Hierarchical Overlapping Belief Estimation by Structured Matrix Factorization

Chaoqi Yang, Jinyang Li, Ruijie Wang, Shuochao Yao, Huajie shao, Dongxin Liu, Shengzhong Liu, Tianshi Wang, Tarek F. Abdelzaher

12 / 08 / 2020, Virtual

2020 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM)

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Content

• Common limitation
• Motivate with an example
• Present our BSMF model
• Problem formulation
• Propose the model (contribution 1)
• Implementation (contribution 2)
• Improve BSMF
• Social convolution module
• Message interpolation module
• Experiment
• Synthetic dataset
• Three real-world dataset

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Common limitation

• Separate a large amount of data into disjoint groups
• Belief separation (belief)
• Opinion mining (opinion)
• Community detection (community)
• Sentiment analysis (sentiment groups)
• …

3

One topic/event

group1

group2

group3

group4

…

disjoint

An example on COVID

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No mask

Reopen everything

Let nature selection work

Plan for herd immunity

Wuhan, China

locked down

Photograph: Leon Neal/AFP via Getty Images

https://www.wsj.com/articles/chinese

-lockdown-redux-11589843868

no action

action

https://en.wikipedia.org/wiki/Social_distancing

Wear mask

Social distancing

quarantine

…

All classes online

Hybrid class model

(about class)

Belief structure

• Structure for the example

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5

Source

Belief

(Unsupervised) belief separation problem

• Input data
• A binary matrix of size
• Who says what
• Claim text (tweets)
• Conceptual belief structure
• Output
• A clustering of
• A clustering of

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The belief model

• : the probability that source endorses claim
• : the probability that source
• : the probability that claim

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For a specific source and a specific claim , will the source endorse the claim?

Belief structed matrix

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Residual part

group

belief

Source

Belief

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Belief structured NMF (BSMF)

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• We design (affiliation) source-group matrix and (affiliation) claim-belief matrix , and assume , , then we can get the following

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• Let the matrix be the matrix of probability

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Belief structured NMF

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x

x

source

claim

claim

source

group

belief

group

belief

Tri-factorization implementation

• Loss function (we want to estimate )

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• Derivative

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• Learning rate for GD (we generalize standard multiplicative update rules)

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Improvement for initial

• Motivation
• is sparse
• Social convolution
• Assumption: similar sources will endorse similar claims
• Extract social relations (adjacency matrix)
• Smooth by graph convolution
• Extension: GNN model
• Message interpolation
• Assumption: the same source might endorse similar claims
• Extract the similarity by bag-of-word (BOW)
• Smooth by interpolation
• Extension: BERT, Transformer
• Details in our paper
• Additional theoretical analysis
• https://drive.google.com/file/d/1REgh3s6taPXjH6OLbijT2APrCTKLm1TR/view?usp=sharing

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Synthetic dataset

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Real-world dataset

• Two datasets
• crawled by Apollo Social Sensing Toolkit

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• Baselines
• Random, DBSCAN, Sentiment140, H-Ncut, NMF, NMTF

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Apollo Social Sensing Toolkit http://apollo2.cs.illinois.edu/

Results (Eurovision2016)

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Results2 (global�warming)

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Conclusion

• identify hierarchical belief structure
• design a belief structure matrix factorization (BSMF) method
• generalize the multiplicative update rules
• conduct informative experiments

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Thanks for Listening��Q & A

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