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SIMLR.R
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# perform the SIMLR clustering algorithm
"SIMLR" <- function( X, c, no.dim = NA, k = 10, if.impute = FALSE, normalize = FALSE, cores.ratio = 1 ) {
# set any required parameter to the defaults
if(is.na(no.dim)) {
no.dim = c
}
# check the if.impute parameter
if(if.impute == TRUE) {
X = t(X)
X_zeros = which(X==0,arr.ind=TRUE)
if(length(X_zeros)>0) {
R_zeros = as.vector(X_zeros[,"row"])
C_zeros = as.vector(X_zeros[,"col"])
ind = (C_zeros - 1) * nrow(X) + R_zeros
X[ind] = as.vector(colMeans(X))[C_zeros]
}
X = t(X)
}
# check the normalize parameter
if(normalize == TRUE) {
X = t(X)
X = X - min(as.vector(X))
X = X / max(as.vector(X))
C_mean = as.vector(colMeans(X))
X = apply(X,MARGIN=1,FUN=function(x) return(x-C_mean))
}
# start the clock to measure the execution time
ptm = proc.time()
# set some parameters
NITER = 30
num = ncol(X)
r = -1
beta = 0.8
cat("Computing the multiple Kernels.\n")
# compute the kernels
D_Kernels = multiple.kernel(t(X),cores.ratio)
# set up some parameters
alphaK = 1 / rep(length(D_Kernels),length(D_Kernels))
distX = array(0,c(dim(D_Kernels[[1]])[1],dim(D_Kernels[[1]])[2]))
for (i in 1:length(D_Kernels)) {
distX = distX + D_Kernels[[i]]
}
distX = distX / length(D_Kernels)
# sort distX for rows
res = apply(distX,MARGIN=1,FUN=function(x) return(sort(x,index.return = TRUE)))
distX1 = array(0,c(nrow(distX),ncol(distX)))
idx = array(0,c(nrow(distX),ncol(distX)))
for(i in 1:nrow(distX)) {
distX1[i,] = res[[i]]$x
idx[i,] = res[[i]]$ix
}
A = array(0,c(num,num))
di = distX1[,2:(k+2)]
rr = 0.5 * (k * di[,k+1] - apply(di[,1:k],MARGIN=1,FUN=sum))
id = idx[,2:(k+2)]
numerator = (apply(array(0,c(length(di[,k+1]),dim(di)[2])),MARGIN=2,FUN=function(x) {x=di[,k+1]}) - di)
temp = (k*di[,k+1] - apply(di[,1:k],MARGIN=1,FUN=sum) + .Machine$double.eps)
denominator = apply(array(0,c(length(temp),dim(di)[2])),MARGIN=2,FUN=function(x) {x=temp})
temp = numerator / denominator
a = apply(array(0,c(length(t(1:num)),dim(di)[2])),MARGIN=2,FUN=function(x) {x=1:num})
A[cbind(as.vector(a),as.vector(id))] = as.vector(temp)
if(r<=0) {
r = mean(rr)
}
lambda = max(mean(rr),0)
A[is.nan(A)] = 0
A0 = (A + t(A)) / 2
S0 = max(max(distX)) - distX
cat("Performing network diffiusion.\n")
# perform network diffiusion
S0 = network.diffusion(S0,k)
# compute dn
S0 = dn(S0,'ave')
S = S0
D0 = diag(apply(S,MARGIN=2,FUN=sum))
L0 = D0 - S
eig1_res = eig1(L0,c,0)
F_eig1 = eig1_res$eigvec
temp_eig1 = eig1_res$eigval
evs_eig1 = eig1_res$eigval_full
# perform the iterative procedure NITER times
converge = vector()
for(iter in 1:NITER) {
cat("Iteration: ",iter,"\n")
distf = L2_distance_1(t(F_eig1),t(F_eig1))
A = array(0,c(num,num))
b = idx[,2:dim(idx)[2]]
a = apply(array(0,c(num,ncol(b))),MARGIN=2,FUN=function(x){ x = 1:num })
inda = cbind(as.vector(a),as.vector(b))
ad = (distX[inda]+lambda*distf[inda])/2/r
dim(ad) = c(num,ncol(b))
# call the c function for the optimization
c_input = -t(ad)
c_output = t(ad)
ad = t(.Call("projsplx_R",c_input,c_output))
A[inda] = as.vector(ad)
A[is.nan(A)] = 0
A = (A + t(A)) / 2
S = (1 - beta) * S + beta * A
S = network.diffusion(S,k)
D = diag(apply(S,MARGIN=2,FUN=sum))
L = D - S
F_old = F_eig1
eig1_res = eig1(L,c,0)
F_eig1 = eig1_res$eigvec
temp_eig1 = eig1_res$eigval
ev_eig1 = eig1_res$eigval_full
evs_eig1 = cbind(evs_eig1,ev_eig1)
DD = vector()
for (i in 1:length(D_Kernels)) {
temp = (.Machine$double.eps+D_Kernels[[i]]) * (S+.Machine$double.eps)
DD[i] = mean(apply(temp,MARGIN=2,FUN=sum))
}
alphaK0 = umkl(DD)
alphaK0 = alphaK0 / sum(alphaK0)
alphaK = (1-beta) * alphaK + beta * alphaK0
alphaK = alphaK / sum(alphaK)
fn1 = sum(ev_eig1[1:c])
fn2 = sum(ev_eig1[1:(c+1)])
converge[iter] = fn2 - fn1
if (iter<10) {
if (ev_eig1[length(ev_eig1)] > 0.000001) {
lambda = 1.5 * lambda
r = r / 1.01
}
}
else {
if(converge[iter]>converge[iter-1]) {
S = S_old
if(converge[iter-1] > 0.2) {
warning('Maybe you should set a larger value of c.')
}
break
}
}
S_old = S
# compute Kbeta
distX = D_Kernels[[1]] * alphaK[1]
for (i in 2:length(D_Kernels)) {
distX = distX + as.matrix(D_Kernels[[i]]) * alphaK[i]
}
# sort distX for rows
res = apply(distX,MARGIN=1,FUN=function(x) return(sort(x,index.return = TRUE)))
distX1 = array(0,c(nrow(distX),ncol(distX)))
idx = array(0,c(nrow(distX),ncol(distX)))
for(i in 1:nrow(distX)) {
distX1[i,] = res[[i]]$x
idx[i,] = res[[i]]$ix
}
}
LF = F_eig1
D = diag(apply(S,MARGIN=2,FUN=sum))
L = D - S
# compute the eigenvalues and eigenvectors of P
eigen_L = eigen(L)
U = eigen_L$vectors
D = eigen_L$values
if (length(no.dim)==1) {
U_index = seq(ncol(U),(ncol(U)-no.dim+1))
F_last = tsne(S,k=no.dim,initial_config=U[,U_index])
}
else {
F_last = list()
for (i in 1:length(no.dim)) {
U_index = seq(ncol(U),(ncol(U)-no.dim[i]+1))
F_last[i] = tsne(S,k=no.dim[i],initial_config=U[,U_index])
}
}
# compute the execution time
execution.time = proc.time() - ptm
cat("Performing Kmeans.\n")
y = kmeans(F_last,c,nstart=200)
ydata = tsne(S)
# create the structure with the results
results = list()
results[["y"]] = y
results[["S"]] = S
results[["F"]] = F_last
results[["ydata"]] = ydata
results[["alphaK"]] = alphaK
results[["execution.time"]] = execution.time
results[["converge"]] = converge
results[["LF"]] = LF
return(results)
}