8 Association

Items and Collections

In transactional data, a collection is associated with each case. A collection defines all possible items that can potentially be present in a transaction. Typically only a tiny subset of all possible items are included. For example, the items present in a market-basket transaction represent only a small fraction of the items available for sale in the store.

Sparse Data

Oracle Data Mining implements collections as nested tables, as shown in Figure 8-2. Each nested row specifies an item name and a value. If the item is present, its value is 1. If the item is not present, its value is null. Many of the item values may be null, since many of the items that could be in the collection are probably not present in any individual transaction.

The null values in nested data indicate sparsity. This means that a high proportion of the item definitions in the collection are not populated. The Oracle Data Mining association algorithm is optimized for processing sparse data.

Frequent Itemset Counting

Table 8-1 shows the frequent itemsets derived from the transactions in Figure 8-1, assuming that ASSO_MAX_RULE_LENGTH is set to 3.

Frequent Itemsets: Minimum Support

Association rules are derived from the frequent itemsets generated by the model. If rules are generated from all possible frequent itemsets, there may be a very high number of rules and the rules may not be very meaningful. Also, the model may take a long time to build. Typically it is desirable to only generate rules from frequent itemsets that are well-represented in the data.

The minimum frequent itemset support is a user-specified percentage that limits the number of frequent itemsets produced by the model. A frequent itemset must appear in at least this percentage of all the transactions if it is to be used as a basis for rules.

The ASSO_MIN_SUPPORT setting specifies the minimum frequent itemset support. It also applies to the rules derived from the frequent itemsets. For details, see Oracle Database PL/SQL Packages and Types Reference.

Table 8-2 shows the frequent itemsets that can be used to generate rules from the transactions in Figure 8-2 if the minimum support is 8%.

Antecedents and Consequents

The IF component of an association rule is known as the antecedent. The THEN component is known as the consequent. The antecedent and the consequent are disjoint; they have no items in common.

Oracle Data Mining supports association rules that have one or more items in the antecedent and a single item in the consequent.

Association Rules: Minimum Confidence

Rules have an associated confidence, which is the conditional probability that the consequent will occur given the occurrence of the antecedent.

The ASSO_MIN_CONFIDENCE setting specifies the minimum confidence for rules. The model eliminates any rules with confidence below the required minimum.

Table 8-3 shows the rules derived from the frequent itemsets listed in Table 8-2. The confidence for each rule is included. For example, the confidence of the rule "If B then D" is 28.5%, because there are seven rules with antecedent B and two of them have D as the consequent (2/7 = 28.5%).

Support

The support of a rule indicates how frequently the items in the rule occur together. For example, cereal and milk might appear together in 40% of the transactions. If so, the following two rules would each have a support of 40%.

cereal implies milk
milk implies cereal

Support is the ratio of transactions that include all the items in the antecedent and consequent to the number of total transactions.

Support can be expressed in probability notation as follows.

support(A implies B) = P(A, B)

Confidence

The confidence of a rule indicates the probability of both the antecedent and the consequent appearing in the same transaction. Confidence is the conditional probability of the consequent given the antecedent. For example, cereal might appear in 50 transactions; 40 of the 50 might also include milk. The rule confidence would be:

cereal implies milk with 80% confidence

Confidence is the ratio of the rule support to the number of transactions that include the antecedent.

Confidence can be expressed in probability notation as follows.

confidence (A implies B) = P (B/A), which is equal to P(A, B) / P(A)

Lift

Both support and confidence must be used to determine if a rule is valid. However, there are times when both of these measures may be high, and yet still produce a rule that is not useful. For example:

Convenience store customers who buy orange juice also buy milk with 
a 75% confidence. 
The combination of milk and orange juice has a support of 30%.

This at first sounds like an excellent rule, and in most cases, it would be. It has very high confidence and very high support. However, what if convenience store customers in general buy milk 90% of the time? In that case, orange juice customers are actually less likely to buy milk than customers in general.

A third measure is needed to evaluate the quality of the rule. Lift indicates the strength of a rule over the random co-occurrence of the antecedent and the consequent, given their individual support. It provides information about the improvement, the increase in probability of the consequent given the antecedent. Lift is defined as follows.

(Rule Support) /(Support(Antecedent) * Support(Consequent))

This can also be defined as the confidence of the combination of items divided by the support of the consequent. So in our milk example, assuming that 40% of the customers buy orange juice, the improvement would be:

30% / (40% * 90%)

which is 0.83 – an improvement of less than 1.

Any rule with an improvement of less than 1 does not indicate a real cross-selling opportunity, no matter how high its support and confidence, because it actually offers less ability to predict a purchase than does random chance.