Introduction to Distribution-based Clustering Answers 1. What advantage do models based on probability distributions have over distance-based approaches? A. They always produce better clusters. B. They can handle outliers more effectively. C. They are easier to implement. D. They require less computational power. Answer: They can handle outliers more effectively. (B) Models based on probability distributions can handle outliers more gracefully than distance-based methods. 2. Which of the following represents a disadvantage of distributionbased clustering methods? A. They are insensitive to initialization. B. They are highly accurate. C. They easily determine the number of clusters. D. They can be computationally intensive. Answer: They can be computationally intensive. (D) Estimating parameters for complex probability distributions can be computationally intensive. 3. In the context of Gaussian Mixture Models (GMMs), what does sensitivity to initialization mean? A. They can only be initialized once. B. The results are not affected by starting conditions. C. The outcomes can vary significantly based on initial parameter values. D. They automatically optimize starting conditions. Answer: The outcomes can vary significantly based on initial parameter values. (C) The performance of GMMs can depend significantly on the initial parameter values. 4. Which application is NOT typically associated with distributionbased clustering? A. Anomaly detection. B. Image segmentation. C. Matrix factorization. D. Customer segmentation. Answer: Matrix factorization. (C) Matrix factorization is not a common application for distribution-based clustering methods. 5. Why is determining the number of clusters in GMMs challenging? A. Due to the mathematical complexity of the models. B. Because cluster count is irrelevant to the data. C. Owing to various interpretative methods used. D. Because they always require a fixed number of clusters. Answer: Due to the mathematical complexity of the models. (A) Selecting the appropriate number of clusters in GMMs can be challenging due to the mathematical complexity involved. 6. What distinguishes distribution-based clustering from distancebased clustering methods? A. Distance-based clustering methods rely on statistical tests. B. Distance-based methods can handle non-spherical cluster shapes. C. Distribution-based clustering models clusters with probability distributions. D. Distribution-based clustering incorporates distance metrics. Answer: Distribution-based clustering models clusters with probability distributions. (C) Distribution-based clustering focuses on modeling data points using probability distributions rather than distance measures. 7. Which of the following describes the role of maximum likelihood estimation (MLE) in distribution-based clustering? A. MLE minimizes the variance across clusters. B. MLE determines the distances between data points. C. MLE serves to categorize data points into predetermined clusters. D. MLE maximizes the probability of the observed data for parameter estimation. Answer: MLE maximizes the probability of the observed data for parameter estimation. (D) MLE is utilized in parameter estimation by maximizing the probability of observing the given data. 8. What is one primary advantage of using Gaussian Mixture Models (GMMs) in clustering? A. GMMs require fewer parameters to estimate than other models. B. GMMs simplify computation by avoiding iterative updating processes. C. GMMs can effectively model arbitrary shapes and varying densities. D. GMMs always provide a single spherical cluster output. Answer: GMMs can effectively model arbitrary shapes and varying densities. (C) GMMs are advantageous as they can handle clusters that are non-spherical and have varying densities. 9. During which phase of the Expectation-Maximization (EM) algorithm are the cluster probabilities estimated? A. Iteration B. M-step C. Initialization D. E-step Answer: E-step (D) The E-step is responsible for estimating the probability of each data point belonging to each cluster. 10. What criterion is typically used to determine the convergence of the EM algorithm in GMMs? A. The stability of cluster centroids B. Consistency in the distance of data points from their cluster means C. The uniformity of the distributions within each cluster D. Change in likelihood or other established metrics Answer: Change in likelihood or other established metrics (D) Convergence is often measured by analyzing the change in likelihood or other relevant metrics. 11. How does distribution-based clustering provide insights into cluster characteristics? A. By visualizing clusters in 3D space B. By estimating a probability density function (PDF) for each cluster C. By enforcing rigid shapes on clusters D. By applying traditional distance measures to cluster assignments Answer: By estimating a probability density function (PDF) for each cluster (B) Distribution-based clustering allows for insight by estimating a PDF that describes the distribution of data points within clusters. 12. What is the initial step in the Gaussian Mixture Models algorithm? A. Re-estimating parameters based on clustering results B. Guessing initial parameters such as mean and variance C. Assigning all data points to a single cluster D. Estimating the likelihood of the observed data Answer: Guessing initial parameters such as mean and variance (B) Initialization involves making initial guesses for parameters like the mean and variance of each Gaussian component. 13. Which of the following is NOT a characteristic of distributionbased clustering? A. Handles arbitrary shapes effectively B. Estimates parameters based on the observed data C. Models clusters using probability distributions D. Relies solely on geometric proximity measures Answer: Relies solely on geometric proximity measures (D) Distribution-based clustering does not rely solely on geometric proximity; it is centered around probability models.