Graph Data Mining Two - Complex Networks - Lecture Slides, Slides of Computer Networks

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Lecture 11:

Graph Data Mining

Graph Data Mining

 DNA sequence

 RNA

Outline

 Graph Pattern Mining

 Mining Frequent Subgraph Patterns  Graph Indexing  Graph Similarity Search

 Graph Classification

 Graph pattern-based approach  Machine Learning approaches

 Graph Clustering

 Link-density-based approach

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Graph Pattern Mining

 Frequent subgraphs

 A (sub)graph is frequent if its support (occurrence frequency) in a given dataset is no less than a minimum support threshold

 Support of a graph g is defined as the percentage of graphs in G which have g as subgraph

 Applications of graph pattern mining

 Mining biochemical structures  Program control flow analysis  Mining XML structures or Web communities  Building blocks for graph classification, clustering, compression, comparison, and correlation analysis

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Example

GRAPH DATASET

FREQUENT PATTERNS (MIN SUPPORT IS 2)

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Graph Mining Algorithms

 Incomplete beam search – Greedy (Subdue)

 Inductive logic programming (WARMR)

 Graph theory-based approaches

 Apriori-based approach  Pattern-growth approach

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Apriori-Based Approach

…

G

G 1

G 2

Gn

k-edge

(k+1)-edge

G’

G’’

Join Prune check the frequency of each candidate

G 1

Gn

Subgraph isomorphism test NP-complete

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Apriori-Based, Breadth-First Search

 AGM (Inokuchi, et al.)  generates new graphs with one more node

 Methodology: breadth-search, joining two graphs

 FSG (Kuramochi and Karypis)  generates new graphs with one more edge

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Graph Pattern Explosion Problem

 If a graph is frequent, all of its subgraphs are frequent

 the Apriori property

 An n -edge frequent graph may have 2 n^ subgraphs

 Among 422 chemical compounds which are confirmed to be active in an AIDS antiviral screen dataset,  there are 1,000,000 frequent graph patterns if the minimum support is 5%

Closed Frequent Graphs

 A frequent graph G is closed

 if there exists no supergraph of G that carries the same support as G

 If some of G’s subgraphs have the same support

 it is unnecessary to output these subgraphs  nonclosed graphs

 Lossless compression

 Still ensures that the mining result is complete

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Scalability Issue

 Naïve solution

 Sequential scan (Disk I/O)  Subgraph isomorphism test (NP-complete)

 Problem: Scalability is a big issue

 An indexing mechanism is needed

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Indexing Strategy

Graph (G)

Substructure

Query graph (Q)

If graph G contains query graph Q, G should contain any substructure of Q

Remarks  Index substructures of a query graph to prune graphs that do not contain these substructures

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Why Frequent Structures?

 We cannot index (or even search) all of substructures

 Large structures will likely be indexed well by their substructures

 Size-increasing support threshold

support

minimum support threshold

size

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Structure Similarity Search

(a) caffeine (b) diurobromine (c) sildenafil

• CHEMICAL COMPOUNDS

• QUERY GRAPH