# Generate Data from Gaussian Mixture Models Generates an $n\times d$ matrix of multivariate normal random vectors with observations (examples) as rows. If $k=1$, all observations belong to the same cluster. If $k>1$ the observations are generated via two-step procedure. First, the cluster membership is drawn from a multinomial distribution, with mixture proportions specified by `pi`. Conditional on cluster membership, the observation is drawn from a multivariate normal distribution, with cluster-specific mean and covariance. The cluster means are provided using `means`, and the cluster covariance matrices are provided using `covs`. If $miss>0$, missingness is introduced, completely at random, by setting that proportion of elements in the data matrix to `NA`. ```r rGMM(n, d = 2, k = 1, pi = NULL, miss = 0, means = NULL, covs = NULL) ``` ## Arguments - `n`: Observations (rows). - `d`: Observation dimension (columns). - `k`: Number of mixture components. Defaults to 1. - `pi`: Mixture proportions. If omitted, components are assumed equiprobable. - `miss`: Proportion of elements missing, $miss\in[0,1)$. - `means`: Either a prototype mean vector, or a list of mean vectors. Defaults to the zero vector. - `covs`: Either a prototype covariance matrix, or a list of covariance matrices. Defaults to the identity matrix. ## Returns Numeric matrix with observations as rows. Row numbers specify the true cluster assignments. ## Examples ```r set.seed(100) # Single component without missingness. # Bivariate normal observations. cov <- matrix(c(1, 0.5, 0.5, 1), nrow = 2) data <- rGMM(n = 1e3, d = 2, k = 1, means = c(2, 2), covs = cov) # Single component with missingness. # Trivariate normal observations. mean_list <- list(c(-2, -2, -2), c(2, 2, 2)) cov <- matrix(c(1, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 1), nrow = 3) data <- rGMM(n = 1e3, d = 3, k = 2, means = mean_list, covs = cov) # Two components without missingness. # Trivariate normal observations. mean_list <- list(c(-2, -2, -2), c(2, 2, 2)) cov <- matrix(c(1, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 1), nrow = 3) data <- rGMM(n = 1e3, d = 3, k = 2, means = mean_list, covs = cov) # Four components with missingness. # Bivariate normal observations. mean_list <- list(c(2, 2), c(2, -2), c(-2, 2), c(-2, -2)) cov <- 0.5 * diag(2) data <- rGMM( n = 1000, d = 2, k = 4, pi = c(0.35, 0.15, 0.15, 0.35), miss = 0.1, means = mean_list, covs = cov) ``` ## See Also For estimation, see `FitGMM`.

rGMM function