双模关联网络中噪声与信号分离的最大熵方法
A maximum entropy approach to separating noise from signal in bimodal affiliation networks
摘要：
在实践中，许多经验网络，包括合著和搭配网络，是二分数据结构的单峰投影，其中一层表示实体，第二层由表示从属关系、属性、组等的多个集合组成，而层间链路指示集合中实体的成员资格。单峰投影中的边权重，我们称之为共生网络，计算两个端点都链接到的集合的数量。解释这种密集的网络需要考虑到基础数据的二分结构的统计分析。在这里，我们开发了一个基于最大熵空模型的统计显著性度量，该模型既保留了个体/实体的频率序列，又保留了集合的大小序列。求解最大熵问题被简化为求解存在快速算法的非线性方程组，从而消除了对昂贵的蒙特卡洛采样技术的需要。我们使用这个指标来修剪和可视化一些经验网络。
英文摘要：
In practice, many empirical networks, including co-authorship and collocation networks are unimodal projections of a bipartite data structure where one layer represents entities, the second layer consists of a number of sets representing affiliations, attributes, groups, etc., and an inter-layer link indicates membership of an entity in a set. The edge weight in the unimodal projection, which we refer to as a co-occurrence network, counts the number of sets to which both end-nodes are linked. Interpreting such dense networks requires statistical analysis that takes into account the bipartite structure of the underlying data. Here we develop a statistical significance metric for such networks based on a maximum entropy null model which preserves both the frequency sequence of the individuals/entities and the size sequence of the sets. Solving the maximum entropy problem is reduced to solving a system of nonlinear equations for which fast algorithms exist, thus eliminating the need for expensive Monte-Carlo sampling techniques. We use this metric to prune and visualize a number of empirical networks.
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