Correlation Search in Graph Databases

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Correlation Search in Graph Databases

• Yiping Ke James Cheng Wilfred Ng
• 
  Presented By Phani Yarlagadda

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Outline

• Motivation
• Challenges
• Problem Definition
• Solution
• Performance Evaluation
• Related Works

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Motivation

• Graph Databases and their importance
• Correlation mining from graph databases
• Structural similarity and statistical similarity

4
Challenges

• Candidate key
• High complexity graph operations
• Vast search space

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Problem Definition

• Pearsons Correlation Coefficient
• Popularly used correlation measure
• Definition
• Given two graphs g1 and g2, the Pearsons
  Correlation Coefficient of g1 and g2, denoted as
  f(g1, g2), is defined as follows
• When supp(g1) or supp(g2) is equal to 0 or
  1, f(g1, g2) is defined to be 0.The range of
  f(g1, g2) falls within -1, 1
• In this paper we are concerned about
  positively correlated graphs only

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Problem Definition

• Correlated Graphs
• Two graphs g1 and g2 are correlated if and
  only if f(g1, g2) ?,
• where ? (0 lt ? 1) is a user-specified
  minimum correlation threshold.

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Problem Definition

• Correlated Graph Search
• Given a graph database D, a correlation query
  graph q and a minimum correlation threshold ?,
  the problem of Correlated Graph Search (CGS) is
  to find the set of all graphs that are correlated
  with q. The answer set of the CGS problem is
  defined as Aq (g,Dg) f(q, g) ?.

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Solution-Candidate Set Generation

• Mine the set of frequent graphs (FGs) from D
  using the thresholds
• Drawbacks
• All existing FG mining algorithms generate graphs
  with higher support before those with lower
  support.
• Not efficient and scalable ,especially when D is
  large or the lower bound is low.

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Solution-Candidate Set Generation

• Mine the set of FGs using the threshold
• Advantages
• Efficient candidate generation.
• Significant reduction in search space.

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Solution-Framework

• The framework of the solution consists of the
  following four steps.
• Obtain the projected database Dq of q.
• Mine the set of candidate graphs C from Dq,
  using lower(q,g)/supp(q) as the minimum support
  threshold.
• Refine C by three heuristic rules.
• For each candidate graph g C,
• Obtain Dg.
• Add (g,Dg) to Aq if f(q, g) ?.

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Solution-Heuristic Rules

• Heuristic Rule 1
• Given a graph g, if g C and g q, then
• g base(Aq)
• Identifies graphs that are guaranteed to be
  answers

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Solution-Heuristic Rules

• Heuristic Rule 2
• Given two graphs g1 and g2,
• where g1 g2 and
• supp(g1, q) supp(g2, q),
• if g1 base(Aq), then g2 base(Aq)
• Helps in reduction of the search space so that
  the unrewarding query costs for false positives.

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Solution-Heuristic Rules

• Heuristic Rule 3
• Given two graphs g1 and g2,
• where g1 g2,
• if supp(g2, q) lt f(supp(g1)),
• then g2 base(Aq)
• Helps in reduction of the search space so that
  the unrewarding query costs for false positives.

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Solution-Algorithm

• Input A graph database D, a query graph q, and a
  correlation threshold ?.
• Output The answer set Aq.
• Obtain Dq
• Mine FGs from Dq using lower(q,g) supp(q) as the
  minimum support threshold and add the FGs to C
• for each graph g C in size-descending order do
• if (g q)
• Add (g,Dg) to Aq
• else
• Obtain Dg
• if (f(q, g) ?)
• Add (g,Dg) to Aq
• else
• H2 ? g C g g, supp(gDq) supp(gDq)
• C ? C-H2
• H3 ? g C g g, supp(gDq) lt
  f(supp(g))/supp(q)
• C ? C-H3

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Solution-Example

• Consider the graph database below

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Solution-Example

• Query q
• Candidate set

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Performance Evaluation

• The dataset contains the compound structures of
  cancer and AIDS data from NCI open database
  compunds.
• The dataset contains about 249k graphs.
• On average each graph in dataset has 21 nodes and
  23 edges. The number of distinct labels for nodes
  and edges is 88.
• We randomly generate four sets of queries, F1,
  F2, F3 and F4 each of which contain 100 queries.
  The support ranges for the queries in F1 to F4
  are 0.02,0.05,(0.05,0.07,(0.07,0.1 and
  (0.1,1.0

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Performance Evaluation

• Effect of candidate generation

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Performance Evaluation

• Effect of

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Performance Evaluation

• Effect of Heuristic Rules

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Performance Evaluation

• Effect of Graph Size

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Related Works

• Raymond proposes an efficient algorithm MCES for
  similarity search.
• Williams proposes an indexing technique that
  adopts graph decomposition method for similarity
  search.
• Zhang and Feigenbaum adopted f correlation
  coefficient to measure the correlated pairs in
  transaction databases.