  Detecting early warning indicators for abrupt dynamical transitions in
complex systems or high-dimensional observation data is essential in many
real-world applications, such as brain diseases, natural disasters, and
engineering reliability. To this end, we develop a novel approach: the directed
anisotropic diffusion map that captures the latent evolutionary dynamics in the
low-dimensional manifold. Then three effective warning signals (Onsager-Machlup
Indicator, Sample Entropy Indicator, and Transition Probability Indicator) are
derived through the latent coordinates and the latent stochastic dynamical
systems. To validate our framework, we apply this methodology to authentic
electroencephalogram (EEG) data. We find that our early warning indicators are
capable of detecting the tipping point during state transition. This framework
not only bridges the latent dynamics with real-world data but also shows the
potential ability for automatic labeling on complex high-dimensional time
series.
