MS-DS Master of Data science Unsupervised Machine Learning Models 3 — Questions and Answers
Question 1: What does the Hopkins statistic measure in cluster analysis?
- The spatial randomness of data — whether data is clusterable at all (Correct answer)
- The optimal number of clusters for k-means
- The within-cluster sum of squares
- The similarity between two dendrograms
Correct answer: The spatial randomness of data — whether data is clusterable at all
The Hopkins statistic tests whether data has a significantly non-random spatial structure, indicating whether it is worth clustering.
Question 2: Which of the following is a key limitation of Principal Component Analysis (PCA) when applied to image data?
- PCA assumes linear relationships and cannot capture nonlinear structure in image manifolds (Correct answer)
- PCA requires labeled image categories to compute components
- PCA cannot reduce images to fewer than 100 dimensions
- PCA is computationally infeasible for images larger than 32x32 pixels
Correct answer: PCA assumes linear relationships and cannot capture nonlinear structure in image manifolds
PCA is a linear method and fails to capture nonlinear manifold structure present in image data, which is why kernel PCA or autoencoders are preferred.
Question 3: In the context of self-organizing maps (SOMs), what does the neighborhood function determine?
- How much surrounding neurons are updated when a best-matching unit is found (Correct answer)
- The distance metric used to compare input vectors
- The number of clusters in the output map
- The learning rate decay schedule
Correct answer: How much surrounding neurons are updated when a best-matching unit is found
The neighborhood function (typically Gaussian) controls how strongly neurons adjacent to the best-matching unit are pulled toward the input during each update.
Question 4: What is the 'cold start' problem in collaborative filtering?
- Inability to make recommendations for new users or items with no interaction history (Correct answer)
- Slow convergence of matrix factorization algorithms on sparse matrices
- Memory overflow when loading large user-item matrices
- Instability in latent factor initialization
Correct answer: Inability to make recommendations for new users or items with no interaction history
The cold start problem occurs when the system cannot generate recommendations for new users or items because no historical interaction data exists.
Question 5: Which property distinguishes agglomerative from divisive hierarchical clustering?
- Agglomerative starts with each point as its own cluster and merges upward; divisive starts with one cluster and splits (Correct answer)
- Agglomerative requires specifying k in advance; divisive does not
- Agglomerative uses density; divisive uses distance
- Agglomerative produces a flat partition; divisive produces a dendrogram
Correct answer: Agglomerative starts with each point as its own cluster and merges upward; divisive starts with one cluster and splits
Agglomerative clustering is bottom-up (merging), while divisive is top-down (splitting); both produce dendrograms but differ in direction.
Question 6: In Independent Component Analysis (ICA), what assumption distinguishes it from PCA?
- ICA assumes statistically independent non-Gaussian sources, whereas PCA assumes uncorrelated Gaussian components (Correct answer)
- ICA maximizes explained variance while PCA minimizes mutual information
- ICA requires more components than the number of observed signals
- ICA is a supervised algorithm while PCA is unsupervised
Correct answer: ICA assumes statistically independent non-Gaussian sources, whereas PCA assumes uncorrelated Gaussian components
ICA exploits statistical independence and non-Gaussianity to separate sources, going beyond the second-order decorrelation that PCA achieves.
Question 7: What does a high average silhouette score (close to 1) indicate about a clustering solution?
- Points are well-matched to their own cluster and poorly matched to neighboring clusters (Correct answer)
- The number of clusters equals the true number of classes in the data
- Within-cluster variance is high and between-cluster variance is low
- The clustering algorithm has converged to a global optimum
Correct answer: Points are well-matched to their own cluster and poorly matched to neighboring clusters
A silhouette score near 1 means each point is much closer to its own cluster's centroid than to any other cluster, indicating dense, well-separated clusters.
MS-DS Master of Data science Unsupervised Machine Learning Models 3
What does the Hopkins statistic measure in cluster analysis?