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Unit 3: Clustering Metrics - Practice Quiz

INT423 — Machine Learning-Ii 50 Questions
0 Correct 0 Wrong 50 Left
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1 What is the range of the Silhouette Coefficient?

A. 0 to infinity
B. -1 to 1
C. -infinity to 1
D. 0 to 1

2 In the context of the Silhouette Score, what does a value near 0 indicate?

A. The clusters are overlapping
B. The sample is far from other clusters
C. The clustering is perfect
D. The sample is assigned to the wrong cluster

3 Which of the following clustering metrics is an 'Internal' evaluation metric (does not require ground truth labels)?

A. Homogeneity Score
B. Adjusted Rand Index
C. V-measure
D. Davies-Bouldin Index

4 For the Davies-Bouldin Index, which of the following represents a better clustering result?

A. A value close to 1
B. A lower value
C. A value close to -1
D. A higher value

5 How is the Dunn Index calculated?

A. Ratio of minimum inter-cluster distance to maximum intra-cluster diameter
B. Average distance between all points
C. Ratio of maximum inter-cluster distance to minimum intra-cluster distance
D. Sum of squared errors

6 The Adjusted Rand Index (ARI) corrects the Rand Index for:

A. Data dimensionality
B. Number of clusters
C. Outliers
D. Chance

7 What is the maximum possible value for the Adjusted Rand Index (ARI)?

A. 1
B. 100
C. Infinity
D. 0

8 Which metric is calculated as the harmonic mean of Homogeneity and Completeness?

A. Silhouette Score
B. F-measure
C. Adjusted Mutual Information
D. V-measure

9 A clustering result satisfies 'Homogeneity' if:

A. The clusters are spherical
B. All members of a given class are assigned to the same cluster
C. The number of clusters equals the number of classes
D. Each cluster contains only members of a single class

10 A clustering result satisfies 'Completeness' if:

A. The entropy of the clusters is zero
B. All members of a given class are assigned to the same cluster
C. Each cluster contains only members of a single class
D. The clusters are well separated

11 Normalized Mutual Information (NMI) is a normalization of the Mutual Information (MI) score to scale the results between:

A. -infinity and infinity
B. 0 and 1
C. -1 and 1
D. 0 and infinity

12 Which metric is the geometric mean of the pairwise precision and recall?

A. Fowlkes-Mallows Index
B. Dunn Index
C. Adjusted Mutual Information
D. V-measure

13 What is the primary advantage of Adjusted Mutual Information (AMI) over Normalized Mutual Information (NMI)?

A. It does not require ground truth
B. It accounts for chance, especially in small samples or large cluster numbers
C. It works better with non-convex clusters
D. It is faster to compute

14 In the Silhouette Score formula , what does 'a' represent?

A. The total number of clusters
B. The variance of the entire dataset
C. The mean distance between a sample and all points in the nearest neighboring cluster
D. The mean distance between a sample and all other points in the same cluster

15 Which of the following metrics requires the knowledge of ground truth labels?

A. Adjusted Rand Index
B. Calinski-Harabasz Index
C. Dunn Index
D. Silhouette Score

16 If the Adjusted Rand Index (ARI) is 0.0, what does this imply?

A. Random labeling
B. Inverse clustering
C. Clustering with 100% error
D. Perfect clustering

17 Which index is most sensitive to noise and outliers because it relies on minimum inter-cluster distances and maximum diameters?

A. V-measure
B. Fowlkes-Mallows Index
C. Silhouette Score
D. Dunn Index

18 The Fowlkes-Mallows Index (FMI) ranges from:

A. 0 to 10
B. -1 to 1
C. 0 to 1
D. -infinity to 0

19 If a clustering algorithm produces a Homogeneity score of 1.0 but a Completeness score of 0.5, what does this likely mean?

A. There is only one cluster
B. Classes are mixed but clusters are large
C. Clusters are pure but classes are split into multiple clusters
D. The algorithm failed completely

20 In the Davies-Bouldin Index calculation, the term represents:

A. The product of cluster sizes
B. The distance to the nearest neighbor
C. The absolute difference in cluster densities
D. The ratio of the sum of cluster dispersions to the distance between cluster centroids

21 When is the Mutual Information (MI) between two clusterings equal to 0?

A. When the two clusterings are independent
B. When the clusterings are identical
C. When the number of clusters is equal
D. When the clusterings are perfectly correlated

22 Which of the following statements about V-measure is FALSE?

A. It is equivalent to Normalized Mutual Information (arithmetic version).
B. It requires ground truth labels.
C. It is symmetric.
D. It ranges from -1 to 1.

23 Which metric is generally preferred when you want to compare clustering solutions with different numbers of clusters on the same dataset, to avoid favoring solutions with more clusters?

A. Purity
B. Sum of Squared Errors
C. Adjusted Mutual Information (AMI)
D. Raw Mutual Information (MI)

24 A Silhouette Score of -1 implies that:

A. The sample is in the correct cluster
B. The sample is a centroid
C. The sample is an outlier
D. The sample is in the wrong cluster

25 Which metric is defined using concepts of entropy and conditional entropy?

A. Silhouette Score
B. Normalized Mutual Information
C. Adjusted Rand Index
D. Dunn Index

26 The Adjusted Rand Index (ARI) is symmetric. This means:

A. ARI(A, B) = -ARI(B, A)
B. ARI values are always positive
C. ARI(A, B) = 1 / ARI(B, A)
D. ARI(A, B) = ARI(B, A)

27 In the calculation of Fowlkes-Mallows Index, 'TP' (True Positive) refers to:

A. Points correctly classified as outliers
B. Pairs of points that are in the same cluster and same class
C. Pairs of points that are in different clusters and different classes
D. Centroids correctly identified

28 Which internal metric assumes that clusters are convex and isotropic (spherical)?

A. Entropy
B. Adjusted Rand Index
C. DBSCAN
D. Silhouette Score

29 What is the primary disadvantage of the Davies-Bouldin Index?

A. It is computationally expensive for small datasets
B. It is always negative
C. It requires ground truth
D. It is limited to spherical clusters

30 If the V-measure is used with a Beta value greater than 1, it places more weight on:

A. Completeness
B. Precision
C. Homogeneity
D. Recall

31 Which of the following is NOT a pair-counting based metric?

A. Rand Index
B. Normalized Mutual Information
C. Adjusted Rand Index
D. Fowlkes-Mallows Index

32 For a perfect clustering where predicted clusters exactly match the ground truth classes, the Normalized Mutual Information (NMI) score is:

A. 0.5
B. Variable depending on dataset size
C. 1.0
D. 0.0

33 When computing the Silhouette Score for an entire dataset, one typically takes:

A. The median of the scores
B. The average of the scores for all samples
C. The minimum score of any point
D. The maximum score of any point

34 The Rand Index (RI) is the percentage of:

A. Information shared
B. Clusters that are pure
C. Correct classifications
D. Pairs of data points for which the two clusterings agree

35 Which metric would be most appropriate if the ground truth labels are not available?

A. V-measure
B. Fowlkes-Mallows Index
C. Silhouette Score
D. Adjusted Rand Index

36 A higher Dunn Index indicates:

A. Overlapping clusters
B. Random clustering
C. High intra-cluster distance and low inter-cluster distance
D. Low intra-cluster distance and high inter-cluster distance

37 Which metric is sensitive to the permutation of cluster labels?

A. Silhouette Score
B. None of the standard clustering metrics
C. Adjusted Rand Index
D. Accuracy (if used naively)

38 In the context of Homogeneity and Completeness, if the ground truth consists of a single class, and the clustering algorithm finds 5 clusters:

A. Both are 1
B. Homogeneity is 1, Completeness is 0
C. Homogeneity is 1, Completeness is < 1
D. Homogeneity is 0, Completeness is 1

39 The Adjusted Mutual Information (AMI) is preferred over NMI when:

A. The number of clusters is small
B. Computation time is critical
C. The clusters are very large
D. The cluster sizes are unbalanced and small samples are used

40 Which component of the Silhouette formula corresponds to 'separation'?

A. a (intra-cluster distance)
B. max(a, b)
C. b - a
D. b (nearest-cluster distance)

41 What is the theoretical minimum of the Adjusted Rand Index?

A. 0
B. -1
C. -0.5
D. It depends on the number of samples

42 Which of the following is a drawback of External Validation metrics like ARI and NMI?

A. They cannot handle outliers
B. They require a labeled dataset
C. They are computationally expensive
D. They are not normalized

43 In the Fowlkes-Mallows Index formula , what is PPV?

A. Recall
B. Precision
C. Accuracy
D. Entropy

44 Which metric essentially measures the similarity between the two partitionings of the data?

A. Silhouette Score
B. Davies-Bouldin Index
C. Dunn Index
D. Adjusted Rand Index

45 If you calculate the Silhouette Score for a dataset with only one cluster, the result is typically defined as:

A. 1
B. 0
C. Undefined or Error
D. -1

46 The V-measure is to Homogeneity and Completeness as the F1-Score is to:

A. TPR and FPR
B. Accuracy and Error
C. Sensitivity and Specificity
D. Precision and Recall

47 Which clustering metric uses the 'max-min' logic (maximize the minimum distance between clusters)?

A. Entropy
B. Davies-Bouldin Index
C. Dunn Index
D. F-measure

48 Why is the Rand Index (unadjusted) often considered optimistic?

A. It favors small clusters
B. It ranges from 0 to infinity
C. It ignores False Positives
D. It does not correct for the agreement that occurs by chance

49 Completeness score of 1.0 implies:

A. The number of clusters equals the number of classes
B. All points of a specific class are assigned to the same cluster
C. All points in a cluster belong to the same class
D. The clusters are perfectly spherical

50 Which of the following metrics calculates the average similarity between each cluster and its most similar one?

A. Dunn Index
B. Calinski-Harabasz Index
C. Silhouette Score
D. Davies-Bouldin Index
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