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.
Question
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.
Solution
The Expectation-Maximization (EM) algorithm serves several purposes in the Gaussian Mixture Model (GMM):
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Initialising the parameters of the Gaussian components: The EM algorithm starts with an initial guess for the parameters (mean and covariance matrices) of the Gaussian components. These parameters can be randomly initialized or based on some heuristic.
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Assigning data points to clusters based on their likelihood: In the Expectation step (E-step), the EM algorithm calculates the posterior probabilities for each data point to belong to each cluster. This is done using the current parameters of the Gaussian components. The data points are then assigned to the cluster that they have the highest probability of belonging to.
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Updating the Gaussian parameters to best fit the data: In the Maximization step (M-step), the EM algorithm updates the parameters of the Gaussian components to maximize the likelihood of the observed data given these parameters. This is done using the cluster assignments from the E-step.
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Calculating the probability density function of the data: The EM algorithm uses the updated parameters of the Gaussian components to calculate the probability density function of the data. This is used to evaluate the quality of the clustering and to decide when to stop the algorithm.
So, the EM algorithm serves to initialize the parameters, assign data points to clusters, update the parameters to best fit the data, and calculate the probability density function of the data in the context of the Gaussian Mixture Model.
Similar Questions
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
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
What is the main goal of the EM algorithm?Select one:a.To maximize the prediction accuracy of the modelb.To minimize the cost or loss function of a modelc.To minimize the error between the predicted and actual values of the datad.To maximize the likelihood of a model given the data
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
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.
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