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Conference Paper

Getting lost in space: Large sample analysis of the resistance distance

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von Luxburg,  U.
Research Group Machines Learning Theory, Max Planck Institute for Intelligent Systems, Max Planck Society;

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Radl,  A.
Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society;

Hein,  M.
Max Planck Society;

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Citation

von Luxburg, U., Radl, A., & Hein, M. (2011). Getting lost in space: Large sample analysis of the resistance distance. In J. Lafferty (Ed.), 24th Annual Conference on Neural Information Processing Systems (NIPS 2010) (pp. 2622-2630). Red Hook, NY: Curran.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0010-4CD3-D
Abstract
The commute distance between two vertices in a graph is the expected time it takes a random walk to travel from the first to the second vertex and back. We study the behavior of the commute distance as the size of the underlying graph increases. We prove that the commute distance converges to an expression that does not take into account the structure of the graph at all and that is completely meaningless as a distance function on the graph. Consequently, the use of the raw commute distance for machine learning purposes is strongly discouraged for large graphs and in high dimensions. As an alternative we introduce the amplified commute distance that corrects for the undesired large sample effects.