Data Mechanics and Coupling Geometry on Binary Bipartite Networks
Data Mechanics and Coupling Geometry on Binary Bipartite Networks
复制标题
DOI：
10.1371/journal.pone.0106154
复制
发表时间：
2014-08-29
期刊：
影响因子：
3.7
通讯作者：
Chen, Chen
中科院分区：
文献类型：
--
作者：
Fushing, Hsieh;Chen, Chen
在二元二部网络的框架下，我们量化了模式的概念，形式化了模式发现的过程。特别关注的模式是在其行轴和列轴上集群之间相互关联的全局相互作用。一个二元二部网络被建立在一个热力学系统中，包含了所有上下自旋构型，这些构型由行和列上的乘积排列定义。该系统在Ising模型电位下具有铁磁能量基态。这种基态，也称为宏观状态，被假定为以多尺度方式聚集嵌入在网络数据中的所有感兴趣的模式。一种用于间接搜索这种宏观状态的新的计算范式，称为数据力学，是通过在行和列空间上迭代地构建具有一对近最优边缘超度量的代理几何系统而设计的。最小化这两种边缘几何的Gromov-Wasserstein距离的耦合措施也被视为在宏观状态附近。由此产生的耦合几何揭示了多尺度块模式信息，这些信息表征了行轴和列轴上集群之间的多层相互作用关系。它是二元二部网络的非参数信息内容。这种耦合几何然后被证明揭示了新的光，并带来解决相互作用的问题，在群落生态学和基因内容为基础的系统发育。其隐含的全球推论预计在许多科学领域具有很高的潜力。
We quantify the notion of pattern and formalize the process of pattern discovery under the framework of binary bipartite networks. Patterns of particular focus are interrelated global interactions between clusters on its row and column axes. A binary bipartite network is built into a thermodynamic system embracing all up-and-down spin configurations defined by product-permutations on rows and columns. This system is equipped with its ferromagnetic energy ground state under Ising model potential. Such a ground state, also called a macrostate, is postulated to congregate all patterns of interest embedded within the network data in a multiscale fashion. A new computing paradigm for indirect searching for such a macrostate, called Data Mechanics, is devised by iteratively building a surrogate geometric system with a pair of nearly optimal marginal ultrametrics on row and column spaces. The coupling measure minimizing the Gromov-Wasserstein distance of these two marginal geometries is also seen to be in the vicinity of the macrostate. This resultant coupling geometry reveals multiscale block pattern information that characterizes multiple layers of interacting relationships between clusters on row and on column axes. It is the nonparametric information content of a binary bipartite network. This coupling geometry is then demonstrated to shed new light and bring resolution to interaction issues in community ecology and in gene-content-based phylogenetics. Its implied global inferences are expected to have high potential in many scientific areas.