© 2008 IBM Corporation Mining Significant Graph Patterns by Leap Search Xifeng Yan (IBM T. J. Watson) Hong Cheng, Jiawei Han (UIUC) Philip S. Yu (UIC)

© 2008 IBM Corporation

Mining Significant Graph Patterns by Leap Search

Xifeng Yan (IBM T. J. Watson) Hong Cheng, Jiawei Han (UIUC) Philip S. Yu (UIC)

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Graph Patterns

Interestingness measures / Objective functions

• Frequency: frequent graph pattern

• Discriminative: information gain, Fisher score

• Significance: G-test

• …

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Frequent Graph Pattern

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Optimal Graph Pattern (this work)

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Objective Functions

Challenge: Not Anti-Monotonic

X

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Challenge: Non Anti-Monotonic

Anti-Monotonic

Non Monotonic

Non-Monotonic: Enumerate all subgraphs then check their score?

Enumerate subgraphs : small-size to large-size

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Frequent Pattern Based Mining Framework

Exploratory task

Graph clustering

Graph classification

Graph index

(SIGMOD’04, ’05)(ISMB’05, ’07)

Graph Database Frequent Patterns Optimal Patterns

1. Bottleneck : millions, even billions of patterns

2. No guarantee of quality

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Direct Pattern Mining Framework

Exploratory task

Graph clustering


Graph index

Graph Database Optimal Patterns

Direct

How?

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Upper-Bound

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Upper-Bound: Anti-Monotonic (cont.)

Rule of Thumb : If the frequency difference of a graph pattern in the positive dataset and the negative dataset increases, the pattern becomes more interesting

We can recycle the existing graph mining algorithms to accommodate non-monotonic functions.

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Vertical Pruning

Larg

e <- s

mall

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Horizontal Pruning: Structural Proximity

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Structural Proximity: Another Perspective

# of frequent patterns >> # of possible frequency pairs

Many patterns share the same score

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Frequency Envelope

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Structural Leap Search

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Frequency Association

Significant patterns often fall into the high-quantile of frequency

Starting with the most frequent patterns

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Descending Leap Mine

1. Structural Leap Searchwith frequency threshold

3. Structural Leap Search

2. Support-Descending Mining

F(g*) converges

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Results: NCI Anti-Cancer Screen Datasets

Name # of Compounds Tumor Description

MCF-7 27,770 Breast

MOLT-4 39,765 Leukemia

NCI-H23 40,353 Non-Small Cell Lung

OVCAR-8 40,516 Ovarian

P388 41,472 Leukemia

PC-3 27,509 Prostate

SF-295 40,271 Central Nerve System

SN12C 40,004 Renal

SW-620 40,532 Colon

UACC257 39,988 Melanoma

YEAST 79,601 Yeast anti-cancer

Link: http://pubchem.ncbi.nlm.nih.gov

Chemical Compounds: anti-cancer or not

# of vertices: 10 ~ 200

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Efficiency

Vertical Pruning

Horizontal Pruning

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Effectiveness (runtime)

frequency descending

frequency descending+ leap mine

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Effectiveness (accuracy)

slightly different

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Graph Classification

Name OA Kernel LEAP OA Kernel (6x) LEAP (6x)

Average (AUC) 0.70 0.72 0.75 0.77

* OA Kernel: Optimal Assignment Kernel LEAP: LEAP search

(6x)

(6x)

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Scalability Means Something !

LEAP

OA

LEAP(6X)

OA(6X)

~20sec

~100sec

~200sec

~8000sec

Linear

Quadratic

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Direct Pattern Mining Framework

Exploratory task

Graph clustering


Graph index

Graph Database Optimal Graph Patterns

Direct

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Beyond Graph Patterns

Exploratory task

Clustering

Classification

Index

itemset/sequence/tree Database Optimal Patterns

Direct

1. Direct mining can be applied to itemsets, sequences, and trees

2. Existing algorithms can be recycled to mine patterns with sophisticated measures.

3. Pattern-based methods including indexing and classification are competitive.

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Thank you

Direct Mining of Discriminative and Essential Graphicaland Itemset Features via Model-based Search Tree

SIGKDD’08 @ Las Vegas

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Graph Classification: Kernel Approach

Kernel-based Graph Classification

Optimal Assignment Kernel (Fröhlich et al. ICML’05)

© 2008 IBM Corporation Mining Significant Graph Patterns by Leap Search Xifeng Yan (IBM T. J. Watson) Hong Cheng, Jiawei Han (UIUC) Philip S. Yu (UIC)

Documents

frequent graph pattern

optimal graph

vertical pruning large

score slide

leap search xifeng yan

work slide

frequency envelope slide

antimonotonic x slide