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Evaluation of Graph Sampling: A Visualization Perspective
Paper by: Yanhong Wu, Nan Cao, Daniel Archambault, Qiaomu Shen, Huamin Qu, and Weiwei Cui
Presentation by: Austin Wallace.March 28, 2017
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What’s better, B or C?
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A little different, right?
● Similar quantitative statistics ● Very different perceptually
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Problem: Analyzing large graphs
● Large graphs are difficult to analyze even with state of the art techniques on high-end clusters
● Can reach hundreds of millions, or even billions of nodes
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One Solution: Graph sampling
● Sampled graph often more desirable than small chunk of original graph
● Makes analysis on large graphs tractable● Can be used for preliminary evaluation
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One more problem: How to sample?
What is the best way to sample?
● Should we pick nodes at random?● Traverse the graph?
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Lots of solutions!
This paper focusses on five of the most widely used:
● Random Node (RN)● Random Edge Node (REN)● Random Walk (RW)● Random Jump (RJ)● Forest Fire (FF)
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What? Why? How?
What:
● Node-link unweighted networks (N: ~1000-20000)
Why:
● Summarize topology
How:
● RN, REN, RW, RJ, FF8
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Key Question: Perceptual Quality
What are the main factors that affect perceptual quality in a sampled graph?
How are those factors affected by the five sampling strategies?
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Important Perceptual Qualities
Three identified:
●
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Important Perceptual Qualities
Three identified:
● Coverage Area●
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Important Perceptual Qualities
Three identified:
● Coverage Area● Cluster Quality●
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Important Perceptual Qualities
Three identified:
● Coverage Area● Cluster Quality● High Degree Nodes, and their preservation
In addition, 20% sampling rate was selected as a fair comparison rate
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Graphs used: BA and Sah
14Power law networks generated by a Barabasi-Albert model
Guaranteed cluster networks generated by Sah et al.’s model
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How did they fare: Coverage Area
● Best: Random Edge Node and Random Jump○ Do not get trapped, but are not as sparse as Random Node
● Random Walk is poorest○ May not explore anywhere near the whole graph, leaving out entire
sections○ Researchers expected Random Node to be poorest
● Forest Fire and Random Walk do better in less modular graphs
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How did they fare: Cluster Quality
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● Best: Random Edge Node and Random Jump perform best
● Poorest: Random Node and Forest Fire ● Random Walk depends on graph modularity, but not
graph size
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How did they fare: High Degree Nodes
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● Best: Random Walk ○ Can visit the same node many times
● Poorest: Random node is consistently poor○ Not at all biased towards high degree nodes
● Random jump does well, but may jump away before fully exploring a high degree node
● Random Edge Nodes is biased towards high degree nodes, so does better
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So, which is best?
● Random Walk to preserve high-degree nodes● Random Jump or Random Edge Node to preserve
global structure and cluster quality● Almost never use Random Node
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Strengths
● Substantial thought given to experiment design and neutralizing potential confounds
● Depth of work: Pilot study, three formal studies● Useful, well explained, and nuanced recommendations
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Weaknesses and limitations
● Does not explore the laying out of graphs post-sampling.
● Only used computer science students/graduates in their studies
● Single sampling rate was tested
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Potential future work
● Improve metrics based on human feedback● Perceptual quality of graph abstraction, as opposed to
sampling● Investigate time to complete tasks on sampled graphs,
as well as accuracy● Investigate false positives, such as a sampled low
degree perceived as high degree21