## IF-THEN Rules

Rule-based classifier make use of set of IF-THEN rules for classification. We can express the rule in the following from:

IF condition THEN conclusion

Let us consider a rule R1,

R1: IF age=youth AND student=yes THEN buy_computer=yes

Points to remember:

- The IF part of the rule is called rule antecedent or precondition.
- The THEN part of the rule is called rule consequent.
- In the antecedent part the condition consist of one or more attribute tests and these tests are logically ANDed.
- The consequent part consist class prediction.

**Note:**

We can also write rule R1 as follows:

R1: (age = youth) ^ (student = yes))(buys computer = yes)

If the condition holds the true for a given tuple, then the antecedent is satisfied.

## Rule Extraction

Here we will learn how to build a rule based classifier by extracting IF-THEN rules from decision tree. Points to remember to extract rule from a decision tree:

- One rule is created for each path from the root to the leaf node.
- To from the rule antecedent each splitting criterion is logically ANDed.
- The leaf node holds the class prediction, forming the rule consequent.

## Rule Induction Using Sequential Covering Algorithm

Sequential Covering Algorithm can be used to extract IF-THEN rules form the training data. We do not require to generate a decision tree first. In this algorithm each rule for a given class covers many of the tuples of that class.

Some of the sequential Covering Algorithms are AQ, CN2, and RIPPER. As per the general strategy the rules are learned one at a time. For each time rules are learned, a tuple covered by the rule is removed and the process continues for rest of the tuples. This is because the path to each leaf in a decision tree corresponds to a rule.

**Note:**The Decision tree induction can be considered as learning a set of rules simultaneously.

The Following is the sequential learning Algorithm where rules are learned for one class at a time. When learning a rule from a class Ci, we want the rule to cover all the tuples from class C only and no tuple form any other class.

Algorithm: Sequential Covering Input: D, a data set class-labeled tuples, Att_vals, the set of all attributes and their possible values. Output: A Set of IF-THEN rules. Method: Rule_set={ }; // initial set of rules learned is empty for each class c do repeat Rule = Learn_One_Rule(D, Att_valls, c); remove tuples covered by Rule form D; until termination condition; Rule_set=Rule_set+Rule; // add a new rule to rule-set end for return Rule_Set;

## Rule Pruning

The rule is pruned is due to the following reason:

- The Assessment of quality are made on the original set of training data. The rule may perform well on training data but less well on subsequent data. That’s why the rule pruning is required.
- The rule is pruned by removing conjunct. The rule R is pruned, if pruned version of R has greater quality than what was assessed on an independent set of tuples.

FOIL is one of the simple and effective method for rule pruning. For a given rule R,

FOIL_Prune = pos-neg/ pos+neg

Where pos and neg is the number of positive tuples covered by R, respectively.

**Note:**This value will increase with the accuracy of R on pruning set. Hence, if the FOIL_Prune value is higher for the pruned version of R, then we prune R.