<s>
Apriori	O
is	O
an	O
algorithm	O
for	O
frequent	O
item	O
set	O
mining	O
and	O
association	B-Algorithm
rule	I-Algorithm
learning	I-Algorithm
over	O
relational	B-Application
databases	I-Application
.	O
</s>
<s>
The	O
frequent	O
item	O
sets	O
determined	O
by	O
Apriori	O
can	O
be	O
used	O
to	O
determine	O
association	B-Algorithm
rules	I-Algorithm
which	O
highlight	O
general	O
trends	O
in	O
the	O
database	O
:	O
this	O
has	O
applications	O
in	O
domains	O
such	O
as	O
market	B-Algorithm
basket	I-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
The	O
Apriori	B-Algorithm
algorithm	I-Algorithm
was	O
proposed	O
by	O
Agrawal	O
and	O
Srikant	O
in	O
1994	O
.	O
</s>
<s>
Apriori	O
is	O
designed	O
to	O
operate	O
on	O
databases	O
containing	O
transactions	O
(	O
for	O
example	O
,	O
collections	O
of	O
items	O
bought	O
by	O
customers	O
,	O
or	O
details	O
of	O
a	O
website	O
frequentation	O
or	O
IP	B-Protocol
addresses	I-Protocol
)	O
.	O
</s>
<s>
Other	O
algorithms	O
are	O
designed	O
for	O
finding	O
association	B-Algorithm
rules	I-Algorithm
in	O
data	O
having	O
no	O
transactions	O
(	O
Winepi	B-Algorithm
and	O
Minepi	O
)	O
,	O
or	O
having	O
no	O
timestamps	O
(	O
DNA	O
sequencing	O
)	O
.	O
</s>
<s>
Given	O
a	O
threshold	O
,	O
the	O
Apriori	B-Algorithm
algorithm	I-Algorithm
identifies	O
the	O
item	O
sets	O
which	O
are	O
subsets	O
of	O
at	O
least	O
transactions	O
in	O
the	O
database	O
.	O
</s>
<s>
Besides	O
,	O
the	O
Apriori	B-Algorithm
algorithm	I-Algorithm
was	O
used	O
to	O
mine	O
associations	O
between	O
various	O
accidents	O
and	O
causative	O
factors	O
and	O
explored	O
the	O
potential	O
laws	O
for	O
reducing	O
subway	O
operation	O
safety	O
accidents	O
.	O
</s>
<s>
Apriori	O
uses	O
breadth-first	B-Algorithm
search	I-Algorithm
and	O
a	O
Hash	B-Application
tree	I-Application
structure	O
to	O
count	O
candidate	O
item	O
sets	O
efficiently	O
.	O
</s>
<s>
Usual	O
set	O
theoretic	O
notation	O
is	O
employed	O
,	O
though	O
note	O
that	O
is	O
a	O
multiset	B-Language
.	O
</s>
<s>
The	O
association	B-Algorithm
rules	I-Algorithm
that	O
can	O
be	O
determined	O
from	O
this	O
database	O
are	O
the	O
following	O
:	O
</s>
<s>
Bottom-up	O
subset	O
exploration	O
(	O
essentially	O
a	O
breadth-first	B-Algorithm
traversal	I-Algorithm
of	O
the	O
subset	O
lattice	O
)	O
finds	O
any	O
maximal	O
subset	O
S	O
only	O
after	O
all	O
of	O
its	O
proper	O
subsets	O
.	O
</s>
