MS-DS Master of Data science Unsupervised Learning Techniques 3

Question 1

What is the computational complexity of a single iteration of k-means on n data points with k clusters and d dimensions?

Accepted Answer

O(nkd)

Answer

Each of the n points must compute distances to each of the k cluster centroids in d dimensions, giving O(nkd) per iteration.

Question 2

Which method is used by UMAP to preserve both local and global structure, distinguishing it from t-SNE?

Accepted Answer

UMAP constructs a fuzzy topological representation and optimizes its cross-entropy with a low-dimensional analog

Answer

UMAP is grounded in Riemannian geometry and algebraic topology, building a fuzzy simplicial complex and minimizing its cross-entropy with a low-dimensional representation, preserving more global structure than t-SNE.

Question 3

What is the 'elbow method' used to determine in unsupervised learning?

Accepted Answer

The appropriate number of clusters k in k-means by plotting inertia vs. k

Answer

The elbow method plots within-cluster sum of squares (inertia) against k; the 'elbow' point where improvement diminishes suggests the optimal k.

Question 4

A researcher applies hierarchical agglomerative clustering with single linkage to data with two elongated, touching clusters. What artifact is likely to occur?

Accepted Answer

Chaining: the two clusters will merge prematurely into one elongated cluster

Answer

Single linkage uses the minimum pairwise distance between clusters, making it susceptible to chaining where a bridge of close points merges two distinct elongated clusters early.

Question 5

In a Variational Autoencoder (VAE), what is the purpose of the reparameterization trick?

Accepted Answer

To allow gradients to flow through the stochastic sampling step during backpropagation

Answer

The reparameterization trick expresses z = μ + σ·ε (ε ~ N(0,I)), making the random node deterministic w.r.t. ε and allowing gradient flow through μ and σ.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Unsupervised Learning Techniques 3