Graph signal and propagation

31 May 2023

Here I take some notes for the graph signal and label propagation as personal review.

The SBM Spectral Visualization

08 Mar 2023

I made a website for see different spectral(Adjacent Matrix, Laplacian Matrix, Bethe Hessian Matrix…) of network generated by SBM model. Please see this website Spectral Visual .

The BP in SBM and Bethe Approximation

02 Dec 2022

Before, we reviewed detectability limitation of community detection. We learn about Belief Propagation, and by see the stability of trivial fixed point of BP in SBM, we can derive the KS-threshold:

The Detectability Limitation of Community(EN)

27 Jul 2022

This is a note mainly about the paper in 2011：Asymptotic analysis of SBM. And also other paper corresponding with this topic: Cristo Moore,

The Detectability Limitation of Community

26 Jul 2022

博士的研究课题是关于网络节点属性可预测性的极限：即在知道了网络的结构后，网络节点属性预测的准确率理论上限能有多高。一个类似的问题是网络社团检测的可检测性，当网络满足某些条件时，网络社团在理论上就是不可检测的。存在一个detectability-undetectability的相变。而且还存在一个easy-hard的相变，即是否存在多项式时间的算法解决社团检测问题。2011年的这篇论文：Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications.比较系统的分析了这一问题，该文涉及到的一些概念Belief Propagation, Bethe free energy, Phase transition比较难以理解。在此做一笔记，作本人对该问题的个人注解，思路梳理。