Subgraph Search Over Uncertain Graphs Erşan Demircioğlu

Motivation – 1/2 A graph structure effectively models a set of items and relations between them. So it has many usage area like modeling – Chemical compounds – Social networks – Network traffic 2

Motivation – 2/2 Generally, the data is modeled to extract some information. – In case of a graph model; frequent or queried sub- graphs are interested. For example, – In bioinformatics, a known gene pattern is queried to identify the organism is pathogenic or not. – For social networks, frequent grouping structure could be interested. 3

Formal Definition of Graph 4

Subgraph and Supgraph Isomorphism 5

Uncertain Graphs In graphs, relation between vertices are certain, two vertices are connected or not. However in real life application, relation between vertices are not certain. – In bioinformatics, we don’t know the gene pattern exactly, but we know probability of connection between proteins 6

Formal Definition of Uncertain Graph 7

Subgraph Search over Graphs 8

Scope of The Presentation Because of verifying subgraph isomorphism is an NP-complete problem, we want to deal with minimal number of candidate graphs. Thus most of studies are focused on pruning uninterested graphs. In the scope of this study, two pruning strategies are investigated. 9

Method Proposed by Chen In this study, – A novel feature structure and – An effective pruning method are proposed. 10

Node Projected Vector – 1/4 11

Node Projected Vector – 2/4 Then, dimensions of graph are extracted – A dimension is generated from a NNT and represents edge between two nodes and its level in NNT. 12

Node Projected Vector – 3/4 13

Node Projected Vector – 4/4 14

Dominated Set Cover Algorithm If Q is subgraph isomorphic to G, then the union of query vectors dominated by G covers all node-projected vectors in Q, – First the dominated vectors for each node of G are computed, – Then, union the dominated vectors of all the nodes of G to get the dominated vector set. 15

Dominated Set Cover Algorithm NPV’s of query graph Q = {NPV(1), NPV(2), NPV(3), NPV(4)} NPV’s of graph G = {NPV(a), NPV(b), NPV(c), NPV(d)} 16

Application on Uncertain Graphs 17

Probability Pruning 18

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Opinion About Method Representing graphs as a feature vector is an innovative idea. – As shown in corresponding paper, feature vectors are effectively used to identify unrelated graphs. – In addition to this, vector representation makes possible to use many classification methodology to classify graphs or extracting frequent sub graphs. 21

Method Proposed by Papapetrou This study is focused on finding frequent supgraphs in uncertain graph database. In this study, – First, each possible exact graphs are generated by using given uncertain graph and probability of these exact graphs are calculated. – Then, expected support value is calculated for a query graph by using possible exact graphs. 22

Calculating Exact Graphs 23

Expected Support 24

Opinion About Method Calculating all possible exact graphs from uncertain graphs removes complexity of uncertainty from problem. However, – Increases dataset size and complexity – Not efficient for large graphs. 25

Questions 26

References Papapetrou, O., Ioannou, E., and Skoutas, D., "Efficient discovery of frequent subgraph patterns in uncertain graph databases." In Proceedings of the 14th International Conference on Extending Database Technology (EDBT/ICDT '11), Anastasia Ailamaki, Sihem Amer-Yahia, Jignesh Pate, Tore Risch, Pierre Senellart, and Julia Stoyanovich (Eds.). ACM, New York, NY, USA, , Chen, L., Wang, C., "Continuous Subgraph Pattern Search over Certain and Uncertain Graph Streams," Knowledge and Data Engineering, IEEE Transactions on, vol.22, no.8, pp , 2010 Shang, H., Zhu, K., Lin, X., Zhang, Y., Ichise, R.;, "Similarity search on supergraph containment," Data Engineering (ICDE), 2010 IEEE 26th International Conference on, vol., no., pp , 1-6 March