Abstract
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 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.
Highlights
Every second cell in our body is a microbial cell
In order to estimate whether the resulting embedding maintains the dynamics of the time-evolving graph, we will compare the metastable states, which we obtained by clustering the two dominant eigenfunctions, with the initial time periods of diarrhea and recovery
Most studies aiming at understanding these dynamics are primarily focused on statistical constitution analysis omitting more complex interactions that can be described as a time-evolving graph
Summary
Every second cell in our body is a microbial cell. We are colonized by a diverse community of bacteria, archaea, and viruses, jointly referred to as the microbiome. About 1.5 kg of microbes live almost everywhere on and in the human body as symbionts, e.g., on the skin, in the mouth, or in the gut. They have a strong influence on both their hosts and environments. The microbiome data, which we will analyze comes from a study about recovery from Vibrio cholerae infection (Hsiao et al 2014). The time-evolving graph from the given OTU table is constructed in the same way as for the MovingPic dataset using the relative abundance vector and Pearson correlation coefficients. The question how to properly construct time-evolving graphs such that both metastable behavior and associations between microbes are taken into consideration need to be considered in future work
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