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Efficient Algorithms for Approximate Member Extraction Using Signature- based Inverted Lists Jialong Han Co-authored with Jiaheng Lu, Xiaofeng Meng Renmin University of China

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 2 Introduction: An Example A dictionary of strings we are interested in E.g. product names, postal addresses… We are going to locate their approximate apparences in a series of documents. See the meaning of approximate apparence in the following example:

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 3 Problem Definition Given a dictionary R and a threshold δ, extract all proper substrings m from input documents S such that there exists r R, and Similarity (r, m) δ(or Distance(r, m) k ). Here we call r a piece of evidence for m. Similarity() is a function measuring the similarity of two strings Strings are viewed as sets of tokens (words) An example for Sim(): Jaccard similarity:

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 4 Outline Introduction State-of-the-art techniques The filtration-verification framework K-signature scheme Inverted Signature-based Hashtable Our algorithms and evaluations Conclusion

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 5 Why pre-pruning is needed We need spot evidence to decide whether a substring m should be extracted Simple verification on all dictionary strings may be inefficient Pre-pruning and post-verifying is beneficial But should it be running-speed-oriented or filtering- power-oriented? Less time or less survivors?

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 6 The issue of compromise comes again Balance between the two stages should be reached: More(less) filtration time Strong(weak) filtration power Fewer(more) candidates Less(more) verification time Overall performance =Tf+Tv ?????

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 7 Outline Introduction State-of-the-art techniques The filtration-verification framework K-signature scheme Inverted Signature-based Hashtable Our algorithms and evaluations Conclusion

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 8 K-signature scheme Proposed by Chakrabarti et al. (SIGMOD 2008) Choose several top-weighted tokens in a string as signatures to represent it: s => Sig(s) Observation: if r cannot match m, r is likely to have insufficient signature overlapping with m K is a parameter for filtration power tuning Potential evidence loss A counter-example found when k=3 We tried and only proved that it works for k=1 and k=

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 9 Outline Introduction State-of-the-art techniques The filtration-verification framework K-signature scheme Inverted Signature-based Hashtable Our algorithms and evaluations Conclusion

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 10 Inverted Signature-based Hashtable Proposed by Chakrabarti et al. (SIGMOD 2008) Each dictionary string encoded into a solid 0-1 matrix An 1 for each occurrence of a tuple (1- rectangle) Bitwise-or all solid matrices to get the matrix of R Observation: if m is an approximate member of R, the matrix of m must have enough intersections with that of R. Formalized into an NPC problem Solution causes too weak filtering power

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 11 Outline Introduction State-of-the-art techniques Our algorithms and evaluations Corrected filtering conditions EvSCAN: Filtration by SIL EvITER: Incremental optimization on EvSCAN Supporting Dynamic Thresholds Conclusion

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 12 If Sim(m,r) δ, what do we have ? wt(Sig(m)Sig(r)) τ(m) wt(Sig(m)Sig(r)) min{τ(m),τ(r) } So the threshold does not remain constant involves unknown evidence Our solution: Use inverted lists to count sig- token overlappings. Note that sig-tokens usually have low document frequency (e.g. IDF as weights) Our proposed theorem Too strict ! Proved by us

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 13 Outline Introduction State-of-the-art techniques Our algorithms and evaluations Corrected filtering conditions EvSCAN: Filtration by SIL EvITER: Incremental optimization on EvSCAN Supporting Dynamic Thresholds Conclusion

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 14 Lists indexed by sig-tokens Each sig-token of a string creates a node (containing the strings id) in the corresponding list. E.g. R = { r1 = canon eos 5d digital camera", r2 =nikon digital slr camera, r3=canon slr camera}. wt(digital, camera, canon, nikon, slr, eos, 5d) = (1, 1, 2, 2, 2, 7,9). Signature-based Inverted Lists 5d, 9.0 canon, 2.0 camera, 1.0 eos, 7.0 nikon, 2.0 slr,

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 15 Filtration by SIL Using an array called accumulator to compute the overlapped sig weight wt(Sig(m)Sig(r)) E.g. m=canon eos digital camera, δ=0.8 5d, 9.0 canon, 2.0 camera, 1.0 eos, 7.0 nikon, 2.0 slr, rid123 wt(Sig(m)Sig(r)) min{τ(m),τ(r) } Accumulator Qualified!

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 16 Outline Introduction State-of-the-art techniques Our algorithms and evaluations Corrected filtering conditions EvSCAN: Filtration by SIL EvITER: Incremental optimization on EvSCAN Supporting Dynamic Thresholds Conclusion

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 17 EvITER: Progressive Computation Recall we are checking all substrings Some of them are quite similar, indicating that they share duplicate computation An intuition: if m have potential evidence r, then m t is very likely to match r Formally we proved that Let ES(m) be the set of potential evidence for m, list[t]={s| all dictionary strings that contain token t} We have ES(m t) ES(m) list[t]

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 18 Example Docoment M: m t …. cannon eos digital camera lens… We know that only r1, r22, r53 are possible to match cannon eos digital camera lens ES(m) {r1} … lens, 3.0 … 2253 List[t]

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 19 Flow of Evidence EvITER for Evidence ITERATION …

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 20 Outline Introduction State-of-the-art techniques Our algorithms and evaluations Corrected filtering conditions EvSCAN: Filtration by SIL EvITER: Incremental optimization on EvSCAN Supporting Dynamic Thresholds Conclusion

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 21 The Static Threshold Problem How does this index work so far? -Get ready forδ=0.8 please. -Please wait 30min for index generation… -Ready! -Document M1,δ=0.8. Go! -…Extraction complete. -Document M2, and I wantδ=0.9… -Sorry, please wait another 30min for index regeneration… -:-(

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 22 The Static Threshold Problem This One Seems Better -Get ready forδ>=0.8 please. -Please wait 30min for index generation… -Ready! -Document M1,δ=0.8. Go! -…Extraction complete. -Document M2, and I wantδ=0.9… -…Extraction complete. :-)

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 23 Supporting Dynamic Thresholds An Observation When δ descends, a string rs tokens fall into Sig(r) one by one, in the order of their weight ranking. I.e. any node is active when δ is below certain threshold u. We record u in each node and sort all nodes in each list according to the descending order of their u value. For any given δ, we only need retrieve a prefix of each list to get all active nodes

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 24 Experimental Datasets DBLP: 274,788 Paper titles 1,838,973 URLs

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 25 Balance should be reached Recall our two stages of filtration and verification

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 26 Performance (DBLP)

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 27 Outline Introduction State-of-the-art techniques Our algorithms and evaluations Corrected filtering conditions EvSCAN: Filtration by SIL EvITER: Incremental optimization on EvSCAN Supporting Dynamic Thresholds Conclusion

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 28 Conclusion Our method causes no false negatives Our method achieves a good balance between the two phases of filtration and verification We also propose EvITER to eliminate duplicate computation Our method has both effective & efficient performance

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 29

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 30 References [1] A. Arasu, V. Ganti, R. Kaushik. Efficient exact set-similarity joins. In VLDB, pages , [2] K. Chakrabarti, S. Chaudhuri, V. Ganti, D. Xin. An efficient filter for approximate membership checking. In SIGMOD Conference, [3] A. Chandel, P. C. Nagesh, and S. Sarawagi. Efficient batch top-k search for dictionary-based entity recognition. In ICDE, page 28, [4] S. Chaudhuri, V. Ganti, and R. Kaushik. A primitive operator for similarity joins in data cleaning. In ICDE, page 5, [5] M.R.Garey and D.S.Johnson. Computers and Intractability: Guidance to the Theory of NP-Completeness. [6] L. Gravano, P. G. Ipeirotis, H. V. Jagadish, N. Koudas, S. Muthukrishnan, and D. Srivastava. Approximate string joins in a database (almost) for free. In VLDB, pages , 2001.

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Jiaheng Lu, Jialong Han, Xiaofeng Meng 31 References [7] C. Li, J. Lu, and Y. Lu. Efficient merging and filtering algorithms for approximate string searches. In ICDE, pages 257–266, [8] C. Li, B,Wang, X. Yang, VGRAM: Improving performance of approximate queries on string collections using variable length grams. In VLDB [9] G. Navarro. A guided tour to approximate string matching. ACM Comput. Surv., 33(1):31–88, [10] S. Sarawagi, A.Kirpal, Efficient set joins on similarity predicates. In SIGMOD Conference, [11] A. Singhal. Modern information retrieval: A brief overview. Bulletin of the IEEE Computer Society Technical Committee on Data Engineering, 24(4):35-43, [12] E. Sutinen and J. Tarhio. On using q-grams locations in approximate string matching. In ESA, pages , [13] W. Wang, C. Xiao, X. Lin, C. Zhang. Efficient approximate entity extraction with edit distance constraints. In SIGMOD Conference, 2009.

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