MS-DS Master of Data science Master of Data science Unsupervised Machine Learning Models 1 — Questions and Answers
Question 1: In hierarchical agglomerative clustering, which linkage criterion defines the distance between two clusters as the maximum distance between any two points in those clusters?
- Single linkage
- Complete linkage (Correct answer)
- Average linkage
- Ward linkage
Correct answer: Complete linkage
Complete linkage (also called maximum linkage) measures the distance between two clusters as the distance between their two farthest-apart points. This tends to produce compact, roughly equal-sized clusters and is less sensitive to outliers than single linkage.
Question 2: Which of the following is NOT an assumption made by the K-Means clustering algorithm?
- Clusters are spherical in shape
- All clusters have roughly equal variance
- The number of clusters K must be specified in advance
- Clusters can have arbitrary non-convex shapes (Correct answer)
Correct answer: Clusters can have arbitrary non-convex shapes
K-Means assumes clusters are convex and isotropic (spherical), with similar variance and roughly equal size. It cannot naturally capture non-convex or irregularly shaped clusters — that is precisely one of its key limitations.
Question 3: When applying Principal Component Analysis (PCA), what property do the resulting principal components always satisfy?
- They are correlated with the original features
- They are orthogonal to one another (Correct answer)
- They each explain an equal proportion of variance
- They preserve pairwise distances between all data points
Correct answer: They are orthogonal to one another
PCA decomposes the covariance matrix via eigendecomposition, producing eigenvectors (principal components) that are mathematically orthogonal — meaning they are uncorrelated with each other. This orthogonality is what makes PCA effective for removing redundant information.
Question 4: An autoencoder trained for dimensionality reduction consists of two main parts. What is the role of the bottleneck (latent) layer?
- To apply dropout regularization to prevent overfitting
- To reconstruct the input with minimal loss
- To force the network to learn a compressed representation of the input (Correct answer)
- To compute the gradient for backpropagation
Correct answer: To force the network to learn a compressed representation of the input
The bottleneck layer has fewer neurons than the input, forcing the encoder to learn a compact, lower-dimensional latent representation. The reconstruction quality depends on how well this compressed code captures the essential structure of the data.
Question 5: Which evaluation metric for clustering does NOT require ground-truth labels to compute?
- Adjusted Rand Index (ARI)
- Normalized Mutual Information (NMI)
- Davies-Bouldin Index (Correct answer)
- Homogeneity score
Correct answer: Davies-Bouldin Index
The Davies-Bouldin Index is an internal evaluation metric that measures the ratio of within-cluster scatter to between-cluster separation using only the data and cluster assignments — no ground-truth labels are needed. ARI, NMI, and homogeneity are all external metrics that require true labels.
Question 6: In the context of unsupervised anomaly detection, what does the Isolation Forest algorithm exploit to identify outliers?
- The distance of a point from the nearest cluster centroid
- The reconstruction error of an autoencoder trained on normal data
- The fact that anomalies require fewer random splits to isolate than normal points (Correct answer)
- The density estimate produced by a Gaussian Mixture Model
Correct answer: The fact that anomalies require fewer random splits to isolate than normal points
Isolation Forest builds an ensemble of random trees by repeatedly splitting data on random features and values. Anomalies, being rare and lying in sparse regions, are isolated closer to the root of the trees (fewer splits needed), resulting in shorter average path lengths that signal outlier status.
MS-DS Master of Data science Master of Data science Unsupervised Machine Learning Models 1
In hierarchical agglomerative clustering, which linkage criterion defines the distance between two clusters as the maximum distance between any two points in those clusters?