In a GMM, what mathematical concept is used to represent the distribution of each cluster? Poisson distributionGaussian distributionUniform distributionExponential distribution

You are tasked with clustering customer data using a Gaussian mixture model (GMM). Which type of clustering does GMM perform?Hierarchical clusteringLinear clusteringSoft clusteringHard clustering

It is proposed to cluster an observed p-dimensional random sample y1, . . . , yn, of size n into g clusters by fitting a mixture model with g multivariate normal components with meanμi and covariance matrix Σi (i = 1, . . . , g) in proportions π1, . . . , πg. In order to reduce the number of parameters in the component-covariance matrices Σi a factor model is to be adopted for the ith-component distribution (i = 1, . . . , g) of Y j (j =1, . . . , n) Specify the component distribution of Y j under the so-called MFA model. Specify the component distribution of Y j under the so-called MCFA model

You are using GMM to cluster a high-dimensional dataset. How is the covariance matrix represented for each cluster?As a diagonal matrixAs a full matrixAs a vectorAs a scalar

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.

Define Poisson distribution. What are its applications.