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246 lines (219 loc) · 7.17 KB
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## ----setup, include=FALSE------------------------------------------------
knitr::opts_chunk$set(echo = TRUE)
## ----echo=FALSE, warning=FALSE, message=FALSE----------------------------
# install.packages("nmfADMM_1.0.tar.gz", repos = NULL, type="source")
library(nmfADMM)
library(NMF)
set.seed(1984)
## ------------------------------------------------------------------------
m <- n <- 1000 # Input size m x n
k = 15 # Rank k approximation
FIXiter = 100 # Fixed the number of iterations for comparison
df = data.frame()
X = matrix(abs(rnorm(n=m*n)), m, n) # A random matrix
sqt = sum(X^2)
# Kmeans
t0=proc.time()
vc = kmeans(t(X),centers=k)
t1=proc.time()
erk = 0
for (i in 1:k) {
erk = erk + sum(apply(X[, vc$cluster==i], 2,
function(x) sum((x-vc$centers[i, ])^2)))
}
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = erk/sqt,
Method="Kmeans"))
# Standard NMF using package "NMF"
t0=proc.time()
def = nmf(X, k, method="lee", nrun=1, maxIter=FIXiter)
t1=proc.time()
Xp = def@fit@W %*% def@fit@H
err0 = sum((Xp-X)^2)/sqt
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = err0,
Method="StandardNMF"))
rc = (1:n)%%k # Random starting cluster assignment
# Standard NMF using ADMM
t0=proc.time()
res = NMF_ADMM(X, k, rc,
fixediter=FIXiter, verbose=0)
t1=proc.time()
Xp = res$W %*% t(res$G)
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = sum((Xp-X)^2)/sqt,
Method="StandardNMF_ADMM"))
# Convex NMF using ADMM
t0=proc.time()
res = ConvexNMF_ADMM(X,k,rc,
fixediter=FIXiter,
verbose=0)
t1=proc.time()
Xp = X %*% res$W %*% res$G
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = sum((Xp-X)^2)/sqt,
Method="ConvexADMM"))
# Symmetric NMF using ADMM (single input version)
t0=proc.time()
res = SymNMF_ADMM(V=X,k=k,cluster=rc,
fixediter=FIXiter,verbose=0)
t1=proc.time()
Xp = res$W %*% t(res$G)
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = sum((Xp-X)^2)/sqt,
Method="SymNMFADMM"))
row.names(df) = NULL
df
## ------------------------------------------------------------------------
m <- n <- 500 # Input size n x n
k = 10 # Rank k approximation
FIXiter = 100 # Fixed the number of iteration for comparison
C = matrix(abs(rnorm(n=m*n)),n,m)
X = C %*% t(C)
sub = round(n/k)
for (j in 1:(k-1)) {
st=(j-1)*sub+1
ed=j*sub
X[st:ed, st:ed] = X[st:ed, st:ed] * (1+runif(1,0.1,2))
}
st = (k-1)*sub+1
ed = n
X[st:ed, st:ed] = X[st:ed, st:ed] * (1+runif(1,0.1,2))
sqt = sum(X^2)
## ----echo = FALSE--------------------------------------------------------
df = data.frame()
# Kmeans
t0=proc.time()
vc = kmeans(t(X),centers=k)
t1=proc.time()
erk = 0
for (i in 1:k) {
erk = erk + sum(apply(X[, vc$cluster==i], 2,
function(x) sum((x-vc$centers[i, ])^2)))
}
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = erk/sqt,
Method="Kmeans"))
# Standard NMF using package "NMF"
t0=proc.time()
def = nmf(X, k, method="lee", nrun=1, maxIter=FIXiter)
t1=proc.time()
Xp = def@fit@W %*% def@fit@H
err0 = sum((Xp-X)^2)/sqt
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = err0,
Method="StandardNMF"))
rc = (1:n)%%k
# Standard NMF using ADMM
t0=proc.time()
res = NMF_ADMM(X, k, rc,
fixediter=FIXiter, verbose=0)
t1=proc.time()
Xp = res$W %*% t(res$G)
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = sum((Xp-X)^2)/sqt,
Method="StandardNMF_ADMM"))
# Convex NMF using ADMM
t0=proc.time()
res = ConvexNMF_ADMM(X,k,rc,
fixediter=FIXiter,
verbose=0)
t1=proc.time()
Xp = X %*% res$W %*% res$G
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = sum((Xp-X)^2)/sqt,
Method="ConvexADMM"))
# Symmetric NMF using ADMM (single input version)
t0=proc.time()
res = SymNMF_ADMM(V=X,k=k,cluster=rc,
fixediter=FIXiter*2,verbose=0)
t1=proc.time()
Xp = res$W %*% t(res$G)
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = sum((Xp-X)^2)/sqt,
Method="SymNMFADMM"))
row.names(df) = NULL
df
## ----echo = FALSE--------------------------------------------------------
simul.mv.gmm <- function(n, lambdas, mus, covs) {
k <- length(lambdas) # k is the number of components
d <- nrow(mus) # d is the dimension of data
stopifnot(k == ncol(mus))
cov.chol = chol(covs)
z <- apply(rmultinom(n, 1, lambdas), 2, which.max)
xi <- matrix(rnorm(n*d), d, n)
x <- matrix(NA, d, n)
for(i in 1:n) {
x[,i] <- (xi[,i] %*% cov.chol) + mus[,z[i]]
}
return(list(x=x,z=z))
}
## ------------------------------------------------------------------------
m <- 100
n <- 500 # Input size m x n
k = 10 # k components with differnet mean
FIXiter = 100 # Fixed the number of iteration for comparison
C = matrix(rnorm(n=m*m),m,m) # Same covariance matrix
CC = cov2cor(C %*% t(C))
sim=simul.mv.gmm(n, rep(1, k), matrix((1:k),m,k,byrow=T), CC)
X = abs(sim$x)
sqt = sum(X^2)
## ----echo = FALSE--------------------------------------------------------
df = data.frame()
# Kmeans
t0=proc.time()
vc = kmeans(t(X),centers=k)
t1=proc.time()
erk = 0
for (i in 1:k) {
erk = erk + sum(apply(X[, vc$cluster==i], 2,
function(x) sum((x-vc$centers[i, ])^2)))
}
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = erk/sqt,
Method="Kmeans"))
# Standard NMF using package "NMF"
t0=proc.time()
def = nmf(X, k, method="lee", nrun=1, maxIter=FIXiter)
t1=proc.time()
Xp = def@fit@W %*% def@fit@H
err0 = sum((Xp-X)^2)/sqt
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = err0,
Method="StandardNMF"))
rc = (1:n)%%k
# Standard NMF using ADMM
t0=proc.time()
res = NMF_ADMM(X, k, rc,
fixediter=FIXiter, verbose=0)
t1=proc.time()
Xp = res$W %*% t(res$G)
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = sum((Xp-X)^2)/sqt,
Method="StandardNMF_ADMM"))
# Convex NMF using ADMM
t0=proc.time()
res = ConvexNMF_ADMM(X,k,rc,
fixediter=FIXiter,
verbose=0)
t1=proc.time()
Xp = X %*% res$W %*% res$G
df=rbind(df, data.frame(n=n, m=m, k=k,
Time=(t1-t0)[3],
RelErr = sum((Xp-X)^2)/sqt,
Method="ConvexADMM"))
row.names(df) = NULL
df