運用高維度連結修正隨機區段模型探索網路中的社群結構

Abstract

考慮一組資料中，我們可以用某種測度去測量每筆資料彼此之間的關係，如此我們就可以把資料轉換成網路的型態。近年來，這種類型的資料開始受到重視：例如蛋白質交互作用網路，或在社交網路的研究上。為了研究這些複雜網路型態的資料，我們必須有一個模型來發掘這些複雜網路的結構。在這篇論文中，我們介紹了一個機率模型──stochastic blockmodel的改良，這個模型在宏觀上可以表現出複雜網路的結構，精細來看也可以反映出各點在網路中的特性。

If the pairwise relationship can be measured, then all data points can be linked or unlinked to each other determined by that pairwise relation. The network structure can be constructed accordingly. The investigation of this kind of network data becomes crucial in understanding the interrelationship that is hidden in the data. Protein–protein interaction networks and large scale social networks are typical examples of this type of data where interrelationships in the data can be hidden and indirect. Consequently, we need flexible models to explain the structure of complex networks. In this study, we introduce a probability model that integrates the important properties of the standard stochastic blockmodel and degree-corrected stochastic blockmodel in literature to form the high dimensional degree corrected stochastic blockmodel. Thus, this model can represent the global structure of networks and reflect the local properties of vertices. Empirical studies are conducted to evaluate the performance of the proposed model for real data.