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6.1 Basic Concepts 245

to the supermarket? This information can lead to increased sales by helping retailers do
selective marketing and plan their shelf space.
Let’s look at an example of how market basket analysis can be useful.

Example 6.1 Market basket analysis. Suppose, as manager of an AllElectronics branch, you would
like to learn more about the buying habits of your customers. Specifically, you wonder,
“Which groups or sets of items are customers likely to purchase on a given trip to the store?”
To answer your question, market basket analysis may be performed on the retail data of
customer transactions at your store. You can then use the results to plan marketing or
advertising strategies, or in the design of a new catalog. For instance, market basket anal-
ysis may help you design different store layouts. In one strategy, items that are frequently
purchased together can be placed in proximity to further encourage the combined sale
of such items. If customers who purchase computers also tend to buy antivirus software
at the same time, then placing the hardware display close to the software display may
help increase the sales of both items.
In an alternative strategy, placing hardware and software at opposite ends of the store
may entice customers who purchase such items to pick up other items along the way. For
instance, after deciding on an expensive computer, a customer may observe security sys-
tems for sale while heading toward the software display to purchase antivirus software,
and may decide to purchase a home security system as well. Market basket analysis can
also help retailers plan which items to put on sale at reduced prices. If customers tend to
purchase computers and printers together, then having a sale on printers may encourage
the sale of printers as well as computers.

If we think of the universe as the set of items available at the store, then each item has a
Boolean variable representing the presence or absence of that item. Each basket can then
be represented by a Boolean vector of values assigned to these variables. The Boolean
vectors can be analyzed for buying patterns that reflect items that are frequently associ-
ated or purchased together. These patterns can be represented in the form of association
rules. For example, the information that customers who purchase computers also tend
to buy antivirus software at the same time is represented in the following association
rule:
computer ⇒ antivirus software [support = 2%,confidence = 60%]. (6.1)

Rule support and confidence are two measures of rule interestingness. They respec-
tively reflect the usefulness and certainty of discovered rules. A support of 2% for
Rule (6.1) means that 2% of all the transactions under analysis show that computer
and antivirus software are purchased together. A confidence of 60% means that 60% of
the customers who purchased a computer also bought the software. Typically, associa-
tion rules are considered interesting if they satisfy both a minimum support threshold
and a minimum confidence threshold. These thresholds can be a set by users or
domain experts. Additional analysis can be performed to discover interesting statistical
correlations between associated items.