An Introduction to the Network Weight Matrix

Ermagun, Alireza; Levinson, David

doi:10.1111/gean.12134

Cited by 27 publications

(16 citation statements)

References 24 publications

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“…These matrices are based on either contiguity or distance and are then used to create spatially lagged variables, applicable to the dependent variable, the independent ones, or the error term [7]. These weight matrices can also be based on networks [36]. Specifications of the model calibration are given in Section 5.…”

Section: Spatial Modelsmentioning

confidence: 99%

Spatial Heterogeneity of Sustainable Transportation Offer Values: A Comparative Analysis of Nantes Urban and Periurban/Rural Areas (France)

Bulteau¹,

Feuillet

Boennec

2018

Urban Science

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Abstract:Innovative solutions have been implemented to promote sustainable mobility in urban areas. In the Nantes area (northwestern part of France), alternatives to single-occupant car use have increased in the past few years. In the urban area, there is an efficient public transport supply, including tramways and a "busway" (Bus Rapid Transit), as well as bike-sharing services. In periurban and rural areas, there are carpool areas, regional buses and the new "tram-train" lines. In this article, we focus on the impact on house prices of these "sustainable" transportation infrastructures and policies, in order to evaluate their values. The implicit price of these sustainable transport offers was estimated through hedonic price functions describing the Nantes urban and periurban/rural housing markets. Spatial regression models (SAR, SEM, SDM and GWR) were carried out to capture the effect of both spatial autocorrelation and spatial heterogeneity. The results show patterns of spatial heterogeneity of transportation offer implicit prices at two scales: (i) between urban and periurban/rural areas, as well as (ii) within each territory. In the urban area, the distance to such offers was significantly associated with house prices. These associations varied by type of transportation system (positive for tramway and railway stations and negative for bike-sharing stations). In periurban and rural areas, having a carpool area in a 1500-m buffer around the home was negatively associated with house prices, while having a regional bus station in a 500-m buffer was non-significant. Distance to the nearest railway station was negatively associated with house prices. These findings provide research avenues to help public policy-makers promote sustainable mobility and pave the way for more locally targeted interventions.

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Section: Spatial Modelsmentioning

confidence: 99%

Spatial Heterogeneity of Sustainable Transportation Offer Values: A Comparative Analysis of Nantes Urban and Periurban/Rural Areas (France)

Bulteau¹,

Feuillet

Boennec

2018

Urban Science

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“…Short-term forecasting of traffic was initially confined to scrutinizing complementary links. In consequence, the competitive nature of traffic links has been overlooked in the spatial weight matrix configuration (Ermagun and Levinson, 2017a).…”

Section: Introductionmentioning

confidence: 99%

Development and application of the network weight matrix to predict traffic flow for congested and uncongested conditions

Ermagun

Levinson

2018

Environment and Planning B: Urban Analytics and City Science

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To capture network dependence between traffic links, we introduce two distinct network weight matrices ([Formula: see text]), which replace spatial weight matrices used in traffic forecasting methods. The first stands on the notion of betweenness centrality and link vulnerability in traffic networks. To derive this matrix, we use an unweighted betweenness method and assume all traffic flow is assigned to the shortest path. The other relies on flow rate change in traffic links. For forming this matrix, we use the flow information of traffic links and employ user equilibrium assignment and the method of successive averages algorithm to solve the network. The components of the network weight matrices are a function not simply of adjacency, but of network topology, network structure, and demand configuration. We test and compare the network weight matrices in different traffic conditions using the Nguyen–Dupuis network. The results lead to a conclusion that the network weight matrices operate better than traditional spatial weight matrices. Comparing the unweighted and flow-weighted network weight matrices, we also reveal that the assigned flow network weight matrices perform two times better than a betweenness network weight matrix, particularly in congested traffic conditions.

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“…Studies of spatial networks have to leverage the embedded direction of edges in order to characterize patterns (Barthelemy, ; Gastner & Newman, ). To incorporate the topology and structure of spatial networks, Ermagun and Levinson () introduced a network weight matrix in which the edge direction is explicitly considered. Road networks are a classic application of spatial networks; Boeing () explored the distribution of road directions in cities and discovered that directional patterns of roads varied among different cities, which can be used as one factor to characterize urban configurations.…”

Section: Where Direction Has Been Consideredmentioning

confidence: 99%

Making direction a first‐class citizen of Tobler's first law of geography

Zhu

Janowicz

Mai

2019

Transactions in GIS

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Waldo Tobler frequently reminded us that the law named after him was nothing more than calling for exceptions. This article discusses one of these exceptions. Spatial relations between points are frequently modeled as vectors in which both distance and direction are of equal prominence. However, in Tobler's first law of geography, such a relation is described only from the perspective of distance by relating the decreasing similarity of observations in some attribute space to their increasing distance in geographic space. Although anisotropic versions of many geographic analysis techniques, such as directional semivariograms, anisotropy clustering, and anisotropic point pattern analysis, have been developed over the years, direction remains on the level of an afterthought. We argue that, compared to distance, directional information is still under‐explored and anisotropic techniques are substantially less frequently applied in everyday GIS analysis. Commonly, when classical spatial autocorrelation indicators, such as Moran's I, are used to understand a spatial pattern, the weight matrix is only built from distance, without direction being considered. Similarly, GIS operations, such as buffering, do not take direction into account either, with distance in all directions being treated equally. In reality, meanwhile, particularly in urban structures and when processes are driven by the underlying physical geography, direction plays an essential role. In this article we ask whether the development of early GIS, data (sample) sparsity, and Tobler's law lead to a theory‐induced blindness for the role of direction. If so, is it possible to envision direction becoming a first‐class citizen of equal importance to distance instead of being an afterthought only considered when the deviation from a perfect circle becomes too obvious to be ignored?

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An Introduction to the Network Weight Matrix

Cited by 27 publications

References 24 publications

Spatial Heterogeneity of Sustainable Transportation Offer Values: A Comparative Analysis of Nantes Urban and Periurban/Rural Areas (France)

Spatial Heterogeneity of Sustainable Transportation Offer Values: A Comparative Analysis of Nantes Urban and Periurban/Rural Areas (France)

Development and application of the network weight matrix to predict traffic flow for congested and uncongested conditions

Making direction a first‐class citizen of Tobler's first law of geography

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