EM algorithm for Spherical Gaussians

Usage

EM_spherical_gaussians(data, k, max.iter = 100, tol = 1e-06)

Arguments

data: n by p matrix, where n is the number of samples and p is the number of features
k: number of clusters
max.iter: maximum iteration of EM
tol: relative change in log-likelihood. If the change is less than tol, then the method terminates early.

Value

a list with elements means, variances, proportions, and log_likelihood for all the respective estimated components of the mixture of Spherical Gaussians

Examples

n <- 500
means <- matrix(c(0, 0, 5, 5), ncol = 2, byrow = TRUE)
covariances <- list(diag(2),
                    diag(2))
proportions <- c(0.5, 0.5)
data <- generate_mixture_gaussians(n, means, covariances, proportions)

# Fit EM algorithm to the generated data
k <- 2 # Number of Gaussian components
em_results <- EM_spherical_gaussians(data, k)
em_results
#> $means
#>          [,1]     [,2]
#> [1,] 5.556755 5.488386
#> [2,] 1.530882 1.444681
#> 
#> $variances
#> [1] 0.5811481 5.5570134
#> 
#> $proportions
#> [1] 0.2305486 0.7694514
#> 
#> $log_likelihood
#> [1] -8.437695e-15
#>