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Distributed Representations of Subgraphs

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Presentation on theme: "Distributed Representations of Subgraphs"β€” Presentation transcript:

1 Distributed Representations of Subgraphs
Bijaya Adhikari, Yao Zhang, Naren Ramakrishnan, and B. Aditya Prakash Department of Computer Science Virginia Tech IEEE ICDM DaMNet, New Orleans, Nov 18th, 2017

2 Adhikari, Zhang, Ramakrishnan, Prakash
Outline Motivation Problem Formulation Method Experiments Conclusion Adhikari, Zhang, Ramakrishnan, Prakash

3 Adhikari, Zhang, Ramakrishnan, Prakash
Motivation Network Embedding Framework Input Network Embeddings Data Mining Tasks Classification Community Detection Link Prediction Anomaly Detection Sense Making … Many Possible Applications! Adhikari, Zhang, Ramakrishnan, Prakash

4 Motivation: Previous work
Most existing works are on node embeddings DeepWalk[Perozzi+, KDD2014] Node2vec[Grover+, KDD 2016] SDNE[Wang+, KDD 2016] LINE[Tang+,WWW 2015] Graph 𝐺(𝑉,𝐸) Vectors How to embed entire subgraphs? Adhikari, Zhang, Ramakrishnan, Prakash

5 Motivation: Our Approach
Given a set of subgraphs from the same graph Learn feature representations of each subgraph Set of Subgraphs Subgraph Embedding β€œPreserve” pre-defined β€œsubgraph property” Adhikari, Zhang, Ramakrishnan, Prakash

6 Adhikari, Zhang, Ramakrishnan, Prakash
Outline Motivation Problem Formulation Method Experiments Conclusion Adhikari, Zhang, Ramakrishnan, Prakash

7 Problem Formulation: Setting
Given A set S= 𝑔 1 , 𝑔 2 , …, 𝑔 𝑛 of subgraphs Typically for the same graph An integer 𝑑 Learn 𝑑-dimensional embedding for each subgraph Such that pre-defined subgraph property is preserved Set of Subgraphs Subgraph Embedding Adhikari, Zhang, Ramakrishnan, Prakash

8 Problem formulation: Challenges
What subgraph property to preserve? How to characterize the property? 𝑔 1 𝑔 2 𝑔 3 Adhikari, Zhang, Ramakrishnan, Prakash

9 Idea: Neighborhood property
Captures neighborhood information within the subgraph 𝑔 1 𝑔 2 𝑔 3 Subgraph 𝑔 1 and 𝑔 2 share neighborhood Subgraph 𝑔 3 does not Adhikari, Zhang, Ramakrishnan, Prakash

10 Capturing neighborhood property
Neighborhood property of a subgraph is defined as the set of all paths annotated by node ids (ID- Paths) in the subgraph {(a,b,a,c), (c,e,a,e), (e,c,a,c), (b,e,c,e), … } {(c,d,d,c), (c,e,a,e), (e,c,a,c), (d,c,d,e), … } {(i,h,j,k), (h,k,i,h), (k,h,j,i), (i,h,k,j), … } Able to capture similarity in the neighborhood Adhikari, Zhang, Ramakrishnan, Prakash

11 Adhikari, Zhang, Ramakrishnan, Prakash
Problem Statement Set of Subgraphs Given: A set of subgraph S= 𝑔 1 , 𝑔 2 , …, 𝑔 𝑛 An integer 𝑑 Learn: An embedding function 𝑓: 𝑔 𝑖 β†’ π’š 𝑖 ∈ 𝑹 𝒅 Subgraph Embedding Such that: The neighborhood property of subgraphs is preserved Adhikari, Zhang, Ramakrishnan, Prakash

12 Adhikari, Zhang, Ramakrishnan, Prakash
Outline Motivation Problem Formulation Method Experiments Conclusion Adhikari, Zhang, Ramakrishnan, Prakash

13 Adhikari, Zhang, Ramakrishnan, Prakash
Subvec Framework Overview Generate samples of Id-paths Enumerating all path is not possible Generate samples of paths Leverage the Id-Paths to learn embeddings Learn the embedding such that nodes in the subgraph can be predicted Adhikari, Zhang, Ramakrishnan, Prakash

14 Adhikari, Zhang, Ramakrishnan, Prakash
Samples of id-paths How to efficiently generate samples of Id-Paths? Subgraph Truncated Random Walks Adhikari, Zhang, Ramakrishnan, Prakash

15 Adhikari, Zhang, Ramakrishnan, Prakash
Feature learning How to learn feature vectors for each subgraphs? Leverage Paragraph2vec’s idea [Quoc+, ICML 2014] SubVec: Distributed Memory Model DM SubVec: Distributed Bag of Nodes DBON Adhikari, Zhang, Ramakrishnan, Prakash

16 Adhikari, Zhang, Ramakrishnan, Prakash
Subvec: DM Models the probability of node occurring in the Id- Path Probability depends on Embedding of the node Embedding of other nodes in the Id-Path Embedding of the subgraph Adhikari, Zhang, Ramakrishnan, Prakash

17 Adhikari, Zhang, Ramakrishnan, Prakash
Subvec: DM Objective The overall objective of SubVec DM is to maximize the log-likelihood Adhikari, Zhang, Ramakrishnan, Prakash

18 Adhikari, Zhang, Ramakrishnan, Prakash
Subvec: DBON Models the probability of a short walk πœƒ appearing in the Id-Path of a subgraph Probability depends on Embedding of the nodes in the walk Embedding of the subgraph Adhikari, Zhang, Ramakrishnan, Prakash

19 Subvec: DBON Objective
The overall objective of SubVec DBON is to maximize the log-likelihood Adhikari, Zhang, Ramakrishnan, Prakash

20 Adhikari, Zhang, Ramakrishnan, Prakash
Complete algorithm The pseudo-code is as following Adhikari, Zhang, Ramakrishnan, Prakash

21 Adhikari, Zhang, Ramakrishnan, Prakash
Outline Motivation Problem Formulation Method Experiments Conclusion Adhikari, Zhang, Ramakrishnan, Prakash

22 Adhikari, Zhang, Ramakrishnan, Prakash
datasets Dataset |V| |E| Domain Workplace 92 757 Contact Cornell 195 304 Web HighSchool 182 2221 Texas 187 328 Washington 230 446 Wisconsin 265 530 PolBlogs 1490 16783 Youtube 1.13M 2.97M Social Adhikari, Zhang, Ramakrishnan, Prakash

23 Community detection using subvec
Problem: Give a network find partitions of the network Such that intra-partition density is high and inter-partitions density is low Adhikari, Zhang, Ramakrishnan, Prakash

24 Community detection: Method
Graph Ego-Nets Embeddings Clusters Adhikari, Zhang, Ramakrishnan, Prakash

25 Community detection: Baselines
Newman [Newman, 2006] Classical Modularity based Community Detection algorithm Louvian [Bondel+, 2008] Fast Modularity based Community Detection algorithm DeepWalk [Perozzi+, 2014] Node embeddings based on vanilla random walk Node2Vec [Grover+, 2014] Node embeddings based on second order random walk Adhikari, Zhang, Ramakrishnan, Prakash

26 Community detection: results
More results in paper Measure Average F1-Score of the communities SubVec outperforms competitors in most datasets Adhikari, Zhang, Ramakrishnan, Prakash

27 Community Detection: Visualization
Ground Truth Communities in HighSchool Dataset Node2vec SubVec Our Framework works well even for dense graphs Adhikari, Zhang, Ramakrishnan, Prakash

28 Case-study: MeMetracker
Memetracker dataset Consists of cascades of memes A meme is a short phrase Cascades flows though news and blog websites Steps Each cascade induces a subgraph in the network Embed the subgraphs enduced by the cascades Cluster the embedding Observe the common β€˜topics’ in each cluster Lipstick on a pig Lipstick on a pig Lipstick on a pig NBC BBC CNN Adhikari, Zhang, Ramakrishnan, Prakash

29 Case-study: MeMetracker
Religious Entertainment Spanish Politics SubVec vectors from meaningful clusters Adhikari, Zhang, Ramakrishnan, Prakash

30 Adhikari, Zhang, Ramakrishnan, Prakash
Case-study: DBLP DBLP is a co-authorship Network We extract subgraphs based on keywords in the title of the papers Keywords include β€˜classification’, β€˜clustering’, β€˜XML’, and so on Each subgraph is annotated by a keyword Steps Embed the subgraphs using SubVec Visualize in 2-dimensions Observe similarity between the keywords Adhikari, Zhang, Ramakrishnan, Prakash

31 Adhikari, Zhang, Ramakrishnan, Prakash
Case-study: DBLP SubVec vectors are meaningful Adhikari, Zhang, Ramakrishnan, Prakash

32 Adhikari, Zhang, Ramakrishnan, Prakash
Scalability More results in paper SubVec scales linearly w.r.t number of subgraphs Adhikari, Zhang, Ramakrishnan, Prakash

33 Adhikari, Zhang, Ramakrishnan, Prakash
Outline Motivation Problem Formulation Method Experiments Conclusion Adhikari, Zhang, Ramakrishnan, Prakash

34 Adhikari, Zhang, Ramakrishnan, Prakash
Conclusion Problem Formulated novel Subgraph Embedding Problem Introduced the Neighborhood Property Algorithm Proposed effective and efficient SubVec Experiments Large Datasets, Performance, Scalability Applications Community Detections Sense Making Adhikari, Zhang, Ramakrishnan, Prakash

35 Adhikari, Zhang, Ramakrishnan, Prakash
Any questions? Funding: Code at: Set of Subgraphs Subgraph Embedding Data Mining Tasks Classification Community Detection Link Prediction Anomaly Detection Sense Making … Adhikari, Zhang, Ramakrishnan, Prakash

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