Introduction to Density-Based Clustering Answers 1. What best defines a core point in density-based clustering? A. A data point that forms a cluster on its own B. A data point that can only be reached via a border point C. A data point with at least a minimum number of points within a given radius D. A data point that is always at the center of a cluster Answer: A data point with at least a minimum number of points within a given radius (C) A core point is defined as a data point that has at least a specified number of other points nearby within a certain distance. 2. What is the primary advantage of density-based clustering over methods like k-means? A. It requires a predetermined number of clusters B. It always produces compact clusters with no noise C. It can only discover spherical clusters D. It automatically determines the number of clusters present in the data Answer: It automatically determines the number of clusters present in the data (D) Density-based clustering methods, such as DBSCAN, can discover the number of clusters automatically, unlike k-means which requires this to be specified. 3. How does DBSCAN handle noise points in the clustering process? A. Noise points are treated as border points B. Noise points are added to the nearest core point cluster C. Noise points are considered as core points in sparse regions D. Noise points are always excluded from any cluster Answer: Noise points are always excluded from any cluster (D) In DBSCAN, noise points are identified as points that are not core or border points, thus they are excluded from clusters. 4. In the context of density-based clustering, what does the ε parameter represent? A. The threshold for determining core points B. The number of dimensions in the dataset C. The maximum distance at which points can be connected D. The minimum number of points needed for a cluster Answer: The maximum distance at which points can be connected (C) The ε parameter defines the radius for the neighborhood around points, which is crucial for determining connections between them. 5. Which scenario represents a common issue when setting a too small ε parameter? A. Excessive number of clusters are discovered B. Identification of too many noisy points C. Clusters merge into one large cluster D. Points within a cluster are not connected Answer: Points within a cluster are not connected (D) When ε is set too small, points close together may not be deemed connected, preventing the identification of real clusters. 6. Which statement about border points is correct? A. They exclusively connect to other border points B. They cannot be part of any cluster C. They lie outside of every core point's ε-neighborhood D. They are not core points but are within the ε-neighborhood of a core point Answer: They are not core points but are within the ε-neighborhood of a core point (D) Border points are defined as those that lie within the neighborhood of a core point but do not meet the criteria to be a core point themselves. 7. What characterizes the clusters discovered using density-based methods? A. They can be of arbitrary shapes and sizes B. They require a predefined structure C. They are always of the same size and shape D. They can only be analyzed in two dimensions Answer: They can be of arbitrary shapes and sizes (A) Density-based clustering methods excel in identifying clusters of varying forms and sizes, unlike some traditional methods. 8. What role does the parameter minPts play in density-based clustering? A. It defines the minimum number of points required to identify a core point B. It sets the maximum allowable distance between core and border points C. It sets the maximum number of clusters allowed D. It controls the overall distance calculation Answer: It defines the minimum number of points required to identify a core point (A) MinPts determines the threshold number of points necessary for a data point to be considered a core point, influencing cluster formation.