arXiv subjects

Zanbo Zhang

Publications and source records attributed to Zanbo Zhang.

4 recordsLinked to original sources

arXiv2023

A Parallel PageRank Algorithm For Undirected Graph

As a measure of vertex importance according to the graph structure, PageRank has been widely applied in various fields. While many PageRank algorithms have been proposed in the past decades, few of them take into account whether the graph under investigation is directed or not. Thus, some important properties of undirected graph\textemdash symmetry on edges, for example\textemdash is ignored. In this paper, we propose a parallel PageRank algorithm specifically designed for undirected graphs that can fully leverage their symmetry. Formally, our algorithm extends the Chebyshev Polynomial approximation from the field of real function to the field of matrix function. Essentially, it reflects the symmetry on edges of undirected graph and the density of diagonalizable matrix. Theoretical analysis indicates that our algorithm has a higher convergence rate and requires less computation than the Power method, with the convergence rate being up to 50\% higher with a damping factor of $c=0.85$. Experiments on six datasets illustrate that our algorithm with 38 parallelism can be up to 39 times faster than the Power method.

cs.NI↗

arXiv2023

An Advanced Parallel PageRank Algorithm

Initially used to rank web pages, PageRank has now been applied in many fields. In general case, there are plenty of special vertices such as dangling vertices and unreferenced vertices in the graph. Existing PageRank algorithms usually consider them as `bad` vertices since they may take troubles. However, in this paper, we propose a parallel PageRank algorithm which can take advantage of these special vertices. For this end, we firstly interpret PageRank from the information transmitting perspective and give a constructive definition of PageRank. Then, based on the information transmitting interpretation, a parallel PageRank algorithm which we call the Information Transmitting Algorithm(ITA) is proposed. We prove that the dangling vertices can increase ITA's convergence rate and the unreferenced vertices and weak unreferenced vertices can decrease ITA's calculations. Compared with the MONTE CARLO method, ITA has lower bandwidth requirement. Compared with the power method, ITA has higher convergence rate and generates less calculations. Finally, experimental results on four data sets demonstrate that ITA is 1.5-4 times faster than the power method and converges more uniformly.

cs.NI↗

arXiv2022

MSTGD:A Memory Stochastic sTratified Gradient Descent Method with an Exponential Convergence Rate

The fluctuation effect of gradient expectation and variance caused by parameter update between consecutive iterations is neglected or confusing by current mainstream gradient optimization algorithms.Using this fluctuation effect, combined with the stratified sampling strategy, this paper designs a novel \underline{M}emory \underline{S}tochastic s\underline{T}ratified Gradient Descend(\underline{MST}GD) algorithm with an exponential convergence rate. Specifically, MSTGD uses two strategies for variance reduction: the first strategy is to perform variance reduction according to the proportion p of used historical gradient, which is estimated from the mean and variance of sample gradients before and after iteration, and the other strategy is stratified sampling by category. The statistic \ $\bar{G}_{mst}$\ designed under these two strategies can be adaptively unbiased, and its variance decays at a geometric rate. This enables MSTGD based on $\bar{G}_{mst}$ to obtain an exponential convergence rate of the form $λ^{2(k-k_0)}$($λ\in (0,1)$,k is the number of iteration steps,$λ$ is a variable related to proportion p).Unlike most other algorithms that claim to achieve an exponential convergence rate, the convergence rate is independent of parameters such as dataset size N, batch size n, etc., and can be achieved at a constant step size.Theoretical and experimental results show the effectiveness of MSTGD

stat.ML↗

arXiv2017

Minimum size of n-factor-critical graphs and k-extendable graphs

We determine the minimum size of $n$-factor-critical graphs and that of $k$-extendable bipartite graphs, by considering Harary graphs and related graphs. Moreover, we determine the minimum size of $k$-extendable non-bipartite graphs for $k=1,\ 2$, and pose a related conjecture for general $k$.

math.CO↗