Unit 6 - Practice Quiz

1 What is the primary difference between internal and external clustering validation metrics?

2 Which of the following is a common example of an external clustering validation metric?

3 Internal clustering validation metrics typically evaluate the quality of clusters based on which two properties?

4 What is the range of possible values for the Silhouette Score?

5 In the context of clustering evaluation, what does "cohesion" measure?

6 What does a Silhouette Score near indicate about a specific data point?

7 What is the primary goal of stability-based evaluation in clustering?

8 Which statistical technique is commonly used to test cluster stability by repeatedly drawing random samples with replacement from the dataset?

9 Why is interpretability often a major challenge in unsupervised learning?

10 Which of the following best describes the role of "domain expertise" in unsupervised learning?

11 In topic modeling (a form of unsupervised learning), why might a human struggle to interpret a discovered topic?

12 Which of the following is a classic real-world application of unsupervised anomaly detection?

13 Unsupervised learning is commonly used in recommendation systems to achieve which goal?

14 In bioinformatics, clustering algorithms are frequently used for what purpose?

15 What is a major ethical risk when unsupervised learning models discover patterns in demographic data?

16 Why is data privacy a significant concern in unsupervised pattern discovery?

17 An unsupervised algorithm clusters banking customers by zip code, which inadvertently groups them by race, leading to unfair loan rejections. This is an example of:

18 Which dimensionality reduction technique is most famous for successfully visualizing the MNIST handwritten digit dataset in 2D or 3D spaces?

19 In a customer segmentation case study, what do the resulting distinct clusters typically represent?

20 When visually plotting the MNIST dataset using t-SNE, what does a dense cluster of points of the same color typically represent?

21 Which of the following metrics is most appropriate for evaluating a clustering algorithm when ground-truth labels are available, and you want to account for chance agreement?

22 The Dunn Index evaluates clustering quality based on cluster compactness and separation. If is the minimum inter-cluster distance and is the maximum intra-cluster distance, how is the Dunn Index interpreted?

23 When using the Davies-Bouldin (DB) Index to evaluate clustering performance, which of the following scenarios represents the best clustering result?

24 Let be the mean intra-cluster distance for a sample, and be the mean nearest-cluster distance. The silhouette score is given by . What does a score of indicate?

25 In the context of cluster cohesion and separation, how does K-Means optimize these two intuitive properties?

26 If a dataset yields a highly negative average Silhouette Score, what is the most likely geometric interpretation of the clusters?

27 Stability-based evaluation involves repeatedly clustering perturbed versions of the dataset. Which parameter is often determined using this method?

28 When comparing two clustering partitions produced during stability-based evaluation via bootstrapping, which metric is commonly used to quantify the agreement between the two partitions?

29 A data scientist applies stability-based evaluation by adding small amounts of Gaussian noise to the dataset. If the resulting clusters change drastically, what does this imply about the original clustering?

30 Why is interpreting the principal components generated by PCA often challenging in high-dimensional domains like genomics?

31 When interpreting cluster centroids obtained from K-Means on a dataset with standardized features (mean 0, variance 1), what does a centroid value of $1.5$ for a specific feature signify?

32 Which of the following describes a common approach to improving the interpretability of an autoencoder's latent space representation?

33 In a real-world anomaly detection case study for credit card fraud, an unsupervised Isolation Forest model is deployed. What is the most significant practical limitation of relying solely on this unsupervised approach?

34 When performing topic modeling (e.g., using LDA) on a large corpus of news articles, how is the quality of the unsupervised topics usually evaluated in a real-world setting?

35 An unsupervised clustering algorithm groups job applicants based on resume text. It ends up creating a cluster that predominantly contains female applicants, despite 'gender' being removed from the data. What ethical issue does this highlight?

36 Why is 'reinforcement of historical bias' a significant concern in Unsupervised Learning algorithms used for pattern discovery?

37 In the context of clustering user data for a targeted advertising system, which of the following poses the greatest risk to user privacy (deanonymization)?

38 When applying t-SNE to visualize the 784-dimensional MNIST handwritten digit dataset in 2D, a data scientist notices that the distance between the cluster of '0's and the cluster of '1's is very large. How should this distance be interpreted?

39 In a customer segmentation case study, a dataset contains 'Age' (ranging 18-80) and 'Annual Income' (ranging $20,000-$150,000). Before applying K-Means clustering, the data scientist forgets to scale the data. What is the most likely consequence?

40 When reducing the dimensionality of the MNIST dataset to 2D for visualization, a researcher compares PCA and UMAP. The PCA plot shows overlapping classes, while the UMAP plot shows clearly distinct islands for each digit. What explains this difference?

41 Suppose you are evaluating a clustering algorithm using the Normalized Mutual Information (NMI) and the Adjusted Rand Index (ARI). The ground truth consists of roughly equal-sized clusters. The algorithm degenerates and places every single data point into its own individual cluster (i.e., clusters for points). How will the Homogeneity, Completeness, and ARI behave in this edge case?

42 The Calinski-Harabasz (CH) Index is defined as . What is the mathematical vulnerability of the CH Index when evaluating algorithms like DBSCAN that can produce an arbitrary number of clusters along with noise points, assuming noise points are assigned to a single 'noise' cluster?

43 Consider the Davies-Bouldin (DB) Index, defined as . If you apply a clustering algorithm to a high-dimensional dataset where the distance metric suffers from the 'curse of dimensionality' (i.e., all pairwise distances converge to a similar value ), what is the asymptotic behavior of the DB Index?

44 Which of the following scenarios describes a theoretical flaw when using the Fowlkes-Mallows Index (FMI) to compare two clusterings of highly imbalanced ground truth data?

45 The Silhouette coefficient for a data point is . Suppose you cluster a dataset consisting of two perfectly concentric circles using DBSCAN, which correctly identifies the inner circle as Cluster 1 and the outer circle as Cluster 2. What will be the general characteristic of the Silhouette scores for the points in Cluster 2 (the outer circle)?

46 A researcher is optimizing the hyperparameter in K-Means by maximizing the average Silhouette score. The dataset fundamentally consists of three clusters: one highly dense spherical cluster of 10,000 points, and two sparse, elongated clusters of 100 points each. How might Silhouette maximization mislead the researcher?

47 By convention, if a cluster contains only a single data point (a singleton), its Silhouette score is set to 0. If this convention were instead evaluated mathematically using the standard formula without overriding, what logical paradox would occur?

48 When using stability-based evaluation to determine the optimal number of clusters , you repeatedly subsample the data and measure the agreement (e.g., using Adjusted Rand Index) between the clusterings. In a dataset drawn from a completely uniform distribution with no true clusters, what is the expected behavior of the stability curve as increases from 2 to ?

49 A modeler applies a stability-based method to evaluate a K-Means clustering model. They bootstrap the dataset times, cluster each sample, and calculate the pairwise Jaccard coefficient of the cluster assignments. Why might bootstrapping introduce a pessimistic bias (underestimating true stability) compared to subsampling without replacement in this specific context?

50 Consider evaluating cluster stability via a Prediction Strength metric. The dataset is split into training and test sets; clusters are found on both. Test points are then assigned to the nearest training cluster centroid. What represents a critical failure mode of this specific evaluation strategy when applied to clusters with highly irregular, non-convex shapes?

51 To improve interpretability in generative unsupervised models, researchers often use a -VAE to enforce disentangled representations. Mathematically, this is achieved by scaling the Kullback-Leibler (KL) divergence term in the ELBO by . What is the primary theoretical trade-off encountered when enforcing this interpretability constraint?

52 A common post-hoc method to interpret a black-box clustering algorithm is to train a surrogate decision tree predicting the cluster labels from the input features. If the underlying clustering algorithm is Spectral Clustering applied to concentric rings (a non-linear manifold), what is the most likely interpretability challenge faced by the surrogate decision tree?

53 In Principal Component Analysis (PCA), the principal components are linear combinations of the original features, which aids interpretability via 'loadings'. In contrast, a deep Autoencoder with non-linear activation functions typically lacks this interpretability. Which mathematical property strictly present in PCA is absent in standard Autoencoders, making the latter's latent space harder to interpret?

54 An unsupervised model is used to segment neighborhoods for targeted marketing. To ensure fairness, the data scientists explicitly remove 'Race' and 'Income' from the dataset. However, an external audit reveals the clusters are still highly correlated with race. Which fundamental phenomenon of unsupervised learning causes this ethical failure?

55 To address fairness in clustering, algorithms like 'Fair K-Means' introduce constraints into the objective function. If is the set of points in cluster , is a protected demographic group, and is the total dataset size, which constraint represents the concept of 'Disparate Impact' mitigation (demographic parity) in Fair K-Means?

56 In a real-world cybersecurity application for anomaly detection, an Isolation Forest is chosen over distance-based methods like K-Nearest Neighbors (KNN). Given a dataset with features where normal traffic forms a dense hyper-sphere and anomalies are sparsely distributed, what is the theoretical justification for this choice?

57 When analyzing single-cell RNA sequencing data (a real-world clustering application), researchers frequently utilize Louvain community detection on a K-Nearest Neighbor (KNN) graph rather than K-Means clustering. Which property of single-cell data makes Louvain biologically more meaningful in this context?

58 When applying t-SNE to the MNIST dataset to visualize digit clusters, the 'perplexity' hyperparameter balances attention between local and global aspects of the data. If a researcher mistakenly sets the perplexity to be equal to (the total number of data points), what will the resulting visualization look like?

59 You are performing customer segmentation using a Gaussian Mixture Model (GMM). Your dataset includes 'Age' and 'Annual Income'. Income is exponentially distributed and skewed, containing extreme outliers. If you use a full, untied covariance matrix for the GMM, what is the most severe mathematical risk you face during Expectation-Maximization (EM)?

60 When applying UMAP to the MNIST handwritten digits dataset, changing the distance metric from Euclidean to Cosine significantly alters the topological embedding. What underlying morphological property of the MNIST digits is fundamentally ignored by the Cosine distance compared to Euclidean distance?