Dimensionality Reduction Quiz

Answers and explanations appear as you take the quiz.

1. Which data-coverage challenge is associated with increasing dimension in the curse of dimensionality?
   • Every added coordinate necessarily improves every model
   • All high-dimensional distances are identical by definition
   • A much larger space can require many more observations to cover densely
   • Every model becomes faster without changing its computation
2. Which directions does PCA prioritize when selecting principal components of centered input data?
   • Directions guaranteed to have the greatest target-label accuracy
   • Directions of high input variance
   • Directions chosen only from column names
   • Directions of minimum variance in every setup
3. Why is PCA called a 'linear' method?
   • It only works on data plotted as straight lines
   • It can only reduce data to exactly one dimension
   • It requires the data to be sorted first
   • It combines features using weighted sums (linear combinations)
4. Which aspect of data do t-SNE and UMAP commonly emphasize in exploratory low-dimensional embeddings?
   • Neighborhood relationships
   • A guarantee of all original pairwise distances
   • An exact encryption of every input file
   • A proof that every visible group is a true category
5. Why might a team evaluate a smaller representation before fitting a downstream model?
   • To guarantee that no useful information is ever lost
   • To compare computational cost and predictive behavior with fewer coordinates
   • To eliminate the need for held-out evaluation
   • To prove that every discarded component is noise
6. Which structure does UMAP use when constructing its representation of nearby input observations?
   • A required list of supervised document labels
   • A file-format encryption key
   • A neighborhood graph
   • A guarantee that all cluster densities are preserved
7. By default, how does the stated scikit-learn PCA transformation preprocess feature means and scales?
   • It centers features but does not scale each to unit variance
   • It both centers and scales every feature to unit variance automatically
   • It scales each feature to unit variance but leaves its mean unchanged
   • It divides every feature by its range without centering
8. Why should visual compactness in an ordinary UMAP plot not be treated as proof of original-space cluster density?
   • UMAP guarantees exact preservation of every original density ratio
   • Plot compactness is automatically calibrated to population frequency
   • The projection preserves every original pairwise distance exactly
   • UMAP does not reliably preserve density in its ordinary embedding