Multifractal approach for comparing road transport network geometry: The case of Spain

Pavón-Domínguez, Pablo; Rincón-Casado, A.; Ruiz, Petronila Oliva; Camacho-Magriñán, P.

doi:10.1016/j.physa.2018.07.034

Cited by 9 publications

(8 citation statements)

References 39 publications

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“…The length of a river network is herein employed as the performance variable with which to assess the performance of river extraction methods. The box-counting method is implemented to calculate the probability distribution of the river network's length [55]. Specifically, N(ε) squares of size ε • ε are used to superimpose a grid over the river network.…”

Section: The Multifractal Methodsmentioning

confidence: 99%

Setting the Flow Accumulation Threshold Based on Environmental and Morphologic Features to Extract River Networks from Digital Elevation Models

Zhang

Loáiciga

Liao

et al. 2021

IJGI

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Determining the flow accumulation threshold (FAT) is a key task in the extraction of river networks from digital elevation models (DEMs). Several methods have been developed to extract river networks from Digital Elevation Models. However, few studies have considered the geomorphologic complexity in the FAT estimation and river network extraction. Recent studies estimated influencing factors’ impacts on the river length or drainage density without considering anthropogenic impacts and landscape patterns. This study contributes two FAT estimation methods. The first method explores the statistical association between FAT and 47 tentative explanatory factors. Specifically, multi-source data, including meteorologic, vegetation, anthropogenic, landscape, lithology, and topologic characteristics are incorporated into a drainage density-FAT model in basins with complex topographic and environmental characteristics. Non-negative matrix factorization (NMF) was employed to evaluate the factors’ predictive performance. The second method exploits fractal geometry theory to estimate the FAT at the regional scale, that is, in basins whose large areal extent precludes the use of basin-wide representative regression predictors. This paper’s methodology is applied to data acquired for Hubei and Qinghai Provinces, China, from 2001 through 2018 and systematically tested with visual and statistical criteria. Our results reveal key local features useful for river network extraction within the context of complex geomorphologic characteristics at relatively small spatial scales and establish the importance of properly choosing explanatory geomorphologic characteristics in river network extraction. The multifractal method exhibits more accurate extracting results than the box-counting method at the regional scale.

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Section: The Multifractal Methodsmentioning

confidence: 99%

Setting the Flow Accumulation Threshold Based on Environmental and Morphologic Features to Extract River Networks from Digital Elevation Models

Zhang

Loáiciga

Liao

et al. 2021

IJGI

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“…There are several methods for evaluating the evolutionary features of a URT. As the fractal approach is an effective way of describing fragmented anthropogenic objects and obtaining scale-independent results [ 10 , 11 ], we used it to assess the evolutionary features of a non-weighted URT network and a transit-weighted network. Fractal concepts were proposed by Mandelbrot [ 10 ], and several definitions of fractal dimensions have been introduced to describe fractality in a quantified way, with application to an urban transport network following nearly a decade later.…”

Section: Introductionmentioning

confidence: 99%

“…Benguigui [ 12 ] first identified the fractal features of an urban transport network and carried out case studies on the London Underground, Paris Metro, Moscow Metro, and Rhine Subway (Germany). Batty [ 13 , 14 ] linked transport analysis to urban geography on the basis of fractal dimensions, after which fractal approaches have been widely applied to different parts of cities including the city center [ 15 ], the whole scope of a city [ 16 ], and conurbations [ 11 ]. Different modes of transport have also been analyzed using fractal methods including traditional surface transport [ 15 ], subway [ 16 ], and the whole public transport network.…”

Section: Introductionmentioning

confidence: 99%

Extracting the Relationship and Evolutionary Rule Connecting Residents’ Travel Demand and Traffic Supply Using Multisource Data

Wang

Chen

Shi

et al. 2021

Sensors

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Urban rail transit (URT) systems are often regarded as the backbone of their respective city. The evolutionary features of URT systems have attracted much attention in recent years, but their evolution and their distinct function in contrast to other transit modes have seldom been investigated, especially quantitatively from the perspective of work–residence separation. Accordingly, we propose a framework for exploring the evolution of URT topological networks and demand-weighted networks, comparing the different impacts of all transit modes on work–residence separation. In this study, a URT passenger flow assignment model was formulated on the basis of travel cost function and an improved logit model was proposed that takes into account the heterogeneity of passengers. This model was used to generate a section load, which is regarded as a weight and able to reflect the residents’ demand for travel by URT. Then, the fractal dimensions for a non-weighted network and demand-weighted network are proposed and their indications for transportation explained. Finally, the Beijing Subway System (BSS) is used as a case study by employing fifty years of network data and ten years of smart card data. Using fractal approaches, the different characteristics illustrated by the two networks were investigated and the reasons behind the observed patterns explained. In addition, the spatial features of the rail network, in terms of fractal indictors, were compared with population distribution and urban mobility for all modes, extracted from phone data as a proxy. Thus, the relationship between the residents’ travel demand and traffic supply can be revealed to some extent. The main finding of this work is that demand must be taken into account when analyzing the fractal features of a transport network, lest the demand side be separated from the supply and important issues missed such as inconsistencies between demand and supply. Additionally, the role of rail transit in work–home imbalance can be investigated in the context of urban mobility for an entire city.

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“…In recent years, some studies have also focused on the MFA of complex networks. MFA has been shown to have better performance than fractal analysis in characterizing the complexity of model and real-world networks [8,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Thus, if a network possesses the multifractal property, we can use the generalized fractal dimensions D q , instead of a single fractal dimension D 0 , to unfold effectively the self-similar structure of the network, thus capturing the fluctuations of local node density in the network.…”

mentioning

confidence: 99%

“…This is because that the sandbox algorithm only randomly selects a number of nodes on a network as the center nodes of sandboxes and then counts the number of nodes in each sandbox within a given radius for MFA. Therefore, the existing sandbox algorithm and its improved versions have been widely used to the calculation of the mass exponents τ q or the generalized fractal dimensions D q of different types of complex networks [10,[26][27][28][30][31][32][33][34]. The calculated results are then used for the investigation into the fractal and multifractal properties of the networks.…”

mentioning

confidence: 99%

A computationally-efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

Ding,

Liu,

et al. 2020

Preprint

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The fractality of complex networks has attracted much attention with extensive investigations over the last 15 years. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful tool to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. One of the widely used methods for fractal analysis is box-covering. It uses the minimum number of covering boxes to calculate the fractal dimension of complex networks, and is known to be NP-hard. More severely, in comparison with fractal analysis algorithms, MFA algorithms have much higher computational complexity. Among various MFA algorithms for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive. Thus, so far it has only been applied to small-scale complex networks of the size of about tens of thousands of nodes. It becomes challenging to implement the MFA for large-scale networks with tens of millions of nodes. It is also not clear whether or not MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally-efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of complex networks, our CESA employs the breadth-first search (BFS) technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. Our CESA's input is a sparse data structure derived from the compressed sparse row (CSR) format designed for compressed storage of the adjacency matrix of large-scale network. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. MFA experiments are performed for typical complex networks to verify our CESA. The CESA is demonstrated to be effective, efficient and feasible through the MFA results of (u,v)-flower model networks from the 5th to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

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Multifractal approach for comparing road transport network geometry: The case of Spain

Cited by 9 publications

References 39 publications

Setting the Flow Accumulation Threshold Based on Environmental and Morphologic Features to Extract River Networks from Digital Elevation Models

Setting the Flow Accumulation Threshold Based on Environmental and Morphologic Features to Extract River Networks from Digital Elevation Models

Extracting the Relationship and Evolutionary Rule Connecting Residents’ Travel Demand and Traffic Supply Using Multisource Data

A computationally-efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

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