模块化最大化在实际环境中的表现
The performance of modularity maximization in practical contexts
摘要：
虽然在实践中被广泛使用，但被称为模块化最大化的流行模块识别技术的行为和准确性在实际环境中并没有得到很好的理解。在这里，我们提出了一个广泛的特点，其性能在这种情况下。首先，我们重新审视并澄清模块化最大化的分辨率极限现象。其次，我们表明，模块度函数Q表现出极端退化：它通常承认指数数量的不同的高分解决方案，通常缺乏一个明确的全球最大值。第三，我们导出了一个无限模块化网络模型的最大模块度Q_max的极限行为，表明它强烈地依赖于网络的大小和它所包含的模块数。最后，使用三个真实世界的代谢网络作为例子，我们表明，退化的解决方案可以从根本上不同意许多，但不是所有的分区属性，如组成的最大模块和模块大小的分布。这些结果意味着，任何模块化最大化程序的输出应谨慎地解释在科学背景下。他们还解释了为什么许多进化论在实践中经常成功地找到高分分区，以及为什么不同的进化论在同一网络的模块化结构上可能存在分歧。最后，我们讨论了减轻这些行为的途径，例如结合来自许多退化解决方案的信息或使用生成模型。
英文摘要：
Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Q_max for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.
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