An Efficient way to Find Frequent

Pattern with Dynamic

Programming Approach

An Efficient way to Find Frequent

Pattern with Dynamic

Programming Approach

Paper ID: 850

Prepared by: Bhalodiya Dharmesh J.

Paper ID: 850

Prepared by: Bhalodiya Dharmesh J.

Frequent Pattern Mining: An ExampleFrequent Pattern Mining: An Example

Given a transaction database DB and a minimum support threshold ξ, find all

frequent patterns (item sets) with support no less than ξ.

INPUT Minimum support: ξ =2 and DB:

OUTPUT All frequent patterns, i.e.,

{I1}, {I2}, {I4}, {I5}, {I1, I2}…,{I4, I5}

Problem Statement: How to efficiently find all frequent patterns?

Given a transaction database DB and a minimum support threshold ξ, find all

frequent patterns (item sets) with support no less than ξ.

INPUT Minimum support: ξ =2 and DB:

OUTPUT All frequent patterns, i.e.,

{I1}, {I2}, {I4}, {I5}, {I1, I2}…,{I4, I5}

Problem Statement: How to efficiently find all frequent patterns?

TID Item set

T1

T2

T3

T4

T5

T6

I1, I2, I5

I2, I3

I1, I5

I2, I4, I5

I1, I2, I4

I4, I5

Apriori StepsApriori Steps

Step 1: Candidate Generation :- Use frequent (k – 1)-itemsets (Lk-1) to

generate candidates of frequent k-itemsets Ck

Step 2: Candidate Test :- Scan database and count each pattern in Ck , get

frequent k-itemsets ( Lk )

E.G. ,

Step 1: Candidate Generation :- Use frequent (k – 1)-itemsets (Lk-1) to

generate candidates of frequent k-itemsets Ck

Step 2: Candidate Test :- Scan database and count each pattern in Ck , get

frequent k-itemsets ( Lk )

E.G. , Apriori iteration

C1 {I1}, {I2}, {I3}, {I4}, {I5}L1 {I1}, {I2}, {I4}, {I5}

C2 {I1,I2},{I1,I3},{I1,I4},{I1,I5},{I2,I3}...,{I4,I5}

L2 {I1, I2},{I1, I5},{I2, I4},{I2, I5},{I4, I5}

Performance Bottlenecks of AprioriPerformance Bottlenecks of Apriori

Candidate Generation :- Generate huge candidate sets

104 frequent 1-itemset will generate 107 candidate 2-itemsets.

To discover a frequent pattern of size 100, e.g., {I1, I2, …, I100}, one needs to generate

2100 1030 candidates.

Candidate Test :- incur multiple scans of database for each candidate.

Candidate Generation :- Generate huge candidate sets

104 frequent 1-itemset will generate 107 candidate 2-itemsets.

To discover a frequent pattern of size 100, e.g., {I1, I2, …, I100}, one needs to generate

2100 1030 candidates.

Candidate Test :- incur multiple scans of database for each candidate.

AprioriDPAprioriDP

Ideas, Construction and DesignIdeas, Construction and Design

AprioriDP: IdeasAprioriDP: Ideas

Use the dynamic table to store 1-itemset and 2-itemset candidate count.

Highly compacted, but complete for frequent pattern mining.

Avoid costly one database scan.

Directly map 2-itemset candidate.

Efficient mapping technique to find frequent itemsets.

Avoid candidate generation

Use the dynamic table to store 1-itemset and 2-itemset candidate count.

Highly compacted, but complete for frequent pattern mining.

Avoid costly one database scan.

Directly map 2-itemset candidate.

Efficient mapping technique to find frequent itemsets.

Avoid candidate generation

AprioriDP : Construction and DesignAprioriDP : Construction and Design

Pair wise scanning.Pair wise scanning. Mapping Technique. Mapping Technique.

AprioriDP : Construction and DesignAprioriDP : Construction and Design

Pair wise scanningPair wise scanning Mapping Technique. Mapping Technique.

AprioriDP : Construction and DesignAprioriDP : Construction and Design

Pair wise scanningPair wise scanning Mapping Technique. Mapping Technique.

AprioriDP : Construction and Design- Final stage.AprioriDP : Construction and Design- Final stage.

Advantages of Dynamic Table structure Advantages of Dynamic Table structure

The most significant advantage of the AprioriDP

Scan the DB only once only.

Bottom-Up approach.

Completeness:

the AprioriDP contains all the information related to mining frequent patterns (2-itemset).

Compactness:

The size of the Table is bounded by the Total No. of items.

Reusable:

Once Dynamic Table fill with occurrence count, we can test candidates at different min_sup.

The most significant advantage of the AprioriDP

Scan the DB only once only.

Bottom-Up approach.

Completeness:

the AprioriDP contains all the information related to mining frequent patterns (2-itemset).

Compactness:

The size of the Table is bounded by the Total No. of items.

Reusable:

Once Dynamic Table fill with occurrence count, we can test candidates at different min_sup.

AprioriDPAprioriDP

Performance EvaluationPerformance Evaluation

Experiment SetupExperiment Setup

Compare the runtime of AprioriDP with Traditional Apriori .

Runtime vs. min_sup.

Runtime per itemset vs. min_sup.

Synthetic data sets : T25.I10.D10K

250 items

avg(transaction size)=25

avg(max/potential frequent item size)=10

10K transactions

Compare the runtime of AprioriDP with Traditional Apriori .

Runtime vs. min_sup.

Runtime per itemset vs. min_sup.

Synthetic data sets : T25.I10.D10K

250 items

avg(transaction size)=25

avg(max/potential frequent item size)=10

10K transactions

Runtime vs. min_sup.Runtime vs. min_sup.

Runtime per itemset vs. min_sup.Runtime per itemset vs. min_sup.