Introduction to Spectral Clustering Answers 1. What is a crucial factor in determining the number of clusters, k, in a clustering algorithm? A. Uniformity of the dataset values B. The number of dimensions in the dataset C. The average distance between data points D. External or domain-specific knowledge Answer: External or domain-specific knowledge (D) The selection of 'k' often requires guidance from external or domain-specific knowledge. 2. Which of the following is a disadvantage of spectral clustering? A. It requires no experimentation with similarity measures B. It may be computationally expensive for large datasets C. It can handle non-convex clusters poorly D. It produces poor results in all cases Answer: It may be computationally expensive for large datasets (B) Spectral clustering can be computationally demanding, particularly for very large datasets. 3. Which statement about the advantages of spectral clustering is true? A. It only supports one type of similarity measure B. It produces results that are always superior to k-means C. It can only cluster convex shapes D. It can effectively handle non-convex clusters Answer: It can effectively handle non-convex clusters (D) One of the benefits of spectral clustering is its ability to handle non-convex clusters effectively. 4. What is one challenge associated with selecting similarity measures in spectral clustering? A. All similarity measures yield similar outcomes B. It leads to perfect cluster separation C. It is straightforward with no required experimentation D. The choice can affect performance significantly Answer: The choice can affect performance significantly (D) The quality of the chosen similarity measures can significantly impact the performance of the spectral clustering algorithm. 5. In k-means clustering, what is a key step taken to improve the clustering process? A. Using a fixed value of k without consideration B. Increasing the number of dimensions C. Reducing the dimensionality of the data D. Employing only one clustering technique Answer: Reducing the dimensionality of the data (C) The clustering process in k-means often relies on techniques that reduce the dimensionality of the dataset. 6. What type of machine learning technique is spectral clustering? A. Unsupervised B. Supervised C. Reinforcement D. Semi-supervised Answer: Unsupervised (A) Spectral clustering is an unsupervised technique that does not rely on prelabeled data. 7. In spectral clustering, the similarity between data points is typically measured using which of the following? A. Mean Squared Error B. Euclidean Distance C. Distance metrics D. Kernel functions Answer: Kernel functions (D) Kernel functions, such as Gaussian kernel, are used to measure similarity in the graph. 8. What does a larger value in the similarity matrix indicate about two data points? A. They are likely closer together. B. They are part of different clusters. C. They correspond to different nodes. D. They have a higher variance. Answer: They are likely closer together. (A) A larger value in the similarity matrix signifies that points are closer and more likely to be in the same cluster. 9. Which matrix is computed to represent the connectivity in the similarity graph? A. Laplacian Matrix B. Eigenvalue Matrix C. Similarity Matrix D. Kernel Matrix Answer: Laplacian Matrix (C) The Laplacian matrix captures the connectivity among nodes in the graph based on the similarity matrix. 10. Which eigenvalues are primarily useful for determining cluster separation in spectral clustering? A. Random eigenvalues B. Higher eigenvalues C. Medium eigenvalues D. Small eigenvalues Answer: Higher eigenvalues (B) Eigenvectors associated with higher eigenvalues are more relevant for capturing local structure and cluster separation. 11. What is the role of the extracted eigenvectors in the spectral clustering algorithm? A. They provide a lower-dimensional representation of the data. B. They increase the dimensionality of the data. C. They cluster the original data points directly. D. They enhance the graphical representation of similarity. Answer: They provide a lower-dimensional representation of the data. (A) The extracted eigenvectors form a lower-dimensional representation that captures the intrinsic structure of the data. 12. What typically follows the extraction of eigenvectors in the spectral clustering process? A. Constructing additional similarity graphs B. Random sampling of data points C. Normalization of the similarity matrix D. Clustering the eigenvectors into groups Answer: Clustering the eigenvectors into groups (D) The extracted eigenvectors are clustered into groups, forming a partition of the dataset. 13. Which of the following statements best describes the advantage of spectral clustering over traditional methods like k-means? A. Improved quality for complex geometries. B. Higher accuracy for linearly separable data. C. Better performance on large datasets. D. Lower computational complexity. Answer: Improved quality for complex geometries. (A) Spectral clustering is particularly useful for complex, non-linearly separable data, producing better quality clusters.