Paper analyzes EM algorithm's trajectory in 2MLR, revealing cycloid behavior.
problem Understanding the convergence and trajectory of EM algorithm in 2MLR.
method Explicit closed-form expressions for EM updates, recurrence relation derivation at population level.
result EM iterations lie on a cycloid trajectory, leading to theoretical estimate of convergence exponent.
Analyzes Gerstner's trochoidal waves and their geometric properties.
problem Understanding the geometry and kinematics of trochoidal waves.
method Derives velocity and arc length conditions for cycloidal, curtate, and prolate trochoids using Galilean transformations.
result Conditions for arc lengths of prolate and curtate trochoids to coincide over a wave cycle.
Cycloids, hipocycloids and epicycloids have an often forgotten common property: they are homothetic to their evolutes. But what if use convex symmetric polygons as unit balls, can we define evolutes and cycloids which are genuinely discrete? Indeed, we can! We define discrete cycloids as eigenvectors of a discrete doub…
The study explores isoptic curves of cycloids and their applications.
problem Understanding isoptic curves of cycloids.
method Definition of isoptic curve, parametric equations, and support function.
result Determination of isoptic curves for hypocycloids and epicycloids.
Given a normed plane P, we call P-cycloids the planar curves which are homothetic to their double P-evolutes. It turns out that the radius of curvature and the support function of a P-cycloid satisfy a differential equation of Sturm-Liouville type. By studying this equati…
Study of timelike surfaces with time-minimizing rulings in Newtonian and relativistic spacetimes.
problem Understanding time-minimizing paths in spacetime geometries.
method Constructing timelike surfaces ruled by geodesics of Finsler or Jacobi metrics.
result Explicit examples of brachistochrone-ruled timelike surfaces in Minkowski and Schwarzschild spacetimes.
We study the problem of discriminative sub-trajectory mining. Given two groups of trajectories, the goal of this problem is to extract moving patterns in the form of sub-trajectories which are more similar to sub-trajectories of one group and less similar to those of the other. We propose a new method called Statistica…
Paper uses deep imitation learning to predict aircraft trajectories accurately.
problem Inefficient and costly Air Traffic Management system limits predictability.
method Generative Adversarial Imitation Learning framework with trajectory clustering and classification.
result Accurate predictions for entire trajectory stages, pre- and tactical.
Paper infers human mobility from sparse trajectories.
problem Modeling and inferring human mobility from sparse trajectory data.
method Proposes a single trajectory inference algorithm and a deep learning architecture for multiple trajectories.
result Deep learning model achieves 2x overall accuracy improvement on sparse trajectories.
Pattern ensembling fills in missing or inaccurate trajectory data.
problem Incompleteness, missing information, and inaccuracies in geolocation data.
method Probabilistically ensemble similar trajectory patterns from the vicinity.
result Reconstructs missing or unreliable trajectory segments effectively.
Study shows magnetic trajectories in Berger spheres are homogeneous.
problem Homogeneity of contact magnetic trajectories in Berger spheres.
method Proved every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow.
result Contact magnetic trajectories in Berger spheres are homogeneous.
Improved trajectory prediction for team sports using sparse outputs.
problem Challenging to train deep learning models for player trajectory prediction.
method Sparse trajectory prediction and constant acceleration interpolation.
result Interpolation improves performance for all tested models.
WS-II algorithm segments trajectories with high accuracy.
problem Trajectory segmentation for diverse data sources.
method Supervised learning with sliding window analysis.
result WS-II outperforms other methods in all datasets.
A framework clusters vehicle motion trajectories efficiently.
problem Costly manual annotation of vehicle motion data.
method Five-stage framework: align, embed, extract, embed, cluster.
result Framework achieves promising results on real-world dataset.
Proposes a CNN-based method for better trajectory owner prediction.
problem Improves trajectory owner prediction for better personalized recommendations and urban planning.
method Connects POIs in a graph, encodes POIs into vectors, transforms trajectories into matrices, and uses a CNN to detect features and predict owners.
result Significantly outperforms existing methods in various metrics.
In this paper we propose a new parameter-free method for trajectory classification which finds the best trajectory partition and dimension combination for robust trajectory classification. Preliminary experiments show that our approach is very promising.
Generative model learns vehicle trajectory distributions for better data generalization.
problem Data sparsity and privacy issues in urban vehicle trajectory analysis.
method Generative adversarial imitation learning framework for urban vehicle trajectory generation.
result TrajGAIL model produces synthetic trajectories similar to real ones, achieving significant performance gains.
Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. In such problems, the way we choose to represent a trajectory underlies algorithms for trajectory prediction and optimization. Interestingly, most all prior work in imitation and reinforcemen…
Method detects trajectory outliers using Hodge Laplacian embeddings.
problem Detecting outliers in trajectory data on simplicial complexes.
method Flow-embeddings using Hodge 1-Laplacian of simplicial complexes.
result Classifies trajectories based on topological behavior.
Study on billiard trajectories with fixed bounces.
problem Counting periodic trajectories with specific bounces.
method Analyzes two-dimensional dispersive billiard systems.
result Asymptotic growth of primitive periodic trajectories.
Representation learning of pedestrian trajectories transforms variable-length timestamp-coordinate tuples of a trajectory into a fixed-length vector representation that summarizes spatiotemporal characteristics. It is a crucial technique to connect feature-based data mining with trajectory data. Trajectory representati…
Method predicts NBA players' multi-modal movement trajectories.
problem Understanding NBA players' decision-making during games.
method LSTM-based architecture with multi-modal loss function.
result Method outperforms state-of-the-art in predicting realistic trajectories.
We address the problem of abnormal event detection from trajectory data. In this paper, a new adversarial approach is proposed for building a deep neural network binary classifier, trained in an unsupervised fashion, that can distinguish normal from abnormal trajectory-based events without the need for setting manual d…
Physics-informed diffusion model detects anomalous trajectories in GPS data.
problem Detecting fake GPS trajectories in international waters.
method Physics-informed diffusion model integrating kinematic constraints.
result Higher prediction accuracy and lower error rate for anomaly detection.
Develops MENT for interpreting and detecting changes in network trajectories.
problem Distortion of network geometry and invalidation of temporal comparisons in dynamic network analysis.
method Develops Multiscale Euclidean Network Trajectories (MENT) framework based on second-moment geometry.
result Validates and interprets network trajectories through isotropic normalization and orthogonal transformations.
Gaussian processes model geospatial trajectories with uncertainty.
problem Interpolating and predicting complex spatiotemporal data.
method Gaussian process models trajectories as multidimensional Gaussian distributions.
result Gaussian processes provide a flexible and probabilistic way to interpolate geospatial data.
The paper defines and analyzes conformal trajectories in 3D space forms.
problem Understanding trajectories in curved 3D spaces.
method Defined conformal trajectories and studied their properties in R3, S3, and H3. result Conformal trajectories in S3 and H3 have constant curvature and torsion. We present CoverNet, a new method for multimodal, probabilistic trajectory prediction for urban driving. Previous work has employed a variety of methods, including multimodal regression, occupancy maps, and 1-step stochastic policies. We instead frame the trajectory prediction problem as classification over a diverse s…
TRAKNN detects rare atmospheric trajectories efficiently.
problem Detecting rare atmospheric anomalies over long periods.
method Unsupervised, recurrence-based kNN algorithm.
result Rare trajectories correspond to physical anomalies.
Algorithm learns mixtures of Markov chains and MDPs from short trajectories.
problem Learning mixtures of Markov chains and MDPs from short unlabeled trajectories.
method Subspace estimation, spectral clustering, EM algorithm, model estimation, classification.
result 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming EM algorithm with random initialization.
DETECT clusters mobility behaviors from trajectories using deep learning.
problem Clustering similar mobility behaviors in large, complex trajectory data.
method DETECT uses deep learning to cluster mobility behaviors from trajectories, transforming and summarizing them to identify similar behaviors.
result DETECT effectively clusters mobility behaviors from real-world datasets.
Homogeneous magnetic trajectories in a special linear group proven.
problem Proving homogeneity of magnetic trajectories in a specific group.
method Using contact magnetic curves and geodesics.
result Every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow.
The study finds billiard trajectories with infinitely many reflections in certain cones.
problem Existence of billiard trajectories with infinitely many reflections.
method Analysis of C3 convex cones and elliptic cones in R3. result Existence of C2 convex cones with billiard trajectories having infinitely many reflections. Paper proposes a method for optimizing local policies for trajectory-centric reinforcement learning.
problem Challenges in global policy optimization for non-linear systems and poor performance of open-loop trajectory optimization.
method Formulates trajectory optimization and local policy synthesis as a single optimization problem and solves it as a nonlinear programming instance.
result Demonstrates improved performance of the proposed technique under simplifying assumptions.
We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.
Study of closed trajectories in hyperbolic plane with specific curvature constraints.
problem Critical trajectories in hyperbolic plane for a specific energy function.
method Classification of critical trajectories based on momentum causal character, proof of existence of closed trajectories.
result Existence of countably many closed trajectories with time-like momentum.
Study magnetic trajectories on 2-step nilpotent Lie groups.
problem Understanding magnetic trajectories on specific Lie groups.
method Formulated magnetic equation, found solutions for invariant Lorentz forces, computed examples in Heisenberg groups.
result Interesting magnetic trajectories involving elliptic integrals found in Heisenberg groups.
A new neural network captures and explains trajectory patterns.
problem Analyzing complex spatial trajectories in urban planning and neuroscience.
method Composite Signal Neural Networks (CompSNN) combining three interpretable ANN modules.
result CompSNN outperforms individual modules and visualizes useful signal parts.
We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.
problem Analyzing and comparing trajectories on Riemannian manifolds.
method Riemannian hierarchical model, Bézier splines, Sasaki metric.
result Spline-based approaches outperform state-of-the-art methods in intensity classification of trajectories.
In this paper, we propose a reinforcement learning-based algorithm for trajectory optimization for constrained dynamical systems. This problem is motivated by the fact that for most robotic systems, the dynamics may not always be known. Generating smooth, dynamically feasible trajectories could be difficult for such sy…
Study on Heisenberg group's Lorentzian problems using Pontryagin's principle.
problem Lorentzian problems on the Heisenberg group.
method Applied Pontryagin's maximum principle to obtain extremal trajectories.
result Parameterization of abnormal and normal extremal trajectories, investigation of reachability sets and existence of optimal trajectories.
End-to-end model predicts multiagent trajectories using game theory and neural nets.
problem Predicting trajectories of interacting agents in complex scenarios.
method Hybrid neural net with game-theoretic reasoning, using implicit layers to map preferences to Nash equilibria.
result Trains an interpretable model that predicts future trajectories and transfers to decision making.
Improved Gaussian Process model for predicting trajectories without independence assumption errors.
problem Incorrect independence assumption in previous work on Gaussian Process uncertainty propagation.
method Proposed a novel piecewise linear approximation to correct the independence assumption in continuous models.
result Corrected the independence assumption in Gaussian Process models for predicting trajectories.
Deep Reinforcement Learning has shown tremendous success in solving several games and tasks in robotics. However, unlike humans, it generally requires a lot of training instances. Trajectories imitating to solve the task at hand can help to increase sample-efficiency of deep RL methods. In this paper, we present a simp…
Critical trajectories in a sphere are found for a specific bending functional.
problem Finding closed trajectories in a sphere for a specific bending functional.
method Existence of infinitely many closed trajectories shown for a given Lagrange multiplier.
result Existence of closed trajectories dependent on a pair of relatively prime natural numbers.
We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph clustering to regroup trajectories with similar profiles. Our experimental stud…
The paper provides uniform length estimates for trajectories on flat cone surfaces.
problem Estimating the length of trajectories on flat cone surfaces.
method Using self-intersection numbers and constants depending only on the flat metric, the paper focuses on convex flat cone spheres with a positive curvature gap and a fixed number of singularities.
result Uniform two-sided estimates for trajectory lengths on convex flat cone spheres are obtained.
Visual observations of dynamic phenomena, such as human actions, are often represented as sequences of smoothly-varying features . In cases where the feature spaces can be structured as Riemannian manifolds, the corresponding representations become trajectories on manifolds. Analysis of these trajectories is challengin…