Linear Discriminant Analysis Quiz

Answers and explanations appear as you take the quiz.

1. Why does common LDA classification produce linear decision boundaries?
   • It uses class-specific covariance matrices in every case
   • It maximizes total feature variance without labels
   • Classes share a covariance matrix in its usual Gaussian model
   • It ignores class priors whenever class sizes differ
2. How does LDA choose projection directions in its supervised reduction role?
   • Maximize total variance without labels
   • Favor class separation relative to within-class variation
   • Choose features only by their marginal variance
   • Keep only the original columns with largest means
3. With K classes and at least K minus one input features, what upper bound applies to the number of useful LDA discriminant directions?
   • K squared
   • K
   • The number of observations
   • K minus one
4. Which objective does PCA optimize in contrast to LDA?
   • High overall variance without using class labels
   • Class posterior probability
   • Maximum class separation using labels
   • Minimum classification error at every threshold
5. When may a low-variance direction matter to LDA?
   • When it has the smallest variance regardless of labels
   • Only when PCA has already chosen it
   • When it separates labeled classes
   • Only when every class has the same mean on it
6. What changes in quadratic discriminant analysis compared with common LDA?
   • Each class must have the same prior probability
   • Each class may have its own covariance matrix
   • Every class mean is constrained to be equal
   • All quadratic terms are removed from the class comparison
7. Why can LDA be numerically difficult when features greatly outnumber examples?
   • The number of classes must automatically become larger
   • Class priors cannot be estimated from any labeled sample
   • The shared-covariance assumption removes every conditioning problem
   • Covariance estimates may be singular or unstable
8. A plot shows separated training groups after LDA projection. What has not yet been established?
   • Reliable generalization on held-out data
   • That labels influenced the projection
   • That a projection was computed
   • That classes were present in training