Related papers: Discovering Heterogeneous Subsequences for Traject…

Trajectory similarity computation is an essential technique for analyzing moving patterns of spatial data across various applications such as traffic management, wildlife tracking, and location-based services. Modern methods often apply…

We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…

High energy physics experiments, in particular experiments at the LHC, require the reconstruction of charged particle trajectories. Methods of reconstructing such trajectories have been known for decades, yet the applications at High…

We propose a data-driven optimization-based pre-compensation method to improve the contour tracking performance of precision motion stages by modifying the reference trajectory and without modifying any built-in low-level controllers. The…

The abundance of vehicle trajectory data offers a new opportunity to compute driving routes between origins and destinations. Current graph-based routing pipelines, while effective, involve substantial costs in constructing, maintaining,…

Heterogeneous but complementary sources of data provide an unprecedented opportunity for developing accurate statistical models of systems. Although the existing methods have shown promising results, they are mostly applicable to situations…

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…

In this paper we present a new classification model in machine learning. Our result is threefold: 1) The model produces comparable predictive accuracy to that of most common classification models. 2) It runs significantly faster than most…

We propose a new first-order method for minimizing nonconvex functions with a Lipschitz continuous gradient and Hessian. The proposed method is an accelerated gradient descent with two restart mechanisms and finds a solution where the…

In this paper we develop a Bayesian optimization based hyperparameter tuning framework inspired by statistical learning theory for classifiers. We utilize two key facts from PAC learning theory; the generalization bound will be higher for a…

We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…

Accurate trajectory prediction has long been a major challenge for autonomous driving (AD). Traditional data-driven models predominantly rely on statistical correlations, often overlooking the causal relationships that govern traffic…

Trajectory clustering enables the discovery of common patterns in trajectory data. Current methods of trajectory clustering rely on a distance measure between two points in order to measure the dissimilarity between two trajectories. The…

Getting tools that allow simple representations and comparisons of a set of categorical trajectories is of major interest for statisticians. Without loosing any information, we associate to each state a binary random indicator function,…

A major challenge in designing neural network (NN) systems is to determine the best structure and parameters for the network given the data for the machine learning problem at hand. Examples of parameters are the number of layers and nodes,…

A key overall goal of biomolecular simulations is the characterization of "mechanism" -- the pathways through configuration space of processes such as conformational transitions and binding. Some amount of heterogeneity is intrinsic to the…

We study the problem of planning collision-free paths for a group of homogeneous robots. We propose a novel approach for turning the paths that were planned egocentrically by the robots, e.g. without taking other robots' moves into account,…

Self-driving vehicles rely on sensory input to monitor their surroundings and continuously adapt to the most likely future road course. Predictive trajectory planning is based on snapshots of the (uncertain) road course as a key input.…