3. Unsupervised Learning

Manifold Learning — Quiz

Test your understanding of manifold learning with 5 practice questions.

Practice Questions

Question 1

Which loss function does UMAP optimize to align high-dimensional and low-dimensional fuzzy simplicial sets?

Question 2

Which graph-theoretic structure does UMAP compute to ensure the high-dimensional nearest-neighbor graph is fully connected?

Question 3

In UMAP’s high-dimensional membership strength formula $w_{ij} = \exp\left(-\frac{d_{ij}-\rho_i}{\sigma_i}\right)$ for $d_{ij}>\rho_i$, if $d_{ij}=0.8$, $\rho_i=0.2$, and $\sigma_i=0.3$, what is $w_{ij}$ approximately?

Question 4

A data scientist has a small dataset with clear but subtle cluster boundaries and wants to explore local groupings in detail. Which technique is more appropriate for this task?

Question 5

What is the intrinsic dimensionality of a 'Swiss roll' dataset embedded in 3D space?