#### DMCA

## Learning Spectral Graph Transformations for Link Prediction

Citations: | 48 - 5 self |

### Citations

906 | The link prediction problem for social networks
- Liben-Nowell, Kleinberg
- 2003
(Show Context)
Citation Context .... Analogously, we also consider a network’s Laplacian matrix as the basis for link prediction. Recently, several link prediction methods have been studied: weighted sums of path counts between nodes (=-=Liben-Nowell & Kleinberg, 2003-=-), the matrix exponential (Wu & Chang, 2004), the von Neumann kernel and diffusion processes (Kandola et al., 2002), the commute time and resistance distance kernels (Fouss et al., 2007), random fores... |

760 |
The structure of scientific collaboration networks
- Newman
(Show Context)
Citation Context ...ask of predicting the edge weights. The network datasets we inspected are summarized in Table 2. DBLP1 is a citation graph. Hep-th is the citation graph of Arxiv’s high energy physics/theory section (=-=Newman, 2001-=-). Advogato is a trust network with three levels of trust (Stewart, 2005). Slashdot is a social network where users tag each other as friends and foes (Kunegis et al., 2009). Epinions is an opinion si... |

438 | Propagation of trust and distrust
- Guha, Kumar, et al.
- 2004
(Show Context)
Citation Context ...ust (Stewart, 2005). Slashdot is a social network where users tag each other as friends and foes (Kunegis et al., 2009). Epinions is an opinion site where users can agree or disagree with each other (=-=Guha et al., 2004-=-). WWW and WT10G are hyperlink network datasets extracted from a subset of the World Wide Web (Albert et al., 1999; Bailey et al., 2003). Eowiki is the bipartite userarticle authorship graph of the Es... |

377 | Eigentaste: A constant time collaborative filtering algorithm
- Goldberg, Roeder, et al.
(Show Context)
Citation Context ...from a subset of the World Wide Web (Albert et al., 1999; Bailey et al., 2003). Eowiki is the bipartite userarticle authorship graph of the Esperanto Wikipedia 2 . Jester is a dataset of rated jokes (=-=Goldberg et al., 2001-=-). MovieLens is a dataset of movie ratings 3 . 6.1. Setup For each network dataset, we split the set of edges into a test and a training set, with the test set containing a third of all edges. For the... |

323 | Application of dimensionality reduction in recommender system-a case study.
- Sarwar, Karypis, et al.
- 2000
(Show Context)
Citation Context ...m forest kernels (Chebotarev & Shamis, 1997) and the heat diffusion kernel (Ito et al., 2005). Similarly, rank reduction of the adjacency matrix has been proposed to implement edge weight prediction (=-=Sarwar et al., 2000-=-). Our main contribution is to generalize these link prediction functions to a common form and to provide a way to reduce the high-dimensional problem of learning the various kernels’ parameters to a ... |

244 | Kernels and regularization on graphs,” in
- Smola, Kondor
- 2003
(Show Context)
Citation Context ... is also known as the Kirchhoff matrix, due to its connection to electrical resistance networks. FCOM(L) = L + FCOM(L) = L + (5) (6) By regularization, we arrive at the regularized Laplacian kernels (=-=Smola & Kondor, 2003-=-): FCOMR(L) = (I + αL) −1 FCOMR(L) = (I + αL) −1 (7) (8) As a special case, the non-normalized regularized Laplacian kernel is called the random forest kernel for α = 1 (Chebotarev & Shamis, 1997). Th... |

222 | Diameter of the world wide web
- ALBERT, JEONG, et al.
- 1999
(Show Context)
Citation Context ..., 2009). Epinions is an opinion site where users can agree or disagree with each other (Guha et al., 2004). WWW and WT10G are hyperlink network datasets extracted from a subset of the World Wide Web (=-=Albert et al., 1999-=-; Bailey et al., 2003). Eowiki is the bipartite userarticle authorship graph of the Esperanto Wikipedia 2 . Jester is a dataset of rated jokes (Goldberg et al., 2001). MovieLens is a dataset of movie ... |

194 | Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation
- Fouss, Pirotte, et al.
- 2007
(Show Context)
Citation Context ...s (Liben-Nowell & Kleinberg, 2003), the matrix exponential (Wu & Chang, 2004), the von Neumann kernel and diffusion processes (Kandola et al., 2002), the commute time and resistance distance kernels (=-=Fouss et al., 2007-=-), random forest kernels (Chebotarev & Shamis, 1997) and the heat diffusion kernel (Ito et al., 2005). Similarly, rank reduction of the adjacency matrix has been proposed to implement edge weight pred... |

176 | Diffusion kernels on graphs and other discrete structures
- Kondor, Lafferty
- 2002
(Show Context)
Citation Context ...ee matrix with Dii = ∑ j Aij. Then A = D −1/2 AD −1/2 is the normalized adjacency matrix. Transformations of the adjacency matrices A and A give rise to the exponential and von Neumann graph kernels (=-=Kondor & Lafferty, 2002-=-; Ito et al., 2005). FEXP(A) = exp(αA) (1) FEXP(A) = exp(αA) (2) FNEU(A) = (I − αA) −1 (3) FNEU(A) = (I − αA) −1 (4) α is a positive parameter. Additionally, the von Neumann kernels require α < 1. 2.2... |

93 | Engineering a multipurpose test collection for web retrieval experiments.
- Bailey, Craswell, et al.
- 2003
(Show Context)
Citation Context ...an opinion site where users can agree or disagree with each other (Guha et al., 2004). WWW and WT10G are hyperlink network datasets extracted from a subset of the World Wide Web (Albert et al., 1999; =-=Bailey et al., 2003-=-). Eowiki is the bipartite userarticle authorship graph of the Esperanto Wikipedia 2 . Jester is a dataset of rated jokes (Goldberg et al., 2001). MovieLens is a dataset of movie ratings 3 . 6.1. Setu... |

85 | The slashdot zoo: mining a social network with negative edges
- Kunegis, Lommatzsch, et al.
- 2009
(Show Context)
Citation Context ...high energy physics/theory section (Newman, 2001). Advogato is a trust network with three levels of trust (Stewart, 2005). Slashdot is a social network where users tag each other as friends and foes (=-=Kunegis et al., 2009-=-). Epinions is an opinion site where users can agree or disagree with each other (Guha et al., 2004). WWW and WT10G are hyperlink network datasets extracted from a subset of the World Wide Web (Albert... |

55 | Learning semantic similarity.
- Kandola, Shawe-Taylor, et al.
- 2002
(Show Context)
Citation Context ...tion methods have been studied: weighted sums of path counts between nodes (Liben-Nowell & Kleinberg, 2003), the matrix exponential (Wu & Chang, 2004), the von Neumann kernel and diffusion processes (=-=Kandola et al., 2002-=-), the commute time and resistance distance kernels (Fouss et al., 2007), random forest kernels (Chebotarev & Shamis, 1997) and the heat diffusion kernel (Ito et al., 2005). Similarly, rank reduction ... |

53 | The matrix-forest theorem and measuring relations in small social groups. Automation and Remote Control,
- Chebatorev, Shamis
- 1997
(Show Context)
Citation Context ...ix exponential (Wu & Chang, 2004), the von Neumann kernel and diffusion processes (Kandola et al., 2002), the commute time and resistance distance kernels (Fouss et al., 2007), random forest kernels (=-=Chebotarev & Shamis, 1997-=-) and the heat diffusion kernel (Ito et al., 2005). Similarly, rank reduction of the adjacency matrix has been proposed to implement edge weight prediction (Sarwar et al., 2000). Our main contribution... |

49 |
Structural models in anthropology.
- Hage, Harary
- 1983
(Show Context)
Citation Context ...eights. The following functions are estimated: red: polynomial; red dashed: nonnegative polynomial; magenta: exponential function; cyan: rank reduction. marized as the enemy of my enemy is my friend (=-=Hage & Harary, 1983-=-). The Laplacian graph kernels can also be applied to signed graphs by using the absolute diagonal degree matrix Dii = ∑ j |Aij| (Hou, 2005). As the unsigned Laplacian, the signed Laplacian is positiv... |

30 |
Application of kernels to link analysis
- Ito, Shimbo, et al.
- 2005
(Show Context)
Citation Context ...and diffusion processes (Kandola et al., 2002), the commute time and resistance distance kernels (Fouss et al., 2007), random forest kernels (Chebotarev & Shamis, 1997) and the heat diffusion kernel (=-=Ito et al., 2005-=-). Similarly, rank reduction of the adjacency matrix has been proposed to implement edge weight prediction (Sarwar et al., 2000). Our main contribution is to generalize these link prediction functions... |

30 |
Social status in an open-source community.
- Stewart
- 2005
(Show Context)
Citation Context ...re summarized in Table 2. DBLP1 is a citation graph. Hep-th is the citation graph of Arxiv’s high energy physics/theory section (Newman, 2001). Advogato is a trust network with three levels of trust (=-=Stewart, 2005-=-). Slashdot is a social network where users tag each other as friends and foes (Kunegis et al., 2009). Epinions is an opinion site where users can agree or disagree with each other (Guha et al., 2004)... |

30 |
A least-squares approach to joint diagonalization
- Wax, Sheinvald
- 1997
(Show Context)
Citation Context ...ntext of joint diagonalization, where given a set of matrices {Ai}, a matrix U is searched that makes the matrices {UAiUT } as diagonal as possible according to a given matrix norm. See for instance (=-=Wax & Sheinvald, 1997-=-). In that context, the task consists of finding an orthogonal matrix U, whereas our approach consists of optimizing the fit by varying the spectrum. 8. Conclusion and Discussion We have presented a m... |

24 |
Bounds for the least Laplacian eigen value of a signed graph.
- Hou
- 2005
(Show Context)
Citation Context ...on. marized as the enemy of my enemy is my friend (Hage & Harary, 1983). The Laplacian graph kernels can also be applied to signed graphs by using the absolute diagonal degree matrix Dii = ∑ j |Aij| (=-=Hou, 2005-=-). As the unsigned Laplacian, the signed Laplacian is positivesemidefinite. Unlike the unsigned Laplacian, the signed Laplacian can be positive-definite. This is the case when each connected component... |