The Part I tutorial, is based on Apriori algorithm and we stated a few about association rules. Today, we will look about association rules, confidence and support.

## Association Rule

If we go by our previous post we defined learning association rule as means finding those items which were bought together most often i.e. single items, pair-wise items, triples etc.

In technical terms, If-then rules about the contents of the basket. Example is below:

Rule for {i1, i2, i3, i4, i5...., iN} -> j means : "

*if a basket contains all of i1,..., iN then its likely to contain an item j.*## Confidence

*of the association rule is the probability of*

**Confidence***j given i1,..., iN*. Simple terms, it's the Ratio of support for

**I**Suppot of I is the number of baskets/transactions containing item I.

*U*{ j } with support for I.### Example

Our Transactions/Baskets |

Now if we want to check the association rule for {2, 4} -> 5.

The confidence is: Ratio of {2, 4}

*U*{5} with support of {2, 4}. Therefore,
Confidence = 3 / 3 => 1

We can say that, {2, 4} -> {5} has a confidence of 1. But, we want to know how interesting the rule is. For this, we have an new parameter called

**Interest.**

**Interest of an association rule**is the difference of it's confidence and the fraction of baskets which contain item j.

I ({2, 4} -> 5) = conf( {2, 4} -> 5) - Fr(5)

= 1 - (3/4)

= 1 - .75

= .25

Therefore, the Interest is just 25 %. It's not an interesting rule.

**Interesting rules are those with high positive or negative interest values.**As high positive or negative values means the presence of I encourages or discourages the presence of j.

fr(5) should be 4/5

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