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APriori.log
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APriori.log
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This is LuaTeX, Version 1.07.0 (TeX Live 2018) (format=lualatex 2018.5.6) 25 DEC 2019 20:02
restricted system commands enabled.
**Chapters/DataMining/APriori.pillar
(./Chapters/DataMining/APriori.pillar
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l.1 !
! A-Priori Algorithm for Mining Frequent Itemsets
?
! Interruption.
\GenericError ...
\endgroup
l.1 !
! A-Priori Algorithm for Mining Frequent Itemsets
?
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[]!!
[]
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l.3 M
odern retailers collect massive amounts of sales data - the logs of onlin...
? q
OK, entering \batchmode...
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[]Modern
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l.5 M
any of these problems can be solved by scanning the database of transacti...
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[]Many
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l.7 B
y finding frequent sets of items, we can also produce association rules b...
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l.9 I
n this chapter, we discuss ''A-Priori'' - a fast and efficient algorithm ...
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[]In
[]
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l.13 !
!! Example: Problem Definition
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[]!!!
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l.16 Y
ou are given a database of transactions {{{$T$}}}:
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[]You
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\OML/cmm/m/it/10 T$\nullfont :
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l.18 |
! TID |! Transaction
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l.26 R
emember that item base is a set of all products.
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[]Remember
[]
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l.29 '
'B'' = =={ eggs, milk, butter, cereal, bacon, bread, avocado, bananas}==
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l.32 Y
our task is to find a set {{{$\mathcal{F}$}}} of all frequent itemsets i...
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[]Your
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l.34 N
ote that in practice, it is faster to encode all items with integers bef...
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[]Note
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l.36 T
urns out, this is not an easy thing to do.
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l.38 !
!! Why This is a Complicated Problem?
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l.40 S
o far, the problem does not seem complicated: you can find all frequent ...
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l.42 [
[[
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l.47 H
owever, the number of possible itemsets grows very quickly as you increa...
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<recently read> \mathbb
l.47 ... called ''powerset'' and denoted {{{$\mathbb
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t :
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l.50 \[
|\mathbb{P}(B)| = \sum_{k=0}^{|B|} C_k^{|B|} = 2^{|B|} \]
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l.53 E
ven for the smallest stores that sells very limited number of products, ...
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l.56 |
! Number of products |! Number of itemsets
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l.62 T
o solve the problem of frequent itemset mining, we must therefore reduce...
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l.64 !
!! Setting the Vocabulary
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[]!!!
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l.67 Y
ou are given a set of items called ''item base''. Think of those items a...
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l.70 \[
B = \{ i_1, \dots, i_n \} \]
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\OML/cmm/m/it/10 B \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 i[]; []
; i[]\OMS/cmsy/m/n/10 g
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l.73 Y
ou are also given a set of ''transactions'' {{{$T$}}} where each transac...
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\OML/cmm/m/it/10 T$
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\OML/cmm/m/it/10 B$\nullfont .
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l.76 \[
T = \{ t_1, \dots, t_m \} \]
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\OML/cmm/m/it/10 T \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 t[]; []
; t[]\OMS/cmsy/m/n/10 g
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\OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 t[] \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 Tt[]
\OMS/cmsy/m/n/10 \OML/cmm/m/it/10 B
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l.80 W
e use the word ''itemset'' to denote any set of items selected from the ...
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l.83 \[
I \subseteq B \]
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\OML/cmm/m/it/10 I \OMS/cmsy/m/n/10 \OML/cmm/m/it/10 B
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l.86 I
n fact, every transaction is an itemset (a set of items that were purcha...
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l.88 W
e say that itemset {{{$I$}}} ''appears'' in transaction {{{$t$}}} if {{{...
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\OML/cmm/m/it/10 I \OMS/cmsy/m/n/10
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l.90 T
he ''count'' of an item set {{{$I$}}} in a set of trasactions {{{$T$}}} ...
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\OML/cmm/m/it/10 T$
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l.93 \[
count(I) = | \{ t_k \in T | I \subseteq t_k \} | \]
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\OML/cmm/m/it/10 count\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 I\OT1/cmr/m/n/10 ) = \O
MS/cmsy/m/n/10 jf\OML/cmm/m/it/10 t[] \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 T\OMS
/cmsy/m/n/10 j\OML/cmm/m/it/10 I \OMS/cmsy/m/n/10 \OML/cmm/m/it/10 t[]\OMS/cm
sy/m/n/10 gj
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l.96 T
he ''support'' of an itemset {{{$I$}}} is the relative frequency of this...
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\OML/cmm/m/it/10 I$
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\OML/cmm/m/it/10 T$
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l.99 \[
support(I) = \frac{count(I)}{|T|} \]
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\OML/cmm/m/it/10 support\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 I\OT1/cmr/m/n/10 ) =
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l.102 w
here {{{$|T|$}}} is the total number of transactions.
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[]where
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\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 T\OMS/cmsy/m/n/10 j$
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l.104 S
upport has a probabilistic interpretation - it is a probability that cu...
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[]Support
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l.106 {{{\[
support(I) = P(I) \]}}}
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\OML/cmm/m/it/10 support\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 I\OT1/cmr/m/n/10 ) =
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 I\OT1/cmr/m/n/10 )
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l.108 G
iven some ''minimum support'' {{{$ minsup \in \mathbb{N} $}}}, an items...
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! Undefined control sequence.
l.108 ...''minimum support'' {{{$ minsup \in \mathbb
{N} $}}}, an itemset {{{$I...
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of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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\OML/cmm/m/it/10 minsup \OMS/cmsy/m/n/10 2
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\OML/cmm/m/it/10 support\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 I\OT1/cmr/m/n/10 )$
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l.110 T
he set of all frequent itemsets in a database of transactions {{{$T$}}}...
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[]The
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