Linear Discriminant Analysis (LDA): Decision Boundaries
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Adapted from an appendix of my MS thesis. Linear Discriminant Analysis Decision Boundary Derivation Decision theory for classification tells us that we need to know the class posteriors P ( G ∣ X ) for optimal classification. Suppose f k ( x ) is the conditional density of X for class G = k , and let π k be the prior probability of class k , with ∑ ℓ = 1 K π ℓ = 1 . Bayes theorem gives us the following [1]. P ( G = k ∣ X = x ) = ∑ ℓ = 1 K f ℓ ( x ) π ℓ f k ( x ) π k . Many…
1Key Takeaways
- Adapted from an appendix of my MS thesis.
- Linear Discriminant Analysis Decision Boundary Derivation Decision theory for classification tells us that we need to know the class posteriors P ( G ∣ X ) for optimal classification.
- Suppose f k ( x ) is the conditional density of X for class G = k , and let π k be the prior probability of class k , with ∑ ℓ = 1 K π ℓ = 1 .
- Bayes theorem gives us the following [1].
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3Why it matters
Coding AI shifts how fast software ships and how much human review each change needs. DEV — ML reports that adapted from an appendix of my MS thesis.
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