arXiv research

Study uses trajectory embedding to measure place function similarity at fine spatial granularity.

We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.

DETECT clusters mobility behaviors from trajectories using deep learning.

Gaussian processes model geospatial trajectories with uncertainty.

Foot-mounted inertial positioning (FMIP) can face problems of inertial drifts and unknown initial states in real applications, which renders the estimated trajectories inaccurate and not obtained in a well defined coordinate system for matching trajectories of different users. In this paper, an approach adopting receiv…

Dynamic time warping (DTW) can be used to compute the similarity between two sequences of generally differing length. We propose a modification to DTW that performs individual and independent pairwise alignment of feature trajectories. The modified technique, termed feature trajectory dynamic time warping (FTDTW), is a…

Trajectory segmentation is the process of subdividing a trajectory into parts either by grouping points similar with respect to some measure of interest, or by minimizing a global objective function. Here we present a novel online algorithm for segmentation and summary, based on point density along the trajectory, and …

Novel framework predicts brain biomarker trajectories with superior performance.

We apply variational inference to learn vehicle trajectory parameters from noisy data.

Paper proposes a new descriptor for early trajectory characterization in matrix iterations.

We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated set of measures of expressivity, unified by the novel notion of trajectory length…

This paper considers the growth in the length of one-dimensional trajectories as they are passed through deep ReLU neural networks, which, among other things, is one measure of the expressivity of deep networks. We generalise existing results, providing an alternative, simpler method for lower bounding expected traject…

Robot motions in the presence of humans should not only be feasible and safe, but also conform to human preferences. This, however, requires user feedback on the robot's behavior. In this work, we propose a novel approach to leverage the user's brain signals as a feedback modality in order to decode the judgment of rob…

Transportation agencies have an opportunity to leverage increasingly-available trajectory datasets to improve their analyses and decision-making processes. However, this data is typically purchased from vendors, which means agencies must understand its potential benefits beforehand in order to properly assess its value…

Develops a method to infer cell trajectories from RNA sequencing data.

We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…

We introduce a mixed-effects model to learn spatiotempo-ral patterns on a network by considering longitudinal measures distributed on a fixed graph. The data come from repeated observations of subjects at different time points which take the form of measurement maps distributed on a graph such as an image or a mesh. Th…

MoNODEs improve neural ODEs by separating dynamic states from static factors.

More than two thirds of mental health problems have their onset during childhood or adolescence. Identifying children at risk for mental illness later in life and predicting the type of illness is not easy. We set out to develop a platform to define subtypes of childhood social-emotional development using longitudinal,…

Paper resolves the debate on process vs. outcome supervision in reinforcement learning.

New algorithm infers trajectories from partial observations using optimal transport.

Active learning selects optimal measurement times for inferring continuous paths from sparse data.

New method models unknown systems with hidden parameters using neural networks.

Measuring similarities between unlabeled time series trajectories is an important problem in domains as diverse as medicine, astronomy, finance, and computer vision. It is often unclear what is the appropriate metric to use because of the complex nature of noise in the trajectories (e.g. different sampling rates or out…

Models for predicting aircraft motion are an important component of modern aeronautical systems. These models help aircraft plan collision avoidance maneuvers and help conduct offline performance and safety analyses. In this article, we develop a method for learning a probabilistic generative model of aircraft motion i…

This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $τ(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a measurable set $E_1$ with positive Lebesgue measure, such that $r(0)\in E_1$ implies t…

Real-time traffic volume inference is key to an intelligent city. It is a challenging task because accurate traffic volumes on the roads can only be measured at certain locations where sensors are installed. Moreover, the traffic evolves over time due to the influences of weather, events, holidays, etc. Existing soluti…

This work tackles uncertainty in multi-agent multi-modal trajectory forecasting.

A new method infers neural trajectories in real-time, improving experimental design.

A method for inferring motility models and heterogeneity from particle trajectories.

This paper evaluates fractal dimension and persistent homology for neural network generalization.

The study characterizes infinite Riemann surfaces and their foliations using quadratic differentials.

Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the collective motion of an ensemble of system trajectories taking into account how traj…

We present a generative approach to classify scarcely observed longitudinal patient trajectories. The available time series are represented as tensors and factorized using generative deep recurrent neural networks. The learned factors represent the patient data in a compact way and can then be used in a downstream clas…

Unsupervised exploration and representation learning become increasingly important when learning in diverse and sparse environments. The information-theoretic principle of empowerment formalizes an unsupervised exploration objective through an agent trying to maximize its influence on the future states of its environme…

We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of a path dependent European option has the same value as the purely probabi…

In this paper we study the typical speed of a generic earthquake trajectory leaving compact sets in the moduli space of the once-punctured torus. Mirzakhani showed that the earthquake flow is measurably equivalent to the horocyclic flow, which has been studied extensively. Our main result shows that the earthquake flow…

New method improves learning from multiple correlated data trajectories.

A new clustering algorithm for functional data using binary trees.

Estimating the effect of a treatment on a given outcome, conditioned on a vector of covariates, is central in many applications. However, learning the impact of a treatment on a continuous temporal response, when the covariates suffer extensively from measurement error and even the timing of the treatments is uncertain…

Unified framework for multi-view diffusion geometries using intertwined diffusion trajectories.

New protocol evaluates synthetic data for temporal consistency.

Scenario-based testing for the safety validation of highly automated vehicles is a promising approach that is being examined in research and industry. This approach heavily relies on data from real-world scenarios to derive the necessary scenario information for testing. Measurement data should be collected at a reason…

Developed a random walk analog of geodesic flow on hyperbolic groups.

In this paper, we present a new location fingerprinting database comprised of Wi-Fi received signal strength (RSS) and geomagnetic field intensity measured with multiple devices at a multi-floor building in Xi'an Jiatong-Liverpool University, Suzhou, China. We also provide preliminary results of localization and trajec…

This work extends entropic optimal transport to non-product reference couplings, focusing on Gaussian cases.

Here we present DIVE: Data-driven Inference of Vertexwise Evolution. DIVE is an image-based disease progression model with single-vertex resolution, designed to reconstruct long-term patterns of brain pathology from short-term longitudinal data sets. DIVE clusters vertex-wise biomarker measurements on the cortical surf…

This study models target trajectories using stochastic processes for efficient tracking.