Space-time prisms

Measuring the structural similarity of network time prisms using temporal signatures with graph indices

New publication: Jaegal Y, Miller HJ. (2019) Measuring the structural similarity of network time prisms using temporal signatures with graph indices. Transactions in GIS. 00:1–24. https ://doi.org/10.1111/tgis.12582

Abstract.  The network‐time prism (NTP) is an extension of the space‐time prism that provides a realistic model of the potential pattern of moving objects in transportation networks. Measuring the similarity among NTPs can be useful for clustering, aggregating, and querying potential mobility patterns. Despite its practical importance, however, there has been little attention given to similarity measures for NTPs. In this research, we develop and evaluate a methodology for measuring the structural similarity between NTPs using the temporal signature approach. The approach extracts the one‐dimensional temporal signature of a selected property of NTPs and applies existing path similarity measures to the signatures. Graph‐theoretic indices play an essential role in summarizing the structural properties of NTPs at each moment. Two extensive simulation experiments demonstrate the feasibility of the approach and compare the performance of graph indices for measuring NTP similarity. An empirical application using bike‐share system data shows that the method is useful for detecting different usage patterns of two heterogenous user groups.

Measuring the geometric and semantic similarity of space–time prisms using temporal signatures

New publication: Miller, H.J., Jaegal, Y. and Raubal, M. (2019) “Measuring the geometric and semantic similarity of space-time prisms using temporal signatures,” Annals of the American Association of Geographers, 109, 730-753.

Well-established techniques exist for measuring the similarity of space–time paths. These measures support clustering and aggregation of space–time paths as well as moving objects database queries based on similar movement patterns or semantics. Little attention has been paid, however, to the analogous problem of measuring space–time prism (STP) similarity, despite comparable applications. This article presents and evaluates a method for measuring STP similarity through dimensionality reduction that leverages their inherent temporal ordering. The technique sweeps an STP along the time axis and derives one-dimensional temporal signatures based on a measured STP property that captures its geometry or semantics. These temporal signatures can be visualized directly as curves. We can also apply existing space–time path similarity measures to these signatures. To demonstrate the feasibility of this approach, we perform two sets of experiments measuring geometric and semantic similarity among STPs and assess the information within these curves using visualization, Fréchet distances, and clustering techniques. Results suggest that the temporal signature curves capture meaningful similarities and differences among STPs.

Measuring the Geometric and Semantic Similarity of Space–Time Prisms Using Temporal Signatures

New publication: Miller, H.J., Jaegal, Y. and Raubal, M., “Measuring the geometric and semantic similarity of space-time prisms using temporal signatures,” Annals of the American Association of Geographers (online first).

Abstract
Well-established techniques exist for measuring the similarity of space–time paths. These measures support clustering and aggregation of space–time paths as well as moving objects database queries based on similar movement patterns or semantics. Little attention has been paid, however, to the analogous problem of measuring space–time prism (STP) similarity, despite comparable applications. This article presents and evaluates a method for measuring STP similarity through dimensionality reduction that leverages their inherent temporal ordering. The technique sweeps an STP along the time axis and derives one-dimensional temporal signatures based on a measured STP property that captures its geometry or semantics. These temporal signatures can be visualized directly as curves. We can also apply existing space–time path similarity measures to these signatures. To demonstrate the feasibility of this approach, we perform two sets of experiments measuring geometric and semantic similarity among STPs and assess the information within these curves using visualization, Fréchet distances, and clustering techniques. Results suggest that the temporal signature curves capture meaningful similarities and differences among STPs.

测量时空路径相似性时，有发展完善的科技。这些方法支持时空路径的集群与聚集，以及根据相似的移动模式或语义的移动物件数据库之提问。尽管具有可比较的应用，但却少有对测量时空稜柱（STP）相似性的类似问题之关注。本文呈现并评估通过维度减少来发挥其内在时间次序以测量STP相似性的一种方法。该技术沿着时间轴延伸STP， 并根据捕捉其几何与语义的测得之STP属性，衍生出单维度时间特徵。这些时间特徵能够直接被视觉化为曲线。我们同时可将既有的时空路径相似性测量应用至这些特徵。为了证实此般方法的可行性，我们执行两组测量STPs之间的几何和语义相似性的实验，并运用可视化、弗雷歇距离以及集群技术，取得这些曲线中的信息。研究结果显示，时间特徵曲线捕捉STPs之间有意义的相似性和差异。

Existen técnicas bien probadas para medir la similitud de las trayectorias espacio–tiempo. Estas medidas soportan agrupamiento y agregación de trayectorias espacio–tiempo lo mismo que consultas de bases de datos de objetos en desplazamiento con base en patrones de movimiento o semántica similares. Sin embargo, poca es la atención que se ha deparado al problema análogo de medir la similitud del prisma espacio–tiempo (STP), a pesar de aplicaciones comparables. Este artículo presenta y evalúa un método para medir la similitud del STP mediante la reducción de dimensionalidad que apalanca su inherente ordenamiento temporal. La técnica barre un STP a lo largo del eje del tiempo y deriva firmas temporales unidimensionales basadas en una propiedad STP medida, que captura su geometría o su semántica. Estas firmas temporales pueden visualizarse directamente como curvas. También podemos aplicar a estas firmas las mediciones existentes de similitud de las trayectorias espacio–tiempo. Para demostrar la viabilidad de este enfoque, realizamos dos conjuntos de experimentos midiendo la similitud geométrica y semántica entre STPs y evaluamos la información dentro de estas curvas usando visualización, distancias Fréchet y técnicas de agrupamiento. Los resultados sugieren que las curvas de firma temporal capturan similitudes significativas y diferencias entre los STPs.