Quadratic Discriminant Analysis

Quadratic discriminant analysis classifies cases into known groups using Gaussian class densities with a separate covariance matrix for each group, giving curved decision boundaries.

이차판별분석은 집단마다 별도의 공분산행렬을 둔 정규분포 밀도로 사례를 이미 알려진 집단에 분류하며, 곡선 형태의 판별 경계를 만듭니다.

My groups have very different spreads on the predictors; is there a discriminant method that does not assume equal covariance matrices?

집단마다 변수들의 퍼짐이 많이 다른데, 공분산이 같다고 가정하지 않는 판별분석이 있나요?

Quadratic discriminant analysis estimates a mean vector and a covariance matrix for each group and assigns each case to the group with the highest posterior probability, so decision boundaries are quadratic. Because it estimates many more parameters than linear discriminant analysis, its cross-validated accuracy should be compared with LDA before choosing it.

When to use Quadratic Discriminant Analysis

• Group covariance matrices differ substantially.
• Each group has many more cases than predictors.
• Classification accuracy matters more than a simple linear description of group differences.

When to use something else

• Groups are small relative to the number of predictors; use linear discriminant analysis instead.
• Predictors are categorical or far from normal; use multinomial logistic regression instead.

Assumptions and requirements

• Multivariate normality of predictors within each group.
• Enough cases per group to estimate a full covariance matrix.
• No perfect multicollinearity within any group.

What the analysis reports

• Cross-validated classification accuracy
• Resubstitution accuracy
• Confusion matrix
• Box's M test as evidence for unequal covariances

How to report it

A quadratic discriminant analysis with [p] predictors and [g] groups (N = [n]) achieved a [k]-fold cross-validated classification accuracy of [value]% (proportional chance [value]%).

Related methods

• Linear Discriminant Analysis
• Gaussian Mixture Model (GMM)
• Multinomial Logistic Regression

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