In general terms, a classifier is an abstract machine or function that realizes some type of grouping or sorting on a set of objects. In a set theoretical definition, classification is the projection of a partition on objects so that they are as homogenous as possible. In categorical terms, a classifier can be defined as a quadruplet (O, X, I, G) where:
O is the set of objects (o1…. on);
X is the set (x1…. xn) of features describing each object O;
I is the set of types (i1…. in);
G is a discriminant function.
In this perspective, a classifier is conceived as a categorical operation defined in the following manner:
For each object O((G(x1…. xn) i)xj).
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