  Reconstructing interactions from observational data is a critical need for
investigating natural biological networks, wherein network dimensionality (i.e.
number of interacting components) is usually high and interactions are
time-varying. These pose a challenge to existing methods that can quantify only
small interaction networks or assume static interactions under steady state.
Here, we proposed a novel approach to reconstruct high-dimensional,
time-varying interaction networks using empirical time series. This method,
named "multiview distance regularized S-map", generalized the state space
reconstruction to accommodate high dimensionality and overcome difficulties in
quantifying massive interactions with limited data. When we evaluated this
method using the time series generated from a large theoretical model involving
hundreds of interacting species, estimated interaction strengths were in good
agreement with theoretical expectations. As a result, reconstructed networks
preserved important topological properties, such as centrality, strength
distribution and derived stability measures. Moreover, our method effectively
forecasted the dynamic behavior of network nodes. Applying this method to a
natural bacterial community helped identify keystone species from the
interaction network and revealed the mechanisms governing the dynamical
stability of bacterial community. Our method overcame the challenge of high
dimensionality and disentangled complex time-varying interactions in large
natural dynamical systems.
