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Recsys RSWeb 2013 paper presentation slides. Paper can be found here: Structural Diversity in Social Recommender Systems

- 1. Structural Diversity in Social Recommender Systems Mitul Tiwari Joint work with Xinyi (Lisa) Huang and Sam Shah LinkedIn
- 2. 2 Who am I
- 3. 3 Outline • Introduction • Motivation • Goal • Structural Diversity in Recommendation • Structural Diversity and User Engagement • Conclusion
- 4. 4 Introduction • Social Networks : important for • Sharing and Discovery • Communication • Networking • Online Social Networks are partially observed • Link Prediction and Recommending entities are important
- 5. 5 Introduction: Network is Important
- 6. 6 Introduction: People You May Know
- 7. 7 Introduction: Goal • How does structural diversity of network plays a role in • Recommendations of people? • User Engagement on the site?
- 8. 8 Outline • Introduction • Motivation • Goal • Structural Diversity in Recommendation • Structural Diversity and User Engagement • Conclusion
- 9. 9 Structural Diversity in PYMK Recommendations • Members in recommendation set mapped to a graph G • Vertices represent members in the recommendation set • Edges are the connections between those members on LinkedIn social graph • 3 measures of structural diversity • Number of connected components • Number of triangles • Average local node degree
- 10. 10 Structural Diversity in Recommendations • A connected component • any pair of vertices are connected by a path or an isolated vertex • Number of connected components • a measure of structural diversity [Ugander et al. 2012] • Smaller number of components => less structural diversity • Effect on Invitation rate or conversion rate • ratio of the number of invitations sent and size of recommended set
- 11. 11 Structural Diversity in Recommendations • Invitation rate increases as the number of components decreases
- 12. 12 Structural Diversity in Recommendations • Members in recommendation set mapped to a graph G • A triangle in graph G • Set of three vertices in Graph G s.t. each vertex is connected to other two • More number of triangles => dense graph • More number of triangles => less structural diversity • Effect on Invitation rate or conversion rate
- 13. 13 Structural Diversity in Recommendations • Invitation rate increases as the number of triangles increases
- 14. 14 Structural Diversity in Recommendations • Members in recommendation set mapped to a graph G • Local node degree • Number of edges incident on the node • Avg local node degree • Average of the local node degree over all nodes • Higher avg local node degree => denser graph • Higher avg local node degree => less structural diversity • Effect on Invitation rate or conversion rate
- 15. 15 Recommendations • Invitation rate increases as the avg local node degree increases
- 16. 16 Structural Diversity in Recommendations • Less diverse the result set, the higher the invitation rates • Explanation: A member knows one person in a recommendation set of connected members then knows other members in the set
- 17. 17 Outline • Introduction • Motivation • Goal • Structural Diversity in Recommendation • Structural Diversity and User Engagement • Conclusion
- 18. 18 Structural Diversity and User Engagement • A member is engaged if visits the site multiple times a week • How does engagement depend on the structure of a member’s immediate connection network? • Connections of a member is mapped to a graph • Vertices represent members in the connections set • Edges are the connections between those members on LinkedIn social graph
- 19. 19 Structural Diversity and User Engagement • K-core decomposition of a graph • Repeatedly remove nodes with less than K neighbors • Eliminate influence from unimportant nodes • K-components • Connected components in K-core decomposition of the graph
- 20. 20 Structural Diversity and User Engagement • Higher engagement with higher number K-core components
- 21. 21 Structural Diversity and User Engagement • Higher engagement with higher number K-core components
- 22. 22 Concluding remarks • Lower structural diversity among recommendation set results in a higher invitation rate • Different form Facebook data study [Ugander et al. 2012] • Use case is slightly different • Effect of structural diversity on recommender system highly depends on the use • Don’t generalize structural diversity effects on one recommender system to all • Higher structural diversity among member’s connection network results in higher engagement • Similar to Facebook data study
- 23. 23 Related Work
- 24. 24 Acknowledgement • http://data.linkedin.com • We are hiring! • Contact: mtiwari[at]linkedin.com
- 25. 25 Questions?

- Hi, I am Mitul Tiwari. Today I am going to present our paper on “Structural Diversity in Social Recommender Systems” This is joint work with Lisa Huang and Sam Shah
- I work in Search, Network, and Analytics group at LinkedIn, and focus on social recommender systems and graph mining problems such as link prediction, etc.
- Here is the outline of my talk. First, I will describe the motivation and the goal behind our work. Next I am going to talk about effects of structural diversity in people recommendation systems such as “People You May Know” at LinkedIn Then I will talk about how structural diversity affects user engagement And finally I will conclude with some remarks drawn from this work
- Social networks have become important for sharing and discovery of content, communication with others, and networking. Any online social network is partially observed as two people might know each other but may not be connected with each other Link prediction and recommending other members to connect with is important to grow your network and social reach
- LinkedIn is the largest professional network with more than 238 million members. Members can connect with each other and maintain their professional network on linkedin.
- LinkedIn exposes it’s link prediction and people recommendation system through a feature called People You May Know or PYMK in short In PYMK we analyze billions of edges to recommend possible connections to you. PYMK is a large scale recommendation system that helps you connect with others.
- In this work we aim to study how structural diversity of connections between recommended set of members in PYMK affects overall invitation or conversion rate Also, we aim to study the structural diversity of connections network affects user engagement on the site
- Next I am going to talk more about how structural diversity of connections between recommended members in PYMK affects the overall invitation or connection rate
- To study structural diversity of connections among the recommended set of members in PYMK, we first map the recommended set of members to a graph G where vertices represents members in the recommendation set, and edges are the connections between those members on LinkedIn social graph We define 3 measures of structural diversity in terms of the number of connected components, the number of triangles, and Average local node degree. I will go into each of these three notions of structural diversity next Todo: a simple graph
- A connected component is defined as a maximal subgraph of the original graph such that any pair of vertices are connected by a path or the subgraph is just an isolated vertex The number of connected components can be used a measure of structural diversity where smaller number of components mean less structural diversity This measure was also used by Ugander et al. in their study where they compared the effect of structural diversity in user recruitment We aim to measure effect on invitation rate or conversion rate, which is defined as the ratio of the number of invitations to connect sent and the size of recommended set in People You May Know (PYMK)
- This figure plots invitation rate vs the number of components for different sizes of recommendation set Data set: PYMK recommendation sets of different sizes: 2, 3, 4, 5 and 6 in this graph For each of this figure, we see that invitation rate increases with decrease in the number of components in the graph That is, invitation rate increases as the recommendation set becomes less structurally diverse
- Next we measure structural diversity in terms of the number of triangles in the graph G, which is obtained by mapping the recommended set of members to a graph G A set of three vertices in a graph form a triangle if any of the vertex is connected with the other two More number of triangles in a graph means denser graph and the graph is less structurally diverse We aim to measure the effect on invitation rate as the number of triangles changes in the graph G
- This figure plots invitation rate with respect to the number of triangles in the graph obtained from the recommendation set A we see the invitation rate increases as the number of triangles increase That is, invitation rate increases as the graph becomes less structurally diverse
- Next we measure structural diversity in terms of average local node degree in Graph G, which is obtained by mapping members in recommendation set to a Graph as before Local node degress is defined as the number of edges incident on the node Avg local node degree is the average of the local node degree over all nodes in Graph G Higher avg local node degree implies denser graph, that means, less structural diversity
- We use the same PYMK data set and measure invitation rate wrt to average local node degree and we observe that invitation rate increases as avg local node degree increases that is, invitation rate increase as the graph becomes less structurally diverse
- In summary, less structurally diverse the recommendation set is the higher the invitation rate Possible explanation: if a member knows one person in a recommendation set, and if the recommendation set of members are strongly connected with each other then, the member knows other members in the set
- Next I am going to talk about structural diversity and its effect on user engagement
- We say a member is engaged if the member visits the site multiple times a week We would like to measure how engagement varies with structural diversity of member’s immediate connection network First, we map connections of a member to a graph, where vertices represent members in the connections set Edges are the connection between those member on the social graph
- We define K-core decomposition of graph as repeatedly removing nodes with less than K neighbors This eliminates influence from unimportant nodes K-components: connected components in K-core decomposition of the graph
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