## Supervised Random Walks: Predicting and Recommending Links in Social Networks

Citations: | 57 - 0 self |

### BibTeX

@MISC{Backstrom_supervisedrandom,

author = {Lars Backstrom and Jure Leskovec},

title = {Supervised Random Walks: Predicting and Recommending Links in Social Networks},

year = {}

}

### OpenURL

### Abstract

Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near future or which existing interactions are we missing. Although this problem has been extensively studied, the challenge of how to effectively combine the information from the network structure with rich node and edge attribute data remains largely open. We develop an algorithm based on Supervised Random Walks that naturally combines the information from the network structure with node and edge level attributes. We achieve this by using these attributes to guide a random walk on the graph. We formulate a supervised learning task where the goal is to learn a function that assigns strengths to edges in the network such that a random walker is more likely to visit the nodes to which new links will be created in the future. We develop an efficient training algorithm to directly learn the edge strength estimation function. Our experiments on the Facebook social graph and large collaboration networks show that our approach outperforms state-of-theart unsupervised approaches as well as approaches that are based on feature extraction.

### Citations

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Citation Context ...ink about it as a task to rank the nodes of the network. The idea is to design an algorithm that will assign higher scores to nodes whichscreated links to than to those thatsdid not link to. PageRank =-=[25]-=- and variants like Personalized PageRank [17, 15] and Random Walks with Restarts [31] are popular methods for ranking nodes on graphs. Thus, one simple idea would be to start a random walk at node s a... |

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Citation Context ...ons—Data mining General Terms: Algorithms; Experimentation. Keywords: Link prediction, Social networks 1. INTRODUCTION Large real-world networks exhibit a range of interesting properties and patterns =-=[7, 20]-=-. One of the recurring themes in this line of research is to design models that predict and reproduce the emergence of such network structures. Research then seeks to develop models that will accurate... |

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Citation Context ...he network. The idea is to design an algorithm that will assign higher scores to nodes whichscreated links to than to those thatsdid not link to. PageRank [25] and variants like Personalized PageRank =-=[17, 15]-=- and Random Walks with Restarts [31] are popular methods for ranking nodes on graphs. Thus, one simple idea would be to start a random walk at node s and compute the proximity of each other node to no... |

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Citation Context ...esearch is to design models that predict and reproduce the emergence of such network structures. Research then seeks to develop models that will accurately predict the global structure of the network =-=[7, 20, 19, 6]-=-. Many types of networks and especially social networks are highly dynamic; they grow and change quickly through the additions of new edges which signify the appearance of new interactions bePermissio... |

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Citation Context ...lational learning community [28, 26]. However, the challenge with these approaches is primarily scalability. Random walks on graphs have been considered for computing node proximities in large graphs =-=[31, 30, 29, 27]-=-. They have also been used for learning to rank nodes in graphs [3, 2, 23, 11]. 2. SUPERVISED RANDOM WALKS Next we describe our algorithm for link prediction and recommendation. The general setting is... |

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Citation Context ...roaches based on network community detection [9, 16] have been tested on small networks. Link prediction in supervised machine learning setting was mainly studied by the relational learning community =-=[28, 26]-=-. However, the challenge with these approaches is primarily scalability. Random walks on graphs have been considered for computing node proximities in large graphs [31, 30, 29, 27]. They have also bee... |

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Citation Context ...including all those with whom s has previously coauthored. Further related work. The link prediction problem in networks comes in many flavors and variants. For example, the network inference problem =-=[13, 24]-=- can be cast as a link prediction problem where no knowledge of the network is given. Moreover, even models of complex networks, like Preferential Attachment [7], Forest Fire model [20] and models bas... |

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Citation Context ... predicting new links in networks. The unsupervised methods for link prediction were extensively evaluated by Liben-Nowell and Kleinberg [21] who found that the Adamic-Adar measure of node similarity =-=[1]-=- performed best. More recently approaches based on network community detection [9, 16] have been tested on small networks. Link prediction in supervised machine learning setting was mainly studied by ... |

52 | Center-Piece Subgraphs: Problem Definition and Fast
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Citation Context ...lational learning community [28, 26]. However, the challenge with these approaches is primarily scalability. Random walks on graphs have been considered for computing node proximities in large graphs =-=[31, 30, 29, 27]-=-. They have also been used for learning to rank nodes in graphs [3, 2, 23, 11]. 2. SUPERVISED RANDOM WALKS Next we describe our algorithm for link prediction and recommendation. The general setting is... |

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Citation Context ...and window z > b: ⎧ ⎪⎨ 0 ifx ≤ −b, h(x) = (x+b) ⎪⎩ 2 /(2z) if−b < x ≤ z −b, (7) (x+b)−z/2 ifx > z −b • Wilcoxon-Mann-Whitney (WMW) loss with width b (Proposed to be used when one aims to maximize AUC =-=[32]-=-): 1 h(x) = 1+exp(−x/b) Each of these loss functions is differentiable and needs to be evaluated for all pairs of nodes d ∈ D and l ∈ L (see Eq. 2). Performing this naively takes approximatelyO(c 2 ) ... |

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Citation Context ...es of the network into a unified link prediction algorithm. We develop a method based on Supervised Random Walks that in a supervised way learns how to bias a PageRank-like random walk on the network =-=[3, 2]-=- so that it visits given nodes (i.e., positive training examples) more often than the others. We achieve this by using node and edge features to learn edge strengths (i.e., random walk transition prob... |

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Citation Context ...lational learning community [28, 26]. However, the challenge with these approaches is primarily scalability. Random walks on graphs have been considered for computing node proximities in large graphs =-=[31, 30, 29, 27]-=-. They have also been used for learning to rank nodes in graphs [3, 2, 23, 11]. 2. SUPERVISED RANDOM WALKS Next we describe our algorithm for link prediction and recommendation. The general setting is... |

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Citation Context ...including all those with whom s has previously coauthored. Further related work. The link prediction problem in networks comes in many flavors and variants. For example, the network inference problem =-=[13, 24]-=- can be cast as a link prediction problem where no knowledge of the network is given. Moreover, even models of complex networks, like Preferential Attachment [7], Forest Fire model [20] and models bas... |

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Citation Context ...es is primarily scalability. Random walks on graphs have been considered for computing node proximities in large graphs [31, 30, 29, 27]. They have also been used for learning to rank nodes in graphs =-=[3, 2, 23, 11]-=-. 2. SUPERVISED RANDOM WALKS Next we describe our algorithm for link prediction and recommendation. The general setting is that we are given a graph and a node s for which we would like to predict/rec... |

16 | Learning random walks to rank nodes in graphs
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Citation Context ...es of the network into a unified link prediction algorithm. We develop a method based on Supervised Random Walks that in a supervised way learns how to bias a PageRank-like random walk on the network =-=[3, 2]-=- so that it visits given nodes (i.e., positive training examples) more often than the others. We achieve this by using node and edge features to learn edge strengths (i.e., random walk transition prob... |

15 | Overview of the 2003 kdd cup
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Citation Context ...it is not practical to incorporate them (a user may have as many as a hundred million nodes at 3 hops). Co-authorship networks. First we consider the co-authorship networks from arXiv e-print archive =-=[12]-=- where we have a time-stamped list of all papers with author names and titles submitted to arXiv during 1992 and 2002. We consider co-authorship networks from four different areas of physics: Astro-ph... |

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Citation Context ...es is primarily scalability. Random walks on graphs have been considered for computing node proximities in large graphs [31, 30, 29, 27]. They have also been used for learning to rank nodes in graphs =-=[3, 2, 23, 11]-=-. 2. SUPERVISED RANDOM WALKS Next we describe our algorithm for link prediction and recommendation. The general setting is that we are given a graph and a node s for which we would like to predict/rec... |

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Citation Context ...ink prediction problem where no knowledge of the network is given. Moreover, even models of complex networks, like Preferential Attachment [7], Forest Fire model [20] and models based on random walks =-=[19, 8]-=-, can be viewed as ways for predicting new links in networks. The unsupervised methods for link prediction were extensively evaluated by Liben-Nowell and Kleinberg [21] who found that the Adamic-Adar ... |

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Citation Context ...re extensively evaluated by Liben-Nowell and Kleinberg [21] who found that the Adamic-Adar measure of node similarity [1] performed best. More recently approaches based on network community detection =-=[9, 16]-=- have been tested on small networks. Link prediction in supervised machine learning setting was mainly studied by the relational learning community [28, 26]. However, the challenge with these approach... |

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Citation Context |

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Citation Context ...ts) between iterations. We arrive at Algorithm 1 that iteratively computes the eigenvector p as well as the partial derivatives of p. Convergence of Algorithm 1 is similar to those of power-iteration =-=[5]-=-. To solve Eq. 4 we further need to compute ∂Qju which is the ∂w partial derivative of entryQju (Eq. 3). This calculation is straightforward. When(j,u) ∈ E we find ∂Qju (1−α) ∂fw(ψ (∑ ju) ∂w and other... |

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Citation Context ...ju and taking the derivative now gives: ∂pu ∂w Notice that pu and ∂pu ∂w = ∑ j ∂pj Qju ∂w +pj ∂Qju ∂w are recursively entangled in the equation. However, we can still compute the gradient iteratively =-=[4, 3]-=-. By (5) (6) Initialize PageRank scores p and partial derivatives ∂pu : ∂wk foreach u ∈ V dop (0) u = 1 |V | foreach u ∈ V,k = 1,...,|w| do ∂pu (0) = 0 ∂wk t = 1 while not converged do foreach u ∈ V d... |