Linear classifier

In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class (or group) it belongs to. A linear classifier achieves this by making a classification decision based on the value of a linear combination of the characteristics. An object's characteristics are also known as feature values and are typically presented to the machine in a vector called a feature vector. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use.

If the input feature vector to the classifier is a real vector ${\displaystyle {\vec {x}}}$, then the output score is

where ${\displaystyle {\vec {w}}}$ is a real vector of weights and f is a function that converts the dot product of the two vectors into the desired output. (In other words, ${\displaystyle {\vec {w}}}$ is a one-form or linear functional mapping ${\displaystyle {\vec {x}}}$ onto R.) The weight vector ${\displaystyle {\vec {w}}}$ is learned from a set of labeled training samples. Often f is a simple function that maps all values above a certain threshold to the first class and all other values to the second class. A more complex f might give the probability that an item belongs to a certain class.

...
Wikipedia