how to do expectation-maximization in r in r

The Expectation-Maximization (EM) algorithm is a statistical method used to find maximum likelihood estimates of the parameters of a probabilistic model in the presence of latent variables. It is widely used for clustering analysis and mixture models.

The Mclust package in R provides several functions for fitting mixture models with EM. In order to use EM for clustering, we need to first define the appropriate probabilistic model for the data. Here is an example of how to perform EM clustering using the Mclust package in R:

main.r
# Load the Mclust library
library(Mclust)

# Generate some data
set.seed(123)
x <- rbind(matrix(rnorm(100, mean = 0), ncol = 2),
           matrix(rnorm(100, mean = 4), ncol = 2))

# Fit a mixture model using EM
fit <- Mclust(x, G = 2)

# Plot the results
plot(fit, what = "classification")
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Here, we generate some two-dimensional data with two distinct groups. We then use the Mclust function to fit a mixture model with two components using EM. Finally, we plot the classification results to show which data points are assigned to each component.

Note that the Mclust function automatically selects the number of components using a Bayesian Information Criterion (BIC) criterion. However, it is also possible to specify the number of components using the G parameter.