Selecting the Right Objective Measure for Association Analysis*

the dependencies between variables. For example, objective measures such as
support, confidence, interest factor, correlation, and entropy have been used extensively
to evaluate the interestingness of association patterns — the stronger
is the dependence relationship, the more interesting is the pattern. These objective
measures are defined in terms of the frequency counts tabulated in a 2 × 2
contingency table, as shown in Table 1.
Table 1. A 2 × 2 contingency table for items A and B.
B
B
A f 11 f 10 f 1+
A f 01 f 00 f 0+
f +1 f +0 N
Although there are numerous measures available for evaluating association
patterns, a significant number of them provide conflicting information about the
interestingness of a pattern. To illustrate this, consider the ten contingency tables,
E1 through E10, shown in Table 2. Table 3 shows the ranking of these tables
according to 21 different measures developed in diverse fields such as statistics,
social science, machine learning, and data mining 1 . The table also shows that
different measures can lead to substantially different rankings of contingency tables.
For example, E10 is ranked highest according to the I measure but lowest
according to the φ-coefficient; while E3 is ranked lowest by the AV measure
but highest by the IS measure. Thus, selecting the right measure for a given
application poses a dilemma because many measures may disagree with each
other.
Table 2. Ten examples of contingency tables.
Contingency table f 11 f 10 f 01 f 00
E1 8123 83 424 1370
E2 8330 2 622 1046
E3 9481 94 127 298
E4 3954 3080 5 2961
E5 2886 1363 1320 4431
E6 1500 2000 500 6000
E7 4000 2000 1000 3000
E8 4000 2000 2000 2000
E9 1720 7121 5 1154
E10 61 2483 4 7452
1 A complete definition of these measures is given in Section 2.