Quadratic Discriminant Analysis

General Description

• Quadratic Discriminant Analysis (QDA) is a supervised classification technique that is typically solved using Bayesian techniques
• QDA uses quadratic decision boundaries to determine the class of an observation, whereas LDA uses linear decision boundaries

Assumptions of QDA

• Observations within each class are drawn from a multivariate Gaussian distribution

• Each class has its own unique mean vector, and each class can have differing variance/covariance

  • This is the primary difference between LDA and QDA
  • This makes QDA more flexible than LDA, which can cause it to perform better generally, but worse if there is a small sample size (typical issues with overfitting)

QDA Compared to LDA

• QDA holds the same assumptions as LDA except that the covariance matrix is not common for each classification
• QDA tends to be more flexible and accurate compared to LDA, since QDA captures non-linear relationshipsto between predictors in the data
• QDA tends to be more computationally expensive compared to LDA
• QDA tends to fall victim to overfitting, due to its added flexibility

References

• QDA Description and Example
• Lecture Notes of QDA
• Example of QDA