Substructure Similarity Search in Graph Databases

1
Substructure Similarity Search in Graph Databases

• By X. Yan P. Yu J.Han
• Ömer Can KOLÇAK

2
Outline

• Introduction
• Preliminary Concepts
• Structural Filtering
• Feature Set Selection
• Algorithm Implementation

3
Introduction

• Data research has been facing a new challenge
  raised by the emergence of complex structural
  data.
• Graphs have broad applications and they are used
  in datasets especially in chemistry-informatics
  and bio-informatics. (eg. ChemIDplus, PDB)
• Also in computer vision and pattern recognition,
  graphs are used to represent complex structures
  such as hand-drawn symbols, 3D objects and
  medical images.

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Introduction

• All these applications indicate the importance
  and the broad usage of graph database and its
  similarity search system.
• While the discovery in graph datasets has been
  studied, a systematic examination of graph query
  systems becomes equally important.

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Structure Search Queries

• Full Structure Search
• Substructure Search
• Full Structure Similarity Search

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Question

• What if no matches occur for a given query graph?

Query Refinement Process
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Query Refinement Process

• manually time consuming
• define the portion of the query for exact
  matching
• and let the system change the portion slightly

RELAXATION RATIO
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Example
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Introduction

• The existing tools such as ChemIDplus, could only
  provide the full structure similarity search and
  the exact substructure search.
• Pairwise substructure similarity computation is
  very expensive.
• For one edge misses, exact substructure search
  may work.
• What if the number of deletions is more than one?

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Graph Similarity Filtering

• GRAFIL
• A feature-based structural filtering algorithm
• no pairwise computation
• Instead, two data structures
• feature-graph matrix
• edge-feature matrix
• filters the dataset by using these matrices
• not on the database, on the matrices

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Contribution of Grafil

• A significant contribution of this study is an
  examination of an inceasingly important search
  problem in graph databases and the proposal of a
  feature-based filtering algorithm for efficient
  substructure similarity search.
• The concept presented in Grafil can be applied to
  searching approximate,non-consequtive sequences,
  trees and other complicated structures as well.

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Preliminary Concepts

• DEFINITION (SUBSTRUCTURE SIMILARITY SEARCH)
• Given a graph database DG1,G2,...,Gn and a
  query graph Q, similarity search is discover all
  the graphs that approximately contain this query
  graph.
• Target Graph Graphs in Dataset

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Preliminary Concepts

• DEFINITION (RELAXATION RATIO)
• Given two graphs G and Q, if P is the maximum
  common subgraph of G and Q, then the substructure
  similarity between G and Q is defined by E(P) /
  E(Q), and 1-E(P) / E(Q) is called
  relaxation ratio.

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Example
Substructure Similarity 11/12 92
Maximum Common Subgraph , P E(P)11
Relaxation Ratio 1-(11/12) 8
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Structural Filtering

• Given a query graph, the major target of our
  algorithm is to filter as many graphs as possible
  using a feature-based approach.
• Features
• Paths
• Discriminative Frequent Structures
• Elementary Structures
• etc...

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Example
This Query Graph contains seven occurences of
these features One fa, two fbs and four fcs
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Feature-Graph Matrix
- easily maintainable
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Framework

• Given a graph database and a query graph, the
  substructure similarity search can be performed
  in the following four steps
• Index Costruction Select small structures as
  features in the graph database, and built the
  feature-graph matrix between the features and the
  graphs in the database.
• Feature Miss Estimation Select a feature set,
  calculate the number of selected features
  contained in the query graph, then compute the
  upper bound of feature misses (dmax) if the query
  graph is relaxed with one edge deletion.

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Framework

• Query Processing Use the feature-graph matrix to
  calculate the difference in the number of
  features between each graph G in the database and
  query Q. If the difference is greater than dmax,
  eliminate graph G. The remaining graphs
  constitute a candidate answer, written as CQ.
• Query Relaxation Relax the query further if the
  user needs more matches than those returned from
  the previous step iterate Steps 2 to 4.

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Feature Miss Estimation
Construct a feature set all features
for k1 dmax4
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Framework on Example

• Given a graph database and a query graph
• Index Construction
• Built the feature graph matrix

• Feature Miss Estimation
• Calculate dmax4

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Framework on Example

• Query Processing
• Calculate the difference in the number of
  features between each graph G and query Q.

Total number of occurrences 7
dmax4
Misses 5
3
2
3
CQG2, G3, G4
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Question

• Should we use all the features together in a
  single filter?
• Does a filter achieve good filtering performance
  if all the features are used together?
• Intuitively, such a strategy would improve the
  performance since all the available information
  is used.
• But, not true

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Question Feature Miss Estimation
for k1 dmax2
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Question Query Processing

• Query Processing

Total number of occurrences 3
dmax2
Misses 3
3
2
2
CQG2, G3
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Answer

• By adding all features in the feature set, we may
  fail to filter some graphs that do not satisfy
  the query requirement.
• To improve the accuracy of the filtering, we
  should select feature sets by grouping the
  features.
• The example implies that the filtering power may
  be weakened if we deploy all the features in one
  filter.
• In order to measure the filtering power,
  selectivity

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Selectivity

• DEFINITION (SELECTIVITY)
• Given a graph database D, a query Q, and a
  feature f, the selectivity is defined by its
  average frequency difference within D and Q.

Occurrence of fa in query graph1
Occurrence of fb in query graph2
Occurrence of fc in query graph4
Selectivity of fa 3/4
Selectivity of fb 7/4
Selectivity of fc 3/4
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Feature Set Selection

• Rule 1. Select a large number of features
• Rule 2. Make sure features cover the query graph
  uniformly.
• Rule 3. Separate features with different
  selectivity.

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Feature Set Selection of Grafil

• Grafil has two types of feature set selection
• Based component (Grafil-base) combines features
  with the same size
• Clustering Component

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Clustering Component

• Grafil first combines the features whose size
  differs at most by 1, and sort them by
  selectivity.
• Hierarchical clustering
• Grafil divides them into three groups with high
  selectivity, medium selectivity and low
  selectivity.

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Grafil Algorithm
-base component -clustering component -pipeline
model
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Conclusion

• We discuss the problem of substructure similarity
  search in large scale graph databases, a problem
  raised by the emergence of massive, complex
  structural data
• Different from the previous work, our solution
  explored the filtering algorithm using indexed
  structural patterns, without doing costly
  structure comparisons
• The successful transformation of the
  structure-based similarity measure to the
  feature-based measure renders our method
  attractive in terms of accuracy and efficiency