**Statistical classification** or **discrimination** is the problem of assigning categories to observations.
If observations are drawn from distinct populations,
and we would like to find a deterministic criterion that assigns the observations to their origin,
the discriminant rule based on maximum likelihood would be \(I(x) = \arg\max_{i \in K} f_i(x)\).
Discriminant analysis are methods that provide estimators $\hat I(x)$ of such discriminant rules.

Notations:
$K$, number of classes.

## Algorithms

**Linear discriminant analysis** (LDA) assumes Gaussian populations with identical covariance matrices,
which gives a linear discriminant rule {Fisher1936}.
**Quadratic discriminant analysis** (QDA) assumes Gaussian populations, giving quadratic discriminant rules.
LDA and QDA are suitable for data with small $n$ or well separated classes, and are capable of $K>2$.

**Naive Bayes**
suitable for data with large $p$

(kernel) **support vector machine** (SVM)
SVM is computationally efficient on nonlinear kernels, suitable for data with well separated classes,
but is limited to $K=2$.

🏷 Category=Computation Category=Machine Learning