# Model-Based Clustering using a Mixture of SAL Distributions Performs model-based clustering using a mixture of SAL distributions. The expectation-maximization (EM) algorithm is used for parameter estimation, the Aitken's acceleration criterion is used to determine convergence, both the BIC and ICL values are given for the considered mixtures. ```r msal(x, G, start = 1, max.it = 10000, eps = 0.01, print.it = F, print.warn = F, print.prmtrs = F) ``` ## Arguments - `x`: A n by p matrix where each row corresponds a p-dimensional observation. - `G`: The desired number of mixture components. - `start`: Specifies how to intialize the zig matrix. If start equals 1, k-means clustering is used. If start equals 2, a random start is used. If start is a vector of length n, then the zig matrix is constructed based from this vector. - `max.it`: The desired number of iterations for the EM algorithm. - `eps`: The desired difference between the asymptotic estimate of the log-likelihood and the current log-likelihood value. - `print.it`: If True, the iteration number of the EM algorithm is printed. - `print.warn`: If True, the observation number that the mean vector is closet too is given. - `print.prmtrs`: If True, the parameter set is printed on each iteration of the EM algorithm. ## Details The mixture of SAL distributions are fitted using an EM algorithm with a ``Set-Back'' procedure to deal with the issue of Infinite Log-Likelihood Values that arise when updating the mean vector (see Section 3.4.2 of Franczak et.al (2014) for details). ## Returns The msal function outputs a list with the following components: - **loglik**: A vector giving the log-likelihood values from each iteration of the considered EM algorithm. - **alpha**: A matrix where each row specifies the direction of skewness in each variable for each mixture component. - **sig**: An array where each matrix specifies the covariance matrix for each mixture component. - **mu**: A matrix where each row gives the mean vector for each mixture component. - **pi.g**: A vector specifying the mixing components. - **bic**: An integer giving the Bayesian Information Criterion (BIC) for the fitted model. - **icl**: An integer giving the Integrated Completed Likelihood (ICL) for the fitted model. - **cluster**: A vector of length n giving the group label for each observation in the considered data set. ## References Franczak et. al (2014). Mixtures of Shifted Asymmetric Laplace Distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 38(6), 1149-1157. ## Author(s) Brian C. Franczak [aut, cre], Ryan P. Browne [aut, ctb], Paul D. McNicholas [aut, ctb] Maintainer: Brian C. Franczak ## Examples ```r ## Clustering Simulated Data alpha <- matrix(c(2,2,1,2),2,2) sig <- array(NA,dim=c(2,2,2)) sig[,,1] <- diag(2) sig[,,2] <- matrix(c(1,0.5,0.5,1),2,2) mu <- matrix(c(0,0,-2,5),2,2) pi.g <- rep(1/2,2) x <- rmsal(n=500,p=2,alpha=alpha,sig=sig,mu=mu,pi.g=pi.g) msal.ex1 <- msal(x=x[,-1],G=2) table(x[,1],msal.ex1$cluster) ## Clustering the Old Faithful Geyser Data data(faithful) msal.ex2 <- msal(x=faithful,G=2) plot(x=faithful,col=msal.ex2$cluster) ## Clustering the Yeast Data data(yeast) msal.ex3 <- msal(x=yeast[,-1],G=2) table(yeast[,1],msal.ex3$cluster) ```