More and more diseases have been found to be strongly correlated with disturbances in the microbiome constitution, e.g., obesity, diabetes, or some cancer types. Thanks to modern high-throughput omics technologies, it becomes possible to directly analyze human microbiome and its influence on the health status. Microbial communities are monitored over long periods of time and the associations between their members are explored. These relationships can be described by a time-evolving graph. In order to understand responses of the microbial community members to a distinct range of perturbations such as antibiotics exposure or diseases and general dynamical properties, the time-evolving graph of the human microbial communities has to be analyzed. This becomes especially challenging due to dozens of complex interactions among microbes and metastable dynamics. The key to solving this problem is the representation of the time-evolving graphs as fixed-length feature vectors preserving the original dynamics. We propose a method for learning the embedding of the time-evolving graph that is based on the spectral analysis of transfer operators and graph kernels. We demonstrate that our method can capture temporary changes in the time-evolving graph on both created synthetic data and real-world data. Our experiments demonstrate the efficacy of the method. Furthermore, we show that our method can be applied to human microbiome data to study dynamic processes.

翻译：越来越多的疾病被发现与微生物结构的干扰密切相关,例如肥胖、糖尿病或某些癌症类型。由于现代高通量肿瘤技术,有可能直接分析人类微生物及其对健康状况的影响。对微生物社区进行长期监测,并探索其成员之间的关联。这些关系可以用一个时间变化的图解来描述。为了了解微生物社区成员对诸如抗生素接触或疾病和一般动态特性等不同范围的扰动性变化的反应,必须分析人类微生物社区的时间变化图。由于微生物和元数据动态之间的数十种复杂互动关系,这变得特别具有挑战性。解决这一问题的关键是将时间变化的图表作为固定的特性矢量进行表述,以保存原始动态。我们提出了一个方法来学习时间变化图的嵌入,该方法基于对转移操作者或疾病以及一般动态特性的光谱分析。我们证明,我们的方法可以将时间变化的人类微生物群落图用于实时的实验,从而显示我们所创造的人类数据在时间变化方法上的变化。我们用的方法可以用来测量我们所创造的模型的模型。