DSE Unsupervised Learning: Clustering 3 — Questions and Answers
Question 1: What does the Calinski-Harabasz Index (Variance Ratio Criterion) measure in clustering evaluation?
- Average distance from points to their centroid
- Ratio of between-cluster dispersion to within-cluster dispersion (Correct answer)
- Number of noise points relative to total points
- Probability of cluster assignment
Correct answer: Ratio of between-cluster dispersion to within-cluster dispersion
Higher Calinski-Harabasz scores indicate dense, well-separated clusters because between-cluster variance far exceeds within-cluster variance.
Question 2: In Gaussian Mixture Models (GMM), what algorithm is used to estimate the model parameters?
- Gradient descent
- Expectation-Maximization (EM) (Correct answer)
- Singular Value Decomposition
- Principal Component Analysis
Correct answer: Expectation-Maximization (EM)
The EM algorithm alternates between assigning soft cluster membership probabilities (E-step) and updating Gaussian parameters (M-step) until convergence.
Question 3: A dendrogram cut at a height of 5 produces 3 clusters, while a cut at height 3 produces 7 clusters. What does this tell you about the data at heights between 3 and 5?
- No merges occur between heights 3 and 5
- Four merges occur between heights 3 and 5 (Correct answer)
- The data has exactly 5 natural clusters
- The linkage criterion changed between cuts
Correct answer: Four merges occur between heights 3 and 5
Going from 7 clusters to 3 requires exactly 4 merge operations, each corresponding to one horizontal line in the dendrogram between those heights.
Question 4: Which parameter in DBSCAN controls the minimum density required for a region to be considered a core region?
- epsilon (ε)
- min_samples (Correct answer)
- bandwidth
- n_clusters
Correct answer: min_samples
min_samples specifies how many points must be within the epsilon radius for a point to qualify as a core point, directly controlling density thresholds.
Question 5: What is 'cluster tendency' and why is it assessed before clustering?
- The tendency of an algorithm to converge quickly
- Whether the data has any meaningful cluster structure (Correct answer)
- The optimal number of clusters in the data
- How well clusters generalize to new data
Correct answer: Whether the data has any meaningful cluster structure
Assessing cluster tendency (e.g., via Hopkins statistic) checks if the data has non-random structure worth clustering before applying any algorithm.
Question 6: In K-Means, what is the objective function being minimized?
- Total between-cluster sum of squares
- Total within-cluster sum of squared distances to centroids (Correct answer)
- Maximum distance between any two points in the same cluster
- Sum of pairwise distances between all cluster centroids
Correct answer: Total within-cluster sum of squared distances to centroids
K-Means minimizes the Within-Cluster Sum of Squares (WCSS), also called inertia, which is the sum of squared Euclidean distances from each point to its assigned centroid.
Question 7: Which of the following scenarios would cause DBSCAN to classify most points as noise?
- Setting epsilon too large
- Setting min_samples too high relative to local density (Correct answer)
- Using Euclidean distance instead of Manhattan distance
- Having perfectly spherical clusters
Correct answer: Setting min_samples too high relative to local density
When min_samples is set too high, most points will fail to meet the density threshold and be labeled as noise, even in genuinely dense regions.
DSE Unsupervised Learning: Clustering 3
What does the Calinski-Harabasz Index (Variance Ratio Criterion) measure in clustering evaluation?