Exploring Generative Models of Tripartite Graphs for Recommendation in Social Media

Charalampos Chelmis, Viktor K Prasanna chelmis@usc.edu

MSM 2013, Paris, France

• Introduction • Structure of Tripartite Graphs • Generative Models of Tripartite Graphs • Social Link Classification Schemes • Evaluation • Conclusion

Overview

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• Social Networking is used for Content organization Content sharing

• Multiple media types • Users' activities

Reveal interests and tastes Hidden structure

• Description of Resources Text Tags / Hashtags

• Social Annotation Collective characterization of resources Use of synonyms for similar recourses Same keywords for different recourses

Introduction

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• How to address issues of synonymy and polysemy? Deal with space size explosion

• How to discover emergent structure in online tagging systems? Hidden topics

• How to capture users’ latent interests? Which subjects a user is mostly interested in? Which users have similar interests?

• How to model the process of social generation of annotations? How to capture the semantics of collaboration

• Why is this useful? Recommend people Recommend Tags / resources Clustering …

Research Questions

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• Set of actors (e.g. users) A={a1, ...,ak} • Set of concepts (e.g. tags) C = {c1, ..., cl} • Set of resources (e.g. photos) R ={r1, ..., rm}

Structure of Tripartite Graphs

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• The User-Concept Model Users are modeled based on their tag usage φ denotes the matrix of topic distributions

− multinomial distribution over N concepts − T topics being drawn independently

θ: the matrix of user-specific mixture weights for these T topics

• Captures users’ latent interests • Ignores Resources • Ignores the social aspect of tagging

• The User-Resource Model Resources become vocabulary terms

• Tags are ignored • Ignores the social aspect of tagging

Reducing the Tripartite Graph to Bipartite Structures

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• Topic-based representation • Model both resources & users’ interests • Multiple users may annotate resource r

• For each tag a user is chosen uniformly at random • Each user is associated with a distribution over

latent topics ɵ • A topic is chosen from a distribution over topics

specific to that user • The tag is generated from the chosen topic

φt: probability distribution of tags for topic t

The User-Resource-Concept Model

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• Tag Recommendation Automatic annotation enhancement Search improvement

• Clustering Community detection Organization of resources/tags in categories

• Navigation and Visualization Social browsing

• Next we focus on recommending people

Recommendation

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• Classification Based on Latent Interests Measure “tastes” distance with respect to latent topics distribution Pointwise squared distance between feature vectors of users u and v Other measures to consider

− Kullback Leibler (KL) divergence − Cosine similarity

• Objective: Minimize the distance between linked users

• Focus on topical homophily Ignore network effects

• Prior work uses network proximity as indicator of link formation

Social Link Recommendation Using Latent Semantics & Network Structure

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]v))(k,-u)(k,(,,v))(1,-u)(1,[( v)F(u, 22 ΘΘΘΘ=

F(u,v) = 0 => u,v have identical distributions

F(u,v) > 0 => distributions diverge

• Latent Topics & Local Structure CN(u,v) = common neighbors between users u and v

− Simplicity and computational efficiency

Latent topics similarity

• Latent Topics & Global Structure SD(u,v) = shortest distance between users u and v

• Non separable training set => inefficient classifiers • Aggregation Strategy

Reduce the number of training samples Produce more efficient classifiers Average latent similarity of user pairs with k common

neighbors:

Social Link Recommendation Using Latent Semantics & Network Structure

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• Objectives Ability to uncover subliminal collective knowledge Evaluate performance of “people” recommendation

• Setting 2.4 GHz Intel Core 2 Duo, 2 GB memory, Windows 7

• Real-world Dataset Last.fm online music system

− social relationships − tagging information − music artist listening information

Statistics − 1,892 users − 25,434 directed user friend relations

− 17,632 artists UR Model vocabulary size − 92,834 user-listened-artist relations

− 11,946 unique tags UC and URC vocabulary size − 186,479 annotations (tuples <user, tag, artist>)

Experimental Analysis

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Sample Topics

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• Evaluate ability to predict tags/resources on new users Perplexity

• Split dataset into two disjoint sets 90% for training

• Lower perplexity indicates better generalization

• URC better overall Exploits more information

• UC Organizes tags in “clusters”

• UR Inferior quality due to noise

Predictive Power

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• Split dataset into two disjoint sets 10%, 25%, 50%, 75% for training, rest for testing

• Evaluation process Randomly sample 12,716 pairs of users 50% true links, 50% negative samples Compute similarity of user pairs Sort users in decreasing order of similarity Add links between users with highest similarity

Recommendation of Social Ties

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• Latent Topics & Shortest Distance Aggregates all true links training similarity values in a single point Least effective

• Ensemble achieves best precision • Over fitting for training size > 50% • Recall drops as dataset size increases

Recommendation of Social Ties

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[Latent Topics & Local Structure]

[Latent Topics]

[Ensemble]

• In social media number of true links << absent links • High performance for both classes

True negatives easier to classify correctly Degradation in performance for true positives

• Reasonable results for practical purposes

How about High Class Imbalance?

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[Latent Topics & Local Structure]

[Latent Topics]

[Ensemble]

• Baselines Cosine Similarity (CS) Maximal Information Path (MIP)

• Evaluation Criterion Area under the receiver-operating characteristic curve (AUC)

• Baselines AUC Computed over the complete dataset Biases the evaluation in favor of the baselines CS AUC = 0.6087 MIP AUC = 0.6256

• Same evaluation process as before • Compute performance lift

% change over best performing baseline Positive % denotes improvement

Comparison to Tag-based similarity metrics

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• Not all schemes can beat the baseline For 10% training data ≤10% AUC loss But, significant speedup due to minimal training dataset

• Latent Topics & Local Structure Scheme consistently better

Comparison to Tag-based similarity metrics

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Training dataset size

[Latent Topics & Local Structure]

[Latent Topics]

• Three generative models of tripartite graphs in social tagging systems

• Modeling of users’ interests in a latent space over resources and metadata

• Limitations Ignore several aspects of real-world annotation process, such as topic

correlation and user interaction

• Achieve great performance in the recommendation task Accurate predictors of social ties in conjunction with structural

evidence Proposed aggregation strategy to reduce number of training samples

• Future work Incorporate other types of resources Automatically identify most discriminative latent topics and discard

uninformative resources and metadata

Concluding Remarks

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• Questions? chelmis@usc.edu

Thank you!

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