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We consider functional outlier detection from a geometric perspective, specifically: for functional data sets drawn from a functional manifold which is defined by the data's modes of variation in amplitude and phase. Based on this manifold,…

Machine Learning · Statistics 2021-09-15 Moritz Herrmann , Fabian Scheipl

We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on $\gamma$-divergence. A novel feature of the…

Methodology · Statistics 2021-10-15 Shonosuke Sugasawa , Daisuke Murakami

Global Navigation Satellite Systems (GNSS) are integrated into many devices. However, civilian GNSS signals are usually not cryptographically protected. This makes attacks that forge signals relatively easy. Considering modern devices often…

Cryptography and Security · Computer Science 2025-05-13 Wenjie Liu , Panos Papadimitratos

Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS), are among the most important sensors for movement analysis. GPS is widely used to record the trajectories of vehicles, animals and human beings.…

Instrumentation and Detectors · Physics 2015-07-15 Peter Ranacher , Richard Brunauer , Wolfgang Trutschnig , Stefan Christiaan Van der Spek , Siegfried Reich

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…

Machine Learning · Statistics 2023-01-18 Thibault Séjourné , Gabriel Peyré , François-Xavier Vialard

Discovering human mobility patterns with geo-location data collected from smartphone users has been a hot research topic in recent years. In this paper, we attempt to discover daily mobile patterns based on GPS data. We view this problem…

Machine Learning · Computer Science 2020-07-02 Weizhu Qian , Fabrice Lauri , Franck Gechter

This article presents a method for estimating the dynamic driving states (position, velocity, acceleration and heading) from noisy measurement data. The proposed approach is effective with both complete and partial observations, producing…

Systems and Control · Electrical Eng. & Systems 2025-04-10 Jonas Torzewski

The analysis of GPS trajectories is a well-studied problem in Urban Computing and has been used to track people. Analyzing people mobility and identifying the transportation mode used by them is essential for cities that want to reduce…

Machine Learning · Computer Science 2020-07-20 I. Cardoso-Pereira , J. B. Borges , P. H. Barros , A. F. Loureiro , O. A. Rosso , H. S. Ramos

Impulsed noise outliers are data points that differs significantly from other observations.They are generally removed from the data set through local regression or Kalman filter algorithm.However, these methods, or their generalizations,…

Methodology · Statistics 2022-08-02 Bertrand Cloez , Bénédicte Fontez , Eliel González García , Isabelle Sanchez

Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some…

Numerical Analysis · Mathematics 2015-11-06 Vishwas Rao , Adrian Sandu , Michael Ng , Elias Nino-Ruiz

Anomaly detection is referred to as a process in which the aim is to detect data points that follow a different pattern from the majority of data points. Anomaly detection methods suffer from several well-known challenges that hinder their…

Machine Learning · Computer Science 2021-08-31 Kasra Babaei , Zhi Yuan Chen , Tomas Maul

Biological oscillations are periodic changes in various signaling processes crucial for the proper functioning of living organisms. These oscillations are modeled by ordinary differential equations, with coefficient variations leading to…

Machine Learning · Computer Science 2024-12-04 Heng Rao , Yu Gu , Jason Zipeng Zhang , Ge Yu , Yang Cao , Minghan Chen

The detection of outliers is of critical importance in the assurance of data quality. Outliers may exist in observed data or in data derived from these observed data, such as estimates and forecasts. An outlier may indicate a problem with…

Methodology · Statistics 2025-10-23 Charles D. Coleman , Thomas Bryan

Surface, image and video data can be considered as functional data with a bivariate domain. To detect outlying surfaces or images, a new method is proposed based on the mean and the variability of the degree of outlyingness at each grid…

Methodology · Statistics 2016-02-01 Mia Hubert , Jakob Raymaekers , Peter J. Rousseeuw , Pieter Segaert

Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…

Pattern Formation and Solitons · Physics 2022-11-24 Per Sebastian Skardal

In a corpus of data, outliers are either errors: mistakes in the data that are counterproductive, or are unique: informative samples that improve model robustness. Identifying outliers can lead to better datasets by (1) removing noise in…

We formulate a statistical flight-pause model for human mobility, represented by a collection of random objects, called motions, appropriate for mobile phone tracking (MPT) data. We develop the statistical machinery for parameter inference…

Methodology · Statistics 2023-07-04 Marcin Jurek , Catherine A. Calder , Corwin Zigler

Mobile sensing enabled by GPS or smart phones has become an increasingly important source of traffic data. For sufficient coverage of the traffic stream, it is important to maintain a reasonable penetration rate of probe vehicles. From the…

Analysis of PDEs · Mathematics 2016-03-29 Benedetto Piccoli , Ke Han , Terry L. Friesz , Tao Yao , Junqing Tang

This work introduces a live anomaly detection system for high frequency and high-dimensional data collected at regional scale such as Origin Destination Matrices of mobile positioning data. To take into account different granularity in time…

Applications · Statistics 2022-05-25 Stefano Maria Iacus , Francesco Sermi , Spyridon Spyratos , Dario Tarchi , Michele Vespe
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