snapnets: automatic segmentation of network sequences with node labels
TRANSCRIPT
SnapNETS: Automatic Segmentation of Network Sequences
with Node Labels
Sorour E. Amiri, Liangzhe Chen, B. Aditya PrakashDepartment of Computer Science
Virginia Tech
AAAI, San Francisco, USA, February 9, 2017
Outline Motivation Alternative Approaches Our Proposed Method: SnapNETS Experiments Conclusion
Amiri, Chen, Prakash 2
Network SequencesEpidemiology: disease spreads over contact networks
Social Media: Information spreads over friendship networks
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Flu
Meme
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G1 G2 G3 G4
G1 G2 G3 G4
Uninfected
Infected
Inactive
Active
Making sense of network sequences
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Flu
when do the infection patterns change?
Star Bridge Near Clique
Reason:• Virus mutation• Vaccination• …
Amiri, Chen, Prakash
G1 G2 G3 G4Uninfected
Infected
Making sense of network sequences
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Meme Reason:• Event• …
Star Clique
when do the activation patterns change?
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G1 G2 G3 G4
Inactive
Active
Problem 1: Network sequence segmentation
Given a sequence of networks with labeled nodes, Find the best segmentation which captures:
Different distribution of node labels.
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Star Bridge Near CliqueAmiri, Chen, Prakash
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In this work: Binary labels {0, 1}
Desirable Properties P1. Parameter-free:
• No threshold, No fixed granularity
P2. Comprehensive: • Use the entire graph
P3. Scalable
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Outline Motivation Alternative Approaches Our Proposed Method: SnapNETS Experiments Conclusion
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Alternative 1: Feature Ext. &Time-series
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0 0 0 … 2F1: #cliques (of active subgraph)
F2: #ladders (of inactive subgraph)
F3: #ladders (of active subgraph)
1 1 0 … 0
0 0 0 … 1
[Henderson et al. 2010] [Likas, Vlassis, and Verbeek 2003] [Li et al. 2009]
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0
1
2
Features time series
F1 F2 F3
Step 1: Feature Extraction
Step 2: Time-series segmentationG1 G2 G3 G4
…
Alternative 1: Feature Ext. &Time-series
Drawbacks: Laborious feature-engineering
o # Cliqueso # Ladders
“Local” change detection:o One aggregation time periodo Threshold
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0
1
2
Features time series
F1 F2 F3
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Alternative 2: Plain-graph-based analysis
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[Shah et al. 2015] [Sun et al. 2007] [Lin et al. 2009] [Qu et al. 2014]
Step 1: Extract active subgraphs
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Step 2: Dynamic graph segmentation
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G1 G2 G3 G4 G1 G2 G3 G4
Alternative 2: Plain-graph-based analysis
Drawbacks: Inactive nodes are important to detect different patterns
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Entire graphDynamic graph segmentation
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G1 G2 G3 G4 G1 G2 G3 G4
Chain Roles are different
Desirable Properties P1. Parameter-free:
• No threshold, No fixed granularity
P2. Comprehensive: • Use the entire graph
P3. Scalable
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Comparison of SnapNETS
Outline Motivation Alternative Approaches Our Proposed Method: SnapNETS
Main Idea and Overview Goal 1: Summarizing Act-snapshots Goal 2: Constructing the segmentation graph Goal 3: Finding the best segmentation
Experiments Conclusion
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Nodes: For each segment there is a node + {Source (‘s’), Target (‘t’)} Source (‘s’) = start time Target (‘t’) = end time
Edges: There is a directed edge between adjacent nodes
Main Idea: Segmentation graph
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Best segmentation problem Path optimization problem
Inpu
t
Segmentation G
raph
Overview of SnapNETS Goal 1. Summarize each graph:
Keep structural and label dependent properties
Goal 2. Construct Segmentation graph:Define nodes and edgesDefining edges weights
o extract the features of summarized graphs
Goal 3. Find the best segmentation:Define the best segmentation (path)Compute the best segmentation
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Technical Challenges Using the entire graph snapshots:
Summarize graph while satisfying P2
Finding the number of segments: Compute segmentation while satisfying P1
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Reminder: P1. Parameter-free P2. Comprehensive P3. Scalable
Amiri, Chen, Prakash
Outline Motivation Alternative Approaches Our Proposed Method: SnapNETS
Main Idea and Overview Goal 1: Summarizing Act-snapshots Goal 2: Constructing the segmentation graph Goal 3: Finding the best segmentation
Experiments Conclusion
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Goal 1: Summarizing graph snapshots
We want to preserve Structural properties Nodes labels
Role of Eigenvalue:
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Epidemic threshold in most diffusion models [Prakash et al. ICDM 2011]
Same Same diffusive properties
Leading eigenvalue of Adjacency matrix
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Our summarization approach We want to get a smaller graph with similar eigenvalues:
Successively merge nodes
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Problem 2: Graph summarization Given: A graph with labeled nodes and a compression ratio. Find: a coarsened graph such that:
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Keep leading eigenvalue Matrix perturbation approach
Based on CoarsNet [Purohit et al. KDD 2014] Successively merge nodes Do not merge nodes with different labels
Our Approach
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Given: A graph with labeled nodes and a compression ratio.Find: a coarsened graph such that:
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0.10.1 0.1
0.2
0.2
…
…
Outline Motivation Alternative Approaches Our Proposed Method: SnapNETS
Main Idea and Overview Goal 1: Summarizing Act-snapshots Goal 2: Constructing the segmentation graph Goal 3: Finding the best segmentation
Experiments Conclusion
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Nodes: For each segment there is a node + {Source (‘s’), Target (‘t’)} Source (‘s’) = start time Target (‘t’) = end time
Edges: There is a directed edge between adjacent nodes
Goal 2: Segmentation graph
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Edge Weights
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How can we measure the distance between two segments?Amiri, Chen, Prakash
w ?
Our Approach Step 1: Extract features from summary graphs:
Easier and more efficient than on original graphs. No complex features
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F = [3.9, 13,..., 2.2]
Step 2: Distance of adjacent segments
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Edge Weights
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w
Outline Motivation Alternative Approaches Our Proposed Method: SnapNETS
Main Idea and Overview Goal 1: Summarizing Act-snapshots Goal 2: Constructing the segmentation graph Goal 3: Finding the best segmentation
Experiments Conclusion
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Goal 3: Finding the best segmentation Observation:
For each segmentation there is a path from ‘s’ to ‘t’For each path from ‘s’ to ‘t’ there is a segmentation
Therefore,• Best segmentation problem Path optimization problem
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Possible approach Longest path? Given a segmentation graph Find the longest path from ‘s’ to ‘t’
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Over segmentation problem
s t. . .
s t0.01 0.01 0.01 0.01
0.9 0.9 0.9
Sum = 3
Sum = 2.7Amiri, Chen, Prakash
Problem 3: Finding the best segmentation
Our idea: Average longest path
Advantages: Parameter free Naturally balances weight of the path with the number of segments.
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Given a segmentation graphFind the average longest path from ‘s’ to ‘t’
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Solving ALP Finding the ALP in general graphs is NP-hard. The segmentation graph is a DAG ALP can be solved in
polynomial time State-of-the-art algorithm [Waggoner et al. WACV 2013]
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Time complexity:
Cubic: Not scalable!
Our Solution: LAYERED-ALP
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Dynamic Programming Optimal solution
lp1 = Longest path with 1 segment
lp2 = Longest path with 2 segments
lp4 = Longest path with 4 segments
Our Solution: LAYERED-ALP
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Time Complexity:
Linear!
Build Layers
Find LP in each layer
Find ALP
Complete algorithm
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Time complexity:
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Sub-quadratic
Complete algorithm: Parallel
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Time complexity:
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Outline Motivation Alternative Approaches Our Proposed Method: SnapNETS
Main Idea and Overview Goal 1: Summarizing Act-snapshots Goal 2: Constructing the segmentation graph Goal 3: Finding the best segmentation
Experiments Conclusion
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Experiments: datasets Different Domains with range of sizes:
BA-degree: Random Barabasi Albert graph AS-Oregon: Autonomous Systems peering information Higgs: Tweets dataset (with the follower-followee network) Portland: Contact network between people of Portland Memetracker: Who-copies-from-whom blog and website network IranElect: Follower-followee network of Twitter related to the Iran
election. DBLP: Co-authorship network related to ‘network’ topic.
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Experiments: baselines DYNAMMO [Li et al. KDD 2009]:
Change point detection ( Reconstruction errors) # segments = # segments of SnapNETS .
K-means [Likas et al. Pattern Recognition 2003]: segment when a new cluster is detected
VOG [Koutra et al. SDM 2014]: 10 most important sub-structures Cut when the set of sub-structures changes significantly
o (threshold = the one gives the best result)
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Feature Extraction & time series
Dynamic graph
Experiments: baselines-variations SN-ORIG: Original graphs instead of summary graphs SN-LP: Longest Path instead of ALP SN-GREEDY: Greedy Approach instead of ALP
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Experiments: Quantitative analysis
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SnapNETS outperforms the baselines Clear patterns in summary graphs
Infection moves to new community
As-Oregon
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Case studies: Memetracker
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Televised vice-presidential debates
Summary graphs are close to the case when all nodes have the same label (f5)
Random nodes are active (f8)
Summary graphs are substantially sparser (f2).
Many active nodes got merged into important nodes such as CNN and BBC to form hubs (f6)
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Can I call you joe?
Case studies: AS-Oregon
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New community New segment
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Scalability
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Scalability of SNAP NETS Speedup by parallelizing construction of segmentation graph
Near-linear
Outline Motivation Alternative Approaches Our Proposed Method: SnapNETS
Main Idea and Overview Goal 1: Summarizing Act-snapshots Goal 2: Constructing the segmentation graph Goal 3: Finding the best segmentation
Experiments Conclusion
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Discussion: SnapNets Patterns:
the ‘placement’ and ‘connection’ of active/inactive nodes:
• structural (e.g. community/role/centrality) • rate changes.
Global method: SnapNETS is a ‘global’ method and not simply a change-point detection method.
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Graph summarization and features
Average Longest Path
Properties: P1. Parameter-freeP2. ComprehensiveP3. Scalable
Future Work Handle dynamic graphs with varying
nodes and edges More node labels and real valued features Work with partially observed graphs
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Any questions?
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Funding:
Code at: https://github.com/SorourAmiri/SnapNETS
Sorour E. Amiri Liangzhe Chen B. Aditya Prakash
Goal 1 Goal 2 Goal 3Finding the best segmentation
Successively merge nodesKeep leading eigenvalueKeep same set of labels
Graph summarization Segmentation graph Nodes Edges Edge weights
ALP
SnapNETS Result