© 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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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Frequent Graph Pattern

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Optimal Graph Pattern (this work)

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Objective Functions

Challenge: Not Anti-Monotonic

X

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

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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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

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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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Direct Pattern Mining Framework

Exploratory task

Graph clustering

Graph classification

Graph index

Graph Database Optimal Patterns

Direct

How?

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Upper-Bound

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

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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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Vertical Pruning

Larg

e <- s

mall

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Horizontal Pruning: Structural Proximity

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Structural Proximity: Another Perspective

# of frequent patterns >> # of possible frequency pairs

Many patterns share the same score

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Graph Pattern Mining | © 2008 IBM Corporation

Frequency Envelope

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Graph Pattern Mining | © 2008 IBM Corporation

Structural Leap Search

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Frequency Association

Significant patterns often fall into the high-quantile of frequency

Starting with the most frequent patterns

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Descending Leap Mine

1. Structural Leap Searchwith frequency threshold

3. Structural Leap Search

2. Support-Descending Mining

F(g*) converges

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

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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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Efficiency

Vertical Pruning

Horizontal Pruning

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Effectiveness (runtime)

frequency descending

frequency descending+ leap mine

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Effectiveness (accuracy)

slightly different

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

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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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Scalability Means Something !

LEAP

OA

LEAP(6X)

OA(6X)

~20sec

~100sec

~200sec

~8000sec

Linear

Quadratic

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Direct Pattern Mining Framework

Exploratory task

Graph clustering

Graph classification

Graph index

Graph Database Optimal Graph Patterns

Direct

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

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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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Thank you

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

SIGKDD’08 @ Las Vegas

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IBM T. J. Watson Research Center

Graph Pattern Mining | © 2008 IBM Corporation

Graph Classification: Kernel Approach

Kernel-based Graph Classification

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