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Getting lost in space: Large sample analysis of the resistance distance
Ulrike von Luxburg · Agnes Radl · Matthias Hein

Mon Dec 06 06:50 PM -- 06:55 PM (PST) @ Regency Ballroom

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.