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CIKM 2009 - Efficient itemset generator discovery over a stream sliding window

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Chuancong Gao

The document describes an algorithm called StreamGen for efficiently mining frequent generator itemsets over data streams using a sliding window model. It introduces the concepts of generator itemsets and why they are important. StreamGen uses a novel enumeration tree structure and optimization techniques. It is the first algorithm that can mine generator itemsets from data streams. Evaluation results show it outperforms other algorithms for related tasks and achieves high classification accuracy when extended to mine classification rules.

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Efficient Itemset Generator Discovery over a Stream Sliding Window Chuancong Gao, Jianyong Wang Database Laboratory Department of Computer Science and Technology Tsinghua University, Beijing 100084, China C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 1 / 28
Outline Introduction What is Generator Why We Need Generators What have We done Related Work The StreamGen Algorithm FP-Tree Enumeration Tree ADD and REMOVE Operations Extension for Mining Classification Rules Evaluation Results Conclusions C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 2 / 28
Introduction What is Generator What is Generator Example: Given the 4 transactions, with the ::::::::: minimum:::::::: support::::::::: threshold::::::::: (supmin) of 2. A B C A D A B C D A B D
Introduction What is Generator What is Generator Example: Given the 4 transactions, with the ::::::::: minimum:::::::: support::::::::: threshold::::::::: (supmin) of 2. A B C A D A B C D A B D Ø : 4 D : 3C : 2B : 3A : 4 ABD : 2ABC : 2 BD : 2BC : 2AD : 3AC : 2AB : 3 Equivalence Class Generator ItemsetClosed Itemset C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 3 / 28
Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; No::::::::::: sub-itemset for a generator itemset in an eqivalence class; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; No::::::::::: sub-itemset for a generator itemset in an eqivalence class; No::::::::::::: super-itemset for a closed itemset in an eqivalence class; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; No::::::::::: sub-itemset for a generator itemset in an eqivalence class; No::::::::::::: super-itemset for a closed itemset in an eqivalence class; Only one closed itemset, while one or more generator itemsets in one same equivalence class. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; No::::::::::: sub-itemset for a generator itemset in an eqivalence class; No::::::::::::: super-itemset for a closed itemset in an eqivalence class; Only one closed itemset, while one or more generator itemsets in one same equivalence class. An itemset could be both a generator itemset and a closed itemset. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; The number is much smaller than all frequent ones; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; The number is much smaller than all frequent ones; The shortest ones in an equivalence class; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; The number is much smaller than all frequent ones; The shortest ones in an equivalence class; The average size tends to be the smallest; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; The number is much smaller than all frequent ones; The shortest ones in an equivalence class; The average size tends to be the smallest; Preferred by ::::: MDL :::::::::: (Minimum::::::::::: Description:::::::: Length) principle. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. Contributions: First algorithm mining frequent itemset generators over stream sliding windows; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. Contributions: First algorithm mining frequent itemset generators over stream sliding windows; Novel :::::::::::: enumeration::::: tree structure and some effective optimization techniques; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. Contributions: First algorithm mining frequent itemset generators over stream sliding windows; Novel :::::::::::: enumeration::::: tree structure and some effective optimization techniques; Extended to directly mine classification rules on a sliding window; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. Contributions: First algorithm mining frequent itemset generators over stream sliding windows; Novel :::::::::::: enumeration::::: tree structure and some effective optimization techniques; Extended to directly mine classification rules on a sliding window; An extensive performance study shows StreamGen outperforms others performing similar tasks, and achieves high classification accuracy. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
Related Work Related Work Itemset Mining Algorithms: Mining frequent patterns without candidate generation: A frequent-pattern tree approach. J. Han, J. Pei, Y. Yin, and R. Mao. Data Min. Knowl. Discov., 2004. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 7 / 28
Related Work Related Work Itemset Mining Algorithms: Mining frequent patterns without candidate generation: A frequent-pattern tree approach. J. Han, J. Pei, Y. Yin, and R. Mao. Data Min. Knowl. Discov., 2004. Closet: An efficient algorithm for mining frequent closed itemsets. J. Pei, J. Han, and R. Mao. SIGMOD Workshop DMKD, 2000. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 7 / 28
Related Work Related Work Itemset Mining Algorithms: Mining frequent patterns without candidate generation: A frequent-pattern tree approach. J. Han, J. Pei, Y. Yin, and R. Mao. Data Min. Knowl. Discov., 2004. Closet: An efficient algorithm for mining frequent closed itemsets. J. Pei, J. Han, and R. Mao. SIGMOD Workshop DMKD, 2000. Minimum description length principle: Generators are preferable to closed patterns. J. Li, H. Li, L. Wong, J. Pei, and G. Dong. AAAI, 2006. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 7 / 28
Related Work Related Work Itemset Mining Algorithms: Mining frequent patterns without candidate generation: A frequent-pattern tree approach. J. Han, J. Pei, Y. Yin, and R. Mao. Data Min. Knowl. Discov., 2004. Closet: An efficient algorithm for mining frequent closed itemsets. J. Pei, J. Han, and R. Mao. SIGMOD Workshop DMKD, 2000. Minimum description length principle: Generators are preferable to closed patterns. J. Li, H. Li, L. Wong, J. Pei, and G. Dong. AAAI, 2006. Mining statistically important equivalence classes and delta-discriminative emerging patterns. J. Li, G. Liu, and L. Wong. SIGKDD, 2007. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 7 / 28
Related Work Related Work Stream Itemset Mining Algorithms: Catch the moment: maintaining closed frequent itemsets over a data stream sliding window. Y. Chi, H. Wang, P. S. Yu, and R. R. Muntz. Knowl. Inf. Syst., 2006. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 8 / 28
Related Work Related Work Stream Itemset Mining Algorithms: Catch the moment: maintaining closed frequent itemsets over a data stream sliding window. Y. Chi, H. Wang, P. S. Yu, and R. R. Muntz. Knowl. Inf. Syst., 2006. Itemset based Classification Algorithms: On mining instance-centric classification rules. J. Wang and G. Karypis. IEEE Trans. Knowl. Data Eng., 2006. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 8 / 28
Related Work Related Work Stream Itemset Mining Algorithms: Catch the moment: maintaining closed frequent itemsets over a data stream sliding window. Y. Chi, H. Wang, P. S. Yu, and R. R. Muntz. Knowl. Inf. Syst., 2006. Itemset based Classification Algorithms: On mining instance-centric classification rules. J. Wang and G. Karypis. IEEE Trans. Knowl. Data Eng., 2006. Discriminative frequent pattern analysis for effective classification. H. Cheng, X. Yan, J. Han, and C.-W. Hsu. ICDE, 2007. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 8 / 28
The StreamGen Algorithm The StreamGen Algorithm Details of our algorithm here. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 9 / 28
The StreamGen Algorithm The StreamGen Algorithm Details of our algorithm here. Example: One running example of stream data containing 6 transaction itemsets and with window size of 4. TimeLine ID Itemset 1 2 3 4 5 6 ABC AD ABCD ABD BCD CD Window#1 Window#2 Window#3 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 9 / 28
The StreamGen Algorithm A Few Basic Theorems Theorem A frequent itemset S is a generator iff there exists no subset with size |S − 1| having the same support with S. Hint: Can be used to check whether an itemset is a generator easily. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 10 / 28
The StreamGen Algorithm A Few Basic Theorems Theorem A frequent itemset S is a generator iff there exists no subset with size |S − 1| having the same support with S. Hint: Can be used to check whether an itemset is a generator easily. Theorem Any subset of a generator would be also a generator. Theorem Any superset of an unpromising itemset must be either unpromising or infrequent. Hint: Help define the border between generators and non-generators; Form the foundation for the enumeration tree. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 10 / 28
The StreamGen Algorithm FP-Tree FP-Tree A modified FP-Tree for store and compress transactions in each sliding window. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 11 / 28
The StreamGen Algorithm FP-Tree FP-Tree A modified FP-Tree for store and compress transactions in each sliding window. Example: FP-Tree of first sliding window in previous example. 1 A B C 2 A D 3 A B C D 4 A B D Ø D:3 C:1 B:1 A:1 C:1 B:1 A:1 1 432 IDTable A:1 B:1 A:1 HeadTable A B D C C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 11 / 28
The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. 3 types of nodes: Infrequent Node; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. 3 types of nodes: Infrequent Node; Unpromising Node. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. 3 types of nodes: Infrequent Node; Unpromising Node. Generator Node. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. 3 types of nodes: Infrequent Node; Unpromising Node. Generator Node. A hash table is prepared for each level of the enumeration tree to accelerate the checking operation. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
The StreamGen Algorithm Enumeration Tree Enumeration Tree Example: Enumeration tree of first sliding window with minimum support 2 1 A B C 2 A D 3 A B C D 4 A B D Ø::4 D:3C:2B:3A:4 BC:2 BD:2 CD:1 Solid border ellipse: Generator Node Dotted border ellipse: Unpromising Node Dotted border rectangle: Infrequent Node C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 13 / 28
The StreamGen Algorithm ADD and REMOVE Operations ADD and REMOVE Operations Core part: Enumeration tree-node status transforming matrix. ADD REMOVE Type x < y x = y x > y x < y x = y x > y G G G G G G/U I/G U U G/U U U U I/U I I I I/G/U I I I x = |itemsetn ∩ T|, y = |itemsetn| − 1 G = Generator, U = Unpromising, I = Infrequent C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 14 / 28
The StreamGen Algorithm ADD and REMOVE Operations Example of ADD Operation Ø::4 D:3C:2B:3A:4 BC:2 BD:2 CD:1 ADD Type x < y x = y x > y G G G G U U G/U U I I I I/G/U x = |itemsetn ∩ T|, y = |itemsetn| − 1 T = B C D 1 A B C 2 A D 3 A B C D 4 A B D 5 B C D + Ø::5 D:4C:3B:4A:4 AB:3 AC:2 ABC:2 AD:2 BC:3 BD:3 CD:2 ACD:1ABD:2 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 15 / 28
The StreamGen Algorithm ADD and REMOVE Operations Example of REMOVE Operation Ø::5 D:4C:3B:4A:4 AB:3 AC:2 ABC:2 AD:2 BC:3 BD:3 CD:2 ACD:1ABD:2 1 A B C − 2 A D 3 A B C D 4 A B D 5 B C D REMOVE Type x < y x = y x > y G G G/U I/G U U U I/U I I I I x = |itemsetn ∩ T|, y = |itemsetn| − 1 T = A B C Ø::4 D:4C:2B:3A:3 AB:2 AC:1 BC:2 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 16 / 28
The StreamGen Algorithm ADD and REMOVE Operations Combine Two Operations For Sliding Window: ADD when window is not full REMOVE when window is full For Incremental Only ADD C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 17 / 28
Extension for Mining Classification Rules Extension for Mining Classification Rules Algorithm 1: StreamGenRules(n) Input : The root node n of the enemuration tree. begin1 nodes ← getGenerators(n);2 sort nodes by info-gain;3 rules ← ∅;4 foreach cn ∈ nodes do5 if ∀r ∈ rules, r ⊂ cn then6 if cn covers at least one transaction then7 rules ← rules ∪ {cn};8 remove covered transactions;9 if no more transactions then10 break;11 return rules;12 end13 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 18 / 28
Evaluation Results Datasets Dataset # Items # tran. # Pos. # Neg. Avg. Len. mushroom 116 8,124 4,208 3,916 21.695 horse 89 368 232 136 16.769 adult 128 48,842 11,687 37,155 13.868 breast 45 699 458 241 8.977 hepatitus 55 155 32 123 17.923 pima 40 768 500 268 8 chess 75 3,196 - - 37 connect 129 67,557 - - 43 pumsb 2,113 49,046 - - 74 The above part is for both runtime evaluation and classification evaluation, The bottom part is only for runtime evaluation. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 19 / 28
Evaluation Results Runtime Comparing with Moment Comparsion with Moment, one frequent closed itemset mining algorithm on sliding windows: 1 10 100 10 20 30 40 50 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = mushroom window size = 2,000 1 10 100 10 20 30 40 50 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = mushroom window size = 4,000 0.1 1 10 100 1000 75 80 85 90 95 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = chess window size = 1,000 0.1 1 10 100 1000 60 70 80 90 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = chess window size = 2,000 10 100 75 80 85 90 95 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = pumsb window size = 2,500 10 100 70 80 90 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = pumsb window size = 10,000 1 10 100 1000 99.333 99.5 99.667 99.833 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = connect window size = 30,000 1 10 100 95 95.833 96.667 97.5 98.333 99.167 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = connect window size = 60,000 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 20 / 28
Evaluation Results Memory Use Comparing with Moment Peak memory uses of Moment and StreamGen in KB: Dataset window size supmin Moment StreamGen mushroom 4,000 0.1 14,476 10,108 mushroom 2,000 0.1 12,504 8,472 chess 2,000 0.6 103,180 31,636 chess 1,000 0.75 34,624 9,176 connect-4 60,000 0.95 141,756 98,236 connect-4 30,000 0.998 73,056 52,372 pumsb 10,000 0.7 1,732,136 75,316 pumsb 2,500 0.75 90,944 23,472 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 21 / 28
Evaluation Results Runtime Comparing with DPM & DDPMine Comparsion with DPM, one frequent generator itemset mining algorithm on static data: 0.1 1 10 100 1000 50 60 70 80 90 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = mushroom window size = 4,000 0.1 1 10 100 1000 75 80 85 90 95 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = chess window size = 1,000 1 10 100 1000 97.015 97.761 98.507 99.254 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = connect window size = 67,000 1 10 89.796 91.837 93.878 95.918 97.959 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = pumsb window size = 49,000 *The runtimes of DPM $ DDPMine are only mearsured on full-sized windows. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 22 / 28
Evaluation Results Runtime Comparing with DPM & DDPMine Comparsion with DPM, one frequent generator itemset mining algorithm on static data: 0.1 1 10 100 1000 50 60 70 80 90 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = mushroom window size = 4,000 0.1 1 10 100 1000 75 80 85 90 95 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = chess window size = 1,000 1 10 100 1000 97.015 97.761 98.507 99.254 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = connect window size = 67,000 1 10 89.796 91.837 93.878 95.918 97.959 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = pumsb window size = 49,000 Comparsion with DDPMine, one frequent itemset based classification rule mining algorithm on static data: 0.1 1 10 100 1000 10000 50 60 70 80 90 Runtime(inseconds) Minimum Support Threshold (in %) DDPMine StreamGen dataset = mushroom window size = 8,000 0.01 0.1 1 10 100 1000 10000 10 20 30 40 50Runtime(inseconds) Minimum Support Threshold (in %) DDPMine StreamGen dataset = horse window size = 600 *The runtimes of DPM $ DDPMine are only mearsured on full-sized windows. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 22 / 28
Evaluation Results Classification Experiment Results Classification Accuracy: Dataset StreamGen DDPMine Accuracy max. len. avg. len. avg. num. Accuracy max. len. avg. len. avg. num. breast 96.708 3 1.551 23.6 95.28 9 2.448 11.6 adult 82.146 3 1.831 13 81.292 14 4.583 7.2 mushroom 98.918 3 1.958 9.6 97.184 22 15.592 16.2 hepatitus 82.006 4 2.387 15 76.986 8 4.8 5 horse 81.512 2 1.389 3.6 81.246 20 4.88 10 pima 74.87 4 1.663 18.4 75.124 7 2.435 12.6 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 23 / 28
Evaluation Results Classification Experiment Results Classification Accuracy: Dataset StreamGen DDPMine Accuracy max. len. avg. len. avg. num. Accuracy max. len. avg. len. avg. num. breast 96.708 3 1.551 23.6 95.28 9 2.448 11.6 adult 82.146 3 1.831 13 81.292 14 4.583 7.2 mushroom 98.918 3 1.958 9.6 97.184 22 15.592 16.2 hepatitus 82.006 4 2.387 15 76.986 8 4.8 5 horse 81.512 2 1.389 3.6 81.246 20 4.88 10 pima 74.87 4 1.663 18.4 75.124 7 2.435 12.6 Rule Example on “mushroom”: StreamGen DDPMine 38 17 39 12 25 5 7 8 11 13 15 16 17 18 19 20 26 13 25 8 17 18 7 67 5 7 9 13 14 15 16 17 18 19 20 40 41 46 53 54 66 2 7 9 11 13 14 15 16 17 18 19 20 21 38 40 44 53 54 76 7 68 2 7 9 11 13 14 15 16 17 18 19 20 28 38 40 44 53 54 76 11 18 2 7 9 11 13 14 15 16 17 18 19 20 32 38 40 53 54 65 76 6 18 37 2 7 9 11 13 14 15 16 17 18 19 20 22 32 38 40 53 54 76 4 53 2 7 9 11 13 14 15 16 17 18 19 20 28 32 38 40 46 53 54 76 2 7 9 11 13 14 15 16 17 18 19 20 21 32 38 40 45 46 53 54 76 2 7 9 11 13 14 15 16 17 18 19 20 21 32 34 38 40 46 48 53 54 76 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 23 / 28
Conclusions Conclusions Explored a new and challenging problem: Mining frequent itemset generators over stream sliding window; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 24 / 28
Conclusions Conclusions Explored a new and challenging problem: Mining frequent itemset generators over stream sliding window; Devised novel enumeration tree structure; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 24 / 28
Conclusions Conclusions Explored a new and challenging problem: Mining frequent itemset generators over stream sliding window; Devised novel enumeration tree structure; Also proposed effective optimization techniques; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 24 / 28
Conclusions Conclusions Explored a new and challenging problem: Mining frequent itemset generators over stream sliding window; Devised novel enumeration tree structure; Also proposed effective optimization techniques; Outperformed other state-of-the-art algorithms in terms of efficiency and classification accuracy. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 24 / 28
Conclusions The End Thank you for Listening! Questions or Comments? C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 25 / 28

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CIKM 2009 - Efficient itemset generator discovery over a stream sliding window

  • 1. Efficient Itemset Generator Discovery over a Stream Sliding Window Chuancong Gao, Jianyong Wang Database Laboratory Department of Computer Science and Technology Tsinghua University, Beijing 100084, China C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 1 / 28
  • 2. Outline Introduction What is Generator Why We Need Generators What have We done Related Work The StreamGen Algorithm FP-Tree Enumeration Tree ADD and REMOVE Operations Extension for Mining Classification Rules Evaluation Results Conclusions C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 2 / 28
  • 3. Introduction What is Generator What is Generator Example: Given the 4 transactions, with the ::::::::: minimum:::::::: support::::::::: threshold::::::::: (supmin) of 2. A B C A D A B C D A B D
  • 4. Introduction What is Generator What is Generator Example: Given the 4 transactions, with the ::::::::: minimum:::::::: support::::::::: threshold::::::::: (supmin) of 2. A B C A D A B C D A B D Ø : 4 D : 3C : 2B : 3A : 4 ABD : 2ABC : 2 BD : 2BC : 2AD : 3AC : 2AB : 3 Equivalence Class Generator ItemsetClosed Itemset C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 3 / 28
  • 5. Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
  • 6. Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
  • 7. Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; No::::::::::: sub-itemset for a generator itemset in an eqivalence class; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
  • 8. Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; No::::::::::: sub-itemset for a generator itemset in an eqivalence class; No::::::::::::: super-itemset for a closed itemset in an eqivalence class; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
  • 9. Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; No::::::::::: sub-itemset for a generator itemset in an eqivalence class; No::::::::::::: super-itemset for a closed itemset in an eqivalence class; Only one closed itemset, while one or more generator itemsets in one same equivalence class. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
  • 10. Introduction What is Generator What is Generator :::::::::::: Equivalence:::::: class: All the frequent :::::::: itemsets contained in the same set of input ::::::::::: transactions ::::::: Closed :::::::: Itemset: The maximal one in equivalence class :::::::::: Generator::::::::: Itemsets: The minimal ones Characteristics: same equivalence class =⇒ same input transactions =⇒ same data distribution =⇒ same ::::::: support value and :::::::::: confidence value; No::::::::::: sub-itemset for a generator itemset in an eqivalence class; No::::::::::::: super-itemset for a closed itemset in an eqivalence class; Only one closed itemset, while one or more generator itemsets in one same equivalence class. An itemset could be both a generator itemset and a closed itemset. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 4 / 28
  • 11. Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
  • 12. Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
  • 13. Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
  • 14. Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; The number is much smaller than all frequent ones; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
  • 15. Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; The number is much smaller than all frequent ones; The shortest ones in an equivalence class; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
  • 16. Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; The number is much smaller than all frequent ones; The shortest ones in an equivalence class; The average size tends to be the smallest; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
  • 17. Introduction Why We Need Generators Why We Need Generators Form a concise representation of equivalence classes together with closed item-sets; As classification rules / features. At least one generator sharing the same support and confidence with others for each equivalence class; The number is much smaller than all frequent ones; The shortest ones in an equivalence class; The average size tends to be the smallest; Preferred by ::::: MDL :::::::::: (Minimum::::::::::: Description:::::::: Length) principle. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 5 / 28
  • 18. Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
  • 19. Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. Contributions: First algorithm mining frequent itemset generators over stream sliding windows; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
  • 20. Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. Contributions: First algorithm mining frequent itemset generators over stream sliding windows; Novel :::::::::::: enumeration::::: tree structure and some effective optimization techniques; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
  • 21. Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. Contributions: First algorithm mining frequent itemset generators over stream sliding windows; Novel :::::::::::: enumeration::::: tree structure and some effective optimization techniques; Extended to directly mine classification rules on a sliding window; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
  • 22. Introduction What have We done What have We done A novel algorithm to mine frequent generator itemsets on stream sliding window. Contributions: First algorithm mining frequent itemset generators over stream sliding windows; Novel :::::::::::: enumeration::::: tree structure and some effective optimization techniques; Extended to directly mine classification rules on a sliding window; An extensive performance study shows StreamGen outperforms others performing similar tasks, and achieves high classification accuracy. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 6 / 28
  • 23. Related Work Related Work Itemset Mining Algorithms: Mining frequent patterns without candidate generation: A frequent-pattern tree approach. J. Han, J. Pei, Y. Yin, and R. Mao. Data Min. Knowl. Discov., 2004. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 7 / 28
  • 24. Related Work Related Work Itemset Mining Algorithms: Mining frequent patterns without candidate generation: A frequent-pattern tree approach. J. Han, J. Pei, Y. Yin, and R. Mao. Data Min. Knowl. Discov., 2004. Closet: An efficient algorithm for mining frequent closed itemsets. J. Pei, J. Han, and R. Mao. SIGMOD Workshop DMKD, 2000. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 7 / 28
  • 25. Related Work Related Work Itemset Mining Algorithms: Mining frequent patterns without candidate generation: A frequent-pattern tree approach. J. Han, J. Pei, Y. Yin, and R. Mao. Data Min. Knowl. Discov., 2004. Closet: An efficient algorithm for mining frequent closed itemsets. J. Pei, J. Han, and R. Mao. SIGMOD Workshop DMKD, 2000. Minimum description length principle: Generators are preferable to closed patterns. J. Li, H. Li, L. Wong, J. Pei, and G. Dong. AAAI, 2006. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 7 / 28
  • 26. Related Work Related Work Itemset Mining Algorithms: Mining frequent patterns without candidate generation: A frequent-pattern tree approach. J. Han, J. Pei, Y. Yin, and R. Mao. Data Min. Knowl. Discov., 2004. Closet: An efficient algorithm for mining frequent closed itemsets. J. Pei, J. Han, and R. Mao. SIGMOD Workshop DMKD, 2000. Minimum description length principle: Generators are preferable to closed patterns. J. Li, H. Li, L. Wong, J. Pei, and G. Dong. AAAI, 2006. Mining statistically important equivalence classes and delta-discriminative emerging patterns. J. Li, G. Liu, and L. Wong. SIGKDD, 2007. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 7 / 28
  • 27. Related Work Related Work Stream Itemset Mining Algorithms: Catch the moment: maintaining closed frequent itemsets over a data stream sliding window. Y. Chi, H. Wang, P. S. Yu, and R. R. Muntz. Knowl. Inf. Syst., 2006. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 8 / 28
  • 28. Related Work Related Work Stream Itemset Mining Algorithms: Catch the moment: maintaining closed frequent itemsets over a data stream sliding window. Y. Chi, H. Wang, P. S. Yu, and R. R. Muntz. Knowl. Inf. Syst., 2006. Itemset based Classification Algorithms: On mining instance-centric classification rules. J. Wang and G. Karypis. IEEE Trans. Knowl. Data Eng., 2006. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 8 / 28
  • 29. Related Work Related Work Stream Itemset Mining Algorithms: Catch the moment: maintaining closed frequent itemsets over a data stream sliding window. Y. Chi, H. Wang, P. S. Yu, and R. R. Muntz. Knowl. Inf. Syst., 2006. Itemset based Classification Algorithms: On mining instance-centric classification rules. J. Wang and G. Karypis. IEEE Trans. Knowl. Data Eng., 2006. Discriminative frequent pattern analysis for effective classification. H. Cheng, X. Yan, J. Han, and C.-W. Hsu. ICDE, 2007. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 8 / 28
  • 30. The StreamGen Algorithm The StreamGen Algorithm Details of our algorithm here. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 9 / 28
  • 31. The StreamGen Algorithm The StreamGen Algorithm Details of our algorithm here. Example: One running example of stream data containing 6 transaction itemsets and with window size of 4. TimeLine ID Itemset 1 2 3 4 5 6 ABC AD ABCD ABD BCD CD Window#1 Window#2 Window#3 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 9 / 28
  • 32. The StreamGen Algorithm A Few Basic Theorems Theorem A frequent itemset S is a generator iff there exists no subset with size |S − 1| having the same support with S. Hint: Can be used to check whether an itemset is a generator easily. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 10 / 28
  • 33. The StreamGen Algorithm A Few Basic Theorems Theorem A frequent itemset S is a generator iff there exists no subset with size |S − 1| having the same support with S. Hint: Can be used to check whether an itemset is a generator easily. Theorem Any subset of a generator would be also a generator. Theorem Any superset of an unpromising itemset must be either unpromising or infrequent. Hint: Help define the border between generators and non-generators; Form the foundation for the enumeration tree. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 10 / 28
  • 34. The StreamGen Algorithm FP-Tree FP-Tree A modified FP-Tree for store and compress transactions in each sliding window. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 11 / 28
  • 35. The StreamGen Algorithm FP-Tree FP-Tree A modified FP-Tree for store and compress transactions in each sliding window. Example: FP-Tree of first sliding window in previous example. 1 A B C 2 A D 3 A B C D 4 A B D Ø D:3 C:1 B:1 A:1 C:1 B:1 A:1 1 432 IDTable A:1 B:1 A:1 HeadTable A B D C C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 11 / 28
  • 36. The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
  • 37. The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. 3 types of nodes: Infrequent Node; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
  • 38. The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. 3 types of nodes: Infrequent Node; Unpromising Node. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
  • 39. The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. 3 types of nodes: Infrequent Node; Unpromising Node. Generator Node. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
  • 40. The StreamGen Algorithm Enumeration Tree Enumeration Tree To help maintain the information of the mined generators and the border between generators and non-generators. 3 types of nodes: Infrequent Node; Unpromising Node. Generator Node. A hash table is prepared for each level of the enumeration tree to accelerate the checking operation. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 12 / 28
  • 41. The StreamGen Algorithm Enumeration Tree Enumeration Tree Example: Enumeration tree of first sliding window with minimum support 2 1 A B C 2 A D 3 A B C D 4 A B D Ø::4 D:3C:2B:3A:4 BC:2 BD:2 CD:1 Solid border ellipse: Generator Node Dotted border ellipse: Unpromising Node Dotted border rectangle: Infrequent Node C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 13 / 28
  • 42. The StreamGen Algorithm ADD and REMOVE Operations ADD and REMOVE Operations Core part: Enumeration tree-node status transforming matrix. ADD REMOVE Type x < y x = y x > y x < y x = y x > y G G G G G G/U I/G U U G/U U U U I/U I I I I/G/U I I I x = |itemsetn ∩ T|, y = |itemsetn| − 1 G = Generator, U = Unpromising, I = Infrequent C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 14 / 28
  • 43. The StreamGen Algorithm ADD and REMOVE Operations Example of ADD Operation Ø::4 D:3C:2B:3A:4 BC:2 BD:2 CD:1 ADD Type x < y x = y x > y G G G G U U G/U U I I I I/G/U x = |itemsetn ∩ T|, y = |itemsetn| − 1 T = B C D 1 A B C 2 A D 3 A B C D 4 A B D 5 B C D + Ø::5 D:4C:3B:4A:4 AB:3 AC:2 ABC:2 AD:2 BC:3 BD:3 CD:2 ACD:1ABD:2 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 15 / 28
  • 44. The StreamGen Algorithm ADD and REMOVE Operations Example of REMOVE Operation Ø::5 D:4C:3B:4A:4 AB:3 AC:2 ABC:2 AD:2 BC:3 BD:3 CD:2 ACD:1ABD:2 1 A B C − 2 A D 3 A B C D 4 A B D 5 B C D REMOVE Type x < y x = y x > y G G G/U I/G U U U I/U I I I I x = |itemsetn ∩ T|, y = |itemsetn| − 1 T = A B C Ø::4 D:4C:2B:3A:3 AB:2 AC:1 BC:2 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 16 / 28
  • 45. The StreamGen Algorithm ADD and REMOVE Operations Combine Two Operations For Sliding Window: ADD when window is not full REMOVE when window is full For Incremental Only ADD C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 17 / 28
  • 46. Extension for Mining Classification Rules Extension for Mining Classification Rules Algorithm 1: StreamGenRules(n) Input : The root node n of the enemuration tree. begin1 nodes ← getGenerators(n);2 sort nodes by info-gain;3 rules ← ∅;4 foreach cn ∈ nodes do5 if ∀r ∈ rules, r ⊂ cn then6 if cn covers at least one transaction then7 rules ← rules ∪ {cn};8 remove covered transactions;9 if no more transactions then10 break;11 return rules;12 end13 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 18 / 28
  • 47. Evaluation Results Datasets Dataset # Items # tran. # Pos. # Neg. Avg. Len. mushroom 116 8,124 4,208 3,916 21.695 horse 89 368 232 136 16.769 adult 128 48,842 11,687 37,155 13.868 breast 45 699 458 241 8.977 hepatitus 55 155 32 123 17.923 pima 40 768 500 268 8 chess 75 3,196 - - 37 connect 129 67,557 - - 43 pumsb 2,113 49,046 - - 74 The above part is for both runtime evaluation and classification evaluation, The bottom part is only for runtime evaluation. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 19 / 28
  • 48. Evaluation Results Runtime Comparing with Moment Comparsion with Moment, one frequent closed itemset mining algorithm on sliding windows: 1 10 100 10 20 30 40 50 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = mushroom window size = 2,000 1 10 100 10 20 30 40 50 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = mushroom window size = 4,000 0.1 1 10 100 1000 75 80 85 90 95 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = chess window size = 1,000 0.1 1 10 100 1000 60 70 80 90 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = chess window size = 2,000 10 100 75 80 85 90 95 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = pumsb window size = 2,500 10 100 70 80 90 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = pumsb window size = 10,000 1 10 100 1000 99.333 99.5 99.667 99.833 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = connect window size = 30,000 1 10 100 95 95.833 96.667 97.5 98.333 99.167 100 Runtime(inseconds) Minimum Support Threshold (in %) Moment StreamGen dataset = connect window size = 60,000 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 20 / 28
  • 49. Evaluation Results Memory Use Comparing with Moment Peak memory uses of Moment and StreamGen in KB: Dataset window size supmin Moment StreamGen mushroom 4,000 0.1 14,476 10,108 mushroom 2,000 0.1 12,504 8,472 chess 2,000 0.6 103,180 31,636 chess 1,000 0.75 34,624 9,176 connect-4 60,000 0.95 141,756 98,236 connect-4 30,000 0.998 73,056 52,372 pumsb 10,000 0.7 1,732,136 75,316 pumsb 2,500 0.75 90,944 23,472 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 21 / 28
  • 50. Evaluation Results Runtime Comparing with DPM & DDPMine Comparsion with DPM, one frequent generator itemset mining algorithm on static data: 0.1 1 10 100 1000 50 60 70 80 90 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = mushroom window size = 4,000 0.1 1 10 100 1000 75 80 85 90 95 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = chess window size = 1,000 1 10 100 1000 97.015 97.761 98.507 99.254 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = connect window size = 67,000 1 10 89.796 91.837 93.878 95.918 97.959 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = pumsb window size = 49,000 *The runtimes of DPM $ DDPMine are only mearsured on full-sized windows. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 22 / 28
  • 51. Evaluation Results Runtime Comparing with DPM & DDPMine Comparsion with DPM, one frequent generator itemset mining algorithm on static data: 0.1 1 10 100 1000 50 60 70 80 90 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = mushroom window size = 4,000 0.1 1 10 100 1000 75 80 85 90 95 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = chess window size = 1,000 1 10 100 1000 97.015 97.761 98.507 99.254 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = connect window size = 67,000 1 10 89.796 91.837 93.878 95.918 97.959 100 Runtime(inseconds) Minimum Support Threshold (in %) DPM StreamGen dataset = pumsb window size = 49,000 Comparsion with DDPMine, one frequent itemset based classification rule mining algorithm on static data: 0.1 1 10 100 1000 10000 50 60 70 80 90 Runtime(inseconds) Minimum Support Threshold (in %) DDPMine StreamGen dataset = mushroom window size = 8,000 0.01 0.1 1 10 100 1000 10000 10 20 30 40 50Runtime(inseconds) Minimum Support Threshold (in %) DDPMine StreamGen dataset = horse window size = 600 *The runtimes of DPM $ DDPMine are only mearsured on full-sized windows. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 22 / 28
  • 52. Evaluation Results Classification Experiment Results Classification Accuracy: Dataset StreamGen DDPMine Accuracy max. len. avg. len. avg. num. Accuracy max. len. avg. len. avg. num. breast 96.708 3 1.551 23.6 95.28 9 2.448 11.6 adult 82.146 3 1.831 13 81.292 14 4.583 7.2 mushroom 98.918 3 1.958 9.6 97.184 22 15.592 16.2 hepatitus 82.006 4 2.387 15 76.986 8 4.8 5 horse 81.512 2 1.389 3.6 81.246 20 4.88 10 pima 74.87 4 1.663 18.4 75.124 7 2.435 12.6 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 23 / 28
  • 53. Evaluation Results Classification Experiment Results Classification Accuracy: Dataset StreamGen DDPMine Accuracy max. len. avg. len. avg. num. Accuracy max. len. avg. len. avg. num. breast 96.708 3 1.551 23.6 95.28 9 2.448 11.6 adult 82.146 3 1.831 13 81.292 14 4.583 7.2 mushroom 98.918 3 1.958 9.6 97.184 22 15.592 16.2 hepatitus 82.006 4 2.387 15 76.986 8 4.8 5 horse 81.512 2 1.389 3.6 81.246 20 4.88 10 pima 74.87 4 1.663 18.4 75.124 7 2.435 12.6 Rule Example on “mushroom”: StreamGen DDPMine 38 17 39 12 25 5 7 8 11 13 15 16 17 18 19 20 26 13 25 8 17 18 7 67 5 7 9 13 14 15 16 17 18 19 20 40 41 46 53 54 66 2 7 9 11 13 14 15 16 17 18 19 20 21 38 40 44 53 54 76 7 68 2 7 9 11 13 14 15 16 17 18 19 20 28 38 40 44 53 54 76 11 18 2 7 9 11 13 14 15 16 17 18 19 20 32 38 40 53 54 65 76 6 18 37 2 7 9 11 13 14 15 16 17 18 19 20 22 32 38 40 53 54 76 4 53 2 7 9 11 13 14 15 16 17 18 19 20 28 32 38 40 46 53 54 76 2 7 9 11 13 14 15 16 17 18 19 20 21 32 38 40 45 46 53 54 76 2 7 9 11 13 14 15 16 17 18 19 20 21 32 34 38 40 46 48 53 54 76 C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 23 / 28
  • 54. Conclusions Conclusions Explored a new and challenging problem: Mining frequent itemset generators over stream sliding window; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 24 / 28
  • 55. Conclusions Conclusions Explored a new and challenging problem: Mining frequent itemset generators over stream sliding window; Devised novel enumeration tree structure; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 24 / 28
  • 56. Conclusions Conclusions Explored a new and challenging problem: Mining frequent itemset generators over stream sliding window; Devised novel enumeration tree structure; Also proposed effective optimization techniques; C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 24 / 28
  • 57. Conclusions Conclusions Explored a new and challenging problem: Mining frequent itemset generators over stream sliding window; Devised novel enumeration tree structure; Also proposed effective optimization techniques; Outperformed other state-of-the-art algorithms in terms of efficiency and classification accuracy. C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 24 / 28
  • 58. Conclusions The End Thank you for Listening! Questions or Comments? C. Gao, J. Wang (Tsinghua Univ.) Efficient Itemset Generator Discovery over a Stream Sliding Window 25 / 28