PARIS: Probabilistic Alignement of Relationships, Instances, and Schema

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PARIS: Probabilistic Alignement of Relationships, Instances, and Schema

Fabian Suchanek Serge Abiteboul Pierre Senellart

15 November 2011

Big-Data Analytics for the Temporal Web

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Outline

Ontology Matching Probabilistic Model Experiments

Challenges for Large Evolving Ontologies Conclusion

(3)

RDF Ontologies

Singer

1935-01-08 plays

type

born Person

An RDF ontology can be seen as a graph of entities

subclassOf

(4)

RDF Ontologies

Singer

1935-01-08 plays

type

born Person

subclassOf classes

relations / properties instances

literals

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RDF Ontologies

instances

relations / properties classes

literals Singer

1935-01-08 plays

type

born Person

subclassOf

Ontologies serve all kinds of purposes:

(6)

Existing Ontologies

There are literally hundreds of ontologies on the Web

1935-01-08 Singer

type

born plays

YAGO

Person subclassOf

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Overlapping Data

birthDate 1935

type RockSinger

marriedTo

YAGO ElvisPedia

1935-01-08 born Singer

type

Many ontologies contain similar or overlapping entities and facts

plays

(8)

Overlapping Data

birthDate 1935

type RockSinger

marriedTo

YAGO ElvisPedia

type

plays

more speciﬁc

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(9)

Overlapping Data

birthDate 1935

type RockSinger

marriedTo

YAGO ElvisPedia

type

plays

more speciﬁc

complementary

(10)

Overlapping Data

birthDate 1935

type RockSinger

marriedTo

YAGO ElvisPedia

type

plays

more speciﬁc

complementary equivalent

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(11)

Problem: Elvis is lonely

ElvisPedia birthDate type

Singer

marriedTo type

YAGO 1935-01-08

born

1935 RockSinger plays

Who is the spouse of the guitar player?

Complementary information cannot be used

?

marriedTo

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Solution: Unify Entities

Singer

marriedTo type

YAGO 1935-01-08

born

?

marriedTo

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Goal: Merging Ontologies

Singer

marriedTo type

YAGO 1935-01-08

born

To merge two ontologies, we have to identify

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Goal: Merging Ontologies

Singer

marriedTo type

YAGO 1935-01-08

born

1935 RockSinger To merge two ontologies, we have to identify

• equivalent instances

plays sameAs

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Goal: Merging Ontologies

subClassOf

Singer

marriedTo type

YAGO 1935-01-08

born

• equivalent or subsuming classes

sameAs plays

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Goal: Merging Ontologies

sameAs subClassOf

Singer

marriedTo type

YAGO 1935-01-08

born

• equivalent or subsuming classes

• equivalent or subsuming relations

subPropertyOf plays

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(17)

Previous work

• uses hard logical constraints, which may be inadequate

• requires parameter tuning

• has not been tried on large ontologies

birthDate marriedTo

1935 RockSinger type type

Singer

1935-01-08 born

(18)

Previous work

• uses hard logical constraints, which may be inadequate

• requires parameter tuning

• has not been tried on large ontologies

birthDate marriedTo

1935 RockSinger type type

Singer

1935-01-08 born

(1)

• has mostly focused on (1) instance matching or (2) schema alignment, ... but not both

(2)

(1) (2)

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PARIS: Aligning Everything At Once

1935-01-08 born There is a synergy between equality of instances, properties and classes!

=> Compute all together!

birthDate marriedTo

1935 type RockSinger type

Singer PARIS

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Outline

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Probabilistic Model

We chose a probabilistic model

the probability that x=y

the probability that is a sub-property of the probability that is a sub-class of

marriedTo

1935 type

1935-01-08

RockSinger

born

type

birthDate Singer

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Literals

For literals, the probability of equality can be estimated upfront:

birthDate RockSinger type

1935 Singer

1935-01-08

type

born

marriedTo

?

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Literals

birthDate RockSinger type

1935 Singer

1935-01-08

type

born

marriedTo

?

• for strings:

string distance

• for numbers:

numeric distance

• for other literals:

domain-speciﬁc

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Literals

• for strings:

string distance

• for numbers:

numeric distance

• for other literals:

domain-speciﬁc ^birthDate

RockSinger type

1935 Singer

1935-01-08

type

born

marriedTo

?

We chose a particularly simple distance:

?

_{24 / 82}

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Equality of Instances

For instances, relations give a hint:

Elvis Presley label

label

born 1935

born

1935 Elvis Presley

marriedTo

?

(26)

Equality of Instances

Elvis Presley label

label

born 1935

born

1935 Elvis Presley

marriedTo

?

Not many people are called Elvis =>

highly indicative

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(27)

Equality of Instances

highly indicative

Elvis Presley label

label

born 1935

born

1935 Elvis Presley

marriedTo

?

Many people are born in 1935 =>

less indicative

(28)

Equality of Instances

highly indicative

Many people are born in 1935 =>

less indicative

Elvis Presley label

label

born 1935

born

1935 Elvis Presley

marriedTo

?

one over the number of incoming links:

The local inverse functionality of a relation with an argument is

| |

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Local Inverse Functionality

Elvis Presley

1935

marriedTo label

1935

born label

born

Elvis Presley Only one person

is called Elvis

The local inverse functionality of a relation with an argument is one over the number of incoming links:

?

| |

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Local Inverse Functionality

Elvis Presley

1935

marriedTo label

1935

born label

born

Elvis Presley Only one person

is called Elvis

The local inverse functionality of a relation with an argument is one over the number of incoming links:

?

10 people are born in 1935

| |

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Global Inverse Functionality

Elvis Presley Elvis Presley marriedTo label

born

1935 1935

label

born

?

the harmonic mean of the local inverse functionalities:

The global inverse functionality of a relation is

Many people share their year of birth Most people have distinct names

(32)

Equality of Instances

marriedTo Elvis Presley Elvis Presley

label label

born born

1935 1935

?

x and x' shall be matched if

Most people have distinct names

Many people share their year of birth

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Equality of Instances

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Equality of Instances

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Equality of Instances

Let's compute the probability of this happening,

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Equality of Instances

Let's compute the probability of this happening,

(adventurous independence assumptions go here)

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Equality of Instances

(adventurous independence assumptions go here) Let's compute the probability of this happening,

(38)

Equality of Instances

label marriedTo

1935 1935

born born

label

Elvis Presley Elvis Presley

?

This evaluates to 1 iﬀ

• There is at least one highly inverse functional r

• There is one shared argument y=y'

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(39)

Equality of Instances

• Literals: precomputed

• Others: recursive

label marriedTo

1935 1935

born born

label

Elvis Presley Elvis Presley

?

(40)

Unequality of Instances

1935 1970

born born

marriedTo How do we guard against inequalities?

?

Elvis Presley label

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(41)

Unequality of Instances

1935 1970

born born

?

Elvis Presley label

These cannot be equal, because they have a diﬀerent value

for a functional relation.

(42)

Unequality of Instances

1935 1970

born born

?

Elvis Presley label

These cannot be equal, because they have a diﬀerent value

for a functional relation.

The functionality is deﬁned analogously to the inverse functionality.

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Unequality of Instances

1935 1970

born born

marriedTo

Every value in one ontology should have a pendant in the other, weighted by the functionality:

?

This factor makes sure that for every y, there is one equivalent y'

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Unequality of Instances

1935 1970

born born

marriedTo

Every value in one ontology should have a pendant in the other, weighted by the functionality:

?

This factor makes sure that for every y, there is one

equivalent y' sang

Lavender Blue Twinkle Twinkle

sang All shook up

Jailhouse Rock

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Equality of Classes

type singer type

Rock-singer

If all instances of one class are instances of the other then the former subsumes the latter

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Equality of Classes

type singer type

Rock-singer

subclassOf

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Equality of Classes

type singer type

Rock-singer subclassOf

| |

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Equality of Classes

type singer type

| |

| | | |

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Equality of Classes

type singer type

| |

| | | |

| |

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Equality of Relations

knows

marriedTo knows

If every pair of one relation is a pair of another relation, then the ﬁrst is a sub-property of the second.

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Equality of Relations

knows

marriedTo knows

marriedTosubpropertyOf knows

(52)

Equality of Relations

knows

marriedTo knows

marriedTo

knows subpropertyOf marriedTo

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Equality of Relations

knows

marriedTo knows

marriedTo

(Those in the intersection)

(Those that have a pendant) knows

subpropertyOf marriedTo

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Algorithm

1. Fix equalities for literals

Literals:

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Algorithm

Literals:

2. Set equalities for relations to a small initial value

Relations:

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Algorithm

Instances:

Relations:

Literals:

3. Iterate the estimations for relations and instances to convergence (*)

(*) We have no proof for convergence, but it seems to happen

Iterate

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Algorithm

Instances:

Relations:

Literals:

Iterate 1. Fix equalities for literals

3. Iterate the estimations for relations and instances to convergence (*) 4. Compute the estimations for classes

ﬁnal Classes: step

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Example

Elvis

dreamsOf label

Elvis

name Elvis Ontology 1 Ontology 2 Ontology 2

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Example

Elvis

dreamsOf label

Elvis

name Elvis Ontology 1 Ontology 2 Ontology 2

label name

Ontology 1 Ontology 2

(60)

Example

Elvis

dreamsOf label

Elvis

name Elvis

label Madonna

name Madonna Ontology 1 Ontology 2 Ontology 2

Ontology 1 Ontology 2 Ciccone

1958 Frozen

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Example

Elvis

dreamsOf label

Elvis

name Elvis

Ciccone 1958 Frozen

label name

Ontology 1 Ontology 2 Ontology 2

(62)

Example

Elvis

dreamsOf label

Elvis

name Elvis

Ciccone 1958 Frozen label

Madonna

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(63)

Example

Elvis

dreamsOf label

Elvis

name Elvis

Ciccone 1958 Frozen

label name

Ontology 1 Ontology 2 Ontology 2

(64)

Example

Elvis

dreamsOf label

Elvis

name Elvis

Ciccone 1958 Frozen label

Madonna

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(65)

Outline

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Experiment: YAGO and DBpedia

Singer

SuperHuman

1977

1935 1935

died born

gender male

born with stillborn twin brother

DBpedia YAGO

1.7m instances 19m facts

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Experiment: YAGO and DBpedia

Singer

SuperHuman

1977

1935 1935

died born

gender male

DBpedia YAGO

2.6m instances 18m facts Independent

class hierarchies

(68)

Experiment: YAGO and DBpedia

Singer

SuperHuman

1977

1935 1935

died born

gender male Independent

class hierarchies

DBpedia YAGO

2.6m instances 18m facts 50% overlap

of instances

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Experiment: YAGO and DBpedia

Singer

SuperHuman

1977

1935 1935

died born

class hierarchies

50% overlap of instances

DBpedia YAGO

2.6m instances 18m facts Independent

properties

(70)

Experiment: YAGO and DBpedia

Singer

SuperHuman

1977

1935 1935

died born

class hierarchies

50% overlap of instances Independent properties

DBpedia YAGO

2.6m instances 18m facts Many

complementary facts

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Experiment: YAGO and DBpedia

Iteration 1 2 3 4

Change -- 12%

1%

0.3%

Time 4:04h 5:06h 5:00h 5:30h

Precision 86%

89%

90%

Recall 69%

73%

Matching the instances:

(72)

Experiment: YAGO and DBpedia

Iteration 1 2 3 4

Change -- 12%

1%

0.3%

Time 4:04h 5:06h 5:00h 5:30h

Precision 86%

89%

90%

Recall 69%

73%

Matching the instances:

Precision: 74%

Aligns roughly half of DBpedia's classes Matching the classes:

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Experiment: YAGO and DBpedia

yago:actedIn = dbpedia:starring- yago:hasChild = dbpedia:child yago:hasChild = dbpedia:parent- yago:created > dbpedia:writer yago:diedIn > dbpedia:placeOfBurial ... and many more. Precision: 96%

Matching the relations:

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Experiment: YAGO and DBpedia

yago:actedIn = dbpedia:starring- yago:hasChild = dbpedia:child yago:hasChild = dbpedia:parent- yago:created > dbpedia:writer yago:diedIn > dbpedia:placeOfBurial ... and many more. Precision: 96%

+ more experiments on OAEI standard datasets and IMDb

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Experiment: YAGO and DBpedia

+ more experiments on OAEI standard datasets and IMDb yago:actedIn = dbpedia:starring-

yago:hasChild = dbpedia:child yago:hasChild = dbpedia:parent- yago:created > dbpedia:writer yago:diedIn > dbpedia:placeOfBurial ... and many more. Precision: 96%

All experiments run with the same settings.

No parameter tuning.

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Outline

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Execution Time

I Essentiallyquadraticalgorithm

∀x1∈O1∀x2∈O2 Pr(x≡x⁰) =. . .

I Optimizations make it possible to only compare entities that have something in common, but only because of our trivial literal matching mechanism

I Lots of random accesses: using aSSDrather than a magnetic hard drive gives us a 25×speedup!

I Still,at the limitof what is processable by a centralized, naïve implementation of our approach

I What if we had 10 million instances? 1 billion instances?

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How to Improve Efficiency

I Parallelization (à la MapReduce) isvery much possible:

I In one iteration, the new value of Pr(x≡y)does not depend on the new value of Pr(x⁰ ≡y⁰)forx⁰ 6=y⁰.

I (Costly)synchronizationneeded at the end of each iteration (similar to PageRank computation)

I Does not solve everything, though: does not change the fact that we deal with anessentially quadratic

computation!

I Clever indexingdefinitely needed, but not trivial, since distance between literals might not be a nice metric

I Samplingprobably the way to go: a human does not need to compare all pairs to determine that two relations are the same.

I What abouton demand matchingof pairs, based on local neighborhoods?

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Evolving Ontologies

I Ontologies arenot static, new facts get added all the time (and some facts get deleted):

I incrementally (e.g., IMDb);

I each time the dataset is regenerated (e.g., YAGO).

I Raises two challenges:

I Can matching be performedincrementallyas well?

I How to deal withtime-dependent equalities(e.g.,Barack ObamaandPresident of the United States) and

time-dependent functional dependencies?

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Outline

(81)

Conclusion

• PARIS matches relations, instances and schema holistically

• PARIS has no parameters to tune

• PARIS shows high precision and recall

marriedTo

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Conclusion

• PARIS matches relations, instances and schema holistically

• PARIS has no parameters to tune

• PARIS shows high precision and recall

• PARIS allows the YAGO Elvis to marry the DBpedia Priscilla

marriedTo equals

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