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Sem 5 Prep
← BI & Data ScienceMarket basket analysis and association rules

Formulas for this chapter

Support

Support(A to B) = P(A and B) = transactions with both / ALL transactions

First measure to compute. Says how widespread the pattern is, and therefore whether it is worth a business decision.

both
Count of transactions containing every item in the rule
ALL
Total number of transactions, the denominator that distinguishes support from confidence

Confidence

Confidence(A to B) = P(B | A) = transactions with both / transactions with A

How reliable the rule is when the antecedent is present. Not symmetric: reversing the rule changes it.

A
The antecedent, the left-hand side
transactions with A
The conditioning denominator

Lift

Lift(A to B) = P(B | A) / P(B) = Confidence(A to B) / Support(B) = P(A and B) / ( P(A) x P(B) ) <- shows it is symmetric > 1 real association | = 1 independent | < 1 negative association

The ranking measure. Always sort rules by lift, then check the count before believing one.

Support(B)
The consequent's own frequency, the baseline being divided out
symmetry
Lift(A to B) = Lift(B to A), so lift cannot tell you which way to act

Apriori in R

rules <- apriori(trans, parameter = list(support = 0.005, confidence = 0.3, minlen = 2)) rules_sorted <- sort(rules, by = "lift", decreasing = TRUE) inspect(head(rules_sorted, 10))

Generating rules in bulk. Minimum count for a rule = support x number of transactions.

support
Minimum fraction of baskets; 0.005 of 10,000 is 50 baskets
confidence
Minimum reliability; 0.3 means the rule must hold 30 % of the time
minlen
Minimum items in the rule; 2 excludes single-item results
Step 3 of 22
The real wordsTheory

The three magic numbers

The professor's own mnemonic: "Think of Support as how often, Confidence as how sure, and Lift as how strong."

Support(A to B) = P(A and B) = transactions with both / all transactions Confidence(A to B) = P(B | A) = transactions with both / transactions with A Lift(A to B) = P(B | A) / P(B) = Confidence(A to B) / Support(B)

All three come from three counts: baskets with both, baskets with A, and baskets with B.

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