1 $What is the range of values for the Silhouette Score?$

A.

-infinity to infinity

B.

-1 to 1

C.

0 to 1

D.

0 to infinity

2 $Which of the following metrics does NOT require ground truth labels (true class labels) to evaluate clustering performance?$

A.

Silhouette Score

B.

Fowlkes-Mallows Index

C.

Normalized Mutual Information

D.

Adjusted Rand Index

3 $In the context of the Davies-Bouldin Index, a lower value indicates:$

A.

Worse clustering

B.

Overfitting

C.

Better clustering

D.

High computational cost

4 $The Dunn Index is defined as the ratio of:$

A.

Minimum inter-cluster distance to maximum intra-cluster distance

B.

Maximum inter-cluster distance to minimum intra-cluster distance

C.

Mean intra-cluster distance to mean inter-cluster distance

D.

Variance of clusters to bias of clusters

5 $Which clustering metric corrects the Rand Index for chance?$

A.

Fowlkes-Mallows Index

B.

Completeness Score

C.

Adjusted Rand Index (ARI)

D.

Silhouette Score

6 $What does a Homogeneity score of 1.0 imply?$

A.

The number of clusters equals the number of samples

B.

All data points of a specific class are assigned to the same cluster

C.

The clusters overlap significantly

D.

All clusters contain data points from only a single class

7 $If all data points belonging to a given class are elements of the same cluster, which metric is maximized?$

A.

Completeness

B.

Dunn Index

C.

Silhouette Score

D.

Homogeneity

8 $The V-measure is the harmonic mean of which two metrics?$

A.

ARI and NMI

B.

Precision and Recall

C.

Silhouette and Dunn Index

D.

Homogeneity and Completeness

9 $Which metric is calculated as the geometric mean of pairwise precision and pairwise recall?$

A.

V-measure

B.

Davies-Bouldin Index

C.

Adjusted Mutual Information

D.

Fowlkes-Mallows Index

10 $Normalized Mutual Information (NMI) is often preferred over Mutual Information (MI) because:$

A.

NMI does not require ground truth

B.

NMI scales the result between 0 and 1, making it comparable across datasets

C.

MI yields negative values

D.

MI is computationally too expensive

11 $What is the primary advantage of Adjusted Mutual Information (AMI) over Normalized Mutual Information (NMI)?$

A.

AMI is faster to compute

B.

AMI can handle negative values

C.

AMI accounts for chance (randomness) in cluster assignment

D.

AMI works without ground truth

12 $In the Silhouette Score formula s = (b - a) / max(a, b), what does 'a' represent?$

A.

The distance to the nearest cluster centroid

B.

The maximum diameter of the cluster

C.

The mean intra-cluster distance (average distance to other points in the same cluster)

D.

The mean nearest-cluster distance

13 $Which of the following indicates a clustering result where samples have been assigned to the wrong clusters according to the Silhouette Score?$

A.

Values near 0

B.

Values near +1

C.

Values near -1

D.

Values exactly 0.5

14 $The Adjusted Rand Index (ARI) yields a score of approximately 0 when:$

A.

The clustering is identical to the ground truth

B.

The number of clusters is equal to the number of samples

C.

The clustering is independent/random compared to the ground truth

D.

The clustering is perfect

15 $Which metric is most sensitive to noise and outliers because it uses maximum diameters and minimum separations?$

A.

V-measure

B.

Silhouette Score

C.

Adjusted Rand Index

D.

Dunn Index

16 $If a clustering algorithm produces 100 clusters for a dataset of 100 samples (each sample is its own cluster), which metric will naturally maximize to 1.0, potentially giving a misleading impression of quality?$

A.

Dunn Index

B.

Silhouette Score

C.

Homogeneity

D.

Completeness

17 $Conversely, if all samples are assigned to a single cluster, which metric will maximize to 1.0?$

A.

Davies-Bouldin Index

B.

Homogeneity

C.

Completeness

D.

Silhouette Score

18 $What is the beta parameter used for in the V-measure calculation?$

A.

To normalize the dataset

B.

To adjust for chance

C.

To weight the importance of Homogeneity versus Completeness

D.

To define the number of clusters

19 $When calculating the Fowlkes-Mallows Index, 'TP' (True Positive) refers to:$

A.

Pairs of points that are in different clusters in both labels

B.

Clusters that are perfectly pure

C.

Pairs of points that are in the same cluster in both the true labels and predicted labels

D.

Points correctly classified as noise

20 $Which of the following is an 'Internal' clustering validity index?$

A.

V-measure

B.

Normalized Mutual Information

C.

Adjusted Rand Index

D.

Davies-Bouldin Index

21 $What is a major limitation of the Silhouette Score when dealing with non-convex clusters (e.g., ring shapes)?$

A.

It requires ground truth

B.

It is computationally cheap

C.

It cannot handle negative values

D.

It tends to give lower scores to density-based clusters that are not spherical

22 $Which component of the Silhouette Score represents the 'separation' of the cluster?$

A.

a (intra-cluster distance)

B.

b (nearest-cluster distance)

C.

max(a, b)

D.

b - a

23 $In the context of NMI, Entropy is used to measure:$

A.

The uncertainty associated with the class or cluster distribution

B.

The number of outliers

C.

The distance between centroids

D.

The geometric shape of the cluster

24 $Which metric is symmetric (i.e., Metric(A, B) = Metric(B, A))?$

A.

Adjusted Rand Index

B.

Homogeneity

C.

Silhouette Score

D.

Completeness

25 $A Davies-Bouldin Index of 0 indicates:$

A.

The worst possible clustering

B.

Random clustering

C.

Ideally separated and compact clusters

D.

Infinite variance

26 $Which of the following is required to calculate the Adjusted Mutual Information (AMI)?$

A.

Centroids of the clusters

B.

Ground truth labels and predicted labels

C.

Euclidean distance matrix

D.

Only the predicted labels

27 $The Fowlkes-Mallows Index is bounded between:$

A.

0 and 1

B.

-1 and 1

C.

-infinity to +infinity

D.

0 and infinity

28 $Why might the Dunn Index be computationally expensive for large datasets?$

A.

It requires calculating eigenvalues

B.

It involves complex integrals

C.

It requires calculating pairwise distances between all points to find min/max distances

D.

It requires ground truth labels

29 $When interpreting Homogeneity (H) and Completeness (C), if H is high and C is low, what does this usually suggest?$

A.

The data is random noise

B.

The clustering is perfect

C.

The algorithm merged distinct classes into one cluster

D.

The algorithm over-segmented the classes (many small clusters for one class)

30 $In the formula for NMI, the Mutual Information I(U, V) is normalized by:$

A.

The arithmetic or geometric mean of the entropies of U and V

B.

The variance of U and V

C.

The number of samples

D.

The maximum distance in the dataset

31 $What happens to the Adjusted Rand Index (ARI) if the class labels are permuted (renamed)?$

A.

The score changes drastically

B.

The score remains the same

C.

The score becomes negative

D.

The score becomes zero

32 $Which external metric suffers less from the 'curse of dimensionality' in its calculation logic (though distances themselves might suffer)?$

A.

Dunn Index

B.

V-measure

C.

Silhouette Score

D.

Davies-Bouldin Index

33 $For a dataset with 'k' ground truth classes, if a clustering algorithm produces 'k' clusters and ARI is 1.0, this means:$

A.

There are outlier points

B.

The clusters perfectly match the ground truth (up to permutation)

C.

The clusters are disjoint but incorrect

D.

The clusters are random

34 $Which metric would be most appropriate to select the optimal number of clusters 'k' in K-Means clustering when true labels are unknown?$

A.

NMI

B.

Silhouette Score

C.

Homogeneity

D.

Adjusted Rand Index

35 $In the calculation of the Davies-Bouldin Index, 'scatter' refers to:$

A.

The average distance of points in a cluster to their centroid

B.

The entropy of the cluster

C.

The distance between cluster centroids

D.

The total number of points

36 $The Rand Index (RI) calculates the percentage of:$

A.

Clusters that have zero entropy

B.

Correctly classified centroids

C.

Points with positive silhouette scores

D.

Decisions where pairs of data points are correctly agreed upon (together or apart)

37 $Does the V-measure prefer a specific number of clusters?$

A.

No, it is independent of cluster count

B.

It only works for k=2

C.

Yes, it favors a single cluster

D.

Yes, it favors a large number of clusters if not adjusted

38 $Which metric is based on the idea that good clusters should be highly similar internally and highly dissimilar externally?$

A.

Silhouette Score

B.

NMI

C.

FMI

D.

ARI

39 $If two different clustering algorithms produce the exact same partition of data, the AMI score between them will be:$

A.

0

B.

1

C.

0.5

D.

Infinity

40 $Which of the following metrics is NOT bounded by 1 (i.e., can it be greater than 1)?$

A.

Silhouette Score

B.

V-measure

C.

Davies-Bouldin Index

D.

Adjusted Rand Index

41 $Homogeneity is equivalent to which classification metric when applied to clusters?$

A.

Accuracy

B.

Precision

C.

Recall

D.

F1 Score

42 $Completeness is equivalent to which classification metric when applied to clusters?$

A.

Accuracy

B.

Specificity

C.

Recall

D.

Precision

43 $Which metric assumes that the best clustering has the minimum sum of similarities between each cluster and its most similar one?$

A.

Silhouette Score

B.

Davies-Bouldin Index

C.

Dunn Index

D.

Calinski-Harabasz Index

44 $When using the Silhouette Score, a value of 0 implies:$

A.

The sample is an outlier

B.

The clustering is perfect

C.

The sample is far away from all clusters

D.

The sample is on or very close to the decision boundary between two neighboring clusters

45 $Why is 'Adjusted' Mutual Information preferred over 'Normalized' Mutual Information in many comparative studies?$

A.

It is easier to calculate

B.

It does not use logarithms

C.

It is always positive

D.

It corrects for the bias toward clusters with many partitions (high k)

46 $The Fowlkes-Mallows index is generally higher when:$

A.

The number of clusters is 1

B.

The clustering and ground truth are highly correlated

C.

The number of clusters is very large

D.

The dataset is very small

47 $In the Dunn Index, the 'diameter' of a cluster usually refers to:$

A.

The radius of the cluster

B.

The maximum distance between any two points in the cluster

C.

The distance to the nearest neighbor

D.

The average distance to the centroid

48 $Which metric is strictly an Information Theoretic measure?$

A.

Normalized Mutual Information (NMI)

B.

Davies-Bouldin Index

C.

Silhouette Score

D.

Dunn Index

49 $If a dataset has highly imbalanced classes, which pair of metrics gives a good view of cluster purity and class coverage?$

A.

Homogeneity and Completeness

B.

Dunn and Variance

C.

Mean and Median

D.

Silhouette and DBI

50 $A negative value for the Adjusted Rand Index (ARI) implies:$

A.

The clustering is perfect

B.

ARI cannot be negative

C.

The clustering is random

D.

The clustering is worse than random assignment

Unit 3 - Practice Quiz