1:4, 1:16] 0 0 0 0 0 0 0 0 0 0 ...
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)
#> Formal class 'omics_network' [package "Patterns"] with 6 slots
#> ..@ omics_network: num [1:100, 1:100] 0 0 0 0 0 0 0 0 0 0 ...
#> ..@ name : chr [1:100] "gene 1" "gene 2" "gene 3" "gene 4" ...
#> ..@ F : num [1:4, 1:4, 1:16] 0 0 0 0 0 0 0 0 0 0 ...
#> ..@ convF : num [1, 1] 0
#> ..@ convO : num 0
#> ..@ time_pt : int [1:4] 1 2 3 4
Plot the simulated 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 the F matrix using the pixmap
package, for high
dimensional F matrices.
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)
#> Formal class 'omics_array' [package "Patterns"] with 7 slots
#> ..@ omicsarray: num [1:100, 1:20] 86.1 -146.8 228.3 505.1 -36.6 ...
#> .. ..- attr(*, "dimnames")=List of 2
#> .. .. ..$ : chr [1:100] "gene 1" "gene 2" "gene 3" "gene 4" ...
#> .. .. ..$ : chr [1:20] "log(S/US) : P1T1" "log(S/US) : P1T2" "log(S/US) : P1T3" "log(S/US) : P1T4" ...
#> ..@ name : chr [1:100] "gene 1" "gene 2" "gene 3" "gene 4" ...
#> ..@ gene_ID : num 0
#> ..@ group : int [1:100] 1 1 1 1 1 1 1 1 1 1 ...
#> ..@ start_time: num 0
#> ..@ time : int [1:4] 1 2 3 4
#> ..@ subject : num 5
Get a summay and plots of the simulated data:
summary(M)
#> log(S/US) : P1T1 log(S/US) : P1T2 log(S/US) : P1T3 log(S/US) : P1T4
#> Min. :-486.823 Min. :-1962.641 Min. :-1923.74 Min. :-3391.76
#> 1st Qu.: -54.618 1st Qu.: -23.300 1st Qu.: -71.99 1st Qu.: -58.69
#> Median : -8.319 Median : 0.000 Median : -3.85 Median : 1.53
#> Mean : 8.799 Mean : 22.064 Mean : 20.72 Mean : 19.82
#> 3rd Qu.: 69.340 3rd Qu.: 9.707 3rd Qu.: 33.00 3rd Qu.: 69.45
#> Max. : 942.229 Max. : 1616.469 Max. : 2899.61 Max. : 3231.17
#> log(S/US) : P2T1 log(S/US) : P2T2 log(S/US) : P2T3 log(S/US) : P2T4
#> Min. :-359.82 Min. :-1126.13 Min. :-600.757 Min. :-797.980
#> 1st Qu.: -39.27 1st Qu.: -14.15 1st Qu.: -49.998 1st Qu.: -73.700
#> Median : 12.54 Median : 0.00 Median : -7.749 Median : -9.760
#> Mean : 21.35 Mean : 20.02 Mean : 23.579 Mean : 8.361
#> 3rd Qu.: 73.02 3rd Qu.: 28.54 3rd Qu.: 67.216 3rd Qu.: 62.297
#> Max. : 451.61 Max. : 946.22 Max. :1869.077 Max. : 935.321
#> log(S/US) : P3T1 log(S/US) : P3T2 log(S/US) : P3T3 log(S/US) : P3T4
#> Min. :-430.696 Min. :-1003.575 Min. :-718.3926 Min. :-1211.592
#> 1st Qu.: -65.939 1st Qu.: -3.637 1st Qu.: -43.3783 1st Qu.: -61.300
#> Median : 1.392 Median : 0.000 Median : -0.3233 Median : -4.124
#> Mean : 4.032 Mean : 11.431 Mean : 19.7553 Mean : 5.993
#> 3rd Qu.: 62.391 3rd Qu.: 36.945 3rd Qu.: 69.6650 3rd Qu.: 62.634
#> Max. : 514.510 Max. : 752.066 Max. :1497.5790 Max. : 1296.563
#> log(S/US) : P4T1 log(S/US) : P4T2 log(S/US) : P4T3 log(S/US) : P4T4
#> Min. :-451.370 Min. :-1113.1785 Min. :-1506.536 Min. :-446.40
#> 1st Qu.: -44.107 1st Qu.: -8.8769 1st Qu.: -48.512 1st Qu.: -56.95
#> Median : 7.193 Median : 0.0000 Median : 4.243 Median : 3.71
#> Mean : 16.034 Mean : 0.9469 Mean : -28.544 Mean : 28.74
#> 3rd Qu.: 62.840 3rd Qu.: 33.2306 3rd Qu.: 46.374 3rd Qu.: 64.89
#> Max. : 657.434 Max. : 844.0070 Max. : 694.220 Max. :1368.62
#> log(S/US) : P5T1 log(S/US) : P5T2 log(S/US) : P5T3 log(S/US) : P5T4
#> Min. :-747.865 Min. :-862.59 Min. :-1493.607 Min. :-1420.740
#> 1st Qu.: -78.166 1st Qu.: -15.10 1st Qu.: -59.853 1st Qu.: -32.799
#> Median : -8.900 Median : 0.00 Median : -2.776 Median : 4.008
#> Mean : -7.693 Mean : 66.20 Mean : -13.865 Mean : -12.332
#> 3rd Qu.: 45.926 3rd Qu.: 31.74 3rd Qu.: 40.324 3rd Qu.: 59.892
#> Max. : 960.419 Max. :1899.57 Max. : 770.655 Max. : 489.916
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)
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1.........................
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.01
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1.........................
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00522
#> We are at step : 3
#> Computing Group (out of 4) :
#> 1.........................
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0034
#> We are at step : 4
#> Computing Group (out of 4) :
#> 1.........................
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00235
#> We are at step : 5
#> Computing Group (out of 4) :
#> 1.........................
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00181
#> We are at step : 6
#> Computing Group (out of 4) :
#> 1.........................
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00142
#> We are at step : 7
#> Computing Group (out of 4) :
#> 1.........................
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00117
#> We are at step : 8
#> Computing Group (out of 4) :
#> 1.........................
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00098
Plot of the inferred F matrix
Heatmap of the inferred coefficients of the Omega matrix
Default values fot the \(F\)
matrices. The Finit
matrix (starting values for the
algorithm). In our case, the Finit
object is an array of
sizes \((T_i,T-i,Ngrp^2)=(4,4,16)\).
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 \(F\) matrix.
The IndicFshape
function allows to design custom F
matrix for cascade networks with equally spaced measurements by
specifying the zero and non zero \(F_{ij}\) cells of the \(F\) 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):
TestIndic=matrix(!((1:(Ti^2))%%(ngrp+1)==1),byrow=TRUE,ngrp,ngrp)
TestIndic
#> [,1] [,2] [,3] [,4]
#> [1,] FALSE TRUE TRUE TRUE
#> [2,] TRUE FALSE TRUE TRUE
#> [3,] TRUE TRUE FALSE TRUE
#> [4,] TRUE TRUE TRUE FALSE
For that choice, we get those init and shape \(F\) matrices.
IndicFinit(Ti,ngrp,TestIndic)
#> , , 1
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 0 0 0 0
#> [3,] 0 0 0 0
#> [4,] 0 0 0 0
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 3
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 4
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 5
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 6
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 0 0 0 0
#> [3,] 0 0 0 0
#> [4,] 0 0 0 0
#>
#> , , 7
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 8
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 9
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 10
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 11
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 0 0 0 0
#> [3,] 0 0 0 0
#> [4,] 0 0 0 0
#>
#> , , 12
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 13
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 14
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 15
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 1 0 0 0
#> [3,] 1 1 0 0
#> [4,] 1 1 1 0
#>
#> , , 16
#>
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 0 0 0 0
#> [3,] 0 0 0 0
#> [4,] 0 0 0 0
IndicFshape(Ti,ngrp,TestIndic)
#> , , 1
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "0" "0" "0" "0"
#> [3,] "0" "0" "0" "0"
#> [4,] "0" "0" "0" "0"
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 3
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 4
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 5
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 6
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "0" "0" "0" "0"
#> [3,] "0" "0" "0" "0"
#> [4,] "0" "0" "0" "0"
#>
#> , , 7
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 8
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 9
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 10
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 11
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "0" "0" "0" "0"
#> [3,] "0" "0" "0" "0"
#> [4,] "0" "0" "0" "0"
#>
#> , , 12
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 13
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 14
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 15
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "a1" "0" "0" "0"
#> [3,] "a2" "a1" "0" "0"
#> [4,] "a3" "a2" "a1" "0"
#>
#> , , 16
#>
#> [,1] [,2] [,3] [,4]
#> [1,] "0" "0" "0" "0"
#> [2,] "0" "0" "0" "0"
#> [3,] "0" "0" "0" "0"
#> [4,] "0" "0" "0" "0"
Those \(F\) 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 \(F\)
matrices we have just introduced.
We now fit the model with an \(F\) matrix that is designed for cascade networks.
Specific Fshape
Net_inf_P_S <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4))
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0074
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00314
#> We are at step : 3
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0019
#> We are at step : 4
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00131
#> We are at step : 5
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00101
#> We are at step : 6
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00081
Plot of the inferred F matrix
Heatmap of the coefficients of the Omega matrix of the network. They reflect the use of a special \(F\) matrix. It is an example of an F matrix specifically designed to deal with cascade networks.
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. :
lars
packageglmnet
package. An
unweighted and a weighted version of the algorithm are availablespls
packageelasticnet
packagec060
package
implementation of stability selectionc060
package implementation of stability selectionlars
package
with light random Gaussian noise added to the explanatory variablesselectboost
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")
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0069
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00229
#> We are at step : 3
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00153
#> We are at step : 4
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00114
#> We are at step : 5
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00086
Plot of the inferred F matrix
Heatmap of the coefficients of the Omega matrix of the network
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)
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0075
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 4e-04
Plot of the inferred F matrix
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")
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0075
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00229
#> We are at step : 3
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00164
#> We are at step : 4
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00123
#> We are at step : 5
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00104
#> We are at step : 6
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00088
Plot of the inferred F matrix
Heatmap of the coefficients of the Omega matrix of the network
Net_inf_P_ELASTICNET <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="ELASTICNET")
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0074
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00396
#> We are at step : 3
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00284
#> We are at step : 4
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00215
#> We are at step : 5
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00168
#> We are at step : 6
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00147
#> We are at step : 7
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00125
#> We are at step : 8
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00114
#> We are at step : 9
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00092
Plot of the inferred F matrix
Heatmap of the coefficients of the Omega matrix of the network
Net_inf_P_stability <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="stability.c060")
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1mc.cores=2
#> 2mc.cores=2.........................
#> 3mc.cores=2.........................
#> 4mc.cores=2.........................
#> The convergence of the network is (L1 norm) : 0.0042
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1mc.cores=2
#> 2mc.cores=2.........................
#> 3mc.cores=2.........................
#> 4mc.cores=2.........................
#> The convergence of the network is (L1 norm) : 0.00095
Plot of the inferred F matrix
Heatmap of the coefficients of the Omega matrix of the network
Net_inf_P_StabWeight <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="stability.c060.weighted", priors=Weights_Net)
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1mc.cores=2
#> 2mc.cores=2 .........................
#> 3mc.cores=2 .........................
#> 4mc.cores=2 .........................
#> The convergence of the network is (L1 norm) : 0.0075
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1mc.cores=2
#> 2mc.cores=2 .........................
#> 3mc.cores=2 .........................
#> 4mc.cores=2 .........................
#> The convergence of the network is (L1 norm) : 0.00034
Plot of the inferred F matrix
Heatmap of the coefficients of the Omega matrix of the network
Net_inf_P_Robust <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="robust")
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0068
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00361
#> We are at step : 3
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00196
#> We are at step : 4
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00125
#> We are at step : 5
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00099
Plot of the inferred F matrix
Heatmap of the coefficients of the Omega matrix of the network
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)
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.0057
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00183
#> We are at step : 3
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00133
#> We are at step : 4
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00095
detach("package:Patterns", unload=TRUE)
library(Patterns)
#>
#> Attaching package: 'Patterns'
#> The following object is masked from 'package:igraph':
#>
#> compare
Plot of the inferred F matrix
Heatmap of the coefficients of the Omega matrix of the network
Net_inf_P_SelectBoostWeighted <- Patterns::inference(M, Finit=CascadeFinit(4,4), Fshape=CascadeFshape(4,4), fitfun="selectboost.weighted",priors=Weights_Net)
#> We are at step : 1
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.007
#> We are at step : 2
#> Computing Group (out of 4) :
#> 1
#> 2.........................
#> 3.........................
#> 4.........................
#> The convergence of the network is (L1 norm) : 0.00044
detach("package:Patterns", unload=TRUE)
library(Patterns)
#>
#> Attaching package: 'Patterns'
#> The following object is masked from 'package:igraph':
#>
#> compare
Plot of the inferred F matrix
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.
data("networkCascade")
set.seed(1)
cutoff(networkCascade)
#> [1] "This computation may be long"
#> [1] "1/10"
#> [1] "2/10"
#> [1] "3/10"
#> [1] "4/10"
#> [1] "5/10"
#> [1] "6/10"
#> [1] "7/10"
#> [1] "8/10"
#> [1] "9/10"
#> [1] "10/10"
#> [1] 0.000 0.007 0.423 0.388 0.236 0.631 0.952 0.976 0.825 0.362
#> $p.value
#> [1] 0.000 0.007 0.423 0.388 0.236 0.631 0.952 0.976 0.825 0.362
#>
#> $p.value.inter
#> [1] -0.04643835 0.14848083 0.28125541 0.36247646 0.33538710 0.60021707
#> [7] 0.92531630 0.98522398 0.79881816 0.37310221
#>
#> $sequence
#> [1] 0.00000000 0.04444444 0.08888889 0.13333333 0.17777778 0.22222222
#> [7] 0.26666667 0.31111111 0.35555556 0.40000000
Analyze the network with a cutoff set to the previouly found 0.133 optimal value.
analyze_network(networkCascade,nv=0.133)
#> node betweenness degree output closeness
#> 1 1 0 3 0.6442821 2.5337730
#> 2 2 8 4 1.3784717 5.4211261
#> 3 3 0 6 1.3308218 6.1428682
#> 4 4 0 9 1.7531528 19.4060065
#> 5 5 0 2 0.6400128 2.5169831
#> 6 6 0 1 0.2725100 3.4520368
#> 7 7 0 0 0.0000000 0.0000000
#> 8 8 0 1 0.1483077 10.4595738
#> 9 9 4 4 0.7969945 3.4810740
#> 10 10 20 7 1.3485173 6.0949803
#> 11 11 0 4 0.8054122 16.2236448
#> 12 12 0 11 2.4624877 10.7417814
#> 13 13 0 0 0.0000000 0.0000000
#> 14 14 0 1 0.1882265 3.8504312
#> 15 15 0 5 1.5808956 13.7135886
#> 16 16 81 24 6.7716649 29.1131750
#> 17 17 0 9 2.0059124 11.2249512
#> 18 18 0 9 1.6083138 6.6506106
#> 19 19 0 0 0.0000000 0.0000000
#> 20 20 0 0 0.0000000 0.0000000
#> 21 21 0 0 0.0000000 0.0000000
#> 22 22 0 0 0.0000000 0.0000000
#> 23 23 0 0 0.0000000 0.0000000
#> 24 24 0 1 0.1607163 0.6320503
#> 25 25 0 0 0.0000000 0.0000000
#> 26 26 0 0 0.0000000 0.0000000
#> 27 27 0 8 3.2710799 13.9045595
#> 28 28 0 2 0.3957891 2.1118782
#> 29 29 0 0 0.0000000 0.0000000
#> 30 30 0 1 0.2255093 0.8868623
#> 31 31 0 0 0.0000000 0.0000000
#> 32 32 0 0 0.0000000 0.0000000
#> 33 33 0 0 0.0000000 0.0000000
#> 34 34 0 0 0.0000000 0.0000000
#> 35 35 0 6 1.4397935 5.6622868
#> 36 36 0 0 0.0000000 0.0000000
#> 37 37 0 0 0.0000000 0.0000000
#> 38 38 0 0 0.0000000 0.0000000
#> 39 39 0 0 0.0000000 0.0000000
#> 40 40 0 0 0.0000000 0.0000000
#> 41 41 0 0 0.0000000 0.0000000
#> 42 42 2 1 0.5205955 2.0473501
#> 43 43 0 0 0.0000000 0.0000000
#> 44 44 0 0 0.0000000 0.0000000
#> 45 45 0 0 0.0000000 0.0000000
#> 46 46 0 0 0.0000000 0.0000000
#> 47 47 0 0 0.0000000 0.0000000
#> 48 48 0 1 0.5096457 2.0042877
#> 49 49 1 1 0.1814386 0.7135450
#> 50 50 0 0 0.0000000 0.0000000
#> 51 51 0 0 0.0000000 0.0000000
#> 52 52 0 0 0.0000000 0.0000000
#> 53 53 0 0 0.0000000 0.0000000
#> 54 54 0 0 0.0000000 0.0000000
#> 55 55 0 0 0.0000000 0.0000000
#> 56 56 0 0 0.0000000 0.0000000
#> 57 57 5 1 0.7142387 2.8088919
#> 58 58 0 0 0.0000000 0.0000000
#> 59 59 0 0 0.0000000 0.0000000
#> 60 60 0 0 0.0000000 0.0000000
#> 61 61 0 0 0.0000000 0.0000000
#> 62 62 0 0 0.0000000 0.0000000
#> 63 63 0 1 0.1668072 0.6560038
#> 64 64 0 0 0.0000000 0.0000000
#> 65 65 0 0 0.0000000 0.0000000
#> 66 66 0 0 0.0000000 0.0000000
#> 67 67 0 0 0.0000000 0.0000000
#> 68 68 0 0 0.0000000 0.0000000
#> 69 69 0 0 0.0000000 0.0000000
#> 70 70 0 0 0.0000000 0.0000000
#> 71 71 0 0 0.0000000 0.0000000
#> 72 72 0 0 0.0000000 0.0000000
#> 73 73 4 1 0.1937648 0.7620205
#> 74 74 0 0 0.0000000 0.0000000
#> 75 75 0 0 0.0000000 0.0000000
#> 76 76 0 0 0.0000000 0.0000000
#> 77 77 0 0 0.0000000 0.0000000
#> 78 78 0 0 0.0000000 0.0000000
#> 79 79 0 0 0.0000000 0.0000000
#> 80 80 0 0 0.0000000 0.0000000
#> 81 81 0 0 0.0000000 0.0000000
#> 82 82 4 2 0.4875471 1.9173803
#> 83 83 4 1 0.2849991 1.1208180
#> 84 84 5 1 0.4477398 1.7608296
#> 85 85 4 1 0.2126269 0.8361995
#> 86 86 0 0 0.0000000 0.0000000
#> 87 87 0 0 0.0000000 0.0000000
#> 88 88 0 0 0.0000000 0.0000000
#> 89 89 0 0 0.0000000 0.0000000
#> 90 90 5 1 0.1522237 0.5986513
#> 91 91 3 1 0.2857613 1.1238157
#> 92 92 0 0 0.0000000 0.0000000
#> 93 93 0 1 0.1784006 0.7015976
#> 94 94 0 0 0.0000000 0.0000000
#> 95 95 0 0 0.0000000 0.0000000
#> 96 96 0 0 0.0000000 0.0000000
#> 97 97 0 0 0.0000000 0.0000000
#> 98 98 0 0 0.0000000 0.0000000
#> 99 99 0 0 0.0000000 0.0000000
#> 100 100 0 0 0.0000000 0.0000000
#> 101 101 0 0 0.0000000 0.0000000
#> 102 102 0 0 0.0000000 0.0000000
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:
Section genes with first significant differential expression at t2:
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)
#> $omicsarray
#> US60 US90 US210
#> 210226_at 0.82417544 0.9166931 0.7310784
#> 233516_s_at -0.27395188 -2.3695246 0.6511830
#> 202081_at 0.60477249 0.6599672 -0.1884742
#> 236719_at -2.07284086 -0.3123747 0.1792494
#> 236019_at -0.08175065 -0.3699708 -0.4315901
#> 1563563_at -1.44513486 1.6869516 -0.4297297
#>
#> $name
#> [1] "210226_at" "233516_s_at" "202081_at" "236719_at" "236019_at"
#> [6] "1563563_at"
#>
#> $gene_ID
#> [1] "210226_at" "233516_s_at" "202081_at" "236719_at" "236019_at"
#> [6] "1563563_at"
#>
#> $group
#> [1] 1 2 1 1 1 1
#>
#> $start_time
#> [1] 1 2 1 1 1 1
#>
#> $time
#> [1] 60 90 210 390
#>
#> $subject
#> [1] 6
Summarize the final selection:
summary(Selection)
#> US60 US90 US210 US390
#> Min. :-2.76841 Min. :-2.369525 Min. :-1.6147 Min. :-2.60480
#> 1st Qu.:-0.18028 1st Qu.:-0.181425 1st Qu.: 0.1985 1st Qu.:-0.03884
#> Median : 0.05675 Median :-0.001924 Median : 0.9886 Median : 0.31766
#> Mean : 0.05764 Mean : 0.278275 Mean : 0.9611 Mean : 0.26428
#> 3rd Qu.: 0.22438 3rd Qu.: 0.664063 3rd Qu.: 1.6918 3rd Qu.: 0.57117
#> Max. : 2.86440 Max. : 4.284675 Max. : 3.6727 Max. : 2.54704
#> US60 US90 US210 US390
#> Min. :-2.7932 Min. :-2.49245 Min. :-1.21606 Min. :-1.74407
#> 1st Qu.:-0.5547 1st Qu.:-0.01944 1st Qu.: 0.07966 1st Qu.:-0.26548
#> Median :-0.3089 Median : 0.14977 Median : 0.72019 Median : 0.03616
#> Mean :-0.2917 Mean : 0.33720 Mean : 0.73063 Mean : 0.06753
#> 3rd Qu.:-0.1725 3rd Qu.: 0.48744 3rd Qu.: 1.26164 3rd Qu.: 0.32496
#> Max. : 2.0267 Max. : 3.37588 Max. : 3.87950 Max. : 2.83321
#> US60 US90 US210 US390
#> Min. :-2.94444 Min. :-0.9721 Min. :-1.9349 Min. :-3.8418
#> 1st Qu.:-0.23136 1st Qu.:-0.1027 1st Qu.: 0.3254 1st Qu.:-0.1592
#> Median :-0.04761 Median : 0.2548 Median : 1.2512 Median : 0.1538
#> Mean : 0.22115 Mean : 0.6479 Mean : 1.0485 Mean : 0.1219
#> 3rd Qu.: 0.33157 3rd Qu.: 1.0737 3rd Qu.: 1.8513 3rd Qu.: 0.6268
#> Max. : 3.31723 Max. : 4.3604 Max. : 4.4860 Max. : 1.9886
#> US60 US90 US210 US390
#> Min. :-2.85438 Min. :-0.90355 Min. :-0.83324 Min. :-0.96834
#> 1st Qu.:-0.06031 1st Qu.:-0.08464 1st Qu.: 0.07605 1st Qu.: 0.01569
#> Median : 0.03601 Median : 0.17135 Median : 0.52176 Median : 0.17370
#> Mean : 0.14593 Mean : 0.41929 Mean : 0.62446 Mean : 0.23854
#> 3rd Qu.: 0.24568 3rd Qu.: 0.75565 3rd Qu.: 1.07821 3rd Qu.: 0.45189
#> Max. : 1.82903 Max. : 3.60640 Max. : 2.27744 Max. : 1.90880
#> US60 US90 US210 US390
#> Min. :-1.38002 Min. :-2.94444 Min. :-1.0271 Min. :-1.3636
#> 1st Qu.:-0.19910 1st Qu.:-0.01758 1st Qu.: 0.1459 1st Qu.:-0.1386
#> Median :-0.07962 Median : 0.16080 Median : 0.7430 Median : 0.1492
#> Mean : 0.12972 Mean : 0.37123 Mean : 0.7972 Mean : 0.1271
#> 3rd Qu.: 0.26113 3rd Qu.: 0.61933 3rd Qu.: 1.3922 3rd Qu.: 0.4825
#> Max. : 2.31074 Max. : 3.24454 Max. : 3.6213 Max. : 1.5979
#> US60 US90 US210 US390
#> Min. :-1.79176 Min. :-3.20791 Min. :-1.4716 Min. :-1.95883
#> 1st Qu.:-0.09822 1st Qu.:-0.03963 1st Qu.: 0.1292 1st Qu.:-0.04786
#> Median : 0.03378 Median : 0.28261 Median : 0.8392 Median : 0.22472
#> Mean : 0.27978 Mean : 0.52529 Mean : 0.7903 Mean : 0.21171
#> 3rd Qu.: 0.33548 3rd Qu.: 1.03256 3rd Qu.: 1.4416 3rd Qu.: 0.42511
#> Max. : 3.16035 Max. : 3.19975 Max. : 2.8027 Max. : 2.14903
Plot the final 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.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.