Question 13
UnclassifiedPrincipal Component Analysis (PCA) is best described as:
Correct answer: B
Explanation
PCA is a linear dimensionality reduction method because it transforms data using linear combinations of the original features. It projects the data onto orthogonal components chosen to capture the maximum variance, which is why it is described as "a linear dimensionality reduction technique that projects data onto orthogonal directions of maximum variance."
Why each option is right or wrong
A. A supervised classification algorithm
B. A linear dimensionality reduction technique that projects data onto orthogonal directions of maximum variance
PCA constructs new variables as linear combinations of the original features, so the transformation is linear rather than nonlinear. The components are chosen by solving an eigenvalue problem on the covariance matrix (or equivalently via SVD), which yields mutually orthogonal axes ordered by descending explained variance; the first component captures the largest possible variance, the second the largest remaining variance subject to orthogonality, and so on.
C. A clustering algorithm
D. A regularization method