Rule models

We can best understand rule models using the principles of discrete mathematics. Let's review some of these principles.

Let X be a set of features, the feature space, and C be a set of classes. We can define the ideal classifier for X as follows:

c: X → C

A set of examples in the feature space with class c is defined as follows:

D = {(x1, c( x1)), ... , (xn, c( xn)) ⊆ X × C

A splitting of X is partitioning X into a set of mutually exclusive subsets X1....Xs, so we can say the following:

X = X1 ∪ .. ∪ Xs

This induces a splitting of D into D1,...Ds. We define Dj where j = 1,...,s and is {(x,c(x) ∈ D | x ∈ Xj)}.

This is just defining a subset in X called Xj where all the members of Xj are perfectly classified.

In the following table we define ...

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