Abstract
Time geography considers that the probability of moving objects distributed in an accessible transportation network is not always uniform, and therefore the probability density function applied to quantitative time geography analysis needs to consider the actual network constraints. Existing methods construct a kernel density function under network constraints based on the principle of least effort and consider that each point of the shortest path between anchor points has the same density value. This, however, ignores the attenuation effect with the distance to the anchor point according to the first law of geography. For this reason, this article studies the kernel function framework based on the unity of the principle of least effort and the first law of geography, and it establishes a mechanism for fusing the extended traditional model with the attenuation model with the distance to the anchor point, thereby forming a kernel density function of time geography under network constraints that can approximate the theoretical prototype of the Brownian bridge and providing a theoretical basis for reducing the uncertainty of the density estimation of the transportation network space. Finally, the empirical comparison with taxi trajectory data shows that the proposed model is effective.
Highlights
Time geography considers that the possibility of moving objects at different accessible locations is not always equal, so quantitative spatiotemporal uncertainty analysis requires measuring the actual visit probability distribution [1]
Downs proposed a time-geographic density estimation (TGDE) method based on the potential path area (PPA) kernel function [8] and extended it to the transportation network to be used in the estimation of missing points in travel itineraries and the evaluation of food availability [9,10]
This paper extends a previous work on the single-layer “ridge” model of the potential network area (PNA) kernel function [26]
Summary
Time geography considers that the possibility of moving objects at different accessible locations is not always equal, so quantitative spatiotemporal uncertainty analysis requires measuring the actual visit probability distribution [1]. A common method is to assign location probabilities to the potential path area (PPA), which is used in time geography to describe the potential range of a moving object during two anchor points [2] In probability theory, this spatiotemporal uncertainty during the period of two anchor points is described by the Brownian bridge [3–6], whose density cloud is similar to a saddle formed by superimposing the bimodal peak on a ridge. The minimum-cost path between two anchor points (corresponding to the focal length in the geographic ellipse, referred to here as the focal line) is assigned the same and maximum density at any point, and the density of other points around the focal line attenuates with cost This kernel function corresponds in form to the base of the saddle-shaped Brown bridge and is effective for such a PNA with multiple paths without intersections except for the endpoints.
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