Multipath tracing with Paris traceroute

Multipath tracing with Paris traceroute

Entity Resolution in the Web of Data Vassilis Christophides INRIA Paris-Roquencourt (MUSE team, France) Joint work with Vasilis Efthymiou (UoC-CSD, Greece) & Kostas Stefanidis (Tampere University, Finland) Matching and Resolving Entities (II): Iterative Resolution Techniques Central vs. Peripheral KBs 3 In Search of Similarity Evidence in KBs [Efthymiou et al. 2016, 2015] Attribute-based unique attributes (e.g., rdfs:label) provide strong evidence >90% of matching pairs have >80% overlap similarity in the values of rdfs:label Content-based comparisons comparisons central KBs: 3-4 common tokens in entity values peripheral KBs: 1-2 common tokens in entity values

blocking algorithms miss up to 30% matches in peripheral KBs Relationships-based comparisons matching neighbors provide positive evidence >92% of pairs with at least one matching neighbor, are matches in most KBs some types of relationships provide strong negative evidence dissimilar values for wasBornIn indicate a non-matching pair 4 Types of Missed Matches (FNs) Type A: a third, matching description (transitivity) applicable to identify matches within a KB Type B: matches of their neighbors directs can identify matches both within a KB and across different KBs isdirected

5 Iterative ER Increase the number of matching entities Blocking Matching Iterative ER: identify new matches based on partial results either of matches or of merges Good for high Variety 6 Iterative ER Approaches Merging-based: new matches can be found by exploiting merged (more complete) descriptions of previously identified matches Idea: ER resembles a database self-join operation (of the initial set of descriptions with itself) But: No knowledge about which descriptions may match, so all pairs of descriptions need to be compared If descriptions related to entity ei are matching to descriptions related to ej, then ei and ej are likely to match Idea: ER resembles to a graph traversal problem in which similarity is propagated until a fixed point is reached Use positive or negative evidence for prioritize similarity recomputation Matching-based:

7 Matching and Resolving Entities (II): Merging-based Iterative Resolution Merging-based ER Formal Definition Let E = {e1, ..., em} a set of entity descriptions and M : E E {true, false} is a match function : E E E is a partial merge function The merging-based (generic) resolution of entities in E is a set of descriptions E, such that: 1.ei, ej E : M(e E : M(ei, ej) = true, eek E : M(e E: (ei, ej) ek 2.ek E : M(e E, el E : M(e E, el ek 3.no strict subset of E satisfies conditions 1 and 2 where el ek means that ek is at least as informative than el, regarding the same real-world entity E E (the merge closure) Condition 1: E cannot produce more than E Condition 2: E produce at least all information of E Condition 3: Minimal solution Note:

Match and Merge Functions: ICAR Properties [Benjelloun et al., 2009] Idempotence: a description always matches itself, and merging it with itself still yields the same description ei E : M(e E if M(ei,ei) = true then (ei,ei) = ei Commutativity: direction of match and merge is irrelevant ei,ej E : M(e E if M(ei,ej) = M(ej,ei) = true then (ei,ej) = (ej,ei) Associativity: order of merge is irrelevant ei,ej,ek E : M(e E if ((ei,ej),ek) and (ei,(ej,ek) exist then ((ei,ej),ek) = (ei,(ej,ek) Representativity: merging does not lose matches; no negative evidence if ek=(ei,ej) then el E : M(e E such that M(ei,el) = true also M(ek,el) = true Transitivity is not assumed! 1

Merge Domination & Monotonicity When the match and merge functions satisfy the ICAR properties, there is a natural domination (partial) order of descriptions Given two descriptions, e and e , we say that e is merge domi1 2 1 nated by e2, denoted e1e2, if M(e1,e2) = true and (e1,e2) = e2 e1 does not add information Merged descriptions always dominates the ones they have derived from e1, e2 E : M(e E such that M(e1,e2) = true, it holds that e1 (e1,e2) and e2 (e1,e2) Match function is monotonic e1, e2, e3 E : M(e E If e1 e2 and M(e1,e3)=true, then M(e2,e3)=true Merge function is monotonic e1, e2, e3 E : M(e E If e1 e2 and M(e1,e3) , then (e1,e3) Entity Resolution with Swoosh F. Naumann 20.6.2013 1 (e ,eGeneric ) What is Best Sequence of Match, Merge Calls that Give us Right Answer? KB1:SKBRK e1 KB1:Stanley_Kubrick KB1:birthPlace KB1:Manhattan

KB1:bornIn 1928-7-26 KB1:parents KB1:Gertrude Kubrick KB1:name S. Kubrick KB1:birthPlace KB1:Manhattan KB1:deathPlace KB1:UnitedKingdom KB1:parents KB1:Jacques Leonard Kubrick KB1:diedIn 1999 rdf:type yago:AmericanFilmDirectors

KB2:SKubrick foaf:name Stanley Kubrick KB2:place_of_birth KB2:MNHT rdf:type foaf:Person KB2:activeYearsEndYear 7/3/1999 KB2:directed KB2:A_Clockwork_Orange M(e1,e2,3)=true e3 e2 M(e2,e3)=true e2,3=(e2,e3 KB12:Stanley_Kubrick birthPlace

Manhattan bornIn 1928-7-26 parents Gertrude Kubrick parents Jacques Leonard Kubrick rdf:type AmericanFilmDirectors activeYearsEndYear 7/3/1999 directed A_Clockwork_Orange 1 R-Swoosh [Benjelloun et al., 2009] Assumes ICAR and merge domination

1: if M(e1,e2) = true we can remove e1 and e2 Whatever would match e1 or e2 now also matches (e1,e2) Representativity and associativity Idea Idea 2: Removal of dominated descriptions is not necessary as a last step in the algorithm Assume e1 and e2 appear in final answer where e1 e2 Then M(e1,e2) = true and (e1,e2) = e2 Thus comparison of e1 and e2 should have generated merged description e2, and e1 should have been eliminated Generic Entity Resolution with Swoosh F. Naumann 20.6.2013 1 R-Swoosh Example E E' E e1 e2 e2

e3 e3 E E' e23 e1 (a) E E' E e1 E' e3 (b) e123 (d) E

E' e1 e2 E' (c) e123 (f) (e) 1 ER with ICAR properties General ER process is guaranteed to be finite Entity descriptions can be matched and merged in any order Dominated entity descriptions can be discarded anytime Union class of match and merge Union-merge: All values are kept in merged descriptions Union-match: At least one of the values in common

e1 e2 e e e e e e e Commutativity of match and merge functions for highly heterogeneous descriptions does not always hold 1 Matching and Resolving Entities (II): Matching-based Iterative Resolution Positive and Negative Match Evidence Evaluated on individual entities Hard Constraints Positive FD: if M(ei, ej) = true then M(ek, Evidence el) = true

Example: if two movies match then their director also match Negative FD: if M(ei, ej) = false then Evidence M(ek, el) = false Example: if two directors dont match then movies directed by them dont also match Negative constraints are usually stated by domain experts Evaluated on interrelated entities Soft Constraints FD: if M(ei, ej) = true then most likely M(ek, el) = true Example: if two movies match then their actors are most likely to match FD: if M(ei, ej) = false then most likely M(ek, el) = false Example: if two movies dont match then their actors are less likely to match Constrains can be recursive L. Getoor, A. Machanavajjhala Entity Resolution for Big Data1 Additional Constraints [Shen et al, 2005] Type

Example Aggregate Subsumption No director has produced more than four movies per year If a movie X from Yago matches a movie Y from IMBD then each studio cited by in Y matches some studio cited by in X Neighborhood If actors X and Y share similar names and some co-actors in a movie, they are likely to match Incompatible No director has filmed a movie in studios both in Africa and Japan Layout If two movies with similar names are mentioned by the same review they are likely to match Key/Uniqueness Actors of the same movie must refer to distinct persons Ordering If two paper citations match, then their authors will be matched in order Individual Victorina Mrida Rojas matches with Victoria Abril 1 Matching-based Iterative ER Pair-wise ER: matching decisions are made independently Deduplication, Linkage Collective ER: matching decisions depend on other matching decisions according to positive and negative evidence (general

constraints) Similarity propagation approaches (more scalable) Dependency graphs of matching decisions Collective relational clustering Probabilistic approaches (scalability is an open issue) Generative Models (for acyclic dependencies between match decisions) Undirected Models based on Markov Networks (sometimes with a first-order logic syntax) Hybrids of constraints and probabilistic models 1 Similarity Propagation Approaches A graph structure for encoding the similarity between entity descriptions and matching decisions, and iteratively assess matching of entities by propagating similarity values Details of how the graph is constructed and traversed and how (content and context) similarity is computed vary Similarity-propagation ER: the match function is re-computed at each iteration step by considering previous matching decisions: Mn(ei,ej) = true, if simn-1(ei,ej) Mn(ei,ej) = false, if simn-1(ei,ej) Mn(ei,ej)= undecided, otherwise Total similarity: sim(ei,ej)= a*simnbr(ei,ej)+(1-a)*simnbr(nbr(ei),nbr(ej)) where nbr(e) denotes the neighborhood (in, out) nodes of e 2

Maintaining the Order of Comparisons In similarity-propagation approaches the order of comparisons is dynamic Graph traversal usually supported by a priority queue (PQ) on the similarity score of nodes As entities are resolved, the PQ is updated for maximizing effectiveness & reducing re-comparisons Different strategies of order maintenance: Based on heuristics type of nodes and edge direction [Dong et al. 2005] degree of nodes [Weis & Naumann 2006] edge weights [Kalashnikov & Mehrotra 2006] Triggered by recent matches [Bhm et al. 2012, LacosteJulien et al. 2013] Lazy maintenance [Herschel et al. 2012, Altowim et al. 2014] 2 Dependency Graph [Dong et al., 2005] Works on an entity graph constructed from the relational records nodes represent similarity comparisons between pairs of records and/or their attribute values (real-valued) edges represent match decisions based on the matching of associated nodes (boolean-valued)

A matching decision is taken when the real-valued similarity score (between 0 and 1) of a node is above a threshold If it exceeds the threshold, it is marked as match, otherwise as undecided, if no more neighbors are undecided, it is marked as non-match Idea 1: consider richer matching evidence Idea 2: propagate similarity between matching decisions Idea 3: Gradually enrich references by merging attribute values (Swoosh-style) 2 Dependency Graph: Example E be a set of entity descriptions A node v = {ei,ej}, where ei,ej E : M(e E, i j An edge e = (va,vb) from va={eai,eaj} to vb = {ebi, ebj} implies ebi , ebj E : M(e values(eai) values(eaj) Let v1 Directed edge when dependency is only in one direction can be stated by domain experts inferred by the data semantics (e.g., keys/forein keys, rdf properties) Include

only nodes whose two entities have the potential to be similar v2 v3 v4 2 Consider Richer Matching Evidence [Dong et al., 2005] Positive evidence (i.e., constraints for match nodes) is captured by the Boolean similarity of neighborhood nodes Strong-boolean: Resolution implies resolution of neighbour E.g., if two movies are matched then director must also be matched Weak-boolean: No direct implication E.g., similarity of two movies increases as their rdf:labels are highly similar Negative evidence (i.e., constraints for nonmatch nodes) is verified after similarity propagation is performed, and inconsistencies are fixed 2

Similarity Propagation [Dong et al., 2005] function for node u: sim(u) = Srv + Ssb + Swb Srv: from real-valued neighbors (decision-tree shape) Ssb: from strong-boolean-valued neighbors Swb: from weak-boolean-valued neighbors Similarity When a node is matched, the similarity score of its neighbors is re-computed Process converges if Similarity score is monotone in the similarity values of neighbors Compute neighbor similarities only if similarity increase is not too small 2 Traversing the ER Graph e a b c

h PQ f a d b c h g Initially all nodes are active and placed in the PQ f A node is processed before its out-neigbors d e g 2 Traversing the ER Graph e a b c

h PQ b c d h d e g g f merged node inactive node 2 Traversing the ER Graph e a b c h PQ c h d

d e g g f 2 Traversing the ER Graph e a b c h PQ h d d e g g f 2 Traversing the ER Graph e a

b c h PQ d e d g g f 3 Traversing the ER Graph e a b c h PQ g b d e

g f 3 Traversing the ER Graph e a b c h PQ b e d g f 3 Traversing the ER Graph e a b c h PQ e c

d g f 3 Traversing the ER Graph e a b c h PQ c d g f 3 Traversing the ER Graph e a b c PQ

h d g f 3 Linda [Bhm et al. 2012] Works on an entity graph constructed from the RDF descriptions exploits the unique mapping constraint between two KBs Key Idea: the more matching neighbors via similar relationships two descriptions have, the more likely it is that they match String similarity of the literal values of entities: checked once Contextual similarity of the graph neighbors:checked iteratively Two square matrices (|E| |E|) are used: X captures the identified matches (binary values) Y captures the pair-wise similarities (real values) Initialization: common neighbors & string similarity of literals Updates: Use the new identified matches of X Until the priority queue (extracted from Y) becomes empty: Get the pair (ei, ej) with the highest similarity: match by default! Update X: matches of ei are also matches of ej Update the similarity of nodes influenced by the new matches 3 Linda Algorithm Example Matches e1 e2 e3

e4 e1 e2 e3 e4 e5 1 PQ 0 0 0 0 e1 e4 1 0 0 0 e2 e4 1

0 0 e1 e3 1 0 e5 e3 1 e2 e3 e5 e3 e4 e2 e1 A priority queue, derived by an initial similarity computation between all pairs, based on their

attribute values e5 3 Linda Algorithm Example Matches e1 e2 e3 e4 e1 e2 e3 e4 e5 1 PQ 0 0 1 0 e1 e4 1

0 0 0 e2 e4 1 0 0 e1 e3 1 0 e5 e3 1 e2 e3 e5 the head of PQ is a match by default

e3 e4 e2 e1 e5 3 Linda Algorithm Example Matches e1 e2 e3 e1 e2 e3 e4 e5 1 0 0 1

0 e2 e4 1 0 0 0 e1 e3 1 0 0 e2 e3 1 0 e5 e3 1 e4

e5 e3 e2 directs directs e4 PQ unique mapping constraint (1-1 Assumption) similarity recomputation, based on the matching neighbors and the names of the links to them e1 e5 3 Linda Algorithm Example Matches e1 e2 e3

e1 e2 e3 e4 e5 1 PQ 0 0 1 0 e2 e3 1 1 0 0 e5 e3 1 0

0 1 0 e4 e5 1 e3 e2 directs directs e4 e1 e5 4 Linda Algorithm Example Matches e1 e2 e3

e1 e2 e3 e4 e5 1 PQ 0 0 1 0 e5 e3 1 1 0 0 1

0 0 1 0 e4 e5 unique mapping constraint (1-1 Assumption) 1 e3 e2 directs directs e4 e1 e5 stops when PQ is empty 4

Linda Distributed Version Matches e1 e1 e2 e3 e4 e5 1 e2 e3 PQ PQ 0 0 0 0 e1 e4 e5 e3 1

0 0 0 e2 e4 e5 e4 1 0 0 e1 e3 1 0 e2 e3 1 e4 e5

Node 2 Node 1 e3 Node 1 e2 knows knows e4 e1 e5 Node 2 The node to hold the PQ entry (a,b) and the respective vertex neighbors is determined by a modulo operation of the first component (a) 4 Matching and Resolving Entities (II): Progressive Resolution Techniques Progressive ER Optimization: maximize benefit (number or type of matches) for

a given cost (number of comparisons, disk/cloud access) Blocking Matching Planning Progressive ER: estimates which part of the data to resolve next and adapts this decision in a pay as you go fashion Good Update for high Velocity 4 Progressive Approach to Relational Entity Resolution [Altowim et al. 2014] Key Idea: divides the ER process into several windows and generates a resolution plan for each window specifies which blocks and entity pairs within these blocks will be resolved during the plan execution phase of a window associates with each identified pair the order in which to apply the similarity functions on the attributes of the two entities

Lazy resolution strategy to resolve pairs with the smallest cost Unlike single entity type resolution a block based prioritization is significantly more important when resolving multiple types4 5 Relational Progressive ER: Example Actors v v v 1 2 Blocks with entities of the same type 3 A1 M11 v 4 A2 D2 Movies

v v v 5 6 7 Directors v v v 9 1 0 1 1D 1 v 8 M2 v

1 2 Altowim et al. Progressive Approach to Relational ER VLDB 2014 4 Matching Probability Estimation The Noisy-OR Model nodes in the ER graph influencing Cause a pair of entities are interpreted as common causes to the same effect Cause Cause The probability that a node is processed Effect at each round depends on the number of cause nodes that are matches and/or not required to know all on the percentage of matching nodes in the causes the block of the effect node Effect: Node considered

for matching v Causes: (a) Influencing i matching nodes x (b) Fraction of matching j pairs in the block of v 4 Altowim et al. Progressive Approach to Relational ER VLDB 2014 Heuristics for Estimating Node Benefit v v v 1 2 3 v v v 5 6 7 A1 M1 v

v A2 D2 M2 Direct A M Benefit 4 8 v v v match non-match 9 1 0 1 1D 1

v 1 2 Indirect Benefit The Impact is estimated for k nodes of the same entity type, as the of their v1 average vnumber M1 direct 2 of matching dependent unresolvedFraction nodes pairs in the block 4 Altowim et al. Progressive Approach to Relational ER VLDB 2014 Traversing the ER Graph (in Blocks) F1 M1 D1 b 0.1 e

0.3 a 0.3 d s(F1)=s(e)= 0.1+0.1*1=0.2 0.1 A1 0.1 s(M1)=s(a)+s(d)= (+*1)*2=4 M2 c 0.2 0.2 h 0.3 D2 f

g s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6 Assign to blocks the sum of their nodes scores: s(B) = Impact(directors) = 3, Impact(actors) = 2, Impact(movies) = 1 Initially, a block of the entity type with the highest outImpact(family) = 1 degree (impact) is selected (in random), since P(v ) i Initial P(vi) = is the same for all nodes (of the same type) Traversing the ER Graph (in Blocks) F1 M1 D1 a 0.3 d b

0.1 e 0.3 s(F1)=s(e)= 0.1+0.1*1=0.2 0.1 0.1 A1 s(M1)=s(a)+s(d)= (+*1)*2=4 M2 c 0.2 0.2 h D2 f g s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.61)=s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6c)+s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6h)=(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.60.1+0.1*2)*2=0.6 Impact(directors) = 3,

Impact(actors) = 2, Impact(movies) = 1 Impact(family) = 1 Initial P(vi) = 0.3 Assign to blocks the sum of their nodes scores: s(B) = Then, update the scores, load the block with the highest score and resolve its nodes Traversing the ER Graph (in Blocks) F1 M1 D1 0.3 b 0.1 a e 0.3 s(F1)=s(e)= 0.1+0.1*1=0.2

0.1 A1 c 0.1 h Impact(directors) = 3, Impact(actors) = 2, Impact(movies) = 1 Impact(family) = 1 Initial P(vi) = s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6M1)=s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6a)+s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6d)= (1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6+*1)+ (1)=s(c)+s(h)=(0.1+0.1*2)*2=0.60.2+0.2*1)=2+0.4 M2 0.2 0.2 d 0.3 D2 f g Assign

to blocks the sum of their nodes scores: s(B) = Then, update the scores, load the block with the highest score and resolve its nodes Traversing the ER Graph (in Blocks) F1 M1 D1 a 0.3 d b 0.1 e 0.3 s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6F1)=s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6e)= 0.1+0.1*1=0.2 0.1 A1

0.1 M2 c h 0.2 0.2 0.3 D2 s(M2)=s(f)= +*1=2 g s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6D2)=s(1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6g)= +*3=4 Impact(directors) = 3, Impact(actors) = 2, Impact(movies) = 1 Then, update Impact(family) = 1 Initial P(vi) = highest score f Assign to blocks the sum of their

nodes scores: s(B) = the scores, load the block with the and resolve its nodes Comparison of ER Graph Traversals Property [Dong et al. 2005] [Bhm et al. 2012] [Altowim et al. 2014] Seed node selection any node with no in-edges the node with the highest content_sim any node of the entity type with the highest out-degree Matching condition similarity is above a threshold value

the highest score (head of PQ) a (black-box) resolve function returns true Similarity/Evidence Update (1)=s(c)+s(h)=(0.1+0.1*2)*2=0.6PQ) weighted sum of in-neighbors similarities weighted sum of matching in-/outneighbors similarities leaky noisy-or of matching inneighbors topological sort advance in the PQ the neighbors (with most similar relationships) of the recent match Backtracking Traversal policy sort PQ based on

#in-matches and #out-neighbors Web-scale Progressive ER: Ongoing Work Relational progressive ER algorithms assume that the more entity pairs are correctly identified, the higher the quality of the result is expected to be We are interested in characterizing the quality of resolved pairs # of real-world entities resolved (shallow strategy) entity-centric search (entity coverage) # of real-world entity graphs resolved (deep strategy) entity-centric recommendation (relationship completeness) # descriptions resolved for the same real-world entity (tail strategy) web-scale knowledge curation (attribute completeness) 5 Matching and Resolving Entities (II): Challenges and Open Issues Challenges and Open Issues Tight

coupling of Blocking with Iterative Matching/Merging Better control of block characteristics w.r.t. the entity similarity subsequently used (see [J. Fisher et al. 2015] Progressive ER with Quality Guarantees guarantees (e.g., coverage) regarding the quality of matches/ merges w.r.t. subsequent entity-centric services and data analysis tasks ER for Big Data Algorithms for high Velocity (see [D. Firmani et al. 2016]), Variety, and Volume entity descriptions (see [Q. Wang et al. 2015] [L. Kolb et al. 2012]) Large-Scale ER Testbeds Real-world ground truth datasets for different match types and open source ER platforms (see [Efthymiou et al. 2015, 2016]) 5 Challenges and Open Issues Crowdsourced ER: reduce the crowdsourcing cost for obtaining ground truth (see [Chai et al. 2016] [Gokhale et al. 2014] [Wang et al. 2012]) Temporal ER: resolve evolving entity descriptions and analyse the history of descriptions (see [Dong & Tan 2015]) Uncertain ER: consider confidence scores when resolving certain & uncertain entity descriptions (see [Gal 2014] [Demartini et al. 2013]) Privacy-aware ER: Trade-off between entity obfuscation techniques and ER results quality (see [Whang & Garcia-Molina 2013])

5 http://www.morganclaypoolpublishers.com/catalog_Orig/product_info.php?products_id=823 The Minoan ER Framework http://csd.uoc.gr/~vefthym/minoanER 6 Questions ? Acknowledgements EU FP7-PEOPLE-2013-IRSES Big Geospatial Data Quality and User Privacy Dfi Mastodons CNRS 2016 6 License These slides are made available under a Creative Commons Attribution-ShareAlike license (CC BY-SA 3.0): http://creativecommons.org/licenses/by-sa/3.0/ You

can share and remix this work, provided that you keep the attribution to the original authors intact, and that, if you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one 6

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