Top-k Set Similarity Joins Chuan Xiao, Wei Wang, Xuemin Lin and Haichuan Shang Univ. of New South Wales, Austrailia ICDE ’09 9 Feb 2011 Taewhi Lee Based on Chuan Xiao’s presentation slides in ICDE ’09

Outline  Introduction  Problem Definition  Existing Approaches  Top-k Join Similarity Join Algorithms  Experiments 2

Motivation  Data Cleaning UniversityCityStatePostal Code University of New South WalesSydneyNSW2052 University of SydneySydneyNSW2006 University of MelbourneMelbourneVictoria3010 University of QueenslandBrisbaneQueensland4072 University of New South ValesSydneyNSW2052 3

More Application  Near duplicate Web page detection Obama Has Busy Final Day Before Taking Office as Bush Says Farewells New York Times Jan 19th, 2009 iht.com Jan 20,

Outline  Introduction  Problem Definition  Existing Approaches  Top-k Join Similarity Join Algorithms  Experiments 5

(Traditional) Set Similarity Join  Each record is tokenized into a set  Given a collection of records, the set similarity join problem is to fi nd all pairs of records,, such that sim(x,y)  t  Common similarity functions: –jaccard: –cosine: –dice: x = {A,B,C,D,E} y = {B,C,D,E,F} 4/6 = /5 = 0.8 8/10 = What if t is unknown beforehand?

What If t is Unknown Beforehand?  Example – using jaccard similarity function –w = {A, B, C, D, E} –x = {A, B, C, E, F} –y = {B, C, D, E, F} –z = {B, C, F, G, H} –If t = 0.7  no results –If t = 0.4 ,,,, (too many results and long running time)  Return the top-k results ranked by their similarity values –if k = 1  7

Top-k Set Similarity Join  Return top-k pairs of records, ranked by similarity scores  Advantages over traditional similarity join –Without specifying a threshold –Output results progressively  benefit interactive applications –Produce most meaningful results under limited resources/time constraints  Can be stopped at any time, but still guarantee sim(output results)  sim(unseen pairs) 8

Outline  Introduction  Problem Definition  Existing Approaches  Top-k Join Similarity Join Algorithms  Experiments 9

Straightforward Solution  Start from a certain t, repeat the following steps: –answer traditional sim-join with t as threshold –if # of results  k, stop and output k results with highest sim –else, decrease t  Example (jaccard, k = 2) –w = {A, B, C, E} –x = {A, B, C, E, F} –y = {B, C, D, E, F} –z = {B, C, F, G, H} –t = 0.9  no result –t = 0.8  –t = 0.7  –t = 0.6 , results don’t change! Which thresholds shall we enumerate? 0.8,

Naïve and Index-Based Algorithms  Na ï ve Algorithm: –Compare every pair of objects -> O(n 2 ) time complexity  Index-based Algorithm [Sarawagi et al. SIGMOD04] : Record Set Index Construction Candidate Generation Verification Result Pairs tokenrecord_id Awxy Bxz … Cyz … <w,x><w,x> <w,y><w,y> <x,y><x,y> <x,z><x,z> … inverted lists 11

 Sort the tokens by a global ordering –increasing order of document frequency  Only need to index the first few tokens (prefix) for each record  Example: jaccard t = 0.8  |x  y|  4 if |x|=|y|=5 AB CD upper bound O(x,y) = 3 < 4! prefix sorted EFG EFG 12 Prefix Filter [Chaudhuri et al. ICDE06, Bayardo et al. WWW07] x y  Must share at least one token in prefix to be a candidate pair –For jaccard, prefix length = |x| * (1 – t) + 1  each t is associated with a prefix length

Outline  Introduction  Problem Definition  Existing Approaches  Top-k Join Similarity Join Algorithms  Experiments 13

Necessary Thresholds  Each prefix is associated with a threshold –the maximum possible similarity a record can achieve with other records ABC x = t x y z

Event-driven Model  Problem: repeated invocation of sim-join algorithm –t is decreasing  run sim-join algorithm in an incremental way  Prefix Event –Initialize prefix length for each record as 1  –For each prefix event  Probe the inverted list of the token for candidate pairs, verify the candi date pairs, and insert them into temp results  Insert x into A ’ s inverted list  Extend prefix by one token  maintain prefix events with a max-heap on t –Stop until t  k-th temp result ’ s similarity 15

Topk-join - Example 16 ABCE ABCEF BCDEF BCFGH w x y z tokenrecord_id Awx Byzxw Cyz inverted list prefix event (w,x) = 0.8 (y,z) = 0.43 (x,y) = 0.67 temporary result jaccard, k=2 verified t wice! t=0.6  2nd temp result’s sim

Optimizations - Verification  In the above example, (w,x) and (y,z) have been verified twice  How to avoid repeated verification? –Memorize all verified pairs with a hash table  too much memory consumption –Check if this pair will be identified again when it is verified for the first time –Keep only those will be identified again before algorithm stops –Guarantee no pair will be verified twice ABDEF ACDEF x y if k-th temp result’s sim = 0.7 won’t be identified again! 17

Optimizations - Indexing  How to reduce inverted list size to save memory? –t is decreasing  calculate the upper bound of similarity for future probings into inverted lists –Don ’ t insert into inverted list if upper bound  k-th temp result ’ s similarity ACDEF BCDEF x y max. similarity = 4/6 = 0.67

Outline  Introduction  Problem Definition  Existing Approaches  Top-k Join Similarity Join Algorithms  Experiments 19

Experiment Settings  Algorithms –topk-join –pptopk: modified ppjoin[ Xiao, et al. WWW08 ], a prefix-filter based approach, with t = 0.95, 0.90,  Measure –Compare topk-join and pptopk (candidate size, running time) –Output results progressively  Dataset dataset# of recordsavg. record size DBLP (author, title)855k14.0 TREC (author, title, abstract)348k130.1 TREC-3GRAM348k868.5 UNIREF-3GRAM (protein seq.)500k

Experiment Results 21

Experiment Results 22

Experiment Results 23

Thank You! Any questions or comments?

Related Work  Index-based approaches –S. Sarawagi and A. Kirpal. Efficient set joins on similarity predicates. In SIG MOD, 2004 –C. Li, J. Lu, and Y. Lu. Efficient merging and filtering algorithms for approxi mate string searches. in ICDE, 2008  Prefix-based approaches –S. Chaudhuri, V. Ganti, and R. Kaushik. A primitive operator for similarity joi ns in data cleaning. In ICDE, 2006 –R. J. Bayardo, Y. Ma, and R. Srikant. Scaling up all pairs similarity search. In WWW, 2007 –C. Xiao, W. Wang, X. Lin, and J. X. Yu. Efficient similarity joins for near duplic ate detection. In WWW, 2008  PartEnum –A. Arasu, V. Ganti, and R. Kaushik. Efficient exact set-similarity joins. In VLD B,