Kernels on Graphs as Proximity Measures

Konstantin Avrachenkov (1) , Pavel Chebotarev (2) , Dmytro Rubanov (1)

1 NEO - Network Engineering and Operations
2 ICS RAS - Trapeznikov Institute of Control Sciences

Kernels and, broadly speaking, similarity measures on graphs are extensively used in graph-based unsupervised and semi-supervised learning algorithms as well as in the link prediction problem. We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This can potentially be useful for recommending the adoption of one or another similarity measure in a machine learning method. Also, we numerically compare various similarity measures in the context of spectral clustering and observe that normalized heat-type similarity measures with log modification generally perform the best.

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]; Apprentissage [cs.LG]

Konstantin Avrachenkov, Pavel Chebotarev, Dmytro Rubanov. Kernels on Graphs as Proximity Measures. Proceedings of the 14th Workshop on Algorithms and Models for the Web Graph (WAW 2017), Jun 2017, Toronto, Canada. ⟨hal-01647915⟩