A GMM assumes that the data is generated from a mixture of several Gaussian distributions with unknown parameters. These parameters include the mean, variance, and the weight of each Gaussian component. The Expectation-Maximization (EM) algorithm is commonly used to estimate these parameters. The steps involved are:
1. Initialization: Guess initial parameters for the means, variances, and weights. 2. Expectation Step (E-step): Calculate the probability that each data point belongs to each Gaussian component. 3. Maximization Step (M-step): Update the parameters based on the probabilities calculated in the E-step. 4. Convergence: Repeat the E-step and M-step until the parameters converge.
