Introduction to Centroid-based Clustering Answers 1. What is the primary metric used in K-means clustering to determine cluster assignments? A. Cosine similarity B. Hamming distance C. Manhattan distance D. Euclidean distance Answer: Euclidean distance (D) K-means clustering uses Euclidean distance to assign data points to the nearest centroid. 2. Which of the following is a primary strength of the K-means algorithm? A. Relatively simple implementation B. Works well with small datasets C. Automatically determines the number of clusters D. Handles missing data effectively Answer: Relatively simple implementation (A) K-means is known for its relatively simple implementation and computational efficiency. 3. What is a common challenge when using K-means clustering? A. It requires far less data than K-medoids. B. It is not sensitive to initial centroid placement. C. It can handle non-spherical clusters effectively. D. It can produce different results based on initial centroid positions. Answer: It can produce different results based on initial centroid positions. (D) K-means is sensitive to initial centroid placement, which can affect clustering results. 4. In K-medoids clustering, what represents the centroid of a cluster? A. The average of all points in the cluster B. The point with the smallest sum of distances to other points C. The closest point to all other points in the cluster D. The point farthest from the cluster mean Answer: The point with the smallest sum of distances to other points (B) The medoid is defined as the data point within a cluster with the smallest sum of distances to all other points in that cluster. 5. Which of these methods is NOT typically used to determine the optimal number of clusters (k)? A. K-nearest neighbors B. Silhouette score C. Elbow method D. Gap statistic Answer: K-nearest neighbors (A) K-nearest neighbors is not used for finding the optimal number of clusters, while the other methods are. 6. What is a significant advantage of K-medoids over K-means? A. It can automatically select the number of clusters B. It is robust to outliers C. It is always faster for large datasets D. It requires fewer data points Answer: It is robust to outliers (B) K-medoids is recognized for its robustness against outliers, making it more suitable in certain conditions than K-means. 7. Which statement about the K-means algorithm is true? A. It assumes all clusters are of equal variance. B. It does not require users to specify the number of clusters beforehand. C. It can perform well on large datasets. D. It is not sensitive to noise and outliers in the data. Answer: It assumes all clusters are of equal variance. (A) K-means performs well on large datasets and assumes that clusters are roughly spherical and of equal variance. 8. Which of the following best describes a limitation of K-means clustering? A. It is dependent on the initial placement of centroids. B. It can easily handle large datasets without any computational cost. C. It provides a probabilistic output for cluster assignment. D. It requires no prior knowledge of the data structure. Answer: It is dependent on the initial placement of centroids. (A) K-means clustering's effectiveness can be significantly affected by the initial placement of centroids.