11 Techniques: PCA - Selected Topics

Question 1

What is the modeling quality Ψq?

Answer 1

the proportion of explained variance by the first q ≤ p principal components

Question 2

What is the modeling quality Ψq if q = p ?

Answer 2

then Ψp = 1

Question 3

What are the charactersitics (mean, covariance) of the normalized principal components matrix Xₛ?

Answer 3

x̅ₛ = 0
^Σ = ^P with Spectral Decomposition ^Γₚ^Λₚ^Γₚᵀ

Question 4

How would you interpret Ψq = x ?

Answer 4

With the first q principal components, we can explain x*100% of the data variation

Question 5

Which values are you looking for when conducting principal components analysis?

Answer 5

estimated:
- μ, Σ,
- Γ (usually given), Λ (usually given),
- principal component Y
- correlation coefficient ρ
- model quality Ψ