# The MLBNCut Clusters the Columns and the Rows Simultaneously of Data from 3 Different Sources. 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. ```r 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. ## Returns 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. ## Examples ```r #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 ``` ## References Sebastian J. Teran Hidalgo and Shuangge Ma. Multilayer Biclustering of Omics Data using MLBNCut. (Work in progress.)

mlbncut function