#### DMCA

## Enhanced statistical rankings via targeted data collection

Citations: | 2 - 0 self |

### Citations

7720 |
Topics in Matrix Analysis
- Horn, Johnson
- 1991
(Show Context)
Citation Context ... i.e., dv = d−, then dv ≤ 2M n and from (6), we obtain λ2(w) ≤ n d− n − 1 ≤ 2M . (7) n − 1 7. Consider the weight w = w0 + δk where δk is the indicator function for edge k. Then using Weyl’s theorem (=-=Horn & Johnson, 1990-=-), we obtain λ2(w) ≤ λ2(w0) + ‖B t diag(δk)B‖ = λ2(w0) + 2. (8) 8. Let G be a weighted graph with weights w ∈ RN and let G ′ be the graph with weights w ′ = w + δk, where δk is the indicator function ... |

226 | The Laplacian spectrum of graphs
- Mohar
- 1991
(Show Context)
Citation Context ...with a discussion. 2. Eigenvalues of the w-weighted graph Laplacian In this section, we review properties of the eigenvalues of the w-weighted graph Laplacian; more extensive treatments are given in (=-=Mohar, 1991-=-; Chung, 1997; Biyikoglu et al., 2007). Let G = (V, E) be the complete graph with |V | = n nodes and let B ∈ RN×n where N := ( ) n 2 be an arcvertex incidence matrix for G, ⎧ ⎪⎨ 1 j = head(k) Bk,j = −... |

101 | Chip-firing games on graphs
- Björner, Lovász, et al.
- 1991
(Show Context)
Citation Context ...on is determined by the algebraic connectivity (Sun et al., 2004). Finally, in the “chipfiring game” of Björner, Lovász and Shor, the algebraic connectivity dictates the length of a terminating game (=-=Björner et al., 1991-=-). Consequently, algebraic connectivity is a performance measure for the convergence rate in sensor networks, data fusion, load balancing, and consensus problems (Olfati-Saber et al., 2007).Enhanced ... |

64 | The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem. - Sun, Boyd, et al. - 2006 |

57 | Growing well-connected graphs, in: - Ghosh, Boyd - 2006 |

55 |
The Perron-Frobenius theorem and the ranking of football teams.
- Keener
- 1993
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Citation Context ...onsider optimal data collection for nonlinear ranking methods, including robust estimators (Osting et al., 2012b), random walker methods (Callaghan et al., 2007), Perron-Frobenius eigenvalue methods (=-=Keener, 1993-=-; Langville & Meyer, 2012), and Elo methods (Elo, 1978; Glickman, 1995; Langville & Meyer, 2012). Secondly, the implementation of a data collection method should be more carefully modeled for particul... |

29 | Active ranking using pairwise comparisons. - Jamieson, Nowak - 2011 |

26 |
Laplacian Eigenvectors of Graphs.
- Bıyıkoglu, Leydold, et al.
- 1915
(Show Context)
Citation Context ...nvalues of the w-weighted graph Laplacian In this section, we review properties of the eigenvalues of the w-weighted graph Laplacian; more extensive treatments are given in (Mohar, 1991; Chung, 1997; =-=Biyikoglu et al., 2007-=-). Let G = (V, E) be the complete graph with |V | = n nodes and let B ∈ RN×n where N := ( ) n 2 be an arcvertex incidence matrix for G, ⎧ ⎪⎨ 1 j = head(k) Bk,j = −1 j = tail(k) (3) ⎪⎩ 0 otherwise, whe... |

23 | An active learning algorithm for ranking from pairwise preferences with an almost optimal query complexity. - Ailon - 2012 |

19 | Maximum algebraic connectivity augmentation is NP-hard,” - Mosk-Aoyama - 2008 |

16 |
Spectral Graph Theory, AMS
- Chung
- 1997
(Show Context)
Citation Context ...sion. 2. Eigenvalues of the w-weighted graph Laplacian In this section, we review properties of the eigenvalues of the w-weighted graph Laplacian; more extensive treatments are given in (Mohar, 1991; =-=Chung, 1997-=-; Biyikoglu et al., 2007). Let G = (V, E) be the complete graph with |V | = n nodes and let B ∈ RN×n where N := ( ) n 2 be an arcvertex incidence matrix for G, ⎧ ⎪⎨ 1 j = head(k) Bk,j = −1 j = tail(k)... |

15 | Adaptive paired comparison design
- Glickman, Jensen
(Show Context)
Citation Context ...ding robust estimators (Osting et al., 2012b), random walker methods (Callaghan et al., 2007), Perron-Frobenius eigenvalue methods (Keener, 1993; Langville & Meyer, 2012), and Elo methods (Elo, 1978; =-=Glickman, 1995-=-; Langville & Meyer, 2012). Secondly, the implementation of a data collection method should be more carefully modeled for particular applications. For instance, for the Yahoo! Movie user rating datase... |

14 | Random walker ranking for NCAA division I-A football
- Callaghan, Mucha, et al.
- 2007
(Show Context)
Citation Context ...e comparison data is an old problem (David, 1963), there have been several recent contributions to the subject (Langville & Meyer, 2012; Osting et al., 2012b; Hirani et al., 2011; Jiang et al., 2010; =-=Callaghan et al., 2007-=-) with broad applications, e.g., problems in social networking, game theory, and e-commerce. Let G = (V, E) denote the complete graph, consisting of a set of n nodes, V = {j} n j=1 , representing alte... |

12 |
Who’s #1?: The Science of Rating and Ranking.
- Langville, Meyer
- 2012
(Show Context)
Citation Context ...spite and possibly as a consequence of these difficulties, although ranking from pairwise comparison data is an old problem (David, 1963), there have been several recent contributions to the subject (=-=Langville & Meyer, 2012-=-; Osting et al., 2012b; Hirani et al., 2011; Jiang et al., 2010; Callaghan et al., 2007) with broad applications, e.g., problems in social networking, game theory, and e-commerce. Let G = (V, E) denot... |

8 | Upper bounds on algebraic connectivity via convex optimization,” - Ghosh, Boyd - 2006 |

7 | Numerical methods for experimental design of largescale linear ill-posed inverse problems, Inverse Problems - Haber, Horesh, et al. |

6 |
Experimental design and analysis for biologists
- Quinn, Keough
- 2002
(Show Context)
Citation Context ... Fisher informativeness of the ranking. Related work. Optimal experiment design (Pukelsheim, 2006) is commonly used in inverse problems, e.g., geophysical (Haber et al., 2008) and biomedical imaging (=-=Quinn & Keough, 2002-=-; Seeger & Nickisch, 2011; Chung & Haber, 2012), for the purpose of reducing the amount of data that must be collected (sparsity). In particular, for inverse problems in imaging, Seeger & Nickisch (20... |

5 | Algebraic connectivity optimization via link addition.
- Wang, Mieghem
- 2008
(Show Context)
Citation Context ...hanced statistical rankings via targeted data collection Algorithm 1 A greedy heuristic for finding edge weights w for which the w-weighted Laplacian has large second eigenvalue (Ghosh & Boyd, 2006b; =-=Wang & Mieghem, 2008-=-). See §2. Input: An initial edge weight w0 ∈ R N defined on the complete graph of n nodes and an integer, ξ. Output: An edge weight, w, such that ‖w − w0‖1 = ξ, and ∆w has large second eigenvalue. Se... |

4 |
Experimental design for biological systems
- Chung, Haber
(Show Context)
Citation Context ... work. Optimal experiment design (Pukelsheim, 2006) is commonly used in inverse problems, e.g., geophysical (Haber et al., 2008) and biomedical imaging (Quinn & Keough, 2002; Seeger & Nickisch, 2011; =-=Chung & Haber, 2012-=-), for the purpose of reducing the amount of data that must be collected (sparsity). In particular, for inverse problems in imaging, Seeger & Nickisch (2011) connect the areas of Bayesian active learn... |

4 |
Least squares ranking on graphs,” arXiv:1011.1716
- Hirani, Kalyanaraman, et al.
- 2010
(Show Context)
Citation Context ...fficulties, although ranking from pairwise comparison data is an old problem (David, 1963), there have been several recent contributions to the subject (Langville & Meyer, 2012; Osting et al., 2012b; =-=Hirani et al., 2011-=-; Jiang et al., 2010; Callaghan et al., 2007) with broad applications, e.g., problems in social networking, game theory, and e-commerce. Let G = (V, E) denote the complete graph, consisting of a set o... |

4 | Visualization of communities in networks - Traud, Frost, et al. - 2009 |

3 | Webscope Dataset: ydata-ymovies-user-movie-ratingscontent-v1 0, http://research.yahoo.com/Academic Relations - Yahoo |

1 | Elo, A. The Rating of Chessplayers, Past and Present - Griffin, Co - 1963 |

1 | Algebraic connectivity of graphs - Pub |

1 | Optimal data collection for improved rankings expose well-connected graphs. submitted - Osting, Brune, et al. |

1 | Statistical ranking using the ℓ 1 -norm on graphs. submitted, 2012b. Pukelsheim, F. Optimal Design of Experiments - Osting, Darbon, et al. |