MS-DS Master of Data science Unsupervised Machine Learning Models 2 — Questions and Answers
Question 1: Which linkage criterion in hierarchical clustering tends to produce compact, spherical clusters?
- Complete linkage
- Single linkage
- Average linkage
- Ward's linkage (Correct answer)
Correct answer: Ward's linkage
Ward's linkage minimizes the total within-cluster variance at each merge step, producing compact and spherical clusters.
Question 2: In DBSCAN, a point is classified as a 'border point' when it:
- Has fewer than MinPts neighbors within epsilon but is reachable from a core point (Correct answer)
- Has more than MinPts neighbors within epsilon
- Is not reachable from any core point
- Has exactly MinPts neighbors within epsilon
Correct answer: Has fewer than MinPts neighbors within epsilon but is reachable from a core point
A border point has fewer than MinPts neighbors within epsilon but falls within the epsilon-neighborhood of a core point.
Question 3: What does the reconstruction error in an autoencoder measure?
- The difference between input and decoder output (Correct answer)
- The KL divergence between latent distributions
- The accuracy of cluster assignments
- The explained variance ratio of components
Correct answer: The difference between input and decoder output
Reconstruction error measures how well the decoder can reproduce the original input from the compressed latent representation.
Question 4: Which of the following best describes the 'manifold hypothesis' as it relates to dimensionality reduction?
- High-dimensional data lies on or near a lower-dimensional manifold embedded in the high-dimensional space (Correct answer)
- All high-dimensional data can be linearly projected to lower dimensions without loss
- Clustering must be performed before dimensionality reduction
- Data variance is uniformly distributed across all dimensions
Correct answer: High-dimensional data lies on or near a lower-dimensional manifold embedded in the high-dimensional space
The manifold hypothesis states that real-world high-dimensional data concentrates near a lower-dimensional curved surface (manifold).
Question 5: In topic modeling with Latent Dirichlet Allocation (LDA), what does the Dirichlet prior control?
- The sparsity of topic-document and word-topic distributions (Correct answer)
- The number of unique words in the corpus
- The maximum number of topics allowed
- The convergence rate of the EM algorithm
Correct answer: The sparsity of topic-document and word-topic distributions
The Dirichlet hyperparameters alpha and beta control the sparsity of per-document topic distributions and per-topic word distributions respectively.
Question 6: What is the primary advantage of using UMAP over t-SNE for dimensionality reduction?
- UMAP better preserves global structure and is significantly faster on large datasets (Correct answer)
- UMAP always produces two-dimensional outputs only
- UMAP requires labeled data to construct the embedding
- UMAP uses a linear projection making it more interpretable
Correct answer: UMAP better preserves global structure and is significantly faster on large datasets
UMAP preserves more global structure than t-SNE and scales better computationally due to its graph-based approximation approach.
Question 7: In a Gaussian Mixture Model, the E-step of the EM algorithm computes:
- The posterior probability that each data point belongs to each Gaussian component (Correct answer)
- The maximum likelihood parameters for each Gaussian
- The number of components using BIC
- The covariance matrix of the full dataset
Correct answer: The posterior probability that each data point belongs to each Gaussian component
The E-step computes the responsibilities — the posterior probabilities (soft assignments) of each point belonging to each mixture component given current parameters.
MS-DS Master of Data science Unsupervised Machine Learning Models 2
Which linkage criterion in hierarchical clustering tends to produce compact, spherical clusters?