data repairing

Data Repairing

Giorgos Flouris, FORTHDecember 11-12, 2012, Luxembourg

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PART I: Problem Statement and

Proposed Solution(D2.2)

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Validity as a Quality Indicator Validity is an important quality indicator

◦ Encodes context- or application-specific requirements◦ Applications may be useless over invalid data◦ Binary concept (valid/invalid)

Two steps to guarantee validity (repair process):1. Identifying invalid ontologies (diagnosis)

Detecting invalidities in an automated manner Subtask of Quality Assessment

2. Remove invalidities (repair) Repairing invalidities in an automated manner Subtask of Quality Enhancement

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DiagnosisExpressing validity using validity rules

over an adequate relational schemaExamples:

◦Properties must have a unique domain◦p Prop(p) a Dom(p,a)◦p,a,b Dom(p,a) Dom(p,b) (a=b)

◦Correct classification in property instances◦x,y,p,a P_Inst(x,y,p) Dom(p,a) C_Inst(x,a)◦x,y,p,a P_Inst(x,y,p) Rng(p,a) C_Inst(y,a)

Diagnosis reduced to relational queries

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Ontology O0Class(Sensor), Class(SpatialThing), Class(Observation)Prop(geo:location)Dom(geo:location,Sensor)Rng(geo:location,SpatialThing)Inst(Item1), Inst(ST1)P_Inst(Item1,ST1,geo:location)C_Inst(Item1,Observation), C_Inst(ST1,SpatialThing)

Example

Correct classification in property instances x,y,p,a P_Inst(x,y,p) Dom(p,a) C_Inst(x,a)

Sensor SpatialThing

Observation

Item1 ST1

geo:location

Schema

Data

Item1 geo:location ST1 Sensor is the domain of geo:locationItem1 is not a Sensor

P_Inst(Item1,ST1,geo:location)O0

Remove P_Inst(Item1,ST1,geo:location)

Add C_Inst(Item1,Sensor)Remove Dom(geo:location,Sensor)

C_Inst(Item1,Sensor)O0

Dom(geo:location,Sensor)O0

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Preferences for Repair– Which repairing option is best?

◦Ontology engineer determines that via preferences

Specified by ontology engineer beforehand

High-level “specifications” for the ideal repair

Serve as “instructions” to determine the preferred (optimal) solution

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Preferences (On Ontologies)

O0

O2

O3

Score: 3

Score: 4

Score: 6

O1

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Preferences (On Deltas)

O0

O1

O2

O3Score: 2

Score: 4

Score: 5

-P_Inst (Item1,ST1, geo:location)

+C_Inst (Item1,Sensor)

-Dom (geo:location,

Sensor)

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PreferencesPreferences on ontologies are result-oriented

◦ Consider the quality of the repair result◦ Ignore the impact of repair◦ Popular options: prefer newest/trustable information,

prefer a specific ontological structurePreferences on deltas are impact-oriented

◦ Consider the impact of repair◦ Ignore the quality of the repair result◦ Popular options: minimize schema changes, minimize

addition/deletion of information, minimize delta sizeProperties of preferences

◦ Preferences on ontologies/deltas are equivalent◦ Quality metrics can be used for stating preferences◦ Metadata on the data can be used (e.g., provenance)◦ Can be qualitative or quantitative

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Generalizing the Approach For one violated constraint

1. Diagnose invalidity2. Determine minimal ways to resolve it3. Determine and return preferred (optimal) resolution

For many violated constraints◦ Problem becomes more complicated◦ More than one resolution steps are required

Issues:1. Resolution order2. When and how to filter non-optimal solutions?3. Constraint (and resolution) interdependencies

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Constraint Interdependencies A given resolution may:

◦ Cause other violations (bad)◦ Resolve other violations (good)

Optimal resolution unknown ‘a priori’◦ Cannot predict a resolution’s ramifications◦ Exhaustive, recursive search required

(resolution tree) Two ways to create the resolution tree

◦ Globally-optimal (GO) / locally-optimal (LO)◦ When and how to filter non-optimal

solutions?

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Resolution Tree Creation (GO)– Find all minimal resolutions

for all the violated constraints, then find the optimal ones

– Globally-optimal (GO)◦ Find all minimal resolutions

for one violation◦ Explore them all◦ Repeat recursively until valid◦ Return the optimal leaves

Optimal repairs (returned)

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Resolution Tree Creation (LO)– Find the minimal and

optimal resolutions for one violated constraint, then repeat for the next

– Locally-optimal (LO)◦ Find all minimal resolutions

for one violation◦ Explore the optimal one(s)◦ Repeat recursively until valid◦ Return all remaining leaves

Optimal repair (returned)

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Comparison (GO versus LO)Characteristics of GO

◦ Exhaustive◦ Less efficient:

large resolution trees◦ Always returns optimal

repairs◦ Insensitive to constraint

syntax◦ Does not depend on

resolution order

Characteristics of LO◦ Greedy◦ More efficient:

small resolution trees◦ Does not always return optimal repairs◦ Sensitive to constraint syntax◦ Depends on resolution order

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PART II: Complexity Analysis andPerformance Evaluation

(D2.2)

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Algorithm and ComplexityDetailed complexity analysis for GO/LO

and various different types of constraints and preferences

Inherently difficult problem◦Exponential complexity (in general)◦Exception: LO is polynomial (in special cases)

Theoretical complexity is misleading as to the actual performance of the algorithms

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Performance in PracticePerformance in practice

◦Linear with respect to ontology size◦Linear with respect to tree size

Types of violated constraints (tree width) Number of violations (tree height) – causes the

exponential blowup Constraint interdependencies (tree height) Preference (for LO): affects pruning (tree width)

Further performance improvement◦Use optimizations◦Use LO with restrictive preference

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Evaluation Parameters Evaluation

1. Effect of ontology size (for GO/LO)2. Effect of tree size (for GO/LO)3. Effect of violations (for GO/LO)4. Effect of preference (relevant for LO only)5. Quality of LO repairs

Evaluation results support our claims:◦ Linear with respect to ontology size◦ Linear with respect to tree size

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Effect of Ontology Size

499999.999999999 4999999.999999991.00

10.00

100.00

1000.00

10000.00

100000.00

1000000.00

10000000.00

Diagnosis GO Repair 16 Violations GO Repair 26 ViolationsLO Repair 16 Violations LO Repair 26 Violations

Triples (x1000)

Exec

utio

n Ti

me

(mse

c)(lo

gsca

le)

(logscale)

20000

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Effect of Tree Size (1/2)

0 30000000 60000000 90000000 120000000 1500000000

200000

400000

600000

800000

1000000

1200000

1400000

1M5M10M15M20M

Nodes (x )

GO E

xecu

tion

Tim

e (s

ec)

610Nodes (x106)

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Effect of Tree Size (2/2)

0 2000 4000 6000 8000 100000

5000

10000

15000

20000

25000

30000

35000

40000

1M5M10M15M20M

# Nodes

LO E

xecu

tion

Tim

e (s

ec)

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Effect of Violations (1/2)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 280

200000

400000

600000

800000

1000000

1200000

1400000

1M5M10M15M20M

# Violations

GO E

xecu

tion

Tim

e (s

ec)

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Effect of Violations (2/2)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 280

5000

10000

15000

20000

25000

30000

35000

40000

1M5M10M15M20M

# Violations

LO E

xecu

tion

Tim

e (s

ec)

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Effect of Preference (LO)

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Quality of LO Repairs (1/2)

0 3 6 9 12 15 18 210

1

2

3

4

5

6

7

GO∩LOGO\LOLO\GO

# Violations

# Pr

ef. R

ep. D

elta

sCCD KB

Max( )

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Quality of LO Repairs (2/2)

0 3 6 9 12 15 18 210

200

400

600

800

1000

1200

1400

GO∩LO

GO\LO

LO\GO

# Violations

# Pr

ef. R

ep. D

elta

sCCD KB

Min( )

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PART III: Application of Repairing

in a Real Setting(D4.4)

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Objectives and Main IdeaEvaluate repairing method in a real LOD

setting◦Using resources from WP4◦Using provenance-related preferences

Validate the utility of WP4 resources for a data quality benchmark

Evaluate the usefulness of provenance, recency etc as metrics/preferences for quality assessment and repair

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SettingUser seeks information on Brazilian cities

◦Fuses Wikipedia dumps from different languages

Guarantees maximal coverage, but may lead to conflicts ◦E.g., city with two different population counts

EN

PT

ES FR

GE

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Main TasksAssess the quality of the resulting dataset

◦Quality assessment frameworkRepair the resulting dataset

◦Using the aforementioned repairing method◦Evaluate the use of provenance-related

preferences Prefer most recent information Prefer most trustworthy information

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ContributionsContributions:

◦Define 5 different metrics based on provenance◦Each metric is used as:

Quality assessment metric (to assess quality) Repairing preference (to “guide” the repair)

◦Evaluate them in a real setting

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Experiments (Setting)Setting

◦ Fused 5 Wikipedias: EN, PT, SP, GE, FR◦ Distilled information about Brazilian cities

Properties considered:◦ populationTotal ◦ areaTotal◦ foundingDate

Validity rules: properties must be functional◦ Repaired invalidities (using our metrics)◦ Checked quality of result◦ Dimensions: consistency, validity, conciseness,

completeness and accuracy

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Metrics for Experiments (1/2)1. PREFER_PT: select conflicting information

based on its source (PT>EN>SP>GE>FR)2. PREFER_RECENT: select conflicting

information based on its recency (most recent is preferred)

3. PLAUSIBLE_PT: ignore “irrational” data (population<500, area<300km2, founding date<1500AD) otherwise use PREFER_PT

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Metrics for Experiments (2/2)4. WEIGHTED_RECENT: select based on

recency, but in cases where the records are almost equally recent, use source reputation (if less than 3 months apart, use PREFER_PT, else use PREFER_RECENT)

5. CONDITIONAL_PT: define source trustworthiness depending on data values (prefer PT for small cities with population<500.000, prefer EN for the rest)

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Consistency, ValidityConsistency

◦Lack of conflicting triples◦Guaranteed to be perfect (by the repairing

algorithm), regardless of preferenceValidity

◦Lack of rule violations◦Coincides with consistency for this example◦Guaranteed to be perfect (by the repairing

algorithm), regardless of preference

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Conciseness, CompletenessConciseness

◦No duplicates in the final result◦Guaranteed to be perfect (by the fuse process),

regardless of preferenceCompleteness

◦Coverage of information◦Improved by fusion◦Unaffected by our algorithm◦Input completeness = output completeness,

regardless of preference◦Measured to be at 77,02%

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AccuracyMost important metric for this experimentAccuracy

◦Closeness to the “actual state of affairs”◦Affected by the repairing choices

Compared repair with the Gold Standard ◦Taken from an official and independent data

source (IBGE)

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en.dbpedia pt.dbpedia

integrated data

GoldStandard

Instituto Brasileiro de Geografia e Estatística

(IBGE)

Fuse/Repair

Compare

Accuracy

dbpedia:areaTotaldbpedia:populationTotaldbpedia:foundingDate

dbpedia:areaTotaldbpedia:populationTotaldbpedia:foundingDate

Accuracy Evaluationfr.dbpedia

…

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Accuracy ExamplesCity of Aracati

◦Population: 69159/69616 (conflicting)◦Record in Gold Standard: 69159◦Good choice: 69159◦Bad choice: 69616

City of Oiapoque◦Population: 20226/20426 (conflicting)◦Record in Gold Standard: 20509◦Optimal approximation choice: 20426◦Sub-optimal approximation choice: 20226

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Accuracy Results

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Accuracy of Input and Output

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Publications Yannis Roussakis, Giorgos Flouris, Vassilis Christophides.

Declarative Repairing Policies for Curated KBs. In Proceedings of the 10th Hellenic Data Management Symposium (HDMS-11), 2011.

Giorgos Flouris, Yannis Roussakis, Maria Poveda-Villalon, Pablo N. Mendes, Irini Fundulaki. Using Provenance for Quality Assessment and Repair in Linked Open Data. In Proceedings of the Joint Workshop on Knowledge Evolution and Ontology Dynamics (EvoDyn-12), 2012.

Yannis Roussakis, Giorgos Flouris, Vassilis Christophides. Preference-Based Repairing of RDF(S) DBs. Under review in TODS Journal.

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BACKUP SLIDES

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Repair Removing invalidities by changing the

ontology in an adequate manner General concerns:

1. Return a valid ontology– Strict requirement

2. Minimize the impact of repair upon the data– Make minor, targeted modifications that repair

the ontology without changing it too much3. Return a “good” repair

– Emulate the changes that the ontology engineer would do for repairing the ontology

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InferenceInference expressed using validity rulesExample:

◦Transitivity of class subsumption◦a,b,c C_Sub(a,b) C_Sub(b,c) C_Sub(a,c)

In practice we use labeling algorithms ◦Avoid explicitly storing the inferred knowledge◦Improve efficiency of reasoning

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Quality Assessment Quality = “fitness for use”

◦ Multi-dimensional, multi-faceted, context-dependent Methodology for quality assessment

◦ Dimensions Aspects of quality Accuracy, completeness, timeliness, …

◦ Indicators Metadata values for measuring dimensions Last modification date (related to timeliness)

◦ Scoring Functions Functions to quantify quality indicators Days since last modification date

◦ Metrics Measures of dimensions (result of scoring function) Can be combined

data repairing

Documents

p domp

location c

locationo0remove p

p rngp

location st1 sensor

locationschema geo

domain of geo

sensordom geo