Efficient Non-Learning Similar Subtrajectory Search

Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires the two checked trajectories are similar to each other in whole. Many real applications (e.g., trajectory clustering and trajectory join) utilize similar subtrajectory search as a basic operator. It is considered that the time complexity is O(mn^2) for exact algorithms to solve the similar subtrajectory search problem under most trajectory distance functions in the existing studies, where m is the length of the query trajectory and n is the length of the data trajectory. In this paper, to the best of our knowledge, we are the first to propose an exact algorithm to solve the similar subtrajectory search problem in O(mn) time for most of widely used trajectory distance functions (e.g., WED, DTW, ERP, EDR and Frechet distance). Through extensive experiments on three real datasets, we demonstrate the efficiency and effectiveness of our proposed algorithms.Comment: VLDB 202

Segmenting trajectories: A framework and algorithms using spatiotemporal criteria

In this paper we address the problem of segmenting a trajectory based on spatiotemporal criteria. We require that each segment is homogeneous in the sense that a set of spatiotemporal criteria are fulfilled. We define different such criteria, including location, heading, speed, velocity, curvature, sinuosity, curviness, and shape. We present an algorithmic framework that allows us to segment any trajectory into a minimum number of segments under any of these criteria, or any combination of these criteria. In this framework, a segmentation can generally be computed in O(n log n) time, where n is the number of edges of the trajectory to be segmented. We also discuss the robustness of our approach.Peer ReviewedPostprint (published version

Segmenting trajectories: A framework and algorithms using spatiotemporal criteria

In this paper we address the problem of segmenting a trajectory based on spatiotemporal criteria. We require that each segment is homogeneous in the sense that a set of spatiotemporal criteria are fulfilled. We define different such criteria including location heading speed velocity curvature sinuosity curviness and shape. We present an algorithmic framework that allows us to segment any trajectory into a minimum number of segments under any of these criteria or any combination of these criteria. In this framework a segmentation can generally be computed in O(n log n) time where n is the number of edges of the trajectory to be segmented. We also discuss the robustness of our approach

A Comparison Between Alignment and Integral Based Kernels for Vessel Trajectories

In this paper we present a comparison between two important types of similarity measures for moving object trajectories for machine learning from vessel movement data. These similarities are compared in the tasks of clustering, classication and outlier detection. The rst similarity type are alignment measures, such as dynamic time warping and edit distance. The second type are based on the integral over time between two trajectories. Following earlier work we dene these measures in the context of kernel methods, which provide state-of-the-art, robust algorithms for the tasks studied. Furthermore, we include the in uence of applying piecewise linear segmentation as pre-processing to the vessel trajectories when computing alignment measures, since this has been shown to give a positive eect in computation time and performance. In our experiments the alignment based measures show the best performance. Regular versions of edit distance give the best performance in clustering and classication, whereas the softmax variant of dynamic time warping works best in outlier detection. Moreover, piecewise linear segmentation has a positive eect on alignments, which seems to be due to the fact salient points in a trajectory, especially important in clustering and outlier detection, are highlighted by the segmentation and have a large in uence in the alignments

Towards optimization methods for movelets extraction in multiple aspect trajectory classification

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Ciência da Computação, Florianópolis, 2023.In the last few years there has been a significant increase in the collection of mobility data. By mobility data we refer to the collection of positioning data, called trajectories, of tracked moving objects. These objects could be humans, animals, vehicles or other devices like Internet of Things (IoT). The analysis of such data has been proved to be useful in several application domains from a urban scenario for traffic prediction or transportation means optimization, to maritime domain analysing vessels paths or environmental domain with the study of hurricanes evolution or animal behavior. One of the most typical and used analysis task on mobility data is classification, where trajectory data is automatically assigned a label or class. The explosion of social media data, sensors, IoT, and Internet-enabled sources allowed the semantic enrichment of such mobility data, which evolved from raw spatio-temporal data to high dimensional data. Mobility analysis, and specifically classification task, on such high dimensional data becomes therefore more challenging. In fact, existing trajectory classification methods have mainly considered space, time, and numerical data, ignoring the large number of semantic dimensions. Only recently research community proposed classification methods based on the concept of movelets that are the parts of a trajectory that better discriminate a class and that can therefore improve classification accuracy. State of the art methods in movelets extraction are computationally inefficient, which makes them unfeasible to be used for real large high dimensional datasets. The objective of this thesis is therefore to develop new algorithms for discovering movelets that are faster than state of the art while maintaining or improving classification accuracy. Our main contribution is a new high performance method for extracting movelets and classifying trajectories, called HiPerMovelets (High-performance Movelets). Experimental results show that HiPerMovelets is 10 times faster than the best state of the art method, reduces the high dimensionality problem, is more scalable, and presents a high classification accuracy in all evaluated datasets. A secondary contribution are the algorithms RandomMovelets and UltraMovelets. RandomMovelets reduces the search space by randomly extracting subtrajectories and evaluating their relevance for classification without exploring the entire dataset. UltraMovelets reduces the combinatorial explosion when exploring subtrajectories. Preliminary results suggest that these methods can reduce the search space, use less computational resources, and are at least 6 times faster than baselines.Nos últimos anos, houve um aumento significativo na coleta de dados de mobilidade. Dados de mobilidade referem-se ao conjunto de dados de posicionamento geográfico, chamados de trajetórias de objetos móveis. Esses objetos podem ser pessoas, animais, veículos ou outros dispositivos como a Internet das Coisas (IoT). A análise deste tipo de dados se revela útil em vários domínios de aplicação, desde um cenário urbano para previsão de tráfego ou otimização de meios de transporte, no domínio marítimo analisando trajetos de embarcações, no domínio ambiental com o estudo da evolução de furacões ou comportamento animal. Uma das tarefas de análise mais comuns e usadas em dados de mobilidade é a classificação, onde os dados de trajetória recebem automaticamente um rótulo ou classe. A explosão de dados de mídia social, sensores, IoT e outras fontes da Internet permitiram o enriquecimento semântico desses dados de mobilidade, que evoluíram de dados espaço-temporais brutos para dados de alta dimensionalidade. A análise de mobilidade, e especificamente a tarefa de classificação, em tais dados de alta dimensionalidade tem se tornado mais desafiadora. De fato, os métodos de classificação de trajetória existentes consideram principalmente espaço, tempo e dados numéricos, ignorando o grande número de dimensões semânticas. Apenas recentemente a comunidade de pesquisa propôs métodos de classificação baseados no conceito de movelets que são as partes de uma trajetória que melhor discriminam uma classe e que podem, portanto, melhorar a precisão da classificação. Métodos de última geração na extração de movelets são computacionalmente ineficientes, o que os torna inviáveis para serem usados em grandes conjuntos de dados de alta dimensão. O objetivo desta tese é, portanto, desenvolver novos algoritmos para descobrir movelets que sejam mais rápidos do que o estado da arte, mantendo ou melhorando a precisão da classificação. Nossa principal contribuição é um novo método de alto desempenho para extração de movelets e classificação de trajetórias, denominado HiPerMovelets (Movelets de alto desempenho). Os resultados experimentais mostram que o HiPerMovelets é 10 vezes mais rápido que o melhor método do estado da arte, reduz o problema de alta dimensionalidade, é mais escalável e apresenta uma alta precisão de classificação em todos os conjuntos de dados avaliados. Uma contribuição secundária são os algoritmos RandomMovelets e UltraMovelets. RandomMovelets reduz o espaço de busca extraindo subtrajetórias aleatoriamente e avaliando sua relevância para classificação sem explorar todo o conjunto de dados. UltraMovelets reduz a explosão combinatória ao explorar subtrajetórias. Os resultados preliminares sugerem que esses métodos podem reduzir o espaço de busca, usar menos recursos computacionais e são pelo menos 6 vezes mais rápidos que a linha de base

Efficient motif discovery in spatial trajectories using discrete Fréchet distance

National Research Foundation (NRF) Singapore under International Research Centres in Singapore Funding Initiativ