Mining Significant Graph Patterns by Leap Search
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1 Mining Significant Graph Patterns by Leap Search Xifeng Yan (IBM T. J. Watson) Hong Cheng, Jiawei Han (UIUC) Philip S. Yu (UIC)
2 Graphs Are Everywhere Magwene et al. Genome Biology :R100 Co-expression Network Program Flow Social Network Chemical Compound Protein Structure 2
3 Graph Pattern Mining 3
4 Graph Patterns Interestingness measures / Objective functions Frequency: frequent graph pattern Discriminative: information gain, Fisher score Significance: G-test 4
5 Frequent Graph Pattern 5
6 Optimal Graph Pattern (this work) 6
7 Objective Functions Challenge: Not Anti-Monotonic X 7
8 Challenge: Non Anti-Monotonic Non Monotonic Anti-Monotonic Enumerate subgraphs : small-size to large-size Non-Monotonic: Enumerate all subgraphs then check their score? 8
9 Frequent Pattern Based Mining Framework Exploratory task Graph clustering Graph classification Graph index Graph Database Frequent Patterns Optimal Patterns (SIGMOD 04, 05) (ISMB 05, 07) 1. Bottleneck : millions, even billions of patterns 2. No guarantee of quality 9
10 Direct Pattern Mining Framework Exploratory task Graph clustering Direct Graph classification Graph index Graph Database Optimal Patterns How? 10
11 Upper-Bound IBM T. J. Watson Research Center 11
12 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. 12
13 Vertical Pruning Large <- small 13
14 Horizontal Pruning: Structural Proximity 14
15 Structural Proximity: Another Perspective # of frequent patterns >> # of possible frequency pairs Many patterns share the same score 15
16 Structural Leap Search 16
17 Frequency Association Significant patterns often fall into the high-quantile of frequency Starting with the most frequent patterns 17
18 Descending Leap Mine 1. Structural Leap Search with frequency threshold F(g*) converges 2. Frequency-Descending Mining 3. Structural Leap Search 18
19 Results: NCI Anti-Cancer Screen Datasets Chemical Compounds: anti-cancer or not # of vertices: 10 ~ 200 Name MCF-7 MOLT-4 NCI-H23 OVCAR-8 P388 PC-3 SF-295 SN12C SW-620 UACC257 YEAST # of Compounds 27,770 39,765 40,353 40,516 41,472 27,509 40,271 40,004 40,532 39,988 79,601 Tumor Description Breast Leukemia Non-Small Cell Lung Ovarian Leukemia Prostate Central Nerve System Renal Colon Melanoma Yeast anti-cancer 19 Link:
20 Efficiency IBM T. J. Watson Research Center Vertical Pruning Vertical Pruning + Horizontal Pruning 20
21 Effectiveness IBM T. J. Watson Research Center frequency descending frequency descending + structural leap search 21
22 Graph Classification Name OA Kernel LEAP OA Kernel (6x) LEAP (6x) Average (AUC) (6x) (6x) * OA Kernel: Optimal Assignment Kernel LEAP: LEAP search 22
23 Scalability Means Something! ~8000sec OA(6X) Quadratic ~200sec ~100sec ~20sec OA LEAP(6X) LEAP Linear 23
24 Beyond Graph Patterns Pattern-based categorical data classification (ICDE 07) 24
25 Beyond Graph Patterns (cont.) 1. Direct mining can be applied to itemsets, sequences, and trees Direct Exploratory task Clustering Classification Index itemset/sequence/tree Database Optimal Patterns 2. Existing algorithms can be recycled to mine patterns with sophisticated measures. 3. Pattern-based methods including indexing and classification are competitive. 25
26 Thank You 26
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