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The meaning of multi-class classification rules

Example: I have two classification rules (Refund is a predictor and Cheat is a binary response):
(Refund, No) → (Cheat, No) Support = 0.4, Confidence = 0.57
(Refund, No) → (Cheat, Yes) Support = 0.3, Confidence = 0.43

=> multi-class classification rules:

(Refund, No) → (Cheat, No) v (Cheat, Yes)

When predicted classification for test data, (Cheat, No) will be selected priority so why we need to have (Cheat, Yes) in multi-class classification rules here?

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(Cheat, No) will be selected (cheat will be classified as No) for the rule (Refund, No).

In a binary response variable like cheat, all the information can be inferred from just the first rule: 

(Refund, No) → (Cheat, No) Support = 0.4, Confidence = 0.57

The other rule is redundant.

However, in the case of a multi-class response variable, we would like to have all the rules written out so we exactly know the likelihood of the rule implying each of the different classes in the response variable. To keep things consistent, this is also done for the case when the response variable is binary.

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  • $\begingroup$ Thanks Nitesh, The purpose (Cheat, Yes) is retained in the multi-layer classification rules to do? $\endgroup$
    – Xuan Dung
    Nov 8, 2014 at 23:03
  • $\begingroup$ @XuanDung: For classification where the response is not binary (multi-class), the confidence of other classes cannot be derived from the confidence of the predicted class (unlike in the binary class version). $\endgroup$
    – Nitesh
    Nov 8, 2014 at 23:05
  • $\begingroup$ I want to know why need to have (Cheat, yes) in this multi-class classification rule, while the predicted classification (Cheat, No) is selected, so (Cheat, Yes) is redundant. $\endgroup$
    – Xuan Dung
    Nov 8, 2014 at 23:12
  • $\begingroup$ Its not just the predicted class, the probability with which its predicted is also important. $\endgroup$
    – Nitesh
    Nov 8, 2014 at 23:20
  • $\begingroup$ I still do not understand why need to have (Cheat, yes) in this multi-class classification rule, you can more explain clean, thanks. $\endgroup$
    – Xuan Dung
    Nov 8, 2014 at 23:26
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It is important to see all the rules if one of the states of target column is more important than others. For example, if you are predicting fraudulent transactions, you might want to flag something as fraud even if is has 5% probability.

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