Community Detection for Correlation Matrices
Community Detection for Correlation Matrices
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DOI：
10.1103/physrevx.5.021006
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发表时间：
2015-04-14
影响因子：
12.5
通讯作者：
Garlaschelli, Diego
中科院分区：
文献类型：
--
作者：
MacMahon, Mel;Garlaschelli, Diego
在复杂系统的研究中，一个具有挑战性的问题是如何在没有先验信息的情况下，解决由单元群决定的突现的、介观的组织，这些单元群的动态活动在内部的相关性比与系统其余部分的相关性更强。现有的过滤相关性的技术并没有明确地面向识别这样的模块，并且可能遭受不可避免的信息丢失。一个有希望的替代方案是使用网络理论中开发的社区检测技术。不幸的是，这种方法主要集中在用相关矩阵替换网络数据上，我们发现，由于与现有算法的零假设不一致，这种方法在本质上是有偏见的。在这里，我们通过基于随机矩阵理论的零模型的一致重新定义，介绍了最流行的社区检测技术的适当的基于相关性的对等体。我们的方法可以过滤掉特定于单元的噪声和系统范围的依赖，并且得到的社区是内部相关的和相互反相关的。我们还实现了多分辨率和多频率方法，揭示了具有“硬”内核和“软”外围的分层嵌套子社区。我们将我们的技术应用于几个金融时间序列，并确定不可简化为标准行业分类的中观股票组；检测在社区之间交替的“软股票”；并讨论投资组合优化和风险管理的含义。
A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that we show to be intrinsically biased because of its inconsistency with the null hypotheses underlying the existing algorithms. Here, we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anticorrelated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested subcommunities with "hard" cores and "soft" peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy; detect "soft stocks" that alternate between communities; and discuss implications for portfolio optimization and risk management.