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
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
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
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
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
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
