Cluster statistics and quasisoliton dynamics in microscopic optimal-velocity models.

Using the non-linear optimal velocity models as an example, we show that there exists an emergent intrinsic scale that characterizes the interaction strength between multiple clusters appearing in the solutions of such models. The interaction characterizes the dynamics of the localized quasisoliton structures given by the time derivative of the headways, and the intrinsic scale is analogous to the "charge" of the quasisolitons, leading to non-trivial cluster statistics from the random perturbations to the initial steady states of uniform headways. The cluster statistics depend both on the quasisoliton charge and the density of the traffic.

A parsimonious mixture of Gaussian trees model for oversampling in imbalanced and multimodal time-series classification.

We propose a novel framework of using a parsimonious statistical model, known as mixture of Gaussian trees, for modeling the possibly multimodal minority class to solve the problem of imbalanced time-series classification. By exploiting the fact that close-by time points are highly correlated due to smoothness of the time-series, our model significantly reduces the number of covariance parameters to be estimated from O(d(2)) to O(Ld), where L is the number of mixture components and d is the dimensionality. Thus, our model is particularly effective for modeling high-dimensional time-series with limited number of instances in the minority positive class.