nips nips2008 nips2008-171 nips2008-171-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Mark Herbster, Guy Lever, Massimiliano Pontil
Abstract: We continue our study of online prediction of the labelling of a graph. We show a fundamental limitation of Laplacian-based algorithms: if the graph has a large diameter then the number of mistakes made by such algorithms may be proportional to the square root of the number of vertices, even when tackling simple problems. We overcome this drawback by means of an efficient algorithm which achieves a logarithmic mistake bound. It is based on the notion of a spine, a path graph which provides a linear embedding of the original graph. In practice, graphs may exhibit cluster structure; thus in the last part, we present a modified algorithm which achieves the “best of both worlds”: it performs well locally in the presence of cluster structure, and globally on large diameter graphs. 1
[1] J. M. Barzdin and R. V. Frievald. On the prediction of general recursive functions. Soviet Math. Doklady, 13:1224–1228, 1972.
[2] M. Belkin and P. Niyogi. Semi-supervised learning on riemannian manifolds. Machine Learning, 56:209– 239, 2004.
[3] A. Blum and S. Chawla. Learning from labeled and unlabeled data using graph mincuts. In Proc. 18th International Conf. on Machine Learning, pages 19–26. Morgan Kaufmann, San Francisco, CA, 2001.
[4] P. Doyle and J. Snell. Random walks and electric networks. Mathematical Association of America, 1984.
[5] J. Fakcharoenphol and B. Kijsirikul. Low congestion online routing and an improved mistake bound for online prediction of graph labeling. CoRR, abs/0809.2075, 2008.
[6] K. Gremban, G. Miller, and M. Zagha. Performance evaluation of a new parallel preconditioner. Parallel Processing Symposium, International, 0:65, 1995.
[7] M. Herbster. Exploiting cluster-structure to predict the labeling of a graph. In The 19th International Conference on Algorithmic Learning Theory, pages 54–69, 2008.
[8] M. Herbster and M. Pontil. Prediction on a graph with a perceptron. In B. Sch¨ lkopf, J. Platt, and o T. Hoffman, editors, Advances in Neural Information Processing Systems 19, pages 577–584. MIT Press, Cambridge, MA, 2007.
[9] M. Herbster, M. Pontil, and L. Wainer. Online learning over graphs. In ICML ’05: Proceedings of the 22nd international conference on Machine learning, pages 305–312, New York, NY, USA, 2005. ACM.
[10] R. Kinderman and J. L. Snell. Markov Random Fields and Their Applications. Amer. Math. Soc., Providence, RI, 1980.
[11] D. Klein and M. Randi´ . Resistance distance. Journal of Mathematical Chemistry, 12(1):81–95, 1993. c
[12] N. Littlestone. Learning when irrelevant attributes abound: A new linear-threshold algorithm. Machine Learning, 2:285–318, 1988.
[13] K. Pelckmans and J. A. Suykens. An online algorithm for learning a labeling of a graph. In In Proceedings of the 6th International Workshop on Mining and Learning with Graphs, 2008.
[14] X. Zhu, Z. Ghahramani, and J. Lafferty. Semi-supervised learning using gaussian fields and harmonic functions. In 20-th International Conference on Machine Learning (ICML-2003), pages 912–919, 2003.