網絡資料的因子模型

Abstract

在科學、工程等眾多重要科學領域都會使用網絡去呈現數據之間的關係。在過去，有眾多的網絡模型被提出去探索網絡資料群集的結構，並對數據資料做分群。此外，還有一些較特殊的結構，像是"Star"和"Bipartite"也是讓科學家感興趣的結構。在本篇論文中，我們提出了一個因子模型來分析網絡資料。在因子模型中，因子代表著是兩個資料點的連結管道，並藉由這兩個資料點的特徵去決定會不會連結。不同的連結函數會建構不同的網絡結構，包含:群集、Star、Bipartite。因此因子模型可以給出合理的理由去解釋為何會產生這些結構。MCM演算法可用於模型的推理。一些模擬和真實資料分析顯示出了模型的有效性。

Network data emerge in science, engineering and many important fields. Numerous network models have been proposed to explore network structure and find node clusters. In addition, link pattern modules such as stars have attracted intensive attention. In this paper, we propose a factor model for analyzing network data. In network, a factor refers a channel for the connection between pairs of nodes to be built based on specific node feature. The edge rate for a pair of nodes can be obtained through a bivariate link function. Different link function yields different types of modules including communities, stars and other patterns. Thus the factor graph model also provides some insight into the rationale of link pattern modules. MCMC procedures can be used for the inference of the model. Some empirical analysis also shows the effectiveness of the model.