True or false: The Expectation Maximisation (EM) algorithm in a Gaussian mixture model (GMM) is employed not only to derive the maximum likelihood estimates of the model parameters but also to ascertain the number of clusters that maximise the data likelihood.TrueFalse

What purpose does the Expectation-Maximisation (EM) algorithm serve in the Gaussian Mixture Model (GMM)?Updating the Gaussian parameters to best fit the data.Calculating the probability density function of the data.Initialising the parameters of the Gaussian components.Assigning data points to clusters based on their likelihood.

While running the Expectation-Maximization algorithm in GMM, what is the purpose of the Expectation step? To terminate the algorithm if convergence is reachedTo update the Gaussian parametersTo calculate the probabilities of data points belonging to each clusterTo assign data points to the nearest cluster

Consider an observed random sample of size n, w1, . . . , wn, from a normal distribution N(µ, σ2 ). To the 75 observations in the dataset Data-A1a.csv apply the EM algorithm to fit via maximum likelihood the two-component normal mixture density with common variances, f(w; Ψ) = X 2 i=1 πi φ(w; µi , σ2 ), where φ(w; µ, σ2 ) = (2πσ2 ) −1/2 exp{−1 2 (w − µ) 2 /σ2 } and Ψ = (π1, µ1, µ2, σ2 ) T . To this end, (i) [1/2 mark] Specify the EM framework

What is a primary advantage of using Gaussian mixture models (GMMs) for clustering?They require fewer computational resources compared to other methods.They are simpler to implement than other clustering algorithms.They can model clusters with different shapes and sizes.They always produce spherical clusters.

What is the EM algorithm used to optimize in the "M" step?Select one:a.The latent variablesb.The model parametersc.The prediction accuracy of the modeld.The likelihood of the model