# Cluster the Columns of X into K Clusters by Giving a Weighted Cluster Membership while shrinking Weights Towards Each Other. This function will output K channels of variables. ```r pwncut(X, K = 2, B = 3000, L = 1000, scale = TRUE, lambda = 1, epsilon = 0, nstarts = 3, start = "default", dist = "gaussian", sigma = 0.1, beta = 1) ``` ## Arguments - `X`: is a n x p matrix of p variables and n observations. - `K`: is the number of clusters. - `B`: is the number of iterations in the simulated annealing algorithm. - `L`: is the temperature coefficient in the simulated annealing algorithm. - `scale`: equals TRUE if data X is to be scaled with mean 0 and variance 1. - `lambda`: the tuning parameter of the penalty. Larger values shrink the weighted cluster membership closer together (default = 1). - `epsilon`: values in the similarity matrix less than epsilon are set to 0 (default = 0). - `nstarts`: the number of starting values also corresponding how many times simulated annealing is run. Larger values provide better results but takes longer. - `start`: if it equals 'default' then the starting value for all weights is 1/K. If 'random' then weights are sampled from a uniform distribution and then scaled to sum 1 per variable. - `dist`: specifies the distance metric used for constructing the similarity matrix. Options are 'gaussian', 'correlation' and 'euclidean' (default = 'gaussian'). - `sigma`: is the bandwidth parameter when the dist metric chosen is 'gaussian' (default = 0.1). - `beta`: when dist='correlation', beta is the exponent applied to each entry of the similarity matrix. ## Details The algorithm minimizes a modified version of NCut through simulated annealing. The clusters correspond to partitions that minimize this objective function. ## Examples ```r # This sets up the initial parameters for the simulation. n <- 100 # Sample size p <- 100 # Number of columns of Y. K <- 3 C0 <- matrix(0,p,K) C0[1:25,1] <- matrix(1,25,1) C0[26:75,1:3] <- matrix(1/3,50,3) C0[76:100,3] <- matrix(1,25,1) A0 <- C0[ ,1]%*%t(C0[ ,1]) + C0[ ,2]%*%t(C0[ ,2]) + C0[ ,3]%*%t(C0[ ,3]) A0 <- A0 - diag(diag(A0)) + diag(p) Z1 <- rnorm(n,0,2) Z2 <- rnorm(n,0,2) Z3 <- rnorm(n,0,2) Y <- matrix(0,n,p) Y[ ,1:25] <- matrix(rnorm(n*25, 0, 2), n, 25) + matrix(Z1, n, 25, byrow=FALSE) Y[ ,26:75] <- matrix(rnorm(n*50, 0, 2), n, 50) + matrix(Z1, n, 50, byrow=FALSE) + matrix(Z2, n, 50, byrow=FALSE) + matrix(Z3, n, 50, byrow=FALSE) Y[ ,76:100] <- matrix(rnorm(n*25, 0, 2), n, 25) + matrix(Z3, n, 25, byrow=FALSE) trial <- pwncut(Y, K = 3, B = 10000, L = 1000, lambda = 1.5, start = 'default', scale = TRUE, nstarts = 1, epsilon = 0, dist = 'correlation', sigma = 10) A1 <- trial[[2]][ ,1]%*%t(trial[[2]][ ,1]) + trial[[2]][ ,2]%*%t(trial[[2]][ ,2]) + trial[[2]][ ,3]%*%t(trial[[2]][ ,3]) A1 <- A1 - diag(diag(A1)) + diag(p) plot(trial[[1]], type='l') errorL <- sum(abs(A0-A1))/p^2 errorL ``` ## References Sebastian J. Teran Hidalgo, Mengyun Wu and Shuangge Ma. Penalized and weighted clustering of gene expression data using PWNCut. (Submitted.)

pwncut function