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A Similarity Skyline Approach for Handling Graph Queries - A Preliminary ReportPowerPoint Presentation

A Similarity Skyline Approach for Handling Graph Queries - A Preliminary Report

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### A Similarity Skyline Approach for Handling GraphQueries - A Preliminary Report

### Thankyou

Katia Abbaci† Allel Hadjali† Ludovic Liétard‡ Daniel Rocacher†

†IRISA/ENSSAT, University of Rennes1

{Katia.Abbaci, Allel.Hadjali, Daniel.Rocacher}@enssat.fr

‡IRISA/IUT, University of Rennes1

Outline

- Introduction
- Background:
- Skyline Query
- Graph Query
- Graph Similarity Measures

- Graph Similarity Skyline
- Refinement Graph Similarity Skyline
- Summary and Outlook

GDM 2011

Introduction (1/3)

Context:

- Graphs: Modeling of structured and complex data
- Application Domains:
- Medicine, Web, Chemistry, Imaging, XML documents, Bioinformatic,...

Chemistry

Web

Imaging

Medicine

GDM 2011

Introduction (2/3)

Main:

- Search Problem of similar graphs to graph query
- Existing approaches: a single similarity measure

- Several methods for measuring the similarity between two graphs:
- Method limited to an application class
- No method fits all

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Introduction (3/3)

Motivations:

- Model for different classes of applications
- Model incorporating multiple features
Contributions:

- Graph Similarity Skyline in order to answer a graph query: optimality in the sense of Pareto
- A Refinement Method of Skyline based on diversity criterion among graphs

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SkylineQuery

- Identification of interesting objects from multi-dimensional dataset
- p = (p1, …, pm),q = (q1, …, qm): multidimensional objects
p Pareto dominatesq, denoted pq, iff:

- on each dimension, 1 ≤ i ≤ m, pi ≤ qi
- on at least one dimension, pj < qj

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SampleSkylineQuery

- Find a cheap hotel and as close as possible to the downtown:

H2

H2

H6

H6

Skyline = {H2, H4, H6}

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Tab. 1 –Sample of hotels

Graph Query

- Twocategories of graph queries:
- Graph containmentsearch:
q: a query, D = {g1, …, gn} a GDB

- Subgraphcontainmentsearch
- Retrieve all graphs gi of D suchthatq ⊆ gi
- Supergraphcontainmentsearch
Retrieve all graphs gi of D suchthatq ⊇ gi

- Graph similaritysearch:
Retrieve structurally similar graphs to the query graph

- Graph containmentsearch:

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Graph SimilarityMeasures

- Several processing methods of graph similarity:
- Edit Distance (DistEd)
- Maximum common subgraph based distance (DistMcs)
- Graph union based distance (DistGu)

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Edit Distance: example

- Transformation of g into g’:
- deletion of the adge (d, e),
- re-labeling the adge (a, d) from 1 to 4,
- re-labeling the node d with e,
- insertion of the adge (a, f) with the label 1.

- Use of the uniform distance:

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Fig. 3 –Example of labeled graphs

Fig. 3 –Example of labeled graphs

Fig. 3 –Example of labeled graphs

Fig. 3 –Example of labeled graphs

Fig. 3 –Example of labeled graphs

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Distances based on Mcs and Gu: example

- Identification of the size of
- Computation of Mcs-based distance:
- Computation of Gu-based distance:

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Fig. 4 –Example of labeled graphs

Fig. 4 –Example of labeled graphs

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Graph Similarity Skyline (1/2)

- Graph compound similarity between two graphs: a vector of local distance measures

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Graph Similarity Skyline (2/2)

- q: a query, D = {g1, …, gn} a GDB
- For i = 1 ton, do:
- Compare
- Extract the Graph Similarity Skyline (GSS):
- Similarity-Dominance Relation
- ∀ i ∈ {1, ..., d}, Disti(g, q) ≤ Disti(g’, q),
- ∃ k ∈ {1, ..., d}, Distk(g, q) < Distk(g’, q).

GDM 2011

Illustrative Example (1/2)

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Fig. 6– Graph databaseD and graph queryq

Fig. 6 – Graph databaseD and graph queryq

Tab. 3 – Information about |Mcs(gi, q)|

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GDM 2011

Illustrative Example (2/2)

- Computation of GCS(gi,q), for i= 1 to 7, do:

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Tab. 4 – Distance Measures

GSS(D, q) = {g1, g4, g5, g7}

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Refinement of Graph Similarity Skyline (1/3)

- Large Skyline
- Need k dissimilar answers
- Solution: diversity criterion
- Extract a subset (S) of size k with a maximal diversity
Provide the user with a global picture of the whole set GSS

- Extract a subset (S) of size k with a maximal diversity

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Refinement of Graph Similarity Skyline (2/3)

- Diversity of a subsetS of size kis:
: diversity in the ith dimension of the subsetS

s. t.:

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Refinement of Graph Similarity Skyline (3/3)

- RefinementAlgorithm:
- For j = 1 to , enumerate , with
- For i = 1 to d, rank-order all Sj in decreasingwayaccording to theirdiversity
Let be the rank of Sj w. r. t. the ith dimension:

- : the best diversity value
- : the worstdiversity value

- EvaluateSj by:
- Extract :

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Illustrative Example6

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- Return the 2 best graphs:

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Fig. 8 – The skyline GSS

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Summary and Outlook

- Skyline approach for searching graphs by similarity
- Extraction of all DB graphs non-dominated by any other graph
- Preserving information about the similarity on different features

- Selection of the subset of graphs with maximal diversity from the skyline
- Implementation: step to demonstrate the effectiveness of the approach on a real database
- Investigation of other similarity measures

GDM 2011

Questions ?

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