Khai thác và lập chỉ mục đồ thị lớn - Luận án tiến sĩ Xifeng Yan

MINING, INDEXING AND SIMILARITY SEARCH IN LARGE GRAPH DATA SETS BY XIFENG YAN B., State University of New York at Stony Brook, 2001 DISSERTATION Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computer Science in the Graduate College of the University of Illinois at Urbana-Champaign, 2006 Urbana, Illinois UMI Number: 3243031 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.

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Box 1346 Ann Arbor, MI 48106-1346 ©by Xifeng Yan, 2006. All rights reserved. CERTIFICATE OF COMMITTEE APPROVAL University of Illinois at Urbana-Champaign Graduate College July 31, 2006 We hereby recommend that the thesis by: XIFENG YAN Entitled: MINING, INDEXING AND SIMILARITY SEARCH IN LARGE GRAPH DATA SETS Be accepted in partial fulfillment of the requirements for the degree of: Doctor of Philosophy eSoe 212.0/2 Director of Research- J IẠWEI HAN Head ofDepartment- Committee Member - Committee Member - * Required for doctoral degree but not for master’s degree Abstract Scalable analytical algorithms and tools for large graph data sets are in great demand across domains from software engineering to computational biology as it is very difficult, if not im- possible, for human beings to manually analyze any reasonably large collection of graphs due to their high complexity. In this dissertation, we investigate two long standing fundamental problems: Given a graph data set, what are the hidden structural patterns and how can we find them? and how can we index graphs and perform similarity search in large graph data sets? Graph pattern mining is an expensive computational problem since subgraph isomorphism is NP-complete.

Previous solutions generate inevitable overheads since they rely on joining two graphs to form larger candidates. We develop a graph canonical labeling system, gSpan, showing both theoretically and empirically that this kind of join operation is unnecessary. Graph indexing, the second problem addressed in this dissertation, may incur an exponential number of index entries if all of the substructures in a graph database are used for indexing. The solution, gIndex, proposes a novel, frequent and discriminative graph mining approach that leads to the development of a compact but effective graph index structure that is orders of magnitude smaller in size but an order of magnitude faster in performance than traditional approaches.

Besides graph mining and search, this dissertation provides thorough investigation of pat- tern summarization, pattern-based classification, constraint pattern mining, and graph similar- ity searching, which could leverage the usage of graph patterns. It also explores several critical applications in bioinformatics, computer systems and software engineering, including gene rel- evance network analysis for functional annotation, and program flow analysis for automated software bug isolation. The developed concepts, theories, and systems may significantly deepen the understanding of data mining principles in structural pattern discovery, interpretation and search. The for- mulation of a general graph information system through this study could provide fundamental supports to graph-intensive applications in multiple domains.

iii To my parents and sister iv Acknowledgments There are no words to express my gratitude to my adviser, Prof. The research presented in this dissertation would not have happened without his support, guidance, and encouragement. Nearly every aspect of my research has been improved due to his mentoring. I was fortunate to spend two summers with Dr.

Yu at IBM Research, who helped me define an important part of my doctoral work. Thanks also to Dr. Jasmine Xianghong Zhou who brought me into the fantastic field of computational biology. It was always inspiring and exciting to work with her.

I also felt honored to be a member in the Database and Information System Lab, where I found many dedicated collaborators: Chao Liu for automated software bug isolation, Hong Cheng and Dong Xin for pattern summarization and interpretation, and Feida Zhu for complexity analysis. It was my honor to have Dr. Christos Faloutsos, Dr. Marianne Winslett, and Dr.

Chengxi- ang Zhai as my Ph. I am very grateful to them for providing insightful comments regarding this dissertation. I am also greatly indebted to many teachers in the past who educated me and got me interested in scientific research. A special thank goes to my primary school teacher Jingzhi Sun and my middle school mathematics teacher Shanshan Wu.

I would like to thank my parents and sister for their love, trust, and encouragement through hard times and for their unconditional support which enables me pursue my interests overseas. This research is funded in part by the U. National Science Foundation grants NSF IIS- 0209199, IIS-0308215, CCR-0325603, and DBI-0515813. Table of Contents List of Figures.

ix List of Tables ca xii Glossary of Notation ©.ààặằaaAa a aaaa aẶRẶ da 1 1. ng gà nà kg vi v ki va 5 1.ee 8 2 Graph Pattern Mining 2. ok cà gà kg va va 10 2.1 Apriori-based Mining.2 Pattern Growth-based Mining.2 Right-Most Extension. cu ee kg xa 16 2.

Quà g v gi kg va 16 2.4 DFS Lexicographic Ôrder. uc cv rà kg va 18 "8s.3 Closed Graph Pattern. cv gà gà va 23 2.2 Failure of Early Termination. ch HH ko 25 2.3 Detecting the Failure of Early Termination.

gà kg kia 28 2.4 Variant Graph PatteTAS. HQ Hạ nàn và kg kia 32 2.1 Contrast Graph Pattern. nạ gà và và 32 2.2 Coherent Graph Pattern. Q Q ng và gà kg va 32 2.3 Discriminative Graph Pattern.4 Dense Graph Pattern 2.

cv Hà gà và ky T va 33 2.5 Approximate Graph Patlern. cu kg va 34 2.2 Relevance-Aware Top-K. và xà vàn a 39 2.6 Pattern-Based Classification. kg ky kg và 41 2.7 Automated Software Bug Isolation.

HQ Quà Tà sa 46 2.1 Uncover “Backtrace” for Noncrashing Bugs. 49 Graph Patterns with ConstrainiS. c c c c c c cv vn ng gà và an a 52 3.1 Highly Connected Graph Patterns. LH Q vn và v22 53 3.1 CloseCut: A Pattern Growth Approach .2 SPLAT: A Pattern Reduction Approach.

v g va k KT kia 60 3.21 Pruning Patte€rnS. cu ng gà kg KV v KÀ 64 3. ch ngà kg kg Nà ko 66 3.3 Gene Relevance Network Analysis. c L vn ng ee 69 Graph Indexing 2.1 Graph Query ProcesSling.

ch HH HH vu vợ kia và va 75 4. ng ng kg ga 77 4.2 Path-based Graph Indexing. ch ng kg ki va 81 `.1 Discriminative Fragment Selection. cà ga v v kg va 84 “.5 Insert/Delete Maintenance.

ch ng cv gi kg kg Và và kia 93 5 Graph Similarity Search. c c c c c cu ng à gg gi.1 Substructure Similarity Search. cu 2 kg ky 101 5. cu gà kg kg k kg 102 5.1 Feature-Graph Matrix.

HQ gà gà kia xa 103 5. - cv kg kg va 104 5.3 Feature Miss EstimatiOn. 0 pee kg va 108 5. HQ HH gu ky 111 5.3 Feature Set Selection.2 Complexity of Optimal Feature Set Seleclion.3 Clustering based Feature Set Selection.6 Substructure Search with Superimposed Distance.2 Framework of Partition-Based Index and Search .3 Fragment-based Index.

Hà kg va 134 5.4 Partition-based Search. c Q Q Q Q ng cu gà k cà ng gà v v v v kg V v v và 157 vill List of Figures 1.1 Program Flow, Protein and Chemical Compound .2 Protein-Protein Interaction Network .1 Program Caller/Callee Graphs.2 Frequent Graph Patterns. Q Q Q Q cu gu g kg kg kg va 11 2.8 Right-Most Extension. v v kg kg va 16 2.7 Lexicographic Search ÏTree.

cu kg ga kg kg 19 2.8 Extended Subgraph lsomorphism.9 Failure of Early Termination. kg ke k kg Ni kg va 26 2.11 Detect the Failure of Early TerminatioOn'.12 Pattern Generation ÔTdđeT. LH gà ky va 28 2.13 Mining Performance in Class CA Compounds.14 Discovered Patterns in Class CA Compounds.16 Pattern Summarization: Top-k, Clustering, and Relevance-aware Top-k .17 Software Behavior Graphs .18 Classification Accuracy Boost.19 Entrance Precision and Exit Precision .20 Precision Boost of Functions .1 Mining Relational Graphs .2 Search Space: Record or Discard .3 Splat: A Pattern Reduction Approach. eee ee ee es 59 3.

cà Và ee 62 3. 0 gà gà v Q k sa 64 3.7 Pruning Properties of Graph Constraints .8 Number of Highly Connected Patterns .9 Size of the Largest Patterns.10 Genes Related with Subtelomerically Encoded Proteins .11 Genes Having Helicase Activity. 0 2 nu ng ga kg kg xa 71 3.12 Genes Involved in Ribosomal Biogenesis .13 Genes Involved in rRNA Processing. 0002 epee eee eee 72 4.

kg kg kg vi k k k va 82 4.5 Size-increasing Support FUnetiOn§S. ee eee ee 83 4. gIndex: Index Size. vu gà xà 94 4.9 gIndex: Sensitivity and Scalability .10 Index Incremental Maintenance.

ee va va 96 4.11 Sampling-based Index Construction. gIndex: Performance on Synthetic Datasets. Q Q Q Q Q Q ng ng ng ga g và NT sa 99 5.4 A Sample Set of Features 2. va gà va 103 5.5 Feature-Graph Matrix Index.

LH ee va 108 5.6 Edge-Feature Matrix. ng Nà va 106 5. c c c Q c n Q ng vn và gà va 115 5.9 Weighted Set System .10 A Query Graph 1n ee 118 5.11 Hierarchical Agglomerative Clustering. cu ng kg kg k kg sa 126 5.13 Grafil: Performance on Chemical DafaAS€f§.

Q Q Q Q Q Q Quà gà kg kg kh kg kia 128 5. EDGE: Performance on Synthetic Datasels. nu ng và va 130 5.19 PIS: Index Construction. ng g kg k KV 135 5.20 The Index Components of PIS 2.

ru và va 136 5.21 Overlapping-Relation Graph. cv ng v v và và 138 5.22 Greedy Partition Selection. 0 ng ng ga gà va 140 5.23 PIS: Performance on Chemical Datasets.24 PIS: Parameter Sensitivity 2. HH kg và v va 144 xi List of Tables 2.1 DFS code for Figures 2.

ee ee eee 18 2.2 Parameters of Synthetic Graph Generator .3 Bug-Relevant Functions with 6 = 20% ©.1 Parameters of Synthetic Relational Graph Generator. ee ee eee 61 4.1 Sufficient Sample Size Given é, d,andp. ee hh hhh h hỢ 92 xii Glossary of Notation ú8AS7Dì set of graphs set of patterns set of real numbers empty set set minus vertex set of graph G edge set of graph G vertex label set edge label set data set supporting data set of pattern a support(a), 6(a) support of a min.support, 6 minimum support P(a) subpattern set of a Or edge extension xill Chapter 1 Introduction Data mining, as well as database systems research, is facing a new challenge raised by the emergence of large volumes of network and graph data, which are pervasive in bioinformatics, chem-informatics, the Web, and many other applications. Due to their adaptive capability of modeling complicated structures, such as proteins, images, documents, and other schemaless data, graph representation of data is well accepted in domains ranging from software engineer- ing to computational biology.

In computer vision, graphs are used to represent the organization of features in images, where the interlinks between features are critical in recognition of scenes and objects. In chemical informatics and bio-informatics, scientists use graphs to represent compounds and proteins. Systems for searching and registering chemical compounds have al- ready been developed.