1. Mining, Indexing and Searching Graphs in Biological Databases
Jiawei Han
Department of Computer Science
&
Institute of Genomic Biology
University of Illinois at Urbana-Champaign
In collaboration with Xifeng Yan (UIUC Ph.D.’06 and IBM Watson), Philip S. Yu (IBM Watson), et al.
(Core material for tutorials at ICDM’05 & KDD’06)
November 20, 2018

2. References: “Covering” Five Papers
X. Yan and J. Han, gSpan: Graph-Based Substructure Pattern Mining, Proc Int. Conf. on Data Mining (ICDM'02) (Google Scholar: ranked #3 out of 83,800 entries on “Graph Pattern Mining” on November 20, 2018)
X. Yan and J. Han, CloseGraph: Mining Closed Frequent Graph Patterns, Proc ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining (KDD'03) (Google Scholar: ranked #1 out of 83,800 entries on “Graph Pattern Mining” on November 20, 2018November 20, 2018)
X. Yan, P. S. Yu, and J. Han, Graph Indexing: A Frequent Structure-based Approach, Proc ACM-SIGMOD Int. Conf. Management of Data (SIGMOD'04) (invited to TODS and published 2005, Google Scholar: ranked #1 out of 39,300 entries on “Graph Indexing” on November 20, 2018)
X. Yan, P. S. Yu, and J. Han, “Substructure Similarity Search in Graph Databases”, Proc ACM-SIGMOD Int. Conf. on Management of Data (SIGMOD'05) (invited and published in ACM TODS’06)
H. Hu, X. Yan, H. Yu, J. Han and X. J. Zhou, “Mining Coherent Dense Subgraphs across Massive Biological Networks for Functional Discovery”, Proc Int. Conf. Intelligent Systems for Molecular Biology (ISMB'05) (Also in Bioinformatics, 2005)
November 20, 2018

3. November 20, 2018

4. Graph, Graph, Everywhere
from H. Jeong et al Nature 411, 41 (2001)
Aspirin
Yeast protein interaction network
November 20, 2018
Co-author network
An Internet Web

5. Why Graph Mining and Searching?
Graphs are ubiquitous
Chemical compounds (Cheminformatics)
Protein structures, biological pathways/networks (Bioinformactics)
Program control flow, traffic flow, and workflow analysis
XML databases, Web, and social network analysis
Graph is a general model
Trees, lattices, sequences, and items are degenerated graphs
Diversity of graphs
Directed vs. undirected, labeled vs. unlabeled (edges & vertices), weighted, with angles & geometry (topological vs. 2-D/3-D)
Complexity of algorithms: many problems are of high complexity!
November 20, 2018

6. Outline Mining frequent graph patterns Graph indexing methods
Similairty search in graph databases
Biological network analysis
Some recent progress on graph mining
November 20, 2018

7. 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
Applications of graph pattern mining
Mining biochemical structures
Program control flow analysis
Mining XML structures or Web communities
Building blocks for graph classification, clustering, comparison, and correlation analysis
November 20, 2018

8. Example: Frequent Subgraphs
Graph Dataset
(A)
(B)
(C)
Frequent Patterns
(min support is 2)
(1)
(2)
November 20, 2018

9. Frequent Subgraph Mining Approaches
Apriori-based approach
AGM/AcGM: Inokuchi, et al. (PKDD’00)
FSG: Kuramochi and Karypis (ICDM’01)
PATH: Vanetik and Gudes (ICDM’02, ICDM’04)
FFSM: Huan, et al. (ICDM’03)
Pattern growth-based approach
MoFa, Borgelt and Berthold (ICDM’02)
gSpan: Yan and Han (ICDM’02)
Gaston: Nijssen and Kok (KDD’04)
November 20, 2018

10. Properties of Graph Mining Algorithms
Search order
breadth vs. depth
Generation of candidate subgraphs
apriori vs. pattern growth
Elimination of duplicate subgraphs
passive vs. active
Support calculation
embedding store or not
Discover order of patterns
path  tree  graph
November 20, 2018

11. Apriori-Based Approach
(k+1)-edge
k-edge G1 G G2 G’ …
G’’ Gn
JOIN
November 20, 2018

12. Pattern Growth-Based Span and Pruning
1-edge
...
2-edge
...
...
If redundant,
prune it!
...
3-edge G1
1: Show that G1=G2  Minimum DFS code of G1 should be equal to Minimum DFS code of G2, thus by calculating the minimum DFS code,
we can tell whether two graphs are the same.
2: MOST IMPORTANT RESULT !!!:
if two graphs G1 and G2 are the same, assume G1 is discovered first, then any graph which is right most extension of graph G2 must
be discovered before. Therefore, we need not check the whole branch under G2 in the search tree. (This is the efficiency comes from)
3: ANOTHER MOST IMPORTANT RESULT:
G2 is presented as a code C, thus we need not even calculate Min(G2), we need only to know whether C is equal to Min(G2). If not, we know
G2 must be discovered before. Very critical for the efficiency.
...
...
PRUNED
...
November 20, 2018

13. gSpan (Yan and Han ICDM’02)
Right-Most Extension
Theorem: Completeness
The Enumeration of Graphs
using Right-most Extension is
COMPLETE
November 20, 2018

14. DFS Code Flatten a graph into a sequence using depth first search
e2: (2,0)
e4: (3,1)
e1: (1,2) 1 2
e5: (2,4)
e3: (2,3) 4 3
November 20, 2018

15. 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 2n 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%
November 20, 2018

16. Closed Frequent Graphs
Motivation: Handling graph pattern explosion problem
Closed frequent graph
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
November 20, 2018

17. CLOSEGRAPH (Yan & Han, KDD’03)
A Pattern-Growth Approach
(k+1)-edge
At what condition, can we
stop searching their children
i.e., early termination? G1
k-edge G2 G
If G and G’ are frequent, G is a subgraph of G’. If in any part of the graph in the dataset where G occurs, G’ also occurs, then we need not grow G, since none of G’s children will be closed except those of G’.
Apriori:
Step1: Join two k-1 edge graphs (these two graphs share a same k-2 edge subgraph) to generate a k-edge graph
Step2: Join the tid-list of these two k-1 edge graphs, then see whether its count is larger than the minimum support
Step3: Check all k-1 subgraph of this k-edge graph to see whether all of them are frequent
Step4: After G successfully pass Step1-3, do support computation of G in the graph dataset, See whether it is really frequent.
gSpan:
Step1: Right-most extend a k-1 edge graph to several k edge graphs.
Step2: Enumerate the occurrence of this k-1 edge graph in the graph dataset, meanwhile, counting these k edge graphs.
Step3: Output those k edge graphs whose support is larger than the minimum support.
Pros:
1: gSpan avoid the costly candidate generation and testing some infrequent subgraphs.
2: No complicated graph operations, like joining two graphs and calculating its k-1 subgraphs.
3. gSpan is very simple
The key is how to do right most extension efficiently in graph. We invented DFS code for graph. … Gn
November 20, 2018

18. Experimental Result
The AIDS antiviral screen compound dataset from NCI/NIH
The dataset contains 43,905 chemical compounds
Among these 43,905 compounds, 423 of them belongs to CA, 1081 are of CM, and the remaining are in class CI
November 20, 2018

19. Discovered Patterns
20%
10% 5%
November 20, 2018

20. Number of Patterns: Frequent vs. ClosedCA
Number of patterns
minimum support
November 20, 2018

21. Runtime: Frequent vs. ClosedCA
runtime (sec)
minimum support
November 20, 2018

22. Do the Odds Beat the Curse of Complexity?
Potentially exponential number of frequent patterns
The worst case complexty vs. the expected probability
Ex.: Suppose Walmart has 104 kinds of products
The chance to pick up one product 10-4
The chance to pick up a particular set of 10 products: 10-40
What is the chance this particular set of 10 products to be frequent 103 times in 109 transactions?
Have we solved the NP-hard problem of subgraph isomorphism testing?
No. But the real graphs in bio/chemistry is not so bad
A carbon has only 4 bounds and most proteins in a network have distinct labels
November 20, 2018

23. Outline Mining frequent graph patterns Graph indexing methods
Similairty search in graph databases
Biological network analysis
Some recent progress on graph mining
November 20, 2018

24. Graph Search: Querying Graph Databases
Given a graph database and a query graph, find all graphs containing this query graph
query graph
graph database
November 20, 2018

25. Scalability Issue Sequential scan Disk I/O
Subgraph isomorphism testing
An indexing mechanism is needed
DayLight: Daylight.com (commercial)
GraphGrep: Dennis Shasha, et al. PODS'02
Grace: Srinath Srinivasa, et al. ICDE'03
(a)
(b)
(c)
Query graph
Sample database
Two issues have to be solved: Disk I/O for false positive and subgraph isomorphism testing for false positive.
Therefore, an indexing mechanism is needed.
The list just shows a partial list of the previous research.
DayLight system is a commercial product targeted for chemical information system. The following is copied from
Once a large graph database is formed, how can we do database management, and further data warehouse and data mining.
2. GraphGrep uses a path-based approach to do graph indexing. Its implementation is available publicly.
3. Grace develops a hierarchical vector space method. It tries to extract features from the graphs in a hierarchical way.
DayLight System
“At Infinity Pharmaceuticals we use the Daylight toolkits for in-house development and have implemented DayCart (as a central component of our chemical registration system. This system has been fully integrated within all aspects of our drug discovery processes and software applications. We have successfully "pushed" the registration process to the chemists; they can quickly and easily register compounds within the context of their electronic notebooks. This has provided a significant enhancement to both the efficiency of data capture and the quality of the data within the chemistry database(s). DayCart integrates well into our overall application and data environment providing a flexible chemical data model which facilitates a data architecture that is tailored to Infinity's processes and scientific approach while at the same time allows speed and scalability. The benefit delivered to Infinity is measured in the strong capability to rapidly and efficiently develop intellectual property and access corporate knowledge effectively. “
November 20, 2018

26. Indexing Strategy Remarks
Query graph (Q)
Graph (G)
If graph G contains query graph Q, G should contain any substructure of Q
Substructure
Remarks
Index substructures of a query graph to prune graphs that do not contain these substructures
Our work, also with all the previous work follows this indexing strategy.
November 20, 2018

27. Framework Two steps in processing graph queries
Step 1. Index Construction
Enumerate structures in the graph database, build an inverted index between structures and graphs
Step 2. Query Processing
Enumerate structures in the query graph
Calculate the candidate graphs containing these structures
Prune the false positive answers by performing subgraph isomorphism test
November 20, 2018

28. Cost Analysis Query Response Time Disk I/O time
Isomorphism testing time
Graph index access time
T_io is the time of fetching a graph from a disk, which may result in one disk block IO. I did not show it in the paper. If the graph dataset can not be held in the main memory, then we need also count the IO time
Our goal is to minimize |Cq|
Size of candidate answer set
Remark: make |Cq| as small as possible
November 20, 2018

29. Path-Based Approach Sample database (a) (b) (c) Paths
0-length: C, O, N, S
1-length: C-C, C-O, C-N, C-S, N-N, S-O
2-length: C-C-C, C-O-C, C-N-C, ...
3-length: ...
Built an inverted index between paths and graphs
November 20, 2018

30. Problems of Path-Based Approach
Sample database
(a)
(b)
(c)
Query graph
Only graph (c) contains this query graph. However, if we only index paths: C, C-C, C-C-C, C-C-C-C, we cannot prune graph (a) and (b).
Only graph (C) contains the query graph. Unfortunately, if we use path only, we cannot prune graphs (a) and (b)
The question is why we use path. The reason is path is very simple, easier to manipulate.
November 20, 2018

31. gIndex: Indexing Graphs by Data Mining
Our methodology on graph index:
Identify frequent structures in the database, the frequent structures are subgraphs that appear quite often in the graph database
Prune redundant frequent structures to maintain a small set of discriminative structures
Create an inverted index between discriminative frequent structures and graphs in the database
The reason of doing frequent graphs is just because the number of frequent graphs is much less than the number
of all subgraphs in the graph database although this number is still too large for indexing.
November 20, 2018

32. IDEAS: Indexing with Two Constraints
discriminative (~103)
frequent (~105)
structure (>106)
November 20, 2018

33. Why Discriminative Subgraphs?
Sample database
(a)
(b)
(c)
All graphs contain structures: C, C-C, C-C-C
Why bother indexing these redundant frequent structures?
Only index structures that provide more information than existing structures
November 20, 2018

34. Discriminative Structures
Pinpoint the most useful frequent structures
Given a set of structures f1, f2, …, fn and a new structure x , we measure the extra indexing power provided by x,
When P is small enough, x is a discriminative structure and should be included in the index
Index discriminative frequent structures only
Reduce the index size by an order of magnitude
November 20, 2018

35. 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
minimum
support threshold
support
size
November 20, 2018

36. Experimental Setting
The AIDS antiviral screen compound dataset from NCI/NIH, containing 43,905 chemical compounds
Query graphs are randomly extracted from the dataset.
GraphGrep: maximum length (edges) of paths is set at 10
gIndex: maximum size (edges) of structures is set at 10
The fingerprint set size is set as large as possible until the program takes 1G memory. Here it is 10K.
Other parameter setting is provided in the paper
November 20, 2018

37. Experiments: Index Size
# OF FEATURES
Remarks:
It shows the raw feature set of path-based approach and structure-based approach. Of course, we can compress the paths into an arbitrary size of index with performance loss. In our experiment setting, we do not compress the path-based index in order to illustrate the best performance it can achieve.
It is also possible to apply discriminative filtering on paths. We have not done experiments on it.
The number of frequent structures or discriminative frequent structures does not change over the different
size of databases.
DATABASE SIZE
November 20, 2018

38. Experiments: Answer Set Size
# OF CANDIDATES
1. That is, the number of graphs containing the query graph is less than 50.
2. Query size are about the number of edges in a query.
3. Answer set size is the number of candidate graphs that may contain the query graph.
4. The actual match is the lower bound that all algorithms can achieve. That is, it is the actual number of graphs that really contain the query graph.
5. The performance of queries whose support is less than 50
QUERY SIZE
November 20, 2018

39. Experiments: Incremental Maintenance
The fact that the number of frequent structures does not change over the different size of databases inspires us to design an algorithm which construct the index incrementally.
2. The black line shows the performance of indexing from the scratch, for example, from a database with 2,000 graphs, 4,000 graphs, 6,000 graphs, 8,000 graphs and 10,000 graphs.
3. The red line shows the performance of incremental indexing, for example, we first built an index for 2,000 graphs, then we add another 2,000 graphs into the database, update the indexing of the original discriminative frequent graphs, then we add another 2,000, … and so on
Frequent structures are stable to database updating
Index can be built based on a small portion of a graph database, but be used for the whole database
November 20, 2018

40. Outline Mining frequent graph patterns Graph indexing methods
Similairty search in graph databases
Biological network analysis
Some recent progress on graph mining
November 20, 2018

41. Structure Similarity Search
CHEMICAL COMPOUNDS
(a) caffeine
(b) diurobromine
(c) viagra
QUERY GRAPH
November 20, 2018

42. Some “Straightforward” Methods
Method1: Directly compute the similarity between the graphs in the DB and the query graph
Sequential scan
Subgraph similarity computation
Method 2: Form a set of subgraph queries from the original query graph and use the exact subgraph search
Costly: If we allow 3 edges to be missed in a 20-edge query graph, it may generate 1,140 subgraphs
November 20, 2018

43. Index: Precise vs. Approximate Search
Precise Search
Use frequent patterns as indexing features
Select features in the database space based on their selectivity
Build the index
Approximate Search
Hard to build indices covering similar subgraphs—explosive number of subgraphs in databases
Idea: (1) keep the index structure
(2) select features in the query space
November 20, 2018

44. Substructure Similarity Measure
Query relaxation measure
The number of edges that can be relabeled or missed; but the position of these edges are not fixed
QUERY GRAPH …
November 20, 2018

45. Substructure Similarity Measure
Feature-based similarity measure
Each graph is represented as a feature vector X = {x1, x2, …, xn}
The similarity is defined by the distance of their corresponding vectors
Advantages
Easy to index
Fast
Rough measure
November 20, 2018

46. Intuition: Feature-Based Similarity Search
Graph (G1)
If graph G contains the major part of a query graph Q, G should share a number of common features with Q
Query (Q)
Graph (G2)
Given a relaxation ratio, calculate the maximal number of features that can be missed !
Suppose we can delete any red edge in the query graph Q.
Substructure
At least one of them
should be contained
November 20, 2018

47. Feature-Graph Matrix
graphs in database G1 G2 G3 G4 G5 f1 1 f2 f3 f4 f5
features
Assume a query graph has 5 features and at most 2 features to miss due to the relaxation threshold
November 20, 2018

48. Edge Relaxation – Feature Misses
If we allow k edges to be relaxed, J is the maximum number of features to be hit by k edges—it becomes the maximum coverage problem
NP-complete
A greedy algorithm exists
We design a heuristic to refine the bound of feature misses
November 20, 2018

49. Query Processing Framework
Three steps in processing approximate graph queries
Step 1. Index Construction
Select small structures as features in a graph database, and build the feature-graph matrix between the features and the graphs in the database
November 20, 2018

50. Framework (cont.) Step 2. Feature Miss Estimation
Determine the indexed features belonging to the query graph
Calculate the upper bound of the number of features that can be missed for an approximate matching, denoted by J
On the query graph, not the graph database
November 20, 2018

51. Framework (cont.) Step 3. Query Processing
Use the feature-graph matrix to calculate the difference in the number of features between graph G and query Q, FG – FQ
If FG – FQ > J, discard G. The remaining graphs constitute a candidate answer set
November 20, 2018

52. Performance Study Database
Chemical compounds of Anti-Aids Drug from NCI/NIH, randomly select 10,000 compounds
Query
Randomly select 30 graphs with 16 and 20 edges as query graphs
Competitive algorithms
Grafil: Graph Filter—our algorithm
Edge: use edges only
All: use all the features
November 20, 2018

53. Comparison of the Three Algorithms
# of candidates
When the number of edge relaxations increases, the performance of Edge and Grafil will be similar, as expected.
Queries with 16 edges
edge relaxation
November 20, 2018

54. Outline Mining frequent graph patterns Graph indexing methods
Similairty search in graph databases
Biological network analysis
Some recent progress on graph mining
November 20, 2018

55. Biological Networks Protein-protein interaction network
Metabolic network
Transcriptional regulatory network
Co-expression network
Genetic Interaction network …
November 20, 2018

56. Data Mining Across Multiple Networksf f a b c d e f g h i j k j j a a h c c h e e b b k k d d i g i g f f f j j a j a h a h c h c c e e e b b k b k k d d g i d i g i g
November 20, 2018

57. Data Mining Across Multiple Networksb d e f g h i j k c a b c d e f g h i j k a b c d e f g h i j k a b c d e f g h i j k f f j a j c h a h c e e b k b k d g i d g i
November 20, 2018

58. Identify Frequent Co-expression Clusters across Multiple Microarray Data Setsb c d e f g h i j k . a b c d e f g h i j k .
c1 c2… cm
g … .2
g … .4 …
g … .2
g … .4
g … .1
g … .5
g … .8
g … .3 .
November 20, 2018

59. Our Solution
We develop a novel algorithm, called CODENSE, to mine frequent coherent dense subgraphs.
The target subgraphs have three characteristics:
All edges occur in >= k graphs (frequency)
All edges should exhibit correlated occurrences in the given graph set (coherency)
The subgraph is dense, where density d is higher than a threshold  and d=2m/(n(n-1)) (density)
m: #edges, n: #nodes
November 20, 2018

60. CODENSE: Mine Coherent Dense Subgraphs
(1) Builds a summary graph by eliminating infrequent edges f a b c d e g h i G3 G2 G6 G5 G4 f a b d e g h i c G1 a b d e g h i c f
summary graph Ĝ
November 20, 2018

61. CODENSE: Mine Coherent Dense Subgraphs
(2) Identify dense subgraphs of the summary graph a b d e g h i c f
summary graph Ĝ
Sub(Ĝ)
Step 2
MODES
Observation: If a frequent subgraph is dense, it must be a dense subgraph in the summary graph. However, the reverse is not true.
November 20, 2018

62. CODENSE: Mine Coherent Dense Subgraphs
(3) Construct the edge occurrence profiles for each dense summary subgraph e g h i c f
Sub(Ĝ)
Step 3 … 1
e-f
c-i
c-h
c-f
c-e G6 G5 G4 G3 G2 G1 E
edge occurrence profiles
November 20, 2018

63. CODENSE: Mine Coherent Dense Subgraphs
(4) builds a second-order graph for each dense summary subgraph … 1
e-f
c-i
c-h
c-f
c-e G6 G5 G4 G3 G2 G1 E
edge occurrence profiles
Step 4
e-h
f-h
e-i
e-g
g-i
h-i
second-order graph S
g-h
f-i
November 20, 2018

64. CODENSE: Mine Coherent Dense Subgraphs
(5) Identify dense subgraphs of the second-order graph
c-f
c-h
c-e
e-h
e-f
f-h
c-i
e-i
e-g
g-i
h-i
second-order graph S
g-h
f-i
Step 4
Sub(S)
Observation: If a subgraph is coherent (its edges show high correlation in their occurrences across a graph set), then its 2nd-order graph must be dense
November 20, 2018

65. CODENSE: Mine Coherent Dense Subgraphs
(6) Identify the coherent dense subgraphs
c-f
c-h
c-e
e-h
e-f
f-h
e-i
e-g
g-i
h-i
Sub(S)
g-h
Step 5 c e f h g i
Sub(G)
November 20, 2018

66. CODENSE: Mine Coherent Dense Subgraphs… 1
e-f
c-i
c-h
c-f
c-e G6 G5 G4 G3 G2 G1 E
edge occurrence profiles c e f h g i
Step 4
Step 5
Sub(G) a b d
e-h
f-h
e-i
e-g
g-i
h-i
second-order graph S
g-h
f-i
Step 1
Step 3
summary graph Ĝ
Sub(Ĝ)
Step 2
Sub(S)
Step 6
MODES
Add/Cut
Restore G and MODES
November 20, 2018

67. Applying CoDense to 39 Yeast Microarray Data Setsf f a j h a h j
c1 c2… cm
g … .2
g … .4 … c c e e b k b k d g i d g i f f
c1 c2… cm
g … .2
g … .4 … a e j a j c h c h e b b k k d g i d g i
c1 c2… cm
g … .1
g … .5 … f f a j h a j c c h e e b b k k d g i d g i f f
c1 c2… cm
g … .8
g … .3 … a j a j h c h c e e b b k k d g i d g i
November 20, 2018

68. Discovery of New Genes Based on Similar Genes
ATP12
MRPL38
MRPL37
MRPL39
FMC1
MRPS18
MRPL32
ACN9
MRPL51
MRP49
YDR115W
PHB1
PET100
ATP17
November 20, 2018

69. Network of Known Similar Genes
ATP17
ATP12
MRPL38
MRPL39
FMC1
MRPS18
MRPL32
ACN9
MRPL51
MRP49
YDR115W
PHB1
PET100
Brown: YDR115W, FMC1, ATP12, MRPL37, MRPS18
GO: (protein metabolism; pvalue = )
November 20, 2018

70. Network Involved in the New Genes
YDR115W
MRP49
PHB1
MRPL51
PET100
ATP12
ATP17
MRPL37
MRPL38
ACN9
MRPL32
MRPL39
MRPS18
FMC1
Red:PHB1,ATP17,MRPL51,MRPL39, MRPL49, MRPL51,PET100
GO: (generation of precursor metabolites and energy; pvalue= )
November 20, 2018

71. Outline Mining frequent graph patterns Graph indexing methods
Similairty search in graph databases
Biological network analysis
Some recent progress on graph mining
November 20, 2018

72. Recent Developments: Graph Mining
Colossal pattern mining: F. Zhu, X. Yan, J. Han, P. S. Yu, and H. Cheng, “Mining Colossal Frequent Patterns by Core Pattern Fusion”, in Proc Int. Conf. on Data Engineering (ICDE'07), April 2007 (Best student paper award)
Constraint-based mining: F. Zhu, X. Yan, J. Han, and P. S. Yu, “gPrune: A Constraint Pushing Framework for Graph Pattern Mining”, in Proc Pacific-Asia Conf. on Knowledge Discovery and Data Mining (PAKDD'07), May 2007 (Best student paper award)
Approximate graph mining: C. Chen, X. Yan, F. Zhu, and J. Han, “gApprox: Mining Frequent Approximate Patterns from a Massive Network”, Proc Int. Conf. on Data Mining (ICDM'07), Oct. 2007
November 20, 2018

73. Recent Developments: Graph Mining
Graph-containment indexing: C. Chen, X. Yan, P. S. Yu, J. Han, D. Zhang, and X. Gu, “Towards Graph Containment Search and Indexing”, in Proc Int. Conf. on Very Large Data Bases (VLDB'07), Vienna, Austria, Sept. 2007
Pattern-based classification: H. Cheng, X. Yan, J. Han, and C.-W. Hsu, “Discriminative Frequent Pattern Analysis for Effective Classification”, in Proc Int. Conf. on Data Engineering (ICDE'07), Istanbul, Turkey, April 2007
DDPMine: H. Cheng, X. Yan, J. Han, and P. S. Yu, "Direct Discriminative Pattern Mining for Effective Classification", Proc Int. Conf. on Data Engineering (ICDE'08), Cancun, Mexico, April 2008
November 20, 2018

74. Discriminative Frequent Pattern Analysis for Effective Classification [ICDE’07]
November 20, 2018

75. Conclusions Graph mining has wide applications
Frequent and closed subgraph mining methods
gSpan and CloseGraph: pattern-growth depth-first search approach
Graph indexing techniques:
Frequent and discirminative subgraphs as indexing fatures
Similairty search in graph databases
Indexing and approximate matching help similar subgraph search
Biological network analysis
Mining coherent, dense, multiple biological networks
Many new developments along the line of graph pattern mining
November 20, 2018

76. Thanks and Questions
November 20, 2018