Editing Statistical classification (section)

==Linear classifiers==
{{main|Linear classifier}}
A large number of [[algorithm]]s for classification can be phrased in terms of a [[linear function]] that assigns a score to each possible category ''k'' by [[linear combination|combining]] the feature vector of an instance with a vector of weights, using a [[dot product]].  The predicted category is the one with the highest score.  This type of score function is known as a [[linear predictor function]] and has the following general form:
<math display=block>\operatorname{score}(\mathbf{X}_i, k) = \boldsymbol\beta_k \cdot \mathbf{X}_i,</math>
where '''X'''<sub>''i''</sub> is the feature vector for instance ''i'', '''β'''<sub>''k''</sub> is the vector of weights corresponding to category ''k'', and score('''X'''<sub>''i''</sub>, ''k'') is the score associated with assigning instance ''i'' to category ''k''.  In [[discrete choice]] theory, where instances represent people and categories represent choices, the score is considered the [[utility]] associated with person ''i'' choosing category ''k''.

Algorithms with this basic setup are known as [[linear classifier]]s.  What distinguishes them is the procedure for determining (training) the optimal weights/coefficients and the way that the score is interpreted.

Examples of such algorithms include
* {{annotated link|Logistic regression}}
** {{annotated link|Multinomial logistic regression}}
* {{annotated link|Probit regression}}
* The [[perceptron]] algorithm
* {{annotated link|Support vector machine}}
* {{annotated link|Linear discriminant analysis}}