BIDE: Efficient Mining of Frequent Closed ... - Semantic Scholar
BIDE: Efficient Mining of Frequent Closed Sequences Jianyong Wang and Jiawei Han University of Illinois at Urbana-Champaign To appear in ICDE 2004 Presented by: Yi-Hung Wu Date: 2004/3/1
Closed Frequent Sequence Mining
Where will data mining research go? Data
Frequent Itemsets, Association Rules, Sequential Patterns, Clusters, Outliers… Knowledge
Text Classification, Web Usage Prediction, Feature Selection, Anomaly Detection, …
Constraint-based Applied DataData Mining Mining Action-oriented Text Mining
Web Mining
Multimedia Mining
Stream Mining
Action Invisible (embedded tool)
Profit
Microarray Classification, “In Vivo” Spam Filtering,…
Biomedical, Financial, Geoscience, Telecom, … P.1
Closed Frequent Sequence Mining
Where will data mining research go? Data
Frequent Itemsets, Association Rules, Sequential Patterns, Clusters, Outliers… Knowledge
Text Classification, Web Usage Prediction, Feature Selection, Anomaly Detection, …
Constraint-based Applied DataData Mining Mining Action-oriented Text Mining
Web Mining
Multimedia Mining
Stream Mining
Action Invisible (embedded tool)
Profit
Microarray Classification, “In Vivo” Spam Filtering,…
Biomedical, Financial, Geoscience, Telecom, … P.1
Closed Frequent Sequence Mining
Which patterns are interesting (applicable)? Relation
Support
M
Interestingness
Confidence All Frequent
Optimal
Itemset Sequence Tree Graph
Only Confident
P.2
Closed Frequent Sequence Mining
Which patterns are interesting (applicable)? Relation M
Support
Interestingness
Confidence All Frequent
Optimal
Itemset Sequence Tree Graph
Only Confident Maximal Frequent Closed Frequent
Top-k Frequent Closed
Non-uniform Support Threshold
Circumstance
P.2
Closed Frequent Sequence Mining
Which patterns are interesting (applicable)? Relation M
Support
Interestingness
Confidence All Frequent
Optimal
Itemset Sequence Tree Graph
Only Confident Maximal Frequent
Correlated Closed Frequent
Top-k Frequent Closed
Non-uniform Support Threshold
Approximate Constraint
Aggregate Constraint
Circumstance
P.2
Closed Frequent Sequence Mining
Which patterns are interesting (applicable)? Relation M
Support
Interestingness
Confidence All Frequent
Optimal
Itemset Sequence Tree Graph
Only Confident Maximal Frequent
Correlated Closed Frequent Frequent
Top-k Frequent Closed
Non-uniform Support Threshold
Circumstance
Approximate Constraint
Aggregate Constraint
Quantity Profitable
P.2
Closed Frequent Sequence Mining
What is “Closed Frequent”? • Take itemset as an example… le… – F ⊇ Closed F ⊇ Max F AC→ →T
P.3
Closed Frequent Sequence Mining
What is “Closed Frequent”? • Take itemset as an example… le… – F ⊇ Closed F ⊇ Max F AC→ →T
P.3
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
What is a Closed Frequent Sequence? • CloSpan [Yang&Han: sdm03] – Lexicographic sequence tree – Pruning! • Common Prefix • Partial Order • Early Termination by Equivalence
P.5
Closed Frequent Sequence Mining
What is a Closed Frequent Sequence? • CloSpan [Yang&Han: sdm03] – Lexicographic sequence tree – Pruning! • Common Prefix • Partial Order • Early Termination by Equivalence
P.5
Closed Frequent Sequence Mining
What is a Closed Frequent Sequence? • CloSpan [Yang&Han: sdm03] – Lexicographic sequence tree – Pruning! • Common Prefix • Partial Order • Early Termination by Equivalence
P.5
Closed Frequent Sequence Mining
What is a Closed Frequent Sequence? • CloSpan [Yang&Han: sdm03] – Lexicographic sequence tree – Pruning! • Common Prefix • Partial Order • Early Termination by Equivalence
P.5
Closed Frequent Sequence Mining
How to mine closed frequent sequences? • Stage 1: Generate candidate sequences – PrefixSpan + Pruning! ⇒ Prefix sequence lattice • Stage 2: Eliminate non-close sequences – Hashing: size, s-id sum • Support equality • Subsumption check
P.6
Closed Frequent Sequence Mining
How to mine closed frequent sequences? • Stage 1: Generate candidate sequences – PrefixSpan + Pruning! ⇒ Prefix sequence lattice • Stage 2: Eliminate non-close sequences – Hashing: size, s-id sum • Support equality • Subsumption check
P.6
Closed Frequent Sequence Mining
How to mine closed frequent sequences? • Stage 1: Generate candidate sequences – PrefixSpan + Pruning! ⇒ Prefix sequence lattice • Stage 2: Eliminate non-close sequences – Hashing: size, s-id sum • Support equality • Subsumption check
P.6
Closed Frequent Sequence Mining
How well does CloSpan perform? • D10C10T2.5N10S6I2.5
P.7
Closed Frequent Sequence Mining
How well does CloSpan perform? • D10C10T2.5N10S6I2.5 S6I2.5
P.7
Closed Frequent Sequence Mining
Can we mine closed frequent sequences without candidate maintenance? • BIDE – BI-Directional Extension • Forward extension events • Backward extension events
– Closure check ck • No FE • No BE
– Pruning! • BackScan P.8
Closed Frequent Sequence Mining
Can we mine closed frequent sequences without candidate maintenance? • BIDE – BI-Directional Extension • Forward extension events • Backward extension events
– Closure check ck • No FE • No BE
– Pruning! • BackScan P.8
Closed Frequent Sequence Mining
Can we mine closed frequent sequences without candidate maintenance? • BIDE – BI-Directional Extension • Forward extension events • Backward extension events
– Closure check ck • No FE • No BE
– Pruning! • BackScan P.8
Closed Frequent Sequence Mining
Where to find forward/backward extensions?
S1: MP11, MP12, MP13 S2: MP21, MP22, MP23 … Sn: MPn1, MPn2, MPn3
P.9
Closed Frequent Sequence Mining
Where to find forward/backward extensions? • FE={locally frequent items with full supports}
S1: MP11, MP12, MP13 S2: MP21, MP22, MP23 … Sn: MPn1, MPn2, MPn3
P.9
Closed Frequent Sequence Mining
Where to find forward/backward extensions? • FE={locally frequent items with full supports} • For prefix ABC, given C1A1A2BC2DA3C3E – Last instance = C1A1A2BC2DA3C3 – LLi: the i-th last-in-last appearance S1: MP11, MP12, MP13 • LL1 = A2, LL2 = B, LL3 = C3
– MPi: the i-th maximum period
S2: MP21, MP22, MP23 … Sn: MPn1, MPn2, MPn3
• MP1 = C1A1, MP2 = A2, MP3 = C2DA3
P.9
Closed Frequent Sequence Mining
Where to find forward/backward extensions? • FE={locally frequent items with full supports} • For prefix ABC, given C1A1A2BC2DA3C3E – Last instance = C1A1A2BC2DA3C3 – LLi: the i-th last-in-last appearance S1: MP11, MP12, MP13 • LL1 = A2, LL2 = B, LL3 = C3
– MPi: the i-th maximum period
S2: MP21, MP22, MP23 … Sn: MPn1, MPn2, MPn3
• MP1 = C1A1, MP2 = A2, MP3 = C2DA3
• BE={items appearing in each of MPi, ∃i)} – Scan backward each of MPi, ∀i ⇒ ScanSkip P.9
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency?
P.10
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency? • BackScan: ABC, C1A1A2BC2DA3C3E – LFi: the i-th last-in-first appearance • LF1 = A2, LF2 = B, LF3 = C2
– SMPi: the i-th semi-maximum period • SMP1 = C1A1, SMP2 = A2, SMP3 = ∅
P.10
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency? • BackScan: ABC, C1A1A2BC2DA3C3E – LFi: the i-th last-in-first appearance • LF1 = A2, LF2 = B, LF3 = C2
– SMPi: the i-th semi-maximum period • SMP1 = C1A1, SMP2 = A2, SMP3 = ∅
• ∃e ∃i, e appears in each of SMPi – Stop projection!
P.10
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency? • BackScan: ABC, C1A1A2BC2DA3C3E – LFi: the i-th last-in-first appearance • LF1 = A2, LF2 = B, LF3 = C2
– SMPi: the i-th semi-maximum period • SMP1 = C1A1, SMP2 = A2, SMP3 = ∅
• ∃e ∃i, e appears in each of SMPi – Stop projection!
P.10
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency? • BackScan: ABC, C1A1A2BC2DA3C3E – LFi: the i-th last-in-first appearance • LF1 = A2, LF2 = B, LF3 = C2
– SMPi: the i-th semi-maximum period • SMP1 = C1A1, SMP2 = A2, SMP3 = ∅
• ∃e ∃i, e appears in each of SMPi – Stop projection!
P.10
Closed Frequent Sequence Mining
Does BIDE perform much better? • BIDE/CloSpan significantly outperforms PrefixSpan/SPADE when support threshold is low • BIDE consumes much less memory and can be an order of magnitude faster than CloSpan • BIDE has linear scalability in terms of data size • BackScan and ScanSkip techniques are very effective in enhancing the performance
P.11
Closed Frequent Sequence Mining
Does BIDE perform much better? • BIDE/CloSpan significantly outperforms PrefixSpan/SPADE when support threshold is low • BIDE consumes much less memory and can be an order of magnitude faster than CloSpan • BIDE has linear scalability in terms of data size • BackScan and ScanSkip techniques are very effective in enhancing the performance
P.11
Closed Frequent Sequence Mining
Does BIDE perform much better? • BIDE/CloSpan significantly outperforms PrefixSpan/SPADE when support threshold is low • BIDE consumes much less memory and can be an order of magnitude faster than CloSpan • BIDE has linear scalability in terms of data size • BackScan and ScanSkip techniques are very effective in enhancing the performance
P.11
Closed Frequent Sequence Mining
Does BIDE perform much better? • BIDE/CloSpan significantly outperforms PrefixSpan/SPADE when support threshold is low • BIDE consumes much less memory and can be an order of magnitude faster than CloSpan • BIDE has linear scalability in terms of data size • BackScan and ScanSkip techniques are very effective in enhancing the performance
P.11
Closed Frequent Sequence Mining
Conclusion Remarks • Closed Frequent has the same expressive power as All Frequent, but provides more compact results and likely better efficiency. • Integrated optimization techniques for database projection, search space pruning, and patternclosure checking are required. • Move candidate-maintenance-and-test paradigm to a new paradigm without candidate maintenance
P.12
Closed Frequent Sequence Mining
Any Question?
3
|
P.13
Closed Frequent Sequence Mining
Any Question? My Questions…
3
|
P.13
Closed Frequent Sequence Mining
Any Question? My Questions… • CloSpan – vs. – D=D=D 3 – D=D=D
|
P.13
Closed Frequent Sequence Mining
Any Question? My Questions… • CloSpan – vs. – D=D=D 3 | – D=D=D • BIDE – How to efficiently compute or maintain MPi/SMPi? – Does it easily adapt BIDE to sequences of itemsets?
P.13
Closed Frequent Sequence Mining
Any Question? My Questions… • CloSpan – vs. – D=D=D 3 | – D=D=D • BIDE – How to efficiently compute or maintain MPi/SMPi? – Does it easily adapt BIDE to sequences of itemsets? • What is the difference between Closed Frequent Sequences and Non-trivial Repeating Patterns? P.13
Closed Frequent Sequence Mining
Where will data mining research go? Data
Frequent Itemsets, Association Rules, Sequential Patterns, Clusters, Outliers… Knowledge
Text Classification, Web Usage Prediction, Feature Selection, Anomaly Detection, …
Constraint-based Applied DataData Mining Mining Action-oriented Text Mining
Web Mining
Multimedia Mining
Stream Mining
Action Invisible (embedded tool)
Profit
Microarray Classification, “In Vivo” Spam Filtering,…
Biomedical, Financial, Geoscience, Telecom, … P.1
Closed Frequent Sequence Mining
Where will data mining research go? Data
Frequent Itemsets, Association Rules, Sequential Patterns, Clusters, Outliers… Knowledge
Text Classification, Web Usage Prediction, Feature Selection, Anomaly Detection, …
Constraint-based Applied DataData Mining Mining Action-oriented Text Mining
Web Mining
Multimedia Mining
Stream Mining
Action Invisible (embedded tool)
Profit
Microarray Classification, “In Vivo” Spam Filtering,…
Biomedical, Financial, Geoscience, Telecom, … P.1
Closed Frequent Sequence Mining
Which patterns are interesting (applicable)? Relation
Support
M
Interestingness
Confidence All Frequent
Optimal
Itemset Sequence Tree Graph
Only Confident
P.2
Closed Frequent Sequence Mining
Which patterns are interesting (applicable)? Relation M
Support
Interestingness
Confidence All Frequent
Optimal
Itemset Sequence Tree Graph
Only Confident Maximal Frequent Closed Frequent
Top-k Frequent Closed
Non-uniform Support Threshold
Circumstance
P.2
Closed Frequent Sequence Mining
Which patterns are interesting (applicable)? Relation M
Support
Interestingness
Confidence All Frequent
Optimal
Itemset Sequence Tree Graph
Only Confident Maximal Frequent
Correlated Closed Frequent
Top-k Frequent Closed
Non-uniform Support Threshold
Approximate Constraint
Aggregate Constraint
Circumstance
P.2
Closed Frequent Sequence Mining
Which patterns are interesting (applicable)? Relation M
Support
Interestingness
Confidence All Frequent
Optimal
Itemset Sequence Tree Graph
Only Confident Maximal Frequent
Correlated Closed Frequent Frequent
Top-k Frequent Closed
Non-uniform Support Threshold
Circumstance
Approximate Constraint
Aggregate Constraint
Quantity Profitable
P.2
Closed Frequent Sequence Mining
What is “Closed Frequent”? • Take itemset as an example… le… – F ⊇ Closed F ⊇ Max F AC→ →T
P.3
Closed Frequent Sequence Mining
What is “Closed Frequent”? • Take itemset as an example… le… – F ⊇ Closed F ⊇ Max F AC→ →T
P.3
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
How to mine closed frequent itemsets? • CHARM [Zaki: sdm02, kdd03] – IT-tree – Pruning!
1. 2. 3. 4.
t(X)=t(Y)→c(X)=c(Y)=c(X∪Y) t(X)⊂t(Y)→c(X)≠c(Y), but c(X)=c(X∪Y) t(X)⊃t(Y)→c(X)≠c(Y), but c(Y)=c(X∪Y) Otherwise→c(X)≠c(Y)≠c(X∪Y) P.4
Closed Frequent Sequence Mining
What is a Closed Frequent Sequence? • CloSpan [Yang&Han: sdm03] – Lexicographic sequence tree – Pruning! • Common Prefix • Partial Order • Early Termination by Equivalence
P.5
Closed Frequent Sequence Mining
What is a Closed Frequent Sequence? • CloSpan [Yang&Han: sdm03] – Lexicographic sequence tree – Pruning! • Common Prefix • Partial Order • Early Termination by Equivalence
P.5
Closed Frequent Sequence Mining
What is a Closed Frequent Sequence? • CloSpan [Yang&Han: sdm03] – Lexicographic sequence tree – Pruning! • Common Prefix • Partial Order • Early Termination by Equivalence
P.5
Closed Frequent Sequence Mining
What is a Closed Frequent Sequence? • CloSpan [Yang&Han: sdm03] – Lexicographic sequence tree – Pruning! • Common Prefix • Partial Order • Early Termination by Equivalence
P.5
Closed Frequent Sequence Mining
How to mine closed frequent sequences? • Stage 1: Generate candidate sequences – PrefixSpan + Pruning! ⇒ Prefix sequence lattice • Stage 2: Eliminate non-close sequences – Hashing: size, s-id sum • Support equality • Subsumption check
P.6
Closed Frequent Sequence Mining
How to mine closed frequent sequences? • Stage 1: Generate candidate sequences – PrefixSpan + Pruning! ⇒ Prefix sequence lattice • Stage 2: Eliminate non-close sequences – Hashing: size, s-id sum • Support equality • Subsumption check
P.6
Closed Frequent Sequence Mining
How to mine closed frequent sequences? • Stage 1: Generate candidate sequences – PrefixSpan + Pruning! ⇒ Prefix sequence lattice • Stage 2: Eliminate non-close sequences – Hashing: size, s-id sum • Support equality • Subsumption check
P.6
Closed Frequent Sequence Mining
How well does CloSpan perform? • D10C10T2.5N10S6I2.5
P.7
Closed Frequent Sequence Mining
How well does CloSpan perform? • D10C10T2.5N10S6I2.5 S6I2.5
P.7
Closed Frequent Sequence Mining
Can we mine closed frequent sequences without candidate maintenance? • BIDE – BI-Directional Extension • Forward extension events • Backward extension events
– Closure check ck • No FE • No BE
– Pruning! • BackScan P.8
Closed Frequent Sequence Mining
Can we mine closed frequent sequences without candidate maintenance? • BIDE – BI-Directional Extension • Forward extension events • Backward extension events
– Closure check ck • No FE • No BE
– Pruning! • BackScan P.8
Closed Frequent Sequence Mining
Can we mine closed frequent sequences without candidate maintenance? • BIDE – BI-Directional Extension • Forward extension events • Backward extension events
– Closure check ck • No FE • No BE
– Pruning! • BackScan P.8
Closed Frequent Sequence Mining
Where to find forward/backward extensions?
S1: MP11, MP12, MP13 S2: MP21, MP22, MP23 … Sn: MPn1, MPn2, MPn3
P.9
Closed Frequent Sequence Mining
Where to find forward/backward extensions? • FE={locally frequent items with full supports}
S1: MP11, MP12, MP13 S2: MP21, MP22, MP23 … Sn: MPn1, MPn2, MPn3
P.9
Closed Frequent Sequence Mining
Where to find forward/backward extensions? • FE={locally frequent items with full supports} • For prefix ABC, given C1A1A2BC2DA3C3E – Last instance = C1A1A2BC2DA3C3 – LLi: the i-th last-in-last appearance S1: MP11, MP12, MP13 • LL1 = A2, LL2 = B, LL3 = C3
– MPi: the i-th maximum period
S2: MP21, MP22, MP23 … Sn: MPn1, MPn2, MPn3
• MP1 = C1A1, MP2 = A2, MP3 = C2DA3
P.9
Closed Frequent Sequence Mining
Where to find forward/backward extensions? • FE={locally frequent items with full supports} • For prefix ABC, given C1A1A2BC2DA3C3E – Last instance = C1A1A2BC2DA3C3 – LLi: the i-th last-in-last appearance S1: MP11, MP12, MP13 • LL1 = A2, LL2 = B, LL3 = C3
– MPi: the i-th maximum period
S2: MP21, MP22, MP23 … Sn: MPn1, MPn2, MPn3
• MP1 = C1A1, MP2 = A2, MP3 = C2DA3
• BE={items appearing in each of MPi, ∃i)} – Scan backward each of MPi, ∀i ⇒ ScanSkip P.9
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency?
P.10
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency? • BackScan: ABC, C1A1A2BC2DA3C3E – LFi: the i-th last-in-first appearance • LF1 = A2, LF2 = B, LF3 = C2
– SMPi: the i-th semi-maximum period • SMP1 = C1A1, SMP2 = A2, SMP3 = ∅
P.10
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency? • BackScan: ABC, C1A1A2BC2DA3C3E – LFi: the i-th last-in-first appearance • LF1 = A2, LF2 = B, LF3 = C2
– SMPi: the i-th semi-maximum period • SMP1 = C1A1, SMP2 = A2, SMP3 = ∅
• ∃e ∃i, e appears in each of SMPi – Stop projection!
P.10
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency? • BackScan: ABC, C1A1A2BC2DA3C3E – LFi: the i-th last-in-first appearance • LF1 = A2, LF2 = B, LF3 = C2
– SMPi: the i-th semi-maximum period • SMP1 = C1A1, SMP2 = A2, SMP3 = ∅
• ∃e ∃i, e appears in each of SMPi – Stop projection!
P.10
Closed Frequent Sequence Mining
How does BIDE improve the mining efficiency? • BackScan: ABC, C1A1A2BC2DA3C3E – LFi: the i-th last-in-first appearance • LF1 = A2, LF2 = B, LF3 = C2
– SMPi: the i-th semi-maximum period • SMP1 = C1A1, SMP2 = A2, SMP3 = ∅
• ∃e ∃i, e appears in each of SMPi – Stop projection!
P.10
Closed Frequent Sequence Mining
Does BIDE perform much better? • BIDE/CloSpan significantly outperforms PrefixSpan/SPADE when support threshold is low • BIDE consumes much less memory and can be an order of magnitude faster than CloSpan • BIDE has linear scalability in terms of data size • BackScan and ScanSkip techniques are very effective in enhancing the performance
P.11
Closed Frequent Sequence Mining
Does BIDE perform much better? • BIDE/CloSpan significantly outperforms PrefixSpan/SPADE when support threshold is low • BIDE consumes much less memory and can be an order of magnitude faster than CloSpan • BIDE has linear scalability in terms of data size • BackScan and ScanSkip techniques are very effective in enhancing the performance
P.11
Closed Frequent Sequence Mining
Does BIDE perform much better? • BIDE/CloSpan significantly outperforms PrefixSpan/SPADE when support threshold is low • BIDE consumes much less memory and can be an order of magnitude faster than CloSpan • BIDE has linear scalability in terms of data size • BackScan and ScanSkip techniques are very effective in enhancing the performance
P.11
Closed Frequent Sequence Mining
Does BIDE perform much better? • BIDE/CloSpan significantly outperforms PrefixSpan/SPADE when support threshold is low • BIDE consumes much less memory and can be an order of magnitude faster than CloSpan • BIDE has linear scalability in terms of data size • BackScan and ScanSkip techniques are very effective in enhancing the performance
P.11
Closed Frequent Sequence Mining
Conclusion Remarks • Closed Frequent has the same expressive power as All Frequent, but provides more compact results and likely better efficiency. • Integrated optimization techniques for database projection, search space pruning, and patternclosure checking are required. • Move candidate-maintenance-and-test paradigm to a new paradigm without candidate maintenance
P.12
Closed Frequent Sequence Mining
Any Question?
3
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P.13
Closed Frequent Sequence Mining
Any Question? My Questions…
3
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P.13
Closed Frequent Sequence Mining
Any Question? My Questions… • CloSpan – vs. – D=D=D 3 – D=D=D
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P.13
Closed Frequent Sequence Mining
Any Question? My Questions… • CloSpan – vs. – D=D=D 3 | – D=D=D • BIDE – How to efficiently compute or maintain MPi/SMPi? – Does it easily adapt BIDE to sequences of itemsets?
P.13
Closed Frequent Sequence Mining
Any Question? My Questions… • CloSpan – vs. – D=D=D 3 | – D=D=D • BIDE – How to efficiently compute or maintain MPi/SMPi? – Does it easily adapt BIDE to sequences of itemsets? • What is the difference between Closed Frequent Sequences and Non-trivial Repeating Patterns? P.13
