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).

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.

Analyzing collective accessibility using average space-time prisms

New publication:  Lee, J. and Miller, H.J. (2019) “Analyzing collective accessibility using average space-time prisms,” Transportation Research Part D: Transport and Environment, 69, 250-264.

Abstract:  The space-time prism (STP) is the envelope of all possible travel paths in space and time between two anchor locations and times, measuring accessibility for an individual given a designated travel and activity episode. Although the STP provides a powerful measure of individual accessibility, transportation researchers often need to analyze accessibility at collective-levels for planning and policy analysis. Deriving a representative STP of a set of individual STPs would provide a general idea of how collective members’ accessibility is performing. However, there is no analytical time geographic method to calculate a collective-level representative STP that is consistent with individual STPs. To fill this gap, this research develops the concept of average space-time prism (ASTP). The ASTP is a representative STP of a group of individual STPs with respect to size, shape, and location. We develop methods for calculating an ASTP using analytical time geography and elliptic Fourier shape analysis techniques. The ASTP provides a geometric and visual summary of collective accessibility: it can be used to generate representative STPs for aggregate geographic units such as neighborhoods and cities based on individual-level data. A possible application of the ASTP is the spatial equity analysis of accessibility. The ASTP can be located at individuals’ anchor locations and overlaid with opportunities, enabling in-situ comparisons between individual versus collective accessibility and accessibility equity analysis considering geographic contexts. We illustrate this ASTP’s capability when measuring the impacts of new transit service on healthcare access equity in a neighborhood in Columbus, Ohio, USA.

Measuring the impacts of new public transit services on space-time accessibility

Lee, J. and Miller, H. J. (2018) “Measuring the impacts of new public transit services on space-time accessibility: An analysis of transit system redesign and new bus rapid transit in Columbus, Ohio, USA,” Applied Geography, 93, 47-63.


  • Lack of access to opportunities contributes to poor social and health outcomes.
  • Columbus, OH introduced a transit route and schedule redesign and bus rapid transit.
  • We analyze impacts on accessibility to opportunities in a deprived neighborhood.
  • Detailed route and schedule data allow high resolution accessibility analysis.
  • The new bus rapid transit has a much greater impact on accessibility


The absence of effective access to opportunities and services is a key contributor to poor socio-economic and health outcomes in underserved neighborhoods in many cities. The city of Columbus, Ohio, USA is attempting to enhance residents’ accessibility by providing new public transit services. These new services include a major Transit System Redesign (TSR) of the conventional bus network and the introduction of a new bus rapid transit, named CMAX. Using a high-resolution space-time accessibility measure, we analyze whether these new public transit services will change residents’ accessibility to job and healthcare in an underserved neighborhood of Columbus. Also, we assess whether enhancing the CMAX service to reduce delays (e.g., reserved lane, off-board payment system) will improve accessibility. The high-resolution space-time accessibility measure in this study uses published public transit schedules via the General Transit Feed Specification (GTFS). We use multiple departure times during a day to account for the temporal fluctuations of accessibility based on the transit schedule changes. We also consider the operating hours of job opportunities and healthcare services. Results suggest that the TSR yields ambiguous benefits for accessibility to jobs and healthcare. However, the new CMAX service and its potential upgrades lead to a substantial increase in both job and healthcare accessibility. The results can be used for city officials and urban planners to evaluate the effectiveness of public transit innovations in improving accessibility.

Keywords: Transportation; Space-time accessibility; Public transit; Bus rapid transit; Jobs; Healthcare