An Efficient Algorithm for Incremental Mining of Association Rules

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An Efficient Algorithm for Incremental Mining of Association Rules

Chin-Chen Chang, Yu-Chiang Li, Jung-San Lee

RIDE-SDMA’05

Speaker ：董原賓 Advisor ：柯佳伶

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Introduction Previous incremental mining algorithms

FUP (Fast Update Algorithm) FUP2 negative border※They all have to rescan the originally database

Problem Publication-like database

EX ： Publication database, web log records, etc. The original database is normally much larger than the incremental database

Solution NFUP (New Fast Update Algorithm)

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Definition

DB ： original database db ： the set of newly added transaction

s DB+ ： DB + db n, Pn ： db is divided into n partitions, db = P1UP2U,…,UPn-1UPn

dbm,n = PmUPm+1U,…,UPn-1UPn

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Definition α set: frequent itemsets in DB+

β set: frequent in dbm,n , (m ≤ n), but infrequent in dbm-1,n

γ set: frequent in dbm,m, but infrequent in dbm+1,n

X.count ： occurrence count

X.start ： partition number when X becomes frequent

X.type ： denotes one of the three types α,β, and γ

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FUP (Fast Update Algorithm)

In case2, itemset is easily calculated In case3, FUP needs to rescan the orig

inal database

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NFUP (New Fast Update Algo.) A backward method that only requires scan

ning incremental database

A frequent itemset in the incremental database is also important even if it is infrequent in the updated database

Partition the incremental database (db) by the time interval

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NFUP The frequent set of itemsets of DB is k

nown in advance

NFUP scans each partition backward, the last partition is scanned first

In each partition, the process is performed like that of Apriori.

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NFUP

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Scan from Pn to P1 and find the α,β,γ itemsets in db

After P1 is scanned, the occurrence count is accumulated with itemsets of DB

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The latest partition is scanned first, initialize variables and accumulate the occurrence

Still frequent in Pm then

accumulate count

Still frequent in dbm,n then accumulate count

Only frequent in dbm+1,n then Remove from α set and addInto β set

Not belong to any set and frequent in Pm then check if Pm is the latest partitionYes α set No γ set

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Example

Scan p2 : 1-itemset

α set startcountβ set startcount γ set startcount

Min sup = 50%

{A: 2} {B: 2} {C: 3}{D: 1} {E: 1} {F: 2}

3 x 0.5 = 1.5

Check if itemset belongs to α setElse check itemset doesn’t belongs to any setCheck if itemset’s count >= 1.5Check if P2 is the latest partition yes α no γ

{A} 2 2

{B} 2 2

{C} 2 3

{F} 2 2

{AB} 2 2

{AC} 2 2

{BC} 2 2

{CF} 2 2

{ABC} 2 2

Run Apriori-gen scan P2 : 2-itemset {AB: 2} {AC: 2} {AF: 1} {BC: 2} {BF: 1} {CF: 2}

Check if itemset belongs to α set Else check itemset doesn’t belong to any set Check if itemset’s count >= 1.5 Check if P2 is the latest partition yes α no γ

{ABC: 2}Scan P2 : 3-itemset

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Example

Scan p1 : 1-itemset

α set startcountβ set startcount γ set startcount

Min sup = 50%

{A: 1} {B: 3} {C: 2}{D: 1} {E: 3} {F: 0}

3 x 0.5 = 1.5

Check if itemset belongs to α set Check itemset doesn’t belongs to any setElse check if itemset’s count >= 1.5Check if P1 is the latest partition yes α no γ

{A} 2 2

{B} 2 2

{C} 2 3

{F} 2 2

{AB} 2 2

{AC} 2 2

{BC} 2 2

{CF} 2 2

{ABC} 2 2

Run Apriori-genscan P1 : 2-itemset {AB: 1} {AC: 0} {BC: 2}{BE: 3} {CE: 2}Check if itemset belon

gs to α set Check itemset doesn’t belong to any set Else check if itemset’s count >= 1.5 Check if P1 is the latest partition yes α no γ

Yesaccumulate countCount < s*|dbm,n| = 0.5x6 = 3 β set

Yesaccumulate countCount < s*|dbm,n| = 0.5x6 = 3 β set

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51

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1{F} 2 2 {E} 1 3

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4

1

1

{AC} 2 2

{CF} 2 2

{BE} 1 3

{CE} 1 2

{ABC} 2 2

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Example

α set startcount

{A} 1 3

{B} 1 5

{C} 1 5

{AB} 1 3

{BC} 1 4

γ set startcount

{E} 1 3

{BE} 1 3

{CE} 1 2

β set startcount

{F} 2 2

{AC} 2 2

{CF} 2 2

{ABC} 2 2

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90

0

0

{AB} 1 3

{BC} 1 4

{ABC} 2 2

{AE} 0 3

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Experiment

Intel Pentium IV 1.5GHz CPU, 640 MB main memory

Microsoft Windows 2000 Professional Synthetic datasets:

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Experiment

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Experiment

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Experiment