Classification test

Given a population whose members can be potentially separated into a number of different sets or classes, a classification rule is a procedure in which the elements of the population set are each assigned to one of the classes. A perfect test is such that every element in the population is assigned to the class it really belongs. An imperfect test is such that some errors appear, and then statistical analysis must be applied to analyse the classification.

A special kind of classification rule are binary classifications.

Having a dataset consisting in couples x and y, where x is each element of the population and y the class it belongs to, a classification rule can be considered as a function that assigns its class to each element. A binary classification is such that the label y can take only one of two values.

A classification rule or classifier is a function h that can be evaluated for any possible value of x, specifically, given the data ${\displaystyle \{(x_{1},y_{1}),\dots ,(x_{n},y_{n})\}}$, h(x) will yields a similar classification ${\displaystyle {\hat {y}}=h(x),}$ as close as possible to the true group label y.

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