Identification-tree building is the most widely used learning method. Thousands of practical identification trees, for applications ranging from medical diagnosis to process control, have been built using the idea.

For a real database of any size, it is unlikely that any test would produce even one completely homogeneous subset. Accordingly, for real databases, one needs a powerful way to measure the total disorder, or inhomogeneity, in the subsets produced by each test. Information theory can be used to compute a measure disorder:

where

nb is the number of samples in branch b,

nt is the total number of samples in all branches,

nbc is the total of samples in branch b of class c.

To see why this borrowed formula works, one needs to focus on the set of samples lying at the end of one branch b. What is required here is a formula involving nb and nbc that gives a high number when a test produces highly inhomogeneous sets and a low number when a test produces completely homogeneous sets. The following formula involving nb and nbc generally works:

The following are the observations of an astute gastronome about the reaction of a group of diners of different ages, weight and height, enjoying chilli peppers in a Mexican restaurant. Mexicans obviously enjoy their national dish, but non-Mexicans appear to have difficulty with the dish:

An dentification trees based on age group, height, weight and nationality (whether or not the indvidual is Mexican) on the above chilli pepper database, is shown below:

The question now is this: What happens when you only select middle aged people from the database? Once the middle-aged people are isolated, the available tests perform as follows:

The Mexican nationality test clearly does the best job of dividing the middle-aged set into homogeneous subsets.

This procedure helps in the generation of of an identification based on the computation of disorder introduced by each of the concepts:

This procedure helps in the conversion of an identification tree into a rule set:

Now if we are asked to consruct an identification tree for determining peoples appetite for chilli peppers, we will come up with:

The following rule set can be derived using PRUNER:

If age_group is middle_aged

and nationality is not Mexican

then the person does_not_like chilli pepper

If age_group is senior_citizen

then the person does_not_like chilli pepper

If no other rule applies

then the person likes chilli pepper

Inductive Learning is sometimes described as a learning that is akin to a heuristic search through a space of symbolic descriptions, generated by an application of various inference rules to the initial observational statements, The inference rules include generalisation rules , which perform generalising transformatins on descriptions, and conventional truth-preserving deductive rules.

Human beings have this capcity ot discover regularities, some would say patterns, in apparently diverse, interacting and noisy collections of observations. There are instances when human beings are guided by a teacher or instructor, who provides facts, and the pupil inductively infers new facts from the given. This is inductive learning.

The key output of inductive learning is a set of production rules.

An arch is conventionally defined as one brick lying on top of, and supported by, of two other bricks with the proviso that the supporting bricks do not touch each other.