| Title: | Active modules for multilayer weighted gene co-expression networks: a continuous optimization approach |
|---|---|
| Description: | A pure data-driven gene network, weighted gene co-expression network (WGCN) could be constructed only from expression profile. Different layers in such networks may represent different time points, multiple conditions or various species. AMOUNTAIN aims to search active modules in multi-layer WGCN using a continuous optimization approach. |
| Authors: | Dong Li, Shan He, Zhisong Pan and Guyu Hu |
| Maintainer: | Dong Li <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.31.0 |
| Built: | 2024-06-30 04:12:36 UTC |
| Source: | https://github.com/bioc/AMOUNTAIN |
Call C version of moduleIdentificationGPFixSS
CGPFixSS(W, z, x0, a = 0.5, lambda = 1, maxiter = 50)CGPFixSS(W, z, x0, a = 0.5, lambda = 1, maxiter = 50)
W |
edge score matrix of the network, n x n matrix |
z |
node score vector of the network, n-length vector |
x0 |
initial solution, n-length vector |
a |
parameter in elastic net the same as in |
lambda |
parameter in objective, coefficient of node score part |
maxiter |
maximal interation of whole procedure |
a list containing function objective vector and the solution
Dong Li, [email protected]
AMOUNTAIN
n = 100 k = 20 theta = 0.5 pp <- networkSimulation(n,k,theta) moduleid <- pp[[3]] ## use default parameters here x <- CGPFixSS(pp[[1]],pp[[2]],rep(1/n,n)) predictedid<-which(x[[2]]!=0) recall <- length(intersect(predictedid,moduleid))/length(moduleid) precise <- length(intersect(predictedid,moduleid))/length(predictedid) Fscore <- (2*precise*recall/(precise+recall))n = 100 k = 20 theta = 0.5 pp <- networkSimulation(n,k,theta) moduleid <- pp[[3]] ## use default parameters here x <- CGPFixSS(pp[[1]],pp[[2]],rep(1/n,n)) predictedid<-which(x[[2]]!=0) recall <- length(intersect(predictedid,moduleid))/length(moduleid) precise <- length(intersect(predictedid,moduleid))/length(predictedid) Fscore <- (2*precise*recall/(precise+recall))
Call C version of moduleIdentificationGPFixSSMultilayer
CGPFixSSMultiLayer(W, listzs, x0, a = 0.5, lambda = 1, maxiter = 50)CGPFixSSMultiLayer(W, listzs, x0, a = 0.5, lambda = 1, maxiter = 50)
W |
edge score matrix of the network, n x n matrix |
listzs |
a list of node score vectors, each layer has a n-length vector |
x0 |
initial solution, n-length vector |
a |
parameter in elastic net the same as in |
lambda |
parameter in objective, coefficient of node score of other layers |
maxiter |
maximal interation of whole procedure |
a list containing solution for network 1 and network 2
Dong Li, [email protected]
AMOUNTAIN
moduleIdentificationGPFixSSMultilayer
n = 100 k = 20 L = 5 theta = 0.5 cpl <- multilayernetworkSimulation(n,k,theta,L) listz <- list() for (i in 1:L){ listz[[i]] <- cpl[[i+2]] } moduleid <- cpl[[2]] ## use default parameters here x <- CGPFixSSMultiLayer(cpl[[1]],listz,rep(1/n,n)) predictedid <- which(x[[2]]!=0) recall <- length(intersect(predictedid,moduleid))/length(moduleid) precise <- length(intersect(predictedid,moduleid))/length(predictedid) Fscore <- (2*precise*recall/(precise+recall))n = 100 k = 20 L = 5 theta = 0.5 cpl <- multilayernetworkSimulation(n,k,theta,L) listz <- list() for (i in 1:L){ listz[[i]] <- cpl[[i+2]] } moduleid <- cpl[[2]] ## use default parameters here x <- CGPFixSSMultiLayer(cpl[[1]],listz,rep(1/n,n)) predictedid <- which(x[[2]]!=0) recall <- length(intersect(predictedid,moduleid))/length(moduleid) precise <- length(intersect(predictedid,moduleid))/length(predictedid) Fscore <- (2*precise*recall/(precise+recall))
Call C version of moduleIdentificationGPFixSSTwolayer
CGPFixSSTwolayer(W1, z1, x0, W2, z2, y0, interlayerA, lambda1 = 1, lambda2 = 1, lambda3 = 1, maxiter = 100, a1 = 0.5, a2 = 0.5)CGPFixSSTwolayer(W1, z1, x0, W2, z2, y0, interlayerA, lambda1 = 1, lambda2 = 1, lambda3 = 1, maxiter = 100, a1 = 0.5, a2 = 0.5)
W1 |
edge score matrix of the network 1, n_1 x n_1 matrix |
z1 |
node score vector of the network 1, n_1-length vector |
x0 |
initial solution of network 1, n_1-length vector |
W2 |
edge score matrix of the network 2, n_2 x n_2 matrix |
z2 |
node score vector of the network 2, n_2-length vector |
y0 |
initial solution of network 2, n_2-length vector |
interlayerA |
inter-layer links weight, n_1 x n_2 matrix |
lambda1 |
parameter in objective, coefficient of node score of network 1 |
lambda2 |
parameter in objective, coefficient of node score of network 2 |
lambda3 |
parameter in objective, coefficient of inter-layer links part |
maxiter |
maximal interation of whole procedure |
a1 |
parameter in elastic net the same as in |
a2 |
parameter in elastic net the same as in |
a list containing solution for network 1 and network 2 and objective
Dong Li, [email protected]
AMOUNTAIN
moduleIdentificationGPFixSSTwolayer
n1=100 k1=20 theta1 = 0.5 n2=80 k2=10 theta2 = 0.5 ppresult <- twolayernetworkSimulation(n1,k1,theta1,n2,k2,theta2) A <- ppresult[[3]] pp <- ppresult[[1]] moduleid <- pp[[3]] netid <- 1:n1 restp<- netid[-moduleid] pp2 <- ppresult[[2]] moduleid2 <- pp2[[3]] ## use default parameters here modres=CGPFixSSTwolayer(pp[[1]],pp[[2]],rep(1/n1,n1), pp2[[1]],pp2[[2]],rep(1/n2,n2),A) predictedid<-which(modres[[1]]!=0) recall = length(intersect(predictedid,moduleid))/length(moduleid) precise = length(intersect(predictedid,moduleid))/length(predictedid) F1 = 2*precise*recall/(precise+recall) predictedid2<-which(modres[[2]]!=0) recall2 = length(intersect(predictedid2,moduleid2))/length(moduleid2) precise2 = length(intersect(predictedid2,moduleid2))/length(predictedid2) F2 = 2*precise2*recall2/(precise2+recall2)n1=100 k1=20 theta1 = 0.5 n2=80 k2=10 theta2 = 0.5 ppresult <- twolayernetworkSimulation(n1,k1,theta1,n2,k2,theta2) A <- ppresult[[3]] pp <- ppresult[[1]] moduleid <- pp[[3]] netid <- 1:n1 restp<- netid[-moduleid] pp2 <- ppresult[[2]] moduleid2 <- pp2[[3]] ## use default parameters here modres=CGPFixSSTwolayer(pp[[1]],pp[[2]],rep(1/n1,n1), pp2[[1]],pp2[[2]],rep(1/n2,n2),A) predictedid<-which(modres[[1]]!=0) recall = length(intersect(predictedid,moduleid))/length(moduleid) precise = length(intersect(predictedid,moduleid))/length(predictedid) F1 = 2*precise*recall/(precise+recall) predictedid2<-which(modres[[2]]!=0) recall2 = length(intersect(predictedid2,moduleid2))/length(moduleid2) precise2 = length(intersect(predictedid2,moduleid2))/length(predictedid2) F2 = 2*precise2*recall2/(precise2+recall2)
Piecewise root finding algorithm for Euclidean projection on elastic net
EuclideanProjectionENNORM(y, t, alpha = 0.5)EuclideanProjectionENNORM(y, t, alpha = 0.5)
y |
constant vector |
t |
radius of elastic net ball |
alpha |
parameter in elastic net: alpha x_1 + (1-alpha)*x_2^2=t |
a list containing network adjacency matrix, node score and module membership
Dong Li, [email protected]
Gong, Pinghua, Kun Gai, and Changshui Zhang. "Efficient euclidean projections via piecewise root finding and its application in gradient projection." Neurocomputing 74.17 (2011): 2754-2766.
y=rnorm(100) x=EuclideanProjectionENNORM(y,1,0.5) sparistyx = sum(x==0)/100y=rnorm(100) x=EuclideanProjectionENNORM(y,1,0.5) sparistyx = sum(x==0)/100
Algorithm for Module Identification on single network
moduleIdentificationGPFixSS(W, z, x0, a = 0.5, lambda = 1, maxiter = 1000)moduleIdentificationGPFixSS(W, z, x0, a = 0.5, lambda = 1, maxiter = 1000)
W |
edge score matrix of the network, n x n matrix |
z |
node score vector of the network, n-length vector |
x0 |
initial solution, n-length vector |
a |
parameter in elastic net the same as in |
lambda |
parameter in objective, coefficient of node score part |
maxiter |
maximal interation of whole procedure |
a list containing function objective vector and the solution
Dong Li, [email protected]
AMOUNTAIN
n = 100 k = 20 theta = 0.5 pp <- networkSimulation(n,k,theta) moduleid <- pp[[3]] ## use default parameters here x <- moduleIdentificationGPFixSS(pp[[1]],pp[[2]],rep(1/n,n)) predictedid<-which(x[[2]]!=0) recall <- length(intersect(predictedid,moduleid))/length(moduleid) precise <- length(intersect(predictedid,moduleid))/length(predictedid) Fscore <- (2*precise*recall/(precise+recall))n = 100 k = 20 theta = 0.5 pp <- networkSimulation(n,k,theta) moduleid <- pp[[3]] ## use default parameters here x <- moduleIdentificationGPFixSS(pp[[1]],pp[[2]],rep(1/n,n)) predictedid<-which(x[[2]]!=0) recall <- length(intersect(predictedid,moduleid))/length(moduleid) precise <- length(intersect(predictedid,moduleid))/length(predictedid) Fscore <- (2*precise*recall/(precise+recall))
Algorithm for Module Identification on multi-layer network sharing the same set of genes
moduleIdentificationGPFixSSMultilayer(W, listz, x0, a = 0.5, lambda = 1, maxiter = 1000)moduleIdentificationGPFixSSMultilayer(W, listz, x0, a = 0.5, lambda = 1, maxiter = 1000)
W |
edge score matrix of the network, n x n matrix |
listz |
a list of node score vectors, each layer has a n-length vector |
x0 |
initial solution, n-length vector |
a |
parameter in elastic net the same as in |
lambda |
parameter in objective, coefficient of node score of other layers |
maxiter |
maximal interation of whole procedure |
a list containing objective values and solution
Dong Li, [email protected]
AMOUNTAIN
moduleIdentificationGPFixSSMultilayer
n = 100 k = 20 L = 5 theta = 0.5 cpl <- multilayernetworkSimulation(n,k,theta,L) listz <- list() for (i in 1:L){ listz[[i]] <- cpl[[i+2]] } moduleid <- cpl[[2]] ## use default parameters here x <- moduleIdentificationGPFixSSMultilayer(cpl[[1]],listz,rep(1/n,n)) predictedid <- which(x[[2]]!=0) recall <- length(intersect(predictedid,moduleid))/length(moduleid) precise <- length(intersect(predictedid,moduleid))/length(predictedid) Fscore <- (2*precise*recall/(precise+recall))n = 100 k = 20 L = 5 theta = 0.5 cpl <- multilayernetworkSimulation(n,k,theta,L) listz <- list() for (i in 1:L){ listz[[i]] <- cpl[[i+2]] } moduleid <- cpl[[2]] ## use default parameters here x <- moduleIdentificationGPFixSSMultilayer(cpl[[1]],listz,rep(1/n,n)) predictedid <- which(x[[2]]!=0) recall <- length(intersect(predictedid,moduleid))/length(moduleid) precise <- length(intersect(predictedid,moduleid))/length(predictedid) Fscore <- (2*precise*recall/(precise+recall))
Algorithm for Module Identification on two-layer network
moduleIdentificationGPFixSSTwolayer(W1, z1, x0, W2, z2, y0, A, lambda1 = 1, lambda2 = 1, lambda3 = 1, maxiter = 1000, a1 = 0.5, a2 = 0.5)moduleIdentificationGPFixSSTwolayer(W1, z1, x0, W2, z2, y0, A, lambda1 = 1, lambda2 = 1, lambda3 = 1, maxiter = 1000, a1 = 0.5, a2 = 0.5)
W1 |
edge score matrix of the network 1, n_1 x n_1 matrix |
z1 |
node score vector of the network 1, n_1-length vector |
x0 |
initial solution of network 1, n_1-length vector |
W2 |
edge score matrix of the network 2, n_2 x n_2 matrix |
z2 |
node score vector of the network 2, n_2-length vector |
y0 |
initial solution of network 2, n_2-length vector |
A |
inter-layer links weight, n_1 x n_2 matrix |
lambda1 |
parameter in objective, coefficient of node score of network 1 |
lambda2 |
parameter in objective, coefficient of node score of network 2 |
lambda3 |
parameter in objective, coefficient of inter-layer links part |
maxiter |
maximal interation of whole procedure |
a1 |
parameter in elastic net the same as in |
a2 |
parameter in elastic net the same as in |
a list containing solution for network 1 and network 2 and objective
Dong Li, [email protected]
AMOUNTAIN
n1=100 k1=20 theta1 = 0.5 n2=80 k2=10 theta2 = 0.5 ppresult <- twolayernetworkSimulation(n1,k1,theta1,n2,k2,theta2) A <- ppresult[[3]] pp <- ppresult[[1]] moduleid <- pp[[3]] netid <- 1:n1 restp<- netid[-moduleid] pp2 <- ppresult[[2]] moduleid2 <- pp2[[3]] ## use default parameters here modres=moduleIdentificationGPFixSSTwolayer(pp[[1]],pp[[2]],rep(1/n1,n1), pp2[[1]],pp2[[2]],rep(1/n2,n2),A) predictedid<-which(modres[[1]]!=0) recall = length(intersect(predictedid,moduleid))/length(moduleid) precise = length(intersect(predictedid,moduleid))/length(predictedid) F1 = 2*precise*recall/(precise+recall) predictedid2<-which(modres[[2]]!=0) recall2 = length(intersect(predictedid2,moduleid2))/length(moduleid2) precise2 = length(intersect(predictedid2,moduleid2))/length(predictedid2) F2 = 2*precise2*recall2/(precise2+recall2)n1=100 k1=20 theta1 = 0.5 n2=80 k2=10 theta2 = 0.5 ppresult <- twolayernetworkSimulation(n1,k1,theta1,n2,k2,theta2) A <- ppresult[[3]] pp <- ppresult[[1]] moduleid <- pp[[3]] netid <- 1:n1 restp<- netid[-moduleid] pp2 <- ppresult[[2]] moduleid2 <- pp2[[3]] ## use default parameters here modres=moduleIdentificationGPFixSSTwolayer(pp[[1]],pp[[2]],rep(1/n1,n1), pp2[[1]],pp2[[2]],rep(1/n2,n2),A) predictedid<-which(modres[[1]]!=0) recall = length(intersect(predictedid,moduleid))/length(moduleid) precise = length(intersect(predictedid,moduleid))/length(predictedid) F1 = 2*precise*recall/(precise+recall) predictedid2<-which(modres[[2]]!=0) recall2 = length(intersect(predictedid2,moduleid2))/length(moduleid2) precise2 = length(intersect(predictedid2,moduleid2))/length(predictedid2) F2 = 2*precise2*recall2/(precise2+recall2)
Simulate a multi-layer weighted network with each layer sharing the same set of nodes but different nodes scores
multilayernetworkSimulation(n, k, theta, L)multilayernetworkSimulation(n, k, theta, L)
n |
number of nodes in each layer of the network |
k |
number of nodes in the conserved module |
theta |
module node score follow the uniform distribution in range [theta,1] |
L |
number of layers |
a list containing all the layers, each as result object of networkSimulation
Dong Li, [email protected]
n = 100 k = 20 theta = 0.5 L = 5 cpl <- multilayernetworkSimulation(n,k,theta,L) ## No proper way to visualize it yetn = 100 k = 20 theta = 0.5 L = 5 cpl <- multilayernetworkSimulation(n,k,theta,L) ## No proper way to visualize it yet
Simulate a single weighted network
networkSimulation(n, k, theta)networkSimulation(n, k, theta)
n |
number of nodes in the network |
k |
number of nodes in the module, n < k |
theta |
module node score follow the uniform distribution in range [theta,1] |
a list containing network adjacency matrix, node score and module membership
Dong Li, [email protected]
pp <- networkSimulation(100,20,0.5) moduleid <- pp[[3]] netid <- 1:100 restp<- netid[-moduleid] groupdesign=list(moduleid,restp) names(groupdesign)=c('module','background') ## Not run: library(qgraph) pg<-qgraph(pp[[1]],groups=groupdesign,legend=TRUE) ## End(Not run)pp <- networkSimulation(100,20,0.5) moduleid <- pp[[3]] netid <- 1:100 restp<- netid[-moduleid] groupdesign=list(moduleid,restp) names(groupdesign)=c('module','background') ## Not run: library(qgraph) pg<-qgraph(pp[[1]],groups=groupdesign,legend=TRUE) ## End(Not run)
Simulate a two-layer weighted network
twolayernetworkSimulation(n1, k1, theta1, n2, k2, theta2)twolayernetworkSimulation(n1, k1, theta1, n2, k2, theta2)
n1 |
number of nodes in the network1 |
k1 |
number of nodes in the module1, n1 < k1 |
theta1 |
module1 node score follow the uniform distribution in range [theta1,1] |
n2 |
number of nodes in the network2 |
k2 |
number of nodes in the module2, n2 < k2 |
theta2 |
module2 node score follow the uniform distribution in range [theta2,1] |
a list containing network1, network2 and a inter-layer links matrix
Dong Li, [email protected]
n1=100 k1=20 theta1 = 0.5 n2=80 k2=10 theta2 = 0.5 ppresult <- twolayernetworkSimulation(n1,k1,theta1,n2,k2,theta2) A <- ppresult[[3]] pp <- ppresult[[1]] moduleid <- pp[[3]] netid <- 1:n1 restp<- netid[-moduleid] pp2 <- ppresult[[2]] moduleid2 <- pp2[[3]] netid2 <- 1:n2 restp2<- netid2[-moduleid2] ## labelling the groups groupdesign=list(moduleid,restp,(moduleid2+n1),(restp2+n1)) names(groupdesign)=c('module1','background1','module2','background2') twolayernet<-matrix(0,nrow=(n1+n2),ncol=(n1+n2)) twolayernet[1:n1,1:n1]<-pp[[1]] twolayernet[(n1+1):(n1+n2),(n1+1):(n1+n2)]<-pp2[[1]] twolayernet[1:n1,(n1+1):(n1+n2)] = A twolayernet[(n1+1):(n1+n2),1:n1] = t(A) ## Not run: library(qgraph) g<-qgraph(twolayernet,groups=groupdesign,legend=TRUE) ## End(Not run)n1=100 k1=20 theta1 = 0.5 n2=80 k2=10 theta2 = 0.5 ppresult <- twolayernetworkSimulation(n1,k1,theta1,n2,k2,theta2) A <- ppresult[[3]] pp <- ppresult[[1]] moduleid <- pp[[3]] netid <- 1:n1 restp<- netid[-moduleid] pp2 <- ppresult[[2]] moduleid2 <- pp2[[3]] netid2 <- 1:n2 restp2<- netid2[-moduleid2] ## labelling the groups groupdesign=list(moduleid,restp,(moduleid2+n1),(restp2+n1)) names(groupdesign)=c('module1','background1','module2','background2') twolayernet<-matrix(0,nrow=(n1+n2),ncol=(n1+n2)) twolayernet[1:n1,1:n1]<-pp[[1]] twolayernet[(n1+1):(n1+n2),(n1+1):(n1+n2)]<-pp2[[1]] twolayernet[1:n1,(n1+1):(n1+n2)] = A twolayernet[(n1+1):(n1+n2),1:n1] = t(A) ## Not run: library(qgraph) g<-qgraph(twolayernet,groups=groupdesign,legend=TRUE) ## End(Not run)