NCutYX (version 0.1.0)

mlbncut: The MLBNCut Clusters the Columns and the Rows Simultaneously of Data from 3 Different Sources.

Description

It clusters the columns of Z,Y and X into K clusters and the samples into R clusters by representing each data type as one network layer. It represents the Z layer depending on Y, and the Y layer depending on X.

Usage

mlbncut(Z, Y, X, K = 2, R = 2, B = 30, N = 500, q0 = 0.25,
  scale = TRUE, dist = "gaussian", sigmas = 1, sigmac = 1)

Arguments

Z

is a n x q matrix of q variables and n observations.

Y

is a n x p matrix of p variables and n observations.

X

is a n x r matrix of r variables and n observations.

K

is the number of column clusters.

R

is the number of row clusters.

B

is the number of iterations.

N

is the number of samples per iterations.

q0

is the quantiles in the cross entropy method.

scale

equals TRUE if data Y is to be scaled with mean 0 and variance 1.

dist

is the type of distance measure use in the similarity matrix. Options are 'gaussian' and 'correlation', with 'gaussian' being the default.

sigmas

is the tuning parameter of the Gaussian kernel of the samples.

sigmac

is the tuning parameter of the Gaussian kernel of the variables.

Value

A list with the final value of the objective function and the clusters.

Details

This function will output K clusters of columns of Z, Y and X and R clusters of the samples.

The algorithm minimizes the NCut through the cross entropy method. The clusters correspond to partitions that minimize this objective function.

References

Sebastian J. Teran Hidalgo and Shuangge Ma. Multilayer Biclustering of Omics Data using MLBNCut. (Work in progress.)

Examples

# NOT RUN {
#This sets up the initial parameters for the simulation.
library(NCutYX)
library(MASS)
library(fields)

n   <- 50
p   <- 50
h   <- 0.15
rho <- 0.15
mu  <- 1

W0 <- matrix(1,p,p)
W0[1:(p/5),1:(p/5)] <- 0
W0[(p/5+1):(3*p/5),(p/5+1):(3*p/5)] <- 0
W0[(3*p/5+1):(4*p/5),(3*p/5+1):(4*p/5)] <- 0
W0[(4*p/5+1):p,(4*p/5+1):p]=0
W0=cbind(W0,W0,W0)
W0=rbind(W0,W0,W0)

W1 <- matrix(1,n,n)
W1[1:(n/2),1:(n/2)] <- 0
W1[(n/2+1):n,(n/2+1):n] <- 0

X <- matrix(0,n,p)
Y <- matrix(0,n,p)
Z <- matrix(0,n,p)

Sigma=matrix(0,p,p)
Sigma[1:(p/5),1:(p/5)] <- rho
Sigma[(p/5+1):(3*p/5),(p/5+1):(3*p/5)] <- rho
Sigma[(3*p/5+1):(4*p/5),(3*p/5+1):(4*p/5)] <- rho
Sigma[(4*p/5+1):p,(4*p/5+1):p] <- rho
Sigma <- Sigma - diag(diag(Sigma))
Sigma <- Sigma + diag(p)

X[1:(n/2),]   <- mvrnorm(n/2,rep(mu,p),Sigma)
X[(n/2+1):n,] <- mvrnorm(n/2,rep(-mu,p),Sigma)

B11 <- matrix(0,p,p)
B12 <- matrix(0,p,p)
B21 <- matrix(0,p,p)
B22 <- matrix(0,p,p)

B11[1:(p/5),1:(p/5)]                     <- runif((p/5)^2,h/2,h)*rbinom((p/5)^2,1,0.5)
B11[(p/5+1):(3*p/5),(p/5+1):(3*p/5)]     <- runif((2*p/5)^2,h/2,h)*rbinom((2*p/5)^2,1,0.5)
B11[(3*p/5+1):(4*p/5),(3*p/5+1):(4*p/5)] <- runif((p/5)^2,h/2,h)*rbinom((p/5)^2,1,0.5)
B11[(4*p/5+1):p,(4*p/5+1):p]             <- runif((1*p/5)^2,h/2,h)*rbinom((1*p/5)^2,1,0.5)

B12[1:(p/5),1:(p/5)]                     <- runif((p/5)^2,-h,-h/2)*rbinom((p/5)^2,1,0.5)
B12[(p/5+1):(3*p/5),(p/5+1):(3*p/5)]     <- runif((2*p/5)^2,-h,-h/2)*rbinom((2*p/5)^2,1,0.5)
B12[(3*p/5+1):(4*p/5),(3*p/5+1):(4*p/5)] <- runif((p/5)^2,-h,-h/2)*rbinom((p/5)^2,1,0.5)
B12[(4*p/5+1):p,(4*p/5+1):p]             <- runif((1*p/5)^2,-h,-h/2)*rbinom((1*p/5)^2,1,0.5)

B21[1:(p/5),1:(p/5)]                     <- runif((p/5)^2,h/2,h)*rbinom((p/5)^2,1,0.5)
B21[(p/5+1):(3*p/5),(p/5+1):(3*p/5)]     <- runif((2*p/5)^2,h/2,h)*rbinom((2*p/5)^2,1,0.5)
B21[(3*p/5+1):(4*p/5),(3*p/5+1):(4*p/5)] <- runif((p/5)^2,h/2,h)*rbinom((p/5)^2,1,0.5)
B21[(4*p/5+1):p,(4*p/5+1):p]             <- runif((1*p/5)^2,h/2,h)*rbinom((1*p/5)^2,1,0.5)

B22[1:(p/5),1:(p/5)]                     <- runif((p/5)^2,-h,-h/2)*rbinom((p/5)^2,1,0.5)
B22[(p/5+1):(3*p/5),(p/5+1):(3*p/5)]     <- runif((2*p/5)^2,-h,-h/2)*rbinom((2*p/5)^2,1,0.5)
B22[(3*p/5+1):(4*p/5),(3*p/5+1):(4*p/5)] <- runif((p/5)^2,-h,-h/2)*rbinom((p/5)^2,1,0.5)
B22[(4*p/5+1):p,(4*p/5+1):p]             <- runif((1*p/5)^2,-h,-h/2)*rbinom((1*p/5)^2,1,0.5)

Y[1:(n/2),]   <- X[1:(n/2),]%*%B11+matrix(rnorm((n/2)*p,0,0.25),n/2,p)
Y[(n/2+1):n,] <- X[(n/2+1):n,]%*%B12+matrix(rnorm((n/2)*p,0,0.25),n/2,p)

Z[1:(n/2),]   <- Y[1:(n/2),]%*%B21+matrix(rnorm((n/2)*p,0,0.25),n/2,p)
Z[(n/2+1):n,] <- Y[(n/2+1):n,]%*%B22+matrix(rnorm((n/2)*p,0,0.25),n/2,p)

trial <- mlbncut(Z,
                 Y,
                 X,
                 K=4,
                 R=2,
                 B=10,
                 N=50,
                 dist='correlation',
                 q0=0.15,
                 scale=TRUE,
                 sigmas=0.05,
                 sigmac=1)

plot(trial[[1]],type='l')
image.plot(trial[[2]])
image.plot(trial[[3]])

errorK <- sum((trial[[3]][,1]%*%t(trial[[3]][,1]) +
                 trial[[3]][,2]%*%t(trial[[3]][,2]) +
                 trial[[3]][,3]%*%t(trial[[3]][,3]) +
                 trial[[3]][,4]%*%t(trial[[3]][,4]))*W0)/(3*p)^2 +
            sum((trial[[2]][,1]%*%t(trial[[2]][,1]) +
                 trial[[2]][,2]%*%t(trial[[2]][,2]))*W1)/(n)^2
errorK
# }