Introduction to Cluster Hierarchy Dendrograms Answers 1. What is a limitation of using dendrograms for data representation? A. They are difficult to interpret with large datasets. B. They always provide complete information about individual clusters. C. Interpreting the dendrogram can be straightforward and objective. D. They require complex software to generate. Answer: They are difficult to interpret with large datasets. (A) Dendrograms can become difficult to interpret with large datasets. 2. In which application are cluster hierarchy dendrograms commonly utilized? A. Creating user interfaces for software B. Analyzing genomic sequences only C. Conducting simple arithmetic operations D. Grouping customers based on purchasing patterns Answer: Grouping customers based on purchasing patterns (D) Market research often uses dendrograms to group customers based on their purchasing patterns. 3. What does the choice of linkage method affect in the creation of a dendrogram? A. The outcome and interpretation of the dendrogram B. The number of clusters that can be formed C. The aesthetic appearance of the dendrogram D. The complexity of the algorithm used Answer: The outcome and interpretation of the dendrogram (A) The choice of linkage method can significantly impact the outcome and interpretation of a dendrogram. 4. Which of the following is NOT a typical application of dendrograms? A. Classifying pixels in image segmentation B. Hierarchical data sorting C. Analyzing protein structures D. Compiling financial reports Answer: Compiling financial reports (D) Compiling financial reports is not a typical application of dendrograms. 5. What is a common challenge when working with dendrograms? A. Their representation can be subjective. B. Finding the optimal number of clusters is not usually complex. C. They are easy to interpret for all users. D. They provide no hierarchical information. Answer: Their representation can be subjective. (A) Interpreting the dendrogram can be subjective, presenting a challenge for users. 6. What does a dendrogram diagrammatically represent? A. The hierarchical relationship between objects or data points B. The linear relationship between data points C. The circular relationship of clusters D. The average distance between all data points Answer: The hierarchical relationship between objects or data points (A) A dendrogram illustrates how clusters are nested within each other in a hierarchical manner. 7. Which clustering method initiates with each data point as a separate cluster? A. Agglomerative Hierarchical Clustering B. K-means Clustering C. Subset Clustering D. Divisive Hierarchical Clustering Answer: Agglomerative Hierarchical Clustering (A) Agglomerative Hierarchical Clustering starts with individual data points as separate clusters. 8. What type of linkage method is characterized by using the shortest distance between data points? A. Single Linkage B. Average Linkage C. Complete Linkage D. Hierarchical Linkage Answer: Single Linkage (A) Single Linkage defines the distance between clusters as the shortest distance between any two data points from different clusters. 9. What does a higher branch height in a dendrogram indicate? A. A stronger connection between clusters B. A greater distance at which clusters were merged C. A lower similarity between clusters D. A more defined cluster separation Answer: A greater distance at which clusters were merged (B) In a dendrogram, higher branches signify that the clusters were merged at a greater distance. 10. Which of the following methods results in wider, potentially lessdefined clusters? A. Single Linkage B. Complete Linkage C. Hierarchical Linkage D. Average Linkage Answer: Complete Linkage (B) Complete Linkage may lead to broader clusters as it considers the longest distance between data points in clusters. 11. When using average linkage, what is measured to determine the distance between two clusters? A. The distance to the centroid of clusters B. The minimum distance between the nearest points C. The average distance between all pairs of points D. The maximum distance between the furthest points Answer: The average distance between all pairs of points (C) Average Linkage uses the average of distances between all paired data points from two clusters. 12. What is a key characteristic of divisive hierarchical clustering? A. It progressively merges clusters to form one B. It uses only two clusters as a basis for further divisions C. It begins with all data points in separate clusters D. It starts with one total cluster and divides recursively Answer: It starts with one total cluster and divides recursively (D) Divisive Hierarchical Clustering starts with all data points in a single cluster and recursively divides them. 13. What is the primary focus of the horizontal dendrogram representation? A. It emphasizes the angle of cluster similarities B. It highlights the vertical height of clusters only C. It shows the three-dimensional distribution of data points D. It visualizes the tree-like structure of data relationships Answer: It visualizes the tree-like structure of data relationships (D) Horizontal dendrograms are used to visualize the hierarchical, tree-like relationships among data points.