Fisher’s direction
Theorem taught in Statistical classifiers and discriminant analysis, part of Statistical learning
Fisher’s direction
| Type | Theorem |
| Taught in | Statistical classifiers and discriminant analysis |
| Part | Statistical learning |
Let \mathbf{d}=\widehat{\boldsymbol\mu}_1-\widehat{\boldsymbol\mu}_2\ne\mathbf{0} and let S be positive definite. Among nonzero directions, the Fisher ratio is maximised by \mathbf{a}\propto S^{-1}\mathbf{d}. If \mathbf{d}=\mathbf{0}, the ratio is zero for every nonzero direction, so it selects no preferred direction.
Used in
- Taught in Statistical classifiers and discriminant analysis, where the derivation and examples are.
- All 8 questions on Statistical classifiers and discriminant analysis
See also
Positive definite matrix · Training data and classifier · Posterior class probability · Zero–one loss and risk · Bayes-optimal rule · Classification problem · Bayes classifier · Error rates and optimal classifiers