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AGSVD.R
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##############################################################################
##############################################################################
AGSVD = function(X, rank_k=2, A, sigma, ku=50, kv=100, niter=100, err=0.0001){
# --------------------------------------------------------------------------
# [n,p] = dim(X), n is the number of samples and p is the number of features
# A: PPI network of genes
# sigma parameter
# --------------------------------------------------------------------------
# Output
n = nrow(X)
p = ncol(X)
U = matrix(0,n,rank_k); D = rep(0,rank_k); V = matrix(0,p,rank_k)
objs = c(); # L = diag(apply(A,1,sum)) - A
tX = X
for(i in 1:rank_k){
out = rank1.AGSVD(tX, A, sigma, ku, kv, niter, err)
U[,i] = out$u; V[,i] = out$v; D[i] = out$d;
temp_objs = norm(tX,"F")^2 - (out$ds)^2
# 2019-7-19: ||X - duv||_F^2 + sigma*|u|^T*L*|u|
# L = diag(apply(A,1,sum)) - A
# sum1 = norm(tX - c(out$d)*out$u%*%t(out$v),"F")^2
# sum2 = sigma*t(abs(out$v))%*%L%*%abs(out$v)
# temp_objs = sum1 + sum2
objs = c(objs,temp_objs)
# update X
tX = tX - c(out$d)*out$u%*%t(out$v)
}
return (list(U=U, D=D, V=V, objs = objs))
}
##############################################################################
##############################################################################
rank1.AGSVD = function(X, A, sigma, ku, kv=2, niter=1000, err=0.0001){
# ------------------
# Initialize u and v
Res = svd(X,1,1)
u0 = Res$u # v0 = v0/norm(v0,'E')
v0 = Res$v
ds = c()
# ------------------
# Iterative algorithm to solve u and v values
for (i in 1:niter){
# update u and v
# u = X%*%v0; u = u/norm(u,'E') # for samples
u = L0project(X%*%v0, ku)
v = AG_project(t(X)%*%u, v0, kv, A, sigma) #for genes
d = t(u)%*%X%*%v
ds = c(ds,d)
# Termination condition
if ((norm(u - u0,'2')<= err)&(norm(v - v0,'2')<= err)){break}
else {
u0 = u;v0 = v}
}
return (list(u=u, v=v, d=d, ds=ds))
}
##############################################################################
##############################################################################
# Sparse Graph-regularized Penalty With Absolute Operator
AG_project = function(z, v0, k, A, sigma){
#------------------------
v0 = abs(v0)
v = abs(z) + sigma*A%*%v0
v = select2(v,k)
#------------------------
if(sum(v^2)==0){return(rep(0,length(v)))}
else{
v = v/sqrt(sum(v^2))
v = sign(z)*v
return(v)}
}
##############################################################################
##############################################################################
# L0 constrained SVD project function
L0project = function(z, k){
absz = abs(z);
u = select2(absz,k)
if(sum(u^2)==0){return(rep(0,length(u)))}
else{
u = u/sqrt(sum(u^2))
u = sign(z)*u
return(u)}
}
# An auxiliary function
select2 = function(x, k){
if(k>=length(x)) return(x)
x[-order(x,decreasing=T)[1:k]] = 0
return(x)
}
##############################################################################
##############################################################################
NetworkEnrichment.of.module = function(PPINetwork,mgIDs){
# module gene IDs
B = PPINetwork
geneNum = dim(B)[1]
Num.mgIDs.edges = sum(B[mgIDs,mgIDs])/2
q = Num.mgIDs.edges-1
m = sum(B)/2
n = geneNum*(geneNum-1)/2-m
k = length(mgIDs)*(length(mgIDs)-1)/2
PValue = phyper(q, m, n, k, lower.tail = F)
FC = (Num.mgIDs.edges/k)/(m/(m+n))
return(c(length(mgIDs),Num.mgIDs.edges,FC,PValue))
}
##############################################################################
##############################################################################
getTable = function(out,METABRIC.gene.network){
V1 = out$V; ds = out$D; moduleEdgeTable = NULL
for(i in 1:ncol(V1)){
M1.geneIDs = which(V1[,i]!=0)
t1 = NetworkEnrichment.of.module(METABRIC.gene.network,M1.geneIDs)
t2 = c(ds[i],t1)
moduleEdgeTable = cbind(moduleEdgeTable,t2)
}
row.names(moduleEdgeTable) = c("d","numGenes","numEdges","FC","Pvalue")
colnames(moduleEdgeTable) = paste("module",1:ncol(V1))
print(round(moduleEdgeTable,2))
return(moduleEdgeTable)
}
##############################################################################
##############################################################################
getNMI.avg = function(out,yanData){
U1 = out$U[,c(1,2)]
res = matrix(rep(0,50),ncol=1)
for(i in 1:50){
set.seed(i)
cl <- kmeans(U1, length(unique(yanData$sample.group)), nstart = 1)
t1 = data.frame(1:length(yanData$sample.group), cl$cluste)
t2 = data.frame(1:length(yanData$sample.group), yanData$sample.group)
res[i,1] = NMI(t1,t2)$value
}
return(list(avg.NMI = mean(res), NMIs = res))
}
getNMI.avg2 = function(out,yanData){
U1 = out$U
print(dim(U1))
res = matrix(rep(0,50),ncol=1)
for(i in 1:50){
set.seed(i)
cl <- kmeans(U1, length(unique(yanData$sample.group)), nstart = 1)
t1 = data.frame(1:length(yanData$sample.group), cl$cluste)
t2 = data.frame(1:length(yanData$sample.group), yanData$sample.group)
res[i,1] = NMI(t1,t2)$value
}
return(list(avg.NMI = mean(res), NMIs = res))
}
##############################################################################
##############################################################################
getFig = function(out, DataName, fileName){
# DataName = "pollen Dataset"
Data = data.frame(out$U[,c(1,2)]);
fig <- ggplot(Data, aes(X1, X2, colour = factor(yanData$sample.group))) +
geom_point(size=I(3)) + ggtitle(DataName) + xlab("PC1")+ylab("PC2") + theme(legend.title=element_blank())
fig = fig +theme(legend.text = element_text(colour = "black", angle = 0,size=12),
axis.title = element_text(colour="black", size=16),
axis.text = element_text(colour = "black",size=16))
ggsave(fig, file=fileName, width=7, height=7)
}
##############################################################################
##############################################################################