Chair of Computer Science 5 RWTH Aachen University Learning Layers Analysis of Overlapping Analysis of Overlapping Communities in Communities in Signed Complex Signed Complex Networks Networks Mohsen Shahriari, Mohsen Shahriari, Ying Li, Ralf Klamma Ying Li, Ralf Klamma Advanced Community Information Systems (ACIS) RWTH Aachen University, Germany shahriari@dbis.rwth-aachen.de Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 1
Agenda Learning Layers Introduction to OCD Analysis of Overlapping Communities in Related Work Signed Complex Networks Motivation & Research Questions Mohsen Overlapping Community Detection (OCD) Algorithms Shahriari, Ying Li, for Signed Networks Ralf Klamma Evaluation Results Conclusion and Outlook Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 2
Introduction to OCD in Signed Networks Learning Layers Community detection as an important part of network Analysis of Overlapping Communities in analysis Signed Complex Networks Two key characteristics of signed social networks - Nodes in the overlapping communities Mohsen Shahriari, + Ying Li, - Relations with signs Ralf Klamma + + + + Community structure + + - - Inside Between Communities Communities + + + - Dense - Negative + - Positive - Sparse + + + + Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 3
Motivation Learning Layers Practical application of OCD in signed networks like Analysis of Overlapping Communities in - Informal learning networks Signed Complex Networks - Review sites - Open source developer networks Mohsen Shahriari, Ying Li, Ralf Klamma Contribute to the current research on OCD in signed networks with the following difficiencies - Few algorithms - No comparison between available algorithms Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 4
Related Work on Community Detection in Signed Graphs Learning Layers Non-overlapping community detection Analysis of Overlapping Communities in - Agent-based finding and extracting communities (FEC) [YaCL07] Signed Complex Networks - Two-step approach by maximizing modularity and minimizing frustration [AnMa12] Mohsen - Clustering re-clustering algorithm (CRA) [AmPi13] Shahriari, Ying Li, Ralf Klamma Overlapping community detection - Signed Disassortative Degree Mixing and Information Diffusion Algorithm (SDMID) [ShKl15] - Signed Probabilistic Mixture Model (SPM) [CWYT14] - Multi-objective Evolutionary Algorithm based on Similarity for Lehrstuhl Informatik 5 Community Detection in Signed Networks (MEA s -SN) [LiLJ14] (Information Systems) Prof. Dr. M. Jarke Slide 5
Research Questions Learning Layers How do Signed Disassortative degree Mixing and Analysis of Overlapping Communities in Information Diffusion (SDMID), Signed Probabilistic Signed Complex Networks Mixture model (SPM) and Multi-objective Evolutionary Algorithm (MEA) perform in comparison with each Mohsen Shahriari, other, in terms of knowledge-driven and statistical Ying Li, Ralf Klamma metrics? What are the structural properties of covers detected by SDMID, SPM and MEA and how do they differ? Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 6
Signed Disassortative Degree Mixing and Information Diffusion Algorithm : Phase 1 Learning Layers Identify leaders Analysis of Overlapping Communities in - Calculate Local Leadership Value (LLD) using effective Signed Complex Networks degree (ED) and normalized disassortativeness (DASS) 𝒌∈𝑶𝒇𝒋(𝒋) 𝐞𝐟𝐡 𝒋 − 𝐞𝐟𝐡(𝒌) 𝑭𝑬 𝒋 = 𝑵𝒃𝒚( 𝒋𝒐 + (𝒋) − 𝒋𝒐 − (𝒋) , 𝟏) 𝑬𝑩𝑻𝑻 𝒋 = 𝒌∈𝑶𝒇𝒋(𝒋) 𝒆𝒇𝒉 𝒋 + 𝒆𝒇𝒉(𝒌) 𝒋𝒐 + (𝒋) + 𝒋𝒐 − (𝒋) Mohsen Shahriari, Ying Li, 𝑴𝑴𝑬 𝒋 = 𝜷 × 𝑬𝑩𝑻𝑻 𝒋 + (𝟐 − 𝜷) × 𝑭𝑬(𝒋) Ralf Klamma - Identify local leaders: ∀𝒌 ∈ 𝑶𝒇𝒋 𝒋 , 𝑴𝑴𝑬(𝒋) ≥ 𝑴𝑴𝑬(𝒌) - Identify global leaders: 𝒌∈𝑴𝑴 𝑮𝑴(𝒌) 𝑮𝑴(𝒋) > 𝑴𝑴 where FL: Follower Set, LL: Local Leader Set Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 7
Signed Disassortative Degree Mixing and Information Diffusion Algorithm : Phase 2 Learning Layers Cascading (network coordination game) Analysis of Overlapping Communities in - Assign a leader node k behavior B and all other nodes behavior A Signed Complex Networks - Node i with current behavior A will change its behavior to that ( B ) of its neighbors, if the potential payoff p B (i) is above a predefined threshold, i.e. LLD: Mohsen Shahriari, Ying Li, 𝒗|𝒗 ∈ 𝑶𝒇𝒋 + 𝒋 𝐛𝐨𝐞 𝒄𝒇𝒊𝒃𝒘𝒋𝒑𝒔 𝒗 = 𝑪 𝒘|𝒘 ∈ 𝑶𝒇𝒋 + 𝒋 𝒃𝒐𝒆 𝒄𝒇𝒊𝒃𝒘𝒋𝒑𝒔 𝒘 = 𝑪 − Ralf Klamma 𝒒 𝑪 (𝒋) = 𝒗|𝒗 ∈ 𝑶𝒇𝒋 + 𝒋 𝒃𝒐𝒆 𝒄𝒇𝒊𝒃𝒘𝒋𝒑𝒔 𝒗 = 𝑪 𝒘|𝒘 ∈ 𝑶𝒇𝒋 + 𝒋 𝒃𝒐𝒆 𝒄𝒇𝒊𝒃𝒘𝒋𝒑𝒔 𝒘 = 𝑪 + + 0.6 + + 0.6 + + + 0.6 + + 0.7 + + 0.7 + 0.7 0.5 + + 0.5 0.5 + + + - + + + - - + + 0.2 0.2 0.2 Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 8
Signed Probabilistic Mixture Model Learning Layers Based on Expectation-Maximization (EM) method Analysis of Overlapping Communities in Maximize the log function of the marginal likelihood of Signed Complex Networks the signed network: + 𝑩 𝒋𝒌 − 𝑩 𝒋𝒌 Mohsen 𝑸 𝑭 𝝏, 𝜾 = 𝝏 𝒔𝒔 𝜾 𝒔𝒋 𝜾 𝒔𝒌 𝝏 𝒔𝒕 𝜾 𝒔𝒋 𝜾 𝒕𝒌 Shahriari, Ying Li, 𝒇 𝒋𝒌 ∈𝑭 𝒔𝒔 𝒔𝒕(𝒔≠𝒕) Ralf Klamma Use 𝜕, 𝜄 to c ompute o The probability of a positive edge from a community r : 𝑞 1 Estimation o The probability of a negative edge from two communities r and s : 𝑞 2 Update 𝜕, 𝜄 with 𝑞 1 and 𝑞 2 by maximizing 𝑚𝑜𝑄(𝐹|𝜕, 𝜄) Maximization Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 9
Multi-Objective Evolutionary Algorithm Based on Similarity for Community Detection in Signed Networks Learning Layers Based upon structural similarity between adjacent nodes Analysis of Overlapping Communities in 𝒚∈𝑪(𝒗)∩𝑪(𝒘) 𝜴(𝒚) Signed Complex s (𝒗, 𝒘) = Networks 𝟑 𝟑 𝒚∈𝑪(𝒗) 𝒙 𝒗𝒚 ∙ 𝒚∈𝑪(𝒘) 𝒙 𝒘𝒚 where 𝛺 𝑦 = 0, if 𝑥 𝑣𝑦 < 0 and 𝑥 𝑤𝑦 < 0; 𝑥 𝑣𝑦 𝑥 𝑤𝑦 , 𝑝𝑢ℎ𝑓𝑠𝑥𝑗𝑡𝑓 Mohsen Shahriari, Objective functions Ying Li, Ralf Klamma - Maximize the sum of positive similarities within communities - Maximize the sum of negative similarities between communities Optimal solution is selected with MOEA/D (multiobjective evolutionary algorithm based on decomposition) [ZhLi07] - Decomposition into scalar optimization Lehrstuhl Informatik 5 (Information Systems) - Simultaneous optimization of these subproblems Prof. Dr. M. Jarke Slide 10
Evaluation Metrics Learning Layers Normalized mutual information : regards 𝑁 𝑗𝑙 , 𝑁 𝑗𝑚 ′ as two random Analysis of Overlapping variables and determines the mutual information ( 𝑁 𝑗 : membership Communities in Signed Complex vector, k: k-th community in detected cover, 𝑚 ′ : 𝑚 ′ -th community in real Networks cover) Signed modularity : measures the strength of a community partition by Mohsen Shahriari, taking into account the degree distribution Ying Li, + 𝒙 𝒌 + − 𝒙 𝒌 − 𝒙 𝒋 𝒙 𝒋 Ralf Klamma 𝟐 𝟑(𝒙 + ) 𝒇 +𝟑|(𝒙 − ) 𝒇 | 𝒇 𝒋𝒌 𝒙 𝒋𝒌 − 𝑹 𝑻𝑷 = 𝟑(𝒙 + ) 𝒇 − 𝜺 𝑫 𝒋 , 𝑫 𝒌 , 𝟑|(𝒙 − ) 𝒇 | where 𝜀 𝐷 𝑗 , 𝐷 𝑘 : No.of communities 𝑓 𝑗𝑘 resides Frustration : normalized weighted weight sum of negative edges inside communities and positive edges between communities − + 𝑮𝒔𝒗𝒕𝒖𝒔𝒃𝒖𝒋𝒑𝒐 = 𝜷 × 𝒙 𝒋𝒐𝒖𝒔𝒃 𝒇 + (𝟐 − 𝜷) × |(𝒙 𝒋𝒐𝒖𝒇𝒔 ) 𝒇 | (𝒙 + ) 𝒇 +|(𝒙 − ) 𝒇 | Lehrstuhl Informatik 5 (Information Systems) Execution time Prof. Dr. M. Jarke Slide 11
Synthetic Network Generator Learning Layers Comes from the idea of [LiLJ14] and is based on the Lancichinetti- Analysis of Overlapping Fortunato-Radicchi (LFR) model (directed and unweighted) and a Communities in Signed Complex Networks model from [YaCL07] Parameters - From LFR: no. of nodes, average/max degree, minus exponents for the Mohsen Shahriari, degree and community size distributions which are power laws, min/max Ying Li, Ralf Klamma community size, no. of overlapping nodes, no. of communities, fraction of edges that each node shares with other communities. - From [YaCL07]: proportion of negative edges inside communities P - and proportion of positive edges between communities P + Generation Negate all Randomly negate P - of Randomly negate P + of Generate a normal inter-community all intra-community all inter-community LFR Network edges edges edges Lehrstuhl Informatik 5 (Information Systems) Prof. Dr. M. Jarke Slide 12
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