# CN2 Induction Algorithm

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A CN2 Induction Algorithm is a rule induction algorithm based on a combination of AQ and ID3.

**Context:**- It can be implemented by a CN2 Induction System to solve a CN2 Induction Task.
- It was initially developed by Clark & Nibblet (1989).
- It outputs a If-Then Rule Set.
- …

**Example(s):****Counter-Example(s):****See:**Pattern Mining Algorithm, Decision Tree Induction Algorithm, Inductive Logic Programming, Propositional Rule, Firs-Order Logic Rule.

## References

### 2019

- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/CN2_algorithm Retrieved:2019-11-3.
- The
**CN2 induction algorithm**is a learning algorithm for rule induction (Clark & Nibblet, 1989). The CN2 induction algorithm. Machine Learning 3(4):261-283. </ref> It is designed to work even when the training data is imperfect. It is based on ideas from the AQ algorithm and the ID3 algorithm. As a consequence it creates a rule set like that created by AQ but is able to handle noisy data like ID3.

- The

### 1989

- (Clark & Nibblet, 1989) ⇒ Peter Clark, and Tim Niblett. (1989). “The CN2 Induction Algorithm”. In: Machine Learning, 3(4) DOI:10.1023/A:1022641700528
- QUOTE: Table 3 presents a summary of the CN2 algorithm. This works in an iterative fashion, each iteration searching for a complex that covers a large number of examples of a single class C and few of other classes...

Let E be a set of classified examples. | ||||

Let SELECTORS be the set of all possible selectors. | ||||

Procedure CN2(E)
| ||||

Let RULE-LIST be the empty list. | ||||

Repeat until BEST_CPX is nil or E is empty:
| ||||

Let BEST_CPX be Find-Best_Complex(E). | ||||

If BEST_CPX is not nil, | ||||

Then let E' be the examples covered by BEST_CPX. | ||||

Remove from E the examples E' covered by BEST_CPX. | ||||

Let C be the most common class of examples in E'. | ||||

Add the rule 'If BEST_CPX then the class is C' | ||||

to the end of RULE-LIST. | ||||

Return RULE-LIST.
| ||||

Procedure Find-Best_Complex(E)
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Let STAR be the set containing the empty complex. | ||||

Let BEST_CPX be nil. | ||||

While STAR is not empty,
| ||||

Specialize all complexes in STAR as follows: | ||||

Let NEWSTAR be the set {x ∧ y|x ∈ STAR, y ∈ SELECTORS}. | ||||

Remove all complexes in NEWSTAR that are either in STAR (i.e., the unspecialized ones) or null (e.g., big = y ∈ big = n). | ||||

For every complex C_{i} in NEWSTAR:
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If C_{i} is statistically significant and better than BEST_CPX by user-defined criteria when tested on E,
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Then replace the current value of BEST_CPX by C_{i.
} | ||||

Repeat until size of NEWSTAR ≤ user-defined maximum:
| ||||

Remove the worst complex from NEWSTAR. | ||||

Let STAR be NEWSTAR. | ||||

Return BEST_CPX.
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