MS-DS Master of Data science Unsupervised Learning Techniques 2 — Questions and Answers
Question 1: Which linkage criterion in hierarchical clustering tends to produce the most compact, spherical clusters?
- Complete linkage
- Single linkage
- Average linkage
- Ward's method (Correct answer)
Correct answer: Ward's method
Ward's method minimizes the total within-cluster variance at each merge step, producing compact, roughly spherical clusters.
Question 2: In the Expectation-Maximization (EM) algorithm for Gaussian Mixture Models, what does the E-step compute?
- The covariance matrices of each Gaussian component
- The posterior probability (responsibility) of each component for each data point (Correct answer)
- The log-likelihood of the observed data
- The number of optimal mixture components
Correct answer: The posterior probability (responsibility) of each component for each data point
The E-step computes the responsibility r_{nk}, the posterior probability that component k generated data point n, given current parameters.
Question 3: What is the primary role of the kernel function in kernel PCA?
- To reduce computational complexity of eigendecomposition
- To implicitly map data into a higher-dimensional feature space where linear PCA is applied (Correct answer)
- To enforce orthogonality among principal components
- To normalize the data before applying PCA
Correct answer: To implicitly map data into a higher-dimensional feature space where linear PCA is applied
The kernel function computes inner products in a high-dimensional (possibly infinite) feature space without explicitly mapping points there, enabling nonlinear dimensionality reduction.
Question 4: Which of the following is a key assumption made by the DBSCAN algorithm?
- Clusters are convex and similarly sized
- Clusters are defined by regions of high density separated by low-density regions (Correct answer)
- The number of clusters must be specified in advance
- Data points belong to exactly one cluster with a hard assignment
Correct answer: Clusters are defined by regions of high density separated by low-density regions
DBSCAN defines clusters as dense regions (cores + reachable points) separated by sparse regions, requiring only epsilon and minPts parameters.
Question 5: In t-SNE, what does the perplexity hyperparameter control?
- The learning rate of the gradient descent optimization
- The balance between local and global structure by setting the effective number of neighbors (Correct answer)
- The number of output dimensions in the embedding
- The number of iterations before convergence
Correct answer: The balance between local and global structure by setting the effective number of neighbors
Perplexity roughly determines how many neighbors each point considers when constructing the high-dimensional probability distribution, balancing local vs. global structure.
Question 6: What does the silhouette coefficient measure for a clustering result?
- The ratio of between-cluster variance to within-cluster variance
- How similar a point is to its own cluster compared to neighboring clusters (Correct answer)
- The probability that a point belongs to its assigned cluster
- The percentage of variance explained by the cluster centroids
Correct answer: How similar a point is to its own cluster compared to neighboring clusters
The silhouette coefficient s(i) = (b(i) - a(i)) / max(a(i), b(i)), where a is intra-cluster distance and b is the nearest-cluster distance.
Question 7: In Independent Component Analysis (ICA), what statistical property distinguishes the independent components from principal components?
- ICA components are orthogonal; PCA components are not necessarily orthogonal
- ICA maximizes non-Gaussianity of components; PCA maximizes variance (Correct answer)
- ICA requires labeled data; PCA does not
- ICA components are always fewer in number than PCA components
Correct answer: ICA maximizes non-Gaussianity of components; PCA maximizes variance
ICA seeks statistically independent, non-Gaussian source signals, while PCA finds orthogonal directions of maximum variance (which are uncorrelated but not necessarily independent).
MS-DS Master of Data science Unsupervised Learning Techniques 2
Which linkage criterion in hierarchical clustering tends to produce the most compact, spherical clusters?