Databases Reference
In-Depth Information
6 An Example
In this section, an example is given to illustrate the proposed mining algo-
rithm. Assume there are four items in a transaction database: milk, bread,
cookies and beverage. The data set includes the six transactions shown in
Table 1.
Assume the maximum possible number (
T
) of fuzzy regions for each item
is set at 4. The actual number of membership functions of each item will be
derived by the proposal mining algorithm. For the data shown in Table 1, the
proposed algorithm proceeds as follows.
STEP 1: Four populations are randomly generated, each for one item. As-
sume the population size is 10 in this example. Each population then includes
10 individuals. Each individual in the first population is a set of membership
functions for item
milk
. Similarly, an individual in the other populations is a
set of membership functions respectively for
bread
,
cookies
,and
beverage
.
STEP 2: Each set of membership functions for an item is encoded into
a chromosome according to the proposed representation. Assume the ten in-
dividuals in each of the four populations are randomly generated as show in
Table 2.
STEP 3: The fitness value of each chromosome is then calculated by the
following substeps. Take the chromosome
C
1
in
Population
3
as an example.
The membership functions in
C
1
for
cookies
are represented as (1 1 1 1, 0 3
5, 3 5 10, 6 13 16, 15 20 20).
STEP 3.1: The quantitative value of each item in each transaction datum
is transformed into a fuzzy set according to the active membership functions
represented by that chromosome. Take the first item in transaction
T
1as
an example. The contents of
T
1 include (
milk
,5),(
bread
, 10), (
cookies
,7),
and (
beverage
, 7). The amount “7” of item cookies is then converted into the
fuzzy set:
0
cookies.Low
+
0
.
6
cookies.LowMiddle
+
0
.
14
cookies.MiddleHigh
+
0
cookies.High
by using the membership functions in
C
1
in
Population
3
. The results for
all the transactions by using chromosome
C
1
in
Population
3
are shown in
Table 3, where the notation
item.term
is called a fuzzy region.
Tabl e 1 .
Six transactions in this example
TID
Items
T1
(milk, 5); (bread, 10); (cookies, 7); (beverage, 7)
T2
(milk, 7); (bread, 14); (cookies, 12)
T3
(bread, 15); (cookies, 12); (beverage, 10)
T4
(milk, 2); (bread, 5); (cookies, 5)
T5
(bread, 9)
T6
(milk, 13); (beverage, 12)
