The algorithm begins by identifying frequent, individual items (items
with a frequency greater than or equal to the given support) in the
database and continues to extend them to larger, frequent itemsets.
Algorithm
The following are the main steps of the algorithm:
1. Calculate the support of item sets (of size k = 1) in the
transactional database (note that support is the frequency of
occurrence of an itemset). This is called generating the
candidate set.
2. Prune the candidate set by eliminating items with a support
less than the given threshold.
3. Join the frequent itemsets to form sets of size k + 1, and repeat
the above sets until no more itemsets can be formed. This will
happen when the set(s) formed have a support less than the
given support.
Let’s go over an example to see the algorithm in action. Suppose that
the given support is 3 and the required confidence is 80%.
K=1: it is called C1(candidate set).
K=2:
K=3:
Now let’s create the association rules. This is where the given
confidence is required. For rule X -> Y, the confidence is calculated
as Support(X and Y)/Support(X)
The following rules can be obtained from the size of two frequent
itemsets (2-frequent itemsets):
I2 -> I3 Confidence = 3/3 = 100%.
2. I3 -> I2 Confidence = 3/4 = 75%
3. I3 -> I4 Confidence = 3/4 = 75%.
4. I4 -> I3 Confidence = 3/3 = 100%
1.
Since our required confidence is 80%, only rules 1 and 4 are
included in the result. Therefore, it can be concluded that customers
who bought item two (I2) always bought item three (I3) with it, and
customers who bought item four (I4) always bought item 3 (I3) with
it.