Effects of embedded distance measurements interacting with modeling approaches on empirical dynamical model predictions

Empirical Dynamic Modeling (EDM) has been a powerful tool for complex ecosystem prediction by providing an equation-free modelling framework. Theoretically, it allows future ecosystem behavior to be predicted by connecting current state to the similar, adjacent and future state on the attractor manifold which is reconstructed by single or multiple time series observed from natural systems. However, the Euclidean distance metric used in these algorithms could bias the true distance on the attractor manifold and consequently decrease the prediction performance. This could become worse if the dimension of the ecosystem is much higher and the system behavior is much complicated so that the reconstructed attractor manifold is more intricate. Therefore, manifold distance metric for both Simplex Projection and S-map was proposed. Our results clearly showed that the prediction accuracy of EDM had a general improvement after manifold distance metric was adopted. Experiments conducted on both synthetic and empirical data proved this advancement. Interestingly, these improvements were unequal for different implementations and the number of variables for embedding. Analysis demonstrated that Smap under multivariate embedding achieved the best prediction performance when manifold distance metric was applied. This suggested that the proposed manifold distance metric can work particularly well for predicting high dimensional ecosystem with complex behaviors. The main contribution of this research is that a new ecological indicator has been developed to more accurately estimate the similarity between ecological states in a reconstructed manifold and therefore provide higher prediction accuracy for EDM framework.