# Computing Heat Kernel Pagerank and a Local Clustering Algorithm

@article{Graham2014ComputingHK,
title={Computing Heat Kernel Pagerank and a Local Clustering Algorithm},
author={Fan Chung Graham and Olivia Simpson},
journal={ArXiv},
year={2014},
volume={abs/1503.03155}
}
• Published 15 October 2014
• Mathematics, Computer Science
• ArXiv
Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating random walks of bounded length and runs in time $$O\big (\frac{\log (\epsilon ^{-1})\log n}{\epsilon ^3\log \log (\epsilon ^{-1})}\big )$$, assuming performing a random walk step and sampling from a distribution with bounded support take constant time.
20 Citations
Computing heat kernel pagerank and a local clustering algorithm
• Mathematics, Computer Science
Eur. J. Comb.
• 2018
It is shown that for a subset S of Cheeger ratio ϕ, many vertices in S may serve as seeds for a heat kernel pagerank vector which will find a cut of conductance O ( ϕ ) .
Distributed Algorithms for Finding Local Clusters Using Heat Kernel Pagerank
• Computer Science
WAW
• 2015
A distributed algorithm is given that computes a local cluster in time that depends only logarithmically on the size of the graph in the CONGEST model when the conductance of the optimal local cluster is known, and that can be computed in the k-machine distributed model in sublinear time.
Local clustering via approximate heat kernel PageRank with subgraph sampling.
• Medicine
Scientific reports
• 2021
This paper presents an algorithm for approximating the heat kernel PageRank on a local subgraph, and shows that the number of computations required is sublinear in terms of the expected size of the local cluster of interest, and that it provides a good approximation of the heat Kernel PageRank.
Solving Local Linear Systems with Boundary Conditions Using Heat Kernel Pagerank
• Mathematics, Computer Science
Internet Math.
• 2015
We present an efficient algorithm for solving local linear systems with a boundary condition using the Green’s function of a connected induced subgraph related to the system. We introduce the method
A Semi-supervised Heat Kernel Pagerank MBO Algorithm for Data Classification
• Mathematics
• 2018
Abstract : We present a very efficient semi-supervised graph-based algorithm for classification of high-dimensional data that is motivated by the MBO method of Garcia-Cardona (2014) and derived using
Efficient Estimation of Heat Kernel PageRank for Local Clustering
• Computer Science
SIGMOD Conference
• 2019
TEA and TEA+, two novel local graph clustering algorithms based on heat kernel PageRank that provide non-trivial theoretical guarantees in relative error of HKPR values and the time complexity and outperforms the state-of-the-art algorithm by more than four times on most benchmark datasets.
Sublinear Algorithms for Local Graph Centrality Estimation
• Computer Science, Mathematics
2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
• 2018
These are the first algorithms yielding worst-case sublinear bounds for general directed graphs and any choice of the target node.
Shortest paths, Markov chains, matrix scaling and beyond : improved algorithms through the lens of continuous optimization
This thesis develops a faster algorithm for the unit capacity minimum cost flow problem, which encompasses the shortest path with negative weights and minimum cost bipartite perfect matching problems, and develops faster algorithms for scaling and balancing nonnegative matrices, two fundamental problems in scientific computing.
Almost-linear-time algorithms for Markov chains and new spectral primitives for directed graphs
The first almost-linear-time directed Laplacian system solver is designed, a notion of approximation is provided for directed graphs, and sparsifiers under this notion always exist are proved.
Exploiting Optimization for Local Graph Clustering
• Mathematics
• 2016
Local graph clustering methods aim to identify well-connected clusters around a given "seed set" of reference nodes. The main focus of prior theoretical work has been on worst-case running time

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