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Description:
More and more diseases have been found to be strongly correlated with disturbances in the microbiome constitution, e.g., obesity, diabetes, and even some types of cancer. Advances in high-throughput omics technologies have made it possible to directly analyze the human microbiome and its impact on human health and physiology. Microbial composition is usually observed over long periods of time and the interactions between their members are explored. Numerous studies have used microbiome data to accurately differentiate disease states and understand the differences in microbiome profiles between healthy and ill individuals. However, most of them mainly focus on various statistical approaches, omitting microbe-microbe interactions among a large number of microbiome species that, in principle, drive microbiome dynamics. Constructing and analyzing time-evolving graphs is needed to understand how microbial ecosystems respond to a range of distinct perturbations, such as antibiotic exposure, diseases, or other general dynamic properties. This becomes especially challenging due to dozens of complex interactions among microbes and metastable dynamics. The key to addressing this challenge lies in representing time-evolving graphs constructed from microbiome data as fixed-length, low-dimensional feature vectors that preserve the original dynamics. Therefore, we propose two unsupervised approaches that map the time-evolving graph constructed from microbiome data into a low-dimensional space where the initial dynamic, such as the number of metastable states and their locations, is preserved. The first method relies on the spectral analysis of transfer operators, such as the Perron--Frobenius or Koopman operator, and graph kernels. These components enable us to extract topological information such as complex interactions of species from the time-evolving graph and take into account the dynamic changes in the human microbiome composition. Further, we study how deep learning techniques can contribute to the study of a complex ...