A.Y. Ng, A.X. Zheng, and M. Jordan. Link Analysis, Eigenvectors, and Stability. In International Joint Conference on Artificial Intelligence (IJCAI-01), 2001.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....alter the graph. We would like small changes in the graph to have a small effect on the weight vector of the algorithm. We capture this requirement by the definition of stability. The notion of stability has been independently considered (but not explicitly defined) in a number of different papers [18, 19, 3, 1]. Given a graph G, we can view a change in graph G, as an operation on graph G, that adds and or removes links so a to produce a new graph G = G. Formally, a change is defined as an operation on the adjacency matrix of the graph G, that alters k entries of the matrix, for some k 0. The ....

....instability can be proven for the class of connected graphs. The proof by Lempel and Moran [16] for the rank instability of Kleinberg algorithm, is the first step towards this direction. Recent work has shown that stability is tightly connected with the spectral properties of the underlying graph [18, 19, 3, 1]. This seems a promising direction for proving stability results. 22 10 Acknowledgments We would like to thank Ronald Fagin, Ronny Lempel, Alberto Mendelzon, and Shlomo Moran for valuable comments and corrections. ....

A. Y. Ng, A. X. Zheng, and M. I. Jordan. Link analysis, eigenvectors, and stability. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), Seattle, Washington, USA, 2001. 23

....[11] consider improvements on the HITS algorithm by using textual information to weight the importance of nodes and links. Rafiei and Mendelzon [42, 38] consider a variation of the HITS algorithm that uses random jumps, similar to SALSA. The same algorithm is also considered by Ng Zheng and Jordan [39, 40], termed Randomized HITS. Extensions of the HITS algorithm that use multiple eigenvectors were proposed by Ng, Zheng and Jordan [40] and Achlioptas et al. 3] Tomlin [51] proposes a generalization of the PAGERANK algorithm that computes flow values for the edges of the Web graph, and a ....

....alter the graph. We would like small changes in the graph to have a small effect on the weight vector of the algorithm. We capture this requirement by the definition of stability. The notion of stability has been independently considered (but not explicitly defined) in a number of different papers [39, 40, 3, 1]. For the definition of stability, we will use some of the terminology employed by Lempel and Moran [35] n be a class of graphs, and let G = P, E) and G # = P, E # ) be two graphs in n . We define the link distance d # between graphs G and G # as follows. d # (G, G # ) E # E # ) ....

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A. Y. Ng, A. X. Zheng, and M. I. Jordan. Link analysis, eigenvectors, and stability. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), Seattle, Washington, USA, 2001.

....alter the graph. We would like small changes in the graph to have a small effect on the weight vector of the algorithm. We capture this requirement by the definition of stability. The notion of stability has been independently considered (but not explicitly defined) in a number of different papers [17, 18, 3, 1]. Given a graph G, we can view a change in graph G, as an operation on graph G, that adds and or removes links so a to produce a new graph G 0 = G. Formally, a change is defined as an operation on the adjacency matrix of the graph G, that alters k entries of the matrix, for some k 0. The ....

....characterized. In our work all the examples for instability are on disconnected graphs. It would be interesting to examine if instability can be proven for the class of connected graphs. Recent work has shown that stability is tightly connected with the spectral properties of the underlying graph [17, 18, 3, 1]. This seems a promising direction for proving stability results. 10 Acknowledgments We would like to thank Ronald Fagin, Ronny Lempel, Alberto Mendelzon, and Shlomo Moran for valuable comments and corrections. 22 ....

A. Y. Ng, A. X. Zheng, and M. I. Jordan. Link analysis, eigenvectors, and stability. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), Seattle, Washington, USA, 2001.

....ABSTRACT The Kleinberg HITS and the Google PageRank algorithms are eigenvector methods for identifying authoritative or influential articles, given hyperlink or citation information. That such algorithms should give reliable or consistent answers is surely a desideratum, and in [10], we analyzed when they can be expected to give stable rankings under small perturbations to the linkage patterns. In this paper, we extend the analysis and show how it gives insight into ways of designing stable link analysis methods. This in turn motivates two new algorithms, whose performance ....

....of particular matrices related to the adjacency graph to determine authority. Understanding the robustness of link analysis algorithms therefore involves an analysis of the stability of these eigenvector calculations. Using ideas from matrix perturbation theory and Markov chain theory, in [10] we formally characterized conditions under which HITS and PageRank are stable. In this paper, we briefly summarize the results derived in [10] and show how they give insight into ways of designing stable link analysis algorithms. This then motivates two new algorithms: Randomized HITS, which ....

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A. Y. Ng, A. X. Zheng, and M. I. Jordan. Link analysis, eigenvectors, and stability. In Proc. 17th International Joint Conference on Artificial Intelligence, 2001.

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A.Y. Ng, A.X. Zheng, and M. Jordan. Link Analysis, Eigenvectors, and Stability. In International Joint Conference on Artificial Intelligence (IJCAI-01), 2001.

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A.Y. Ng, A.X. Zheng, and M. Jordan. Link Analysis, Eigenvectors, and Stability. In International Joint Conference on Artificial Intelligence (IJCAI-01), 2001.

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A.Y. Ng, A.X. Zheng, and M. Jordan. Link Analysis, Eigenvectors, and Stability. In International Joint Conference on Artificial Intelligence (IJCAI-01), 2001.

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A.Y. Ng, A.X. Zheng, and M. Jordan. Link Analysis, Eigenvectors, and Stability. In International Joint Conference on Artificial Intelligence (IJCAI-01), 2001.

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