Frequent itemset mining methods

Frequent Item-set Mining
Methods
Prepared By- Mr.Nilesh Magar

Data Mining:
Data mining is the efficient discovery of
valuable, non obvious information from a
large collection of data.

 Most important concepts in Data-mining
 Item-set & frequent item-set:
 Market Basket model
Frequent Item-set:

Example Of Market basket Model:
B1 = {m, c, b} B2 = {m, p, j} B3 = {m, b} B4 = {c, j}
B5 = {m, p, b} B6 = {m, c, b, j} B7 = {c, b, j} B8 = {b, c}
Suppose Min support =3
Frequent item-sets: {m:5}, {c:5}, {b:6}, {j:4}, {m, b:4}, {c,
b:4}, {j, c:3}.

Association Rule:
 Medical diagnosis dataset-symptoms and illness.
 A rule is define as an implication of the form X Y where X,Y
I (Items). Or in other words: if { i1, i2,…, ik} j, means: if a
basket contains all of i1,…, ik then it is likely to Contain j.
 The probability of finding Y for us to accept this rule is called
the confidence of the rule.
 Conf(X Y)=SUPP(X U Y)/SUPP(X)
 {m,b}c ::: Confidence = 2/4 = 50%
 Thus Association mining is 2 step Process:
Find all frequent item-sets:
Generate Strong association rules from frequent item-setPrepared By- Mr.Nilesh Magar

The Apriori algorithm
 Mining frequent item-set for Boolean association rule
 Prior knowledge
 Iterative approach known as level-wise search k-item-
sets are used to explore (k+1)-item-sets
 One full scan of the database required to find lK , L1->
Items with Min Support. L2-> generating 2-item-set etc.

 Two steps:
Join
finding Lk, a set of candidate k-itemsets is generated
by joining Lk-1 with itself
Prune
To reduce the size of Ck the Apriori property is used:
if any (k-1) subset of a candidate k-itemset is not in
Lk-1, then the candidate cannot be frequent either,so
it can be removed from Ck. – subset testing.

Join & prune
Step

Example:
TID List of item_IDs
T100 I1, I2, I5
T200 I2, I4
T300 I2, I3
T400 I1, I2, I4
T500 I1, I3
T600 I2, I3
T700 I1, I3
T800 I1, I2, I3, I5
T900 I1, I2, I3Prepared By- Mr.Nilesh Magar

 Scan D for count of each candidate
 C1: I1 – 6, I2 – 7, I3 -6, I4 – 2, I5 - 2
 Compare candidate support count with minimum support count (min_sup=2)
 L1: I1 – 6, I2 – 7, I3 -6, I4 – 2, I5 - 2
 Generate C2 candidates from L1 and scan D for count of each candidate
 C2: {I1,I2} – 4, {I1, I3} – 4, {I1, I4} – 1, …
 Compare candidate support count with minimum support count
 L2: {I1,I2} – 4, {I1, I3} – 4, {I1, I5} – 2, {I2, I3} – 4, {I2, I4} - 2, {I2, I5} – 2
 Generate C3 candidates from L2 using the join and prune steps:
 Join: C3=L2xL2={{I1, I2, I3}, {I1, I2, I5}, {I1, I3, I5}, {I2, I3, I4}, {I2, I3, I5}, {I2, I4,
I5}}
 Prune: C3: {I1, I2, I3}, {I1, I2, I5}
 Scan D for count of each candidate
 C3: {I1, I2, I3} - 2, {I1, I2, I5} – 2
 Compare candidate support count with minimum support count
 L3: {I1, I2, I3} – 2, {I1, I2, I5} – 2
 Generate C4 candidates from L3
 C4=L3xL3={I1, I2, I3, I5}
 This itemset is pruned, because its subset {{I2, I3, I5}} is not frequent => C4=null

Generating association rules from
frequent item-sets: from Slide 5
Finding the frequent item-sets from
transactions in a database D
Generating strong association rules:
Confidence(A=>B)=P(B|A)=
support_count(AUB)/support_count(A)
support_count(AUB) – number of transactions
containing the itemsets AUB
support_count(A) - number of transactions containing
the itemsets A

 Example:
 lets have l={I1, I2, I5}
 The nonempty subsets are {I1, I2}, {I1, I5}, {I2, I5}, {I1}, {I2}, {I5}.
 Generating association rules:
I1 and I2=>I5 conf=2/4=50%
I1 and I5=>I2 conf=2/2=100%
I2 and I5=> I1 conf=2/2=100%
I1=>I2 and I5 conf=2/6=33%
I2=>I1 and I5 conf=2/7=29%
I5=>I1 and I2 conf=2/2=100%
If min_conf is 70%, then only the second, third and last rules above
are output.

Advantages & Disadvantages:
 Adv:
 1) Uses Large item-set
Property
 2) Easily parallelized
 3) Easy to implement
Dis-Adv:
1) Assumes
transaction
database is
memory resident
Requires up to ‘m’
database scan.

Mining Frequent Itemsets without
candidate generation
The candidate generate and test method
It may need to generate a huge number of
candidate sets
It may need to repeatedly scan the database
and check a large set of candidates by pattern
matching
Frequent-pattern growth method(FP-
growth) – frequent pattern tree(FP-tree)

Step-1:
Item Count
I1 6
I2 7
I3 6
I4 2
I5 2
Step-2:Arrange Transaction in descending order
TID List of item
(Before)
List of item
(After)
T100 I1, I2, I5 I2,I1,I5
T200 I2, I4 I2,I4
T300 I2, I3 I2,I3
T400 I1, I2, I4 I2,I1,I4
T500 I1, I3 I1,I3
T600 I2, I3 I2,I3
T700 I1, I3 I1,I3
T800 I1, I2, I3, I5 I2,I1,I3,I5
T900 I1, I2, I3 I2,I1,I3

FP-TREE

Item Conditional
Pattern Base
Conditional
FP-tree
Frequent Pattern
Generated
I5 {{I2, I1:1}, {I2,
I1, I3:1}}
(I2:2, I1:2) {I2, I5:2}, {I1,
I5:2}, {I2, I1, I5:2}
I4 {{I2, I1:2},
{I2:1}}
(I2:2) {I2, I4:2}
I3 {{I2, I1:2},
{I2:2}, {I1:2}}
(I2:4, I1:2),
(I1:2),
{I2, I3:4}, {I1,
I3:4}, {I2, I1, I3:2}
I1 {{I2:4}} (I2:4) {I2, I1:4}

Mining frequent itemsets using vertical
data format
 Transforming the horizontal data format of the
transaction database D into a vertical data
format:
Itemset TID_set
I1 {T100, T400, T500, T700, T800, T900}
I2 {T100, T200, T300, T400, T600, T800, T900}
I3 {T300, T500, T600, T700, T800, T900}
I4 {T200, T400}
I5 {T100, T800}

Example For Practice

Minimum support threshold is 3

T List of item
(After)
T1 f,c,a,m,p
T2 f,c,a,b,m
T3 f,b
T4 c,b,p
T5 f,c,a,p,m

{}
f:4 c:1
b:1
p:1
b:1c:3
a:3
b:1m:2
p:2 m:1
Header Table
Item frequency head
f 4
c 4
a 3
b 3
m 3
p 3
FP-Growth Example

FP-Growth Example
EmptyEmptyf
{(f:3)}|c{(f:3)}c
{(f:3, c:3)}|a{(fc:3)}a
Empty{(fca:1), (f:1), (c:1)}b
{(f:3, c:3, a:3)}|m{(fca:2), (fcab:1)}m
{(c:3)}|p{(fcam:2), (cb:1)}p
Conditional FP-treeConditional pattern-baseItem

FP-Tree Algorithm:
Input: DB, min_support
Output: FP-Tree
1. Scan DB & count all frequent items.
2. Create null root & set as current node.
3. For each Transaction T
 Sort T’s items.
 For each sorted Item I
 Insert I into tree as a child of current node.
 Connect new tree node to header list.

FP- Growth Algorithm:

Adv. & disAdv. Of FP- Growth:
Adv:
1) Only 2 Passes Over Data-set
2) No Candidate Generation
3) Much Faster Than Apriori
DisAdv:
• FP-Tree may not fit in memory.
• FP-Tree is expensive to build

Subjects
1) U.M.L.
2) P.P.L.
3) D.M.D.W.
4) O.S.
5) Programming Languages
6) RDBMS
Mr. Nilesh Magar
Lecturer at MIT, Kothrud, Pune.
9975155310.
Prepared By - Mr. Nilesh Magar

Thank You
Prepared By - Mr. Nilesh Magar

Frequent itemset mining methods

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