Location, location, usage: How different notions of centrality can predict land usage in Singapore

Journal Pre-proof Location, location, usage: How different notions of centrality can predict land usage in Singapore? Francisco Benita, Georgios Piliouras

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S0378-4371(19)31808-4 https://doi.org/10.1016/j.physa.2019.123221 PHYSA 123221

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Physica A

Received date : 1 March 2019 Revised date : 26 August 2019 Please cite this article as: F. Benita and G. Piliouras, Location, location, usage: How different notions of centrality can predict land usage in Singapore?, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123221. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier B.V.

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Location, location, usage: How different notion of centrality can predict land usage in cities?

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Relatively strong links between street connectivity and street centrality. Atypical behavior of the land allocated to street, closeness and information centrality. Combination of the two types of indicators to characterize land use and geographical regions.

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*Manuscript Click here to view linked References

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Location, location, usage: How different notions of centrality can predict land usage in Singapore? Francisco Benitaa , Georgios Piliourasa Systems and Design, Singapore University of Technology and Design, 8 Somapah Road Singapore, 487372

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Abstract

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The concepts of street connectivity, street centrality, and how they relate to the land use, have gained increasing appeal among city planners and complex systems researchers. This paper examines the relationship between these two types of street network indicators and land-use types in Singapore. Despite the fact that both approaches have been carried out in parallel and semi-independently, the findings suggest that rather than focusing specifically on single-type of indicators, the combination of both may provide more intuitive results to planning authorities as they are able to better correlate with the geographical division and land use of the city. Keywords: Connectivity, centrality, street networks, land use

1. Introduction

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Quantifying the relationship between the road street network and built environment is increasingly important for urban design because the street network structure has impact not only on city’s economic performance (Porta et al., 2009, 2012; Shen and Karimi, 2017) but also on residents’ safety and well-being (Lau, 2011; Owen and Wong, 2013; Moeinaddini et al., 2014; Zhu and Diao, 2016). There is a reciprocal relationship between land use and transportation system determining the urban morphology of the cities. Recent studies investigating this link have been able to provide intuitive results built mainly on mathematical models (Ozbil et al., 2011; Rui and Ban, 2014), but there is still limited evidence from both, the methodological and the empirical view point. This task becomes even harder if one looks at the approaches of how the street network structure is measured. On the one hand, the street connectivity, emerged from the urban planning literature, is based on street-connectivity indicators. For instance, the Street Connectivity Index (SCI) proposed by the United Nations Human Settlements Programme (UN-Habitat) includes street density, the land allocated to street and street intersection density among its indicators (UN-Habitat, 2016). This index, its components and other similar metrics have been extensively investigated in previous studies that address a number of urban planning and design concerns including active transportation behavior (Berrigan et al., 2010), property value (Diao and Ferreira, 2010), housing price patterns (Shen and Karimi, 2017), vehicle miles traveled (Handy et al., 2005; Diao and Ferreira, 2014) and so on. But some other researchers have been more skeptical in terms of its consistency and robustness (Knight and Marshall, 2015). Email addresses: francisco [email protected] (Francisco Benita), [email protected] (Georgios Piliouras)

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On the other hand, based on complex network theory, a second approach sets the road street network as the backbone of the city and uses tools from graph theory to compute street-centrality indicators. Among them, degree centrality, closeness centrality, betweenness centrality and information centrality are the most widely used (Porta et al., 2006; Crucitti et al., 2006; Kirkley et al., 2018; Lee and Jung, 2018). Some authors have explored the relationship between street-centrality and land use (Rui and Ban, 2014), economic activities (Porta et al., 2009, 2012), urban morphology (Moeinaddini et al., 2014; Masucci and Molinero, 2016) or walkability (Bielik et al., 2018). Some others have raised concerns with respect to validity and reliability of real-life problems such as traffic flow prediction (Gao et al., 2013). It seems that both approaches have been carried out in parallel and semi-independently. The street-connectivity relates more to architectural-based conceptualizations addressed by the space syntax (Hillier et al., 2010). Alternatively, the street-centrality is closer to non-spatial networks which look at different patterns in nature like power law distributions (Clauset et al., 2009). In this vein, the present study focused on two open research questions: (i) How these two types of indicators are related to each other, and; (ii) How they relate the land use patterns of the city. Notice that both type of indicators cannot be considered as the sole driving forces of land use, however, past research suggests that higher levels of these indicators can explain a significant amount of the landuse intensity. The empirical evidence supports the occurrence of the synchronization phenomena in different cities from Netherlands (Geurs et al., 2006), Italy (Porta et al., 2009) or China (Wang et al., 2011a; Shen and Karimi, 2017). This is important because relationships between urban form, mobility practices and sustainability of a metropolitan area can be established. Land development is consequence of human activities and connectivity/centrality is therefore associated with cities’ functionality and the presence, density and topology of the located activities and land use. Using Singapore as an example, it is intended to investigate the link among regional divisions of the city, land use, and street-connectivity/centrality indicators. In doing so, two types of geographical units are analyzed, say (large) planing areas and (small) subzones as depicted by Figure 1 in Section 3. Latent Profile Analysis (LPA) is implemented to create classes of geographical units based on its street-connectivity/centrality and then compared against land use and regional divisions. LPA is a form of mixture modeling that creates a set of classes that are maximally different. It uses probabilities for class members and allows to specify classes based on theory and then compare the models based on fit statistics. The empirical findings from Section 5 suggest that, rather to restricting to a single approach of street network structure, the combination of both type of indicators yields more intuitive results that better explain both, the regional division of the city as well as the land use. The reason behind this is because the classes generated by LPA are more similar to the true (label) land use and regional division patterns when both connectivity and centrality indicators are taken into account. Conversely, the use of single-type of indicators raise issues in areas of special use like parks, reservoirs or industrial districts. This is the case of land allocated to street, with extremely high values in areas of special use, or closeness and information centrality, with a significant power-law behavior, see Figure 3 and Table 4 in Section 4.2. In addition, the outcomes of this work provide practical information on the benefits and limitations of both type of indicators. It also illustrates, in its Section 4.3, how they relate to socio-demographics (average monthly household income or population density) and economic activities (number of companies). The paper is organized as follows. In the next section, it is discussed the existing theoretical and empirical research on this topic. Section 3 introduces the study area and sources of information. In Section 4 an exploratory analysis is conducted to examine simple correlations between streetconnectivity/centrality indicators as well as its statistical characteristics and properties like power law of degree distribution. Section 5 made use of LPA to characterize geographical units based on its street network structure. Then, the Normalized Mutual Information measures are obtained to 2

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compare similarities between different profiles. This article concludes in Section 6 with the related discussion, potential implications, and suggestions for the future efforts. 2. Background 2.1. Street connectivity

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The street connectivity have been widely used in the literature as a comprehensive resource for improving street connectivity in developed and developing countries. More street connectivity create a more efficient transportation system, and can improve a wide range of community aspects reaching into health (Wang et al., 2013), safety (Moeinaddini et al., 2014), economic activity (Shen and Karimi, 2017) and quality of life (Owen and Wong, 2013). Furthermore, the link between street connectivity and land use has been explored by Matthews and Turnbull (2007) and Shen and Karimi (2017) for residential areas. A popular version of this street connectivity is captured by the SCI, proposed by the UN-Habitat in 2012 (UN-Habitat, 2016). The SCI provides a framework for measuring street connectivity which is a key aspect of urban mobility. Better connectivity implies ease of commuting between places and more destinations that can be reached by more and shorter routes. Thus, well-connected road street networks are characterized by many short links, several intersections, and less dead-ends. The original SCI considers three indicators, nevertheless, this work adds the percentage of four-way intersections as it has received increasing attention in the literature (Cervero and Kockelman, 1997; Diao and Ferreira, 2010, 2014). • Street density: The length of roads and/or streets in km per sq. km. • Land allocated to street: The total area allocated to street as a proportion of the total surface of the built-up area. • Street intersection density: The number of intersections per sq. km of land. • Four-way proportion: The percentage of intersections that are four-way.

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Street density is important for the spatial plans of cities as it defines the socio-dynamics of an urban area by constraining the location of roads and human settlements. Based on estimations from UN-Habitat Global Urban Observatory, urban areas with values of street density about 20km of streets per sq. km are characterized by high street density. However, penalties should be applied for higher or lower values as it has been found that in both conditions mobility is negatively affected (UN-Habitat, 2016). The land allocated to street is a relevant indicator because transportation systems consume large amount of land for circulation. This indicator was already studied in the early work of Cervero and Kockelman (1997) and Handy et al. (2002) in the form of vertical land-use mixing within parcels and ratio of building heights to street width, respectively. According to the UN-Habitat report, the top cities with more than 25% of the land allocated to street are considered as highly connected areas. In general, these types of areas are historically planned cities. Conversely, low connected areas typically have values of less than 15% whereas low to moderate and moderate to high have 15-20% and 20-25%, respectively. The street intersection density indicates that the more connected the road street network the less barriers in accessibility to different urban areas, leading in an increase in urban circulation. The UN-Habitat Global Urban Observatory suggests at least 100 intersections per sq. km values for well-connected urban areas. 3

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Lastly, the incidence of four-way intersections is a proxy for grid-like patterns and a good predictor of whether an area reflects neotraditional design elements. Previous studies have shown that these four street-connectivity indicators are highly correlated (Berrigan et al., 2010). Nevertheless, having data on only one of them is not enough to assess the street connectivity. For instance, if considering the land allocated to street only, an urban area can have wide streets in a very limited road street network and low intersection density, which does not always imply high connectivity. Similarly, lengthy road street network and dense intersections on very narrow streets do not also promote high connectivity. Therefore, a combination of the four indicators is required to capture the degree of connectivity of a road street network and this is precisely what the SCI does.

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2.2. Centrality analysis of the road street network Centrality indicators are static predictors of congestion and load on networks. These measures are adopted from the graph theory and they have been used in a number of social (Newman, 2003), economic (Kali and Reyes, 2007), biological (Pastor-Satorras et al., 2015) and transportation (Wang et al., 2011b; Laxe et al., 2012; Lee and Jung, 2018; Kirkley et al., 2018) studies. Under this approach, the street network structure is viewed as a topological graph composed of nodes and edges. Nodes indicate characteristics of the intersections and edges point out the connectivity among nodes as they represent the streets. Street-centrality indicators measure the relative importance of a node within the road street network. It is worth noticing that conversely to street-connectivity indicators, centrality metrics have often been used to asses the physical form of cities and its implications for land use. Four measures of this type are often used in studies addressing the network structure and nodal centrality of urban areas (Crucitti et al., 2006; Laxe et al., 2012; Wang et al., 2011b; Masucci and Molinero, 2016; Lee and Jung, 2018; Bielik et al., 2018): • Degree centrality: It is based on the idea that important nodes have the largest number of ties to other nodes. • Closeness centrality: Measures the degree of proximity to all other nodes.

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• Betweenness centrality: Indicates the significance of a node or edge in terms of the shortest paths. • Information centrality: Measures the decreasing amount of the efficiency when the specific node is deactivated.

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Degree centrality (being central as being incident to others) represents the importance of the node in the street network structure as it provides connectivity and popularity of an intersection with respect to spatially neighboring intersections. It gives information of how many other nodes are connected with a particular node. For example, nodes with degree 1 stand for dead ends while nodes with degrees 2, 3, 4 or 5 represent intersections. Closeness centrality (being central as being close to others) measures the extent to which a node is close to all other nodes along the shortest path. It reflects its accessibility in the road street network, and it gives alternative routes within the network. The closeness analysis helps to understand how the graph behaves locally in terms of transportation efficiency on the raw street network structure (Masucci and Molinero, 2016). The nodes near to the geometrical centroid of the network are much more likely to have high closeness scores. The betweenness centrality (being central as being between others) is a path-based measure of the importance of a node in terms of the amount of flow passing through it (Kirkley et al., 2018). 4

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A node that is between many others is assumed to have a higher likelihood of being able to control traffic flow in the road street network. For instance, in the case where all of the vehicles on the road follow the rule that they have to pass by the node or edge only along with the shortest path, then the betweenness approximately represents the volume of traffic (Lee and Jung, 2018; Kirkley et al., 2018), although this result has been questioned by Gao et al. (2013) and may others. Information centrality (being central as being critical for all other as a group) relates a node’s importance to the ability to respond to deactivation of that node (Porta et al., 2006). This indicator embeds both, closeness and betweenness in a single quantity, and leads to another distinct concept of being central as being critical for others. The measure depends on the length of the alternative paths that are used once a node is deactivated. Similar to the street-connectivity indicators, these four centrality measures have been show to exhibit large positive correlation in the context of street networks as early explained in Crucitti et al. (2006). The formulas to compute each centrality indicator are provided in the Appendix A.1. 3. Data and study area

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It is used data from Singapore for the street network structure comparison. Singapore is a densely-populated tropical island city-state, located at the southern tip of Peninsular Malaysia in South East Asia. The country is home to 5.6 million people, with only an area of 712 sq. km, this is half the size of Los Angeles and about 2/3 the size of New York City. Singapore has been often described as a highly planned city where land development is strictly controlled, and land use is taken seriously (Tun¸cer et al., 2017; Benita et al., 2019b). The government authorities have responded to the challenge of land scarcity in different ways such as its comprehensive road pricing system or its intensive public transport improvements (Monnot et al., 2017). The city has 164 km of expressways and 698 km of arterial roads which currently account for 12% of the land. The trade-off between the use of land for roads, and other activities has become an important issue for the planning authorities. The street network is obtained from the Land Transportation Authority and the graph has 107,501 nodes and 65,696 edges. There are used the tools from Benita et al. (2019a) to remove all nodes that are not intersection or dead-ends, hence, the simplified graph has 28,098 nodes and 33,694 edges. The analysis is presented by considering two types of geographical units: (large) planning areas and (small) subzones. This strategy would allow to investigate the land use patterns and street connectivity/centrality indicators in more detail. The planning authority of the city divides Singapore into 5 regions (Central, East, North-East, North and West), 55 planning areas and 323 subzones. Subzones are the main urban planning and census divisions of Singapore and they are divisions within a planning area. There can be more than 10 subzones within a planning area. Each planning area has a population of about 150,000 and served by a town center and several neighborhood commercial/shopping centers. The number of planning areas within a region ranges from 6 to 22 depending on the distribution of population within the region. To obtain land use information it is used the data from the Master Plan 2014 of the city. The document has granular land use of 31 types of zoning notations reflecting the permissible predominant use of land within the demarcated area. The zoning notations ranges from residential to commercial, business park, park, reservoirs, road street and special use, which can be used to compute the land allocated to street. The land use is aggregated such that each geographical unit is single-type in land use. Although this assumption is rather strong for planning areas, which are larger spatial units as shown in Figure 1, the analysis by subzone allows to relax such consideration. This is, each geographical unit is labeled with its corresponding land use. As detailed in Table 1, four (six) types of land use are considered for planning areas (subzones). There were excluded from the analysis three (21) planing 5

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areas (subzones) due to they are mainly small islands or reservoir areas with either no road street network or one dead-end node only. Table 1: Land use description

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Description Residential developments Business park operations General industrial uses Reservoirs and areas used or intended to be used for special purposes Residential developments without any commercial use Mixed residential and commercial purposes Commercial buildings, shopping complex and convention/exhibition centers Business park operations General industrial uses Reservoirs and areas used or intended to be used for special purposes

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Planning areas (52) Residential (31) Business (4) Industrial (3) Special use (14) Subzones (302) Residential (124) Residential mix (41) Commercial (32) Business (9) Industrial (43) Special use (53)

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Figure 1 displays the regions, planing areas and subzones, the different types of land use and the corresponding average value of each indicator. To compute street-centrality measures by geographical unit, the average value of the nodes inside each polygon were used as the referent. The raw centrality scores can be appreciated in Figure A1 of the Appendix A.1. The average values of betweenness (information) centrality have been divided (multiplied) by 100 (10) for visualization purposes. It is interesting to observe how in the case of planning areas, residential zones have the highest mean values of street density and street intersection density. Conversely, for subzones, industrial zones are the ones with the highest mean values of these two indicators. The patterns of the average values of centrality indicators are also different, and this is precisely why the link between land use, street-connectivity and street-centrality indicators needs to be investigated at different spatial units.

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4. Exploratory analysis 4.1. Descriptive statistics and simple correlations

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Figure 2 displays the average value and standard deviation of each indicator by region. The exercise allows to highlight considerable variations in mean values when the analysis is performed by planning area or by subzone. For example, the Central region (22 planning areas and 125 subzones) is the region devoted mainly to residential, commercial and business uses. This region has the highest mean values of street density, street intersection density, closeness centrality and information centrality. On the other hand, the West region (11 planning areas and 67 subzones), designed for industrial usage, has small average values of land allocated to street together with large values of four-way proportion and degree centrality. However, larger standard deviations of centrality indicators are presented at the planning area level. This is because averaging centrality makes one centrality value as a dominant factor. Overall, one can observe that in Singapore, the land allocated to street is highly efficient because the average values are larger than 25%, regardless the region and land use (see Figure 1). The street intersection density seems to report low average scores (lower than 20km of streets per sq. km) apart from the Central region. This can be explained by the fact that the city is generally cover by

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(a) Planning areas

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(b) Subzones

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Figure 1: Singapore’s planning areas and subzones

Figure 2: Average indicators’ value by region

surrounding parks and green spaces, particularly in special use areas, which do not allow for direct

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travel between destinations and require commuters to travel longer and more circuitous routes. Mean differences of degree and information centrality appear to be quite small among regions whereas closeness and betweenness present larger variations. The finding suggest that the road street network of the Central and North-East regions is highly efficient as large values of closeness are generally associated with high accessibility of a place (Porta et al., 2012). Despite the fact that some studies have shown the difficulties in linking betweenness and real dynamic traffic flows, low average values of this indicator are signal that there are very few nodes playing an important role in the network. Under the static case, this setting is a general result of planned traffic intervention (Kirkley et al., 2018). Table 2: Correlation between indicators

Land to str.

Int. den.

-0.29 (0.13) 0.89 (0.94) 0.12 (-0.18) 0.44 (-0.06) 0.66 (0.21) 0.10 (0.06) 0.32 (0.22)

-0.03 (0.15) -0.13 (-0.04) -0.43 (-0.34) 0.06 (0.15) 0.11 (-0.03) 0.07 (0.27)

0.20 (-0.14) 0.16 (-0.09) 0.69 (0.24) 0.13 (0.05) 0.45 (0.25)

Four-way p.

Int. den. Four-way p. Deg. Clo. Betw. Inf.

-0.04 (-0.06) -0.01 (-0.06) 0.06 (-0.04) 0.36 (0.05)

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Str. den. Str. den.

-0.03 (-0.04) 0.02 (-0.07) -0.38 (-0.40)

0.40 (0.32) 0.69 (0.62)

0.36 (0.27)

Notes: Correlations at the subzone level in brackets. Values significant at p < 0.01 are bold.

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Table 2 displays the correlation matrix of the eight indicators. In regards with the streetconnectivity, it is interesting to notice that street density and street intersection density have the strongest positive correlation (r = 0.89 for planning areas and r = 0.94 for subzones). The land allocated to street has a totally different pattern as it is negatively correlated with the other three connectivity indicators, but only significant with four-way proportion and street density. The results also show that degree is not correlated with closeness or betweenness. But the correlations between closeness, betweenness and information centrality are positive and significant. This finding is consistent with previous studies (Crucitti et al., 2006). The (linear) correlation between streetconnectivity/centrality indicators is interesting to analyze as it is found that street density and street intersection density have high positive correlation with the centrality indicators. Again, the land allocated to street shows mixed results. In summary, at least in the case of Singapore, it seems that apart from land allocated to street and degree centrality, there is a clear trend showing positive correlation of street-connectivity/centrality indicators.

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4.2. Statistical distributions Figure 3 reports the distribution of the eight indicators by type of land use. The distributions are analyzed by planing areas only because at the subzone level the power of the statistical tests, which are performed later on in this section, would decrease if the observations are subzones due to these polygons contains a smaller number of nodes. 8

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Figure 3(a) displays the histogram of the four street-connectivity indicators, and as one can see, residential areas have the largest values of street density and four-way proportion compared to business, industrial and special use areas. They also have right-skewed distribution of intersection density and optimal values of land allocated to street. The special use planing areas have low values of street density and street intersection density, combined with very high values of land allocated to street. Intuitively, the results here indicate that special use areas permit for comprehensive planning consisting mainly in streets and roads.

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(a) Histograms of street-connectivity indicators

(b) Complementary cumulative distribution function (CDF) of street-centrality indicators. Each line corresponds to one planning area. Each figure also shows the log-log plots aggregated by land use. The estimated exponents by least square that fits on slopes for street-centrality are shown in dotted lines

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Figure 3: Histograms and complementary cumulative distribution function (CDF) of street-connectivity indicators and street-centrality indicators; planning areas

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Figure 3(b) displays the complementary cumulative distribution function (CDF) of the centrality indicators for each one of the 52 planning areas. This type of plots is often used in complex network theory because they allow to explore possible power law distribution of centrality (also called scalefree networks). Each figure contains a subfigure with log-log plots grouped by land use which illustrates how the power low actually fits the centrality. In general, identifying power law fits in street-centrality is important because they can give an idea of possible highly uneven distribution of the centrality over self-organized networks. This means that most nodes have low centrality scores and coexist with a few nodes with high values of centrality. The statistical analysis of the power law tests is shown in Appendix A.2 and Table 3 gives the results. The set of alternative distributions to test include log-normal, exponential, stretched exponential and power-law with exponential cut-off (i.e., a power law distribution multiplied by an exponential distribution). The values of the table provide evidence that the distributions of closeness and information have a good fit to a power law. In the case of closeness in special use areas, the log-normal distribution is better than the power-law distribution. Note that the results also suggest that the power law with cut-off distribution is empirically indistinguishable from the power-law 9

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distribution as all the p − values are always larger than 0.1. In the case of degree and betweenness one can conclude that they do not fit well by a power-law model and there is no plausible alternative model for it. Table 3: Tests of power-law behavior in the centrality indicators Stretched exponential NLR p Degree 0.926 -0.561 0.575 0.220 0.278 0.781 0.924 -0.093 0.926 0.514 -0.078 0.938 Closeness 0.193 -0.777 0.437 0.003 1.800 0.072 0.099 1.652 0.099 0.010 1.305 0.192 Betweenness 0.023 2.137 0.033 0.003 2.725 0.006 0.006 2.351 0.019 <0.001 5.944 <0.001 Information 0.700 0.043 0.966 0.645 0.042 0.967 0.858 0.027 0.979 0.837 0.028 0.978

Exponential NLR p

<0.001 0.001 0.003 0.001

-0.520 -0.046 -0.090 -0.111

0.603 0.964 0.928 0.912

-0.092 1.226 0.096 0.653

Residential Business Industrial Special use

0.177 0.190 0.159 0.167

-0.741 -1.042 -1.184 -3.410

0.459 0.297 0.236 0.001

-1.302 2.957 1.649 2.567

Residential Business Industrial Special use

<0.001 <0.001 <0.001 <0.001

-0.810 -1.076 -0.944 -0.363

0.418 0.282 0.345 0.716

2.280 2.972 2.745 4.098

Residential Business Industrial Special use

0.179 0.157 0.184 0.171

0.001 0.001 0.001 0.001

0.999 0.999 0.999 0.999

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Residential Business Industrial Special use

0.386 0.461 0.179 0.206

Power law with cut-off LR p

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Log-normal NLR p

-0.782 -0.060 -0.037 -0.057

Support for power law

0.211 0.729 0.786 0.735

none none none none

-0.449 <0.001 <0.001 -0.007

0.343 0.998 0.999 0.904

good good good moderate

<0.001 <0.001 <0.001 <0.001

0.992 0.999 0.999 0.999

none none none none

-0.111 -0.141 -0.037 -0.046

0.638 0.638 0.786 0.762

good good good good

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Power law p

Notes: The normalized log-likelihoo ratio test (NLR) is directly used to calculate the p − value (p) while for the power law with exponential cut-off it is given the the log-likelihood ratio (LR). The column “support for power law” labels the good fit of the power law model according to the four categories proposed by Clauset et al. (2009): (i) none (the data is probably not power-law distributed); (ii) moderate (the power law is a good fit but that there are other plausible alternatives); (iii) good (the power law is a good fit and none of the alternatives considered is plausible), and; (iv) with cut-off (a power law with exponential cut-off is favored over a pure power law). Values significant at the 10% are bold.

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Table 4 reports the results of the scaling parameter α after 2,500 iterations. The calculations are performed for closeness and information only as their power law behavior have been demonstrated in Table 3. The estimated α ˆ parameters correspond with the dotted lines slopes in Figure 3(b) and the power law patterns of the centrality measures only occur when x ≥ xmin . An interesting property of the power law distributions is that, when α ≤ 2, the first moment (the mean) is infinite, along with all the higher moments. In fact, empirical studies suggest that in real networks α ∈ (2, 3) (Crucitti et al., 2006; Kirkley et al., 2018). In other words, the magnitude of α is important because it tells us when the mean and the variance of the distribution can be used to characterize it and when it cannot. For example, for α > 2, as all cases in Table 4, the mean is well defined. This type of analysis implies useful consequences because one can use the well-known 80:20 rule: W = P (α−2/α−1) , (1) which indicates that the W proportion of the total centrality is concentrated in the P percent of the nodes. For example, 64% (14%) of the total information (closeness) in residential areas is concentrated in only 10% of the nodes, and as α → 2 this asymmetry gets progressively more extreme as it is the case of closeness in industrial areas. Useful insights to understand the origin of 10

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Table 4: Basic parameters of centrality indicators along with their power-law fits

Residential Business Industrial Special use

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Residential Business Industrial Special use

α ˆ ntail Closeness 60 8.63 65 7 5.98 18 5 2.90 104 4 3.20 142 Information 134 2.24 51 22 5.08 11 22 5.02 26 22 9.39 21

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this heterogeneity, can be derived by the preferential attachment process (Crucitti et al., 2006; Porta et al., 2006). This process suggests that new nodes generated by the transportation authorities, such as intersections, attach preferentially to already well-connected nodes. The procedure results in a street network structure with skewed centrality distribution. 4.3. Relation with socio-economic indicators

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In Singapore, there is evidence not only that the less wealthy households spend more income and time in transportation because they are located in peripheral areas (Lau, 2011), but also that high-income households have better access to the urban rail transit system (Zhu and Diao, 2016). Figure 4 takes a step in this direction. By using Principal Component Analysis, there are computed four indexes (connectivity-planning areas; connectivity-subzones; centrality-planning areas, and; centrality-subzones). This technique searches for axes, called principal components, along which projected observations show the highest variance. The resulting first principal components are often used to explore the structure of variation in the sample. Principal Component Analysis is based on an eigenvalue problem and the technique is particularly relevant because it decorrelates the original measurements shown in Table 2, and it provides a projection of the data that maximizes the differences of connectivity/centrality between geographical areas. Each version of the index is an optimal linear combination of the measures used to summarize their interrelationships. The approach of introducing an overall connectivity/centrality index by means of Principal Component Analysis have been used before by Strano et al. (2013), among others. Appendix A.3 documents in detail the construction of the index. The first version of the index, called Street connectivity index uses the four traditional streetconnectivity indicators while the other one, called Street centrality index, is constructed from the four centrality-based indicators. Table 5 summarizes the main information related to each index. In every case, two components are used to generate the overall index and each explains more than 70% of the original variance of the data. The left-hand side of Figures 4 plots both indexes, and one can clearly see a positive association between them. Nevertheless, the relationship is not straightforward. Each doth represents one of the planning areas and subzones, respectively. The normal 95% confidence ellipse clusters similar observations so that observations outside the ellipse are atypical points. In other words, they score relatively well in one version of the index but relatively bad in the other version.

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(a) Planning areas

(b) Subzones

Figure 4: Street connectivity/centrality index and its correlation with other indicators Table 5: Eigenvalues and cummulative contribution of the street connectivity/centrality index

Eigenvalue

Variance (%)

Cumm. Cont. (%)

Planning areas

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Str. Con. Ind. (two components) 2.01 50.16 1.02 25.52 Str. Cen. Ind. (two components) 1 2.04 50.98 2 1.09 27.15

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1 2

50.16 75.68 50.98 78.13

Subzones

Str. Con.Ind. (two components) 1.96 49.08 1.03 25.62 Str. Cen. Ind.(two components) 1 1.94 48.45 2 1.02 25.54

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1 2

49.08 74.70 48.45 73.99

The right-hand side of Figure 4 explores the relation between the indexes and other socioeconomic and geographical indicators. The analysis is disaggregated by type of land use and the data

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sources are: (i) the General Household Survey 2015 (for average income and population density); (ii) the average monthly rental price index by subzone computed in Benita et al. (2019a); (iii) postal code data of 454,368 new registered companies between 2012 and 2018 according to the Accounting and Corporate Regulatory Authority (for total companies), and; (iv) the Master Plan 2014 (for percentage of green areas). Among the results, at the planning area level, there is a strong positive (negative) association between connectivity (centrality) and the number of companies in industrial areas. This is, industrial areas with larger number of companies tend to exhibit good (poor) street connectivity (centrality). Conversely, apart from centrality in commercial zones, the granular analysis by subzone reveals that this correlation is positive in both version of the index for business, industrial and commercial zones. The result is in line with Porta et al. (2009) and Porta et al. (2012) who reported that local centrality scores (represented by buffers inside cells of a grid) are associated with characteristics of the economic activities such as larger number of companies or concentration of specific industries. With respect to the percentage of green space in special use areas, one can observe that the indexes do not correlated with the variable. It is interesting to observe that contrary to previous empirical investigations, both indexes seem to be either negative or weakly positive associated with income levels. The exception is the average rental price in residential mix subzones (r = 0.47). A possible explanation is that this work uses aggregated results of street-connectivity/centrality by planning area and subzone while past research made us of more granular data at the household level. Hence, if one thinks of Singapore as a set of self-organized and well-delimited neighborhoods, as the case of planning areas and subzones, one can conclude that the less wealthy areas are as well connected in terms of the road street network as the wealthier ones (typically located at the Central region). 5. Latent Profile Analysis on street-connectivity and street-centrality

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The final stage of the analysis consists in finding answer to the question of whether streetconnectivity/centrality indicators can be used to classify urban areas according to meaningful and intuitive groups such as regions or types of land use as shown in Figure 1. This classification task is relevant in light of the emerging hypothesis that, at least in some common types of cities, commercial uses and land-use intensity are subject to the distributed attraction exercised by the connectivity/centrality of the street network (Porta et al., 2009; Wang et al., 2011a). Gaining a deeper understanding of these interactions is critical in today’s rapidly transforming urban environments because it is not clear whether the planned land use pattern and the proposed street layout follows a systematic spatial logic (Geurs et al., 2006; Xiao et al., 2017). Hence, the profiling exercise in this section can be seen as a generalization of the above mentioned hypothesis as there are considered not only commercial areas but also residential, business, industrial and special use areas. In doing so, there are created homogeneous clusters or profiles of according to their streetconnectivity/centrality characteristics. For this task, LPA is of great utility. The technique is a special case of mixture models in which it is assumed that the population consists of unobserved profiles. The model is based on a categorical latent variable, say, profiles, and continuous indicators, say street-connectivity/centrality indicators. The number and the nature of the profiles are unknown and must be inferred from the data. The purpose of LPA is to find a solution with a sufficient number of profiles that reveals a distinctive pattern of responses between the different profiles but relatively homogeneous responses within each profile. Thus, the number of profiles or clusters will be defined by the algorithm. To compare models with different sizes of clusters and select the best configuration it is used the Bayesian Information Criterion. Appendix A.4 describes in detail the process of the LPA algorithm. 13

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Three types of settings are tested, namely: street-connectivity indicators, street-centrality indicators, and all eight indicators. The idea is to compare how similar or different the results are. This comparison of similarity among profiles can be made by means of the Normalized Mutual Information (NMI). The NMI ∈ [0 − 1] measures the mutual information entropy between resulted planning areas/subzones profiles and ground truth labels (Lancichinetti and Fortunato, 2009). The NMI is an extremely useful tool to compare profile outputs between different configurations. When NMI is close to 1 it means that two configurations are allocating the observations in the same profiles, whereas values close to 0 indicate that the two configurations give completely different results. The interested reader is referred to Appendix A.5 for a more formal definition of NMI. Table 6: Normalized Mutual Information results

1 0.10 0.46 0.19 0.07

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Str. con. ind. (7 profiles) Str. cen. ind. (7 profiles) All eight ind. (5 profiles) Land use (6 types) Regions (5 regions)

Planning areas Str. cen. ind. All eight ind. 1 0.42 0.27 0.31 Subzones

Pr e-

Str. con. ind. (5 profiles) Str. cen. ind. (5 profiles) All eight ind. (5 profiles) Land use (4 types) Regions (5 regions)

Str. con. ind. 1 0.36 0.66 0.50 0.29

1 0.17 0.12 0.23

Land use

Regions

1 0.45 0.39

1.00 0.14

1.00

1 0.22 0.09

1.00 0.13

1.00

Notes: Best configurations for land use and regions (by row) in bold font.

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The main results from the profile analysis are summarized in Table 6. First, one needs to notice the (dis)similarity between regions and land use which gives NMI = 0.14(0.13) for planning areas (subzones). This means that regions do share mixed land use. Second, one can observe what happens if the street-connectivity/centrality indicators are used to classify the geographical units. From the table, connectivity outperforms centrality at explaining the land use of planning areas (0.50 vs 0.27). Interestingly, the combination of both type of indicators can yield a better classification performance (0.22) than connectivity (0.19) or centrality (0.12) only. Similarly, in regards with the regions, the findings are also mixed as the combination of indicators works better for planning areas (0.39) whereas for subzones, centrality indicators do a better job (0.23). The magnitude of the difference in NMI values is important to highlight as it is not marginal and one can truly appreciate the improvements of the best configuration with respect to the alternatives. Lastly, a very important remark is that, when the “all eight indicators” model is ruled out, one always have that land use is better explained by street-connectivity whereas regions are better explained by street-centrality. By computing the similarity between street-connectivity and street-centrality profiles, one gets 0.10 by subzones, which means that each classifications splits these areas into completely different profiles. The result was somehow expected as the (linear) correlation between both type of indicators is relative low at these highly disaggregated geographical units. See for example Table 2, the small correlation between degree/betweenness with respect to street density/street intersection density/four-way proportion. Finally, Figure 5 illustrates the best configurations. Note that the original data was standardized to have mean 0 and standard deviation of 1 because the unit measure of all indicators is different 14

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(a) Profiles that best explain land use by planning areas and subzones. Average z-scores.

(b) Profiles that best explain regions by planning areas and subzones. Average z-scores.

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Figure 5: Planning areas’ and subzones’ profiles

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and the z-scored is the most widely used method of standardization. Higher average z-scores are associated with large values of the indicator. By taking the example of regions by planning areas, the left-hand side of Figure 5(b) illustrates how profiles 3 and 5 are associated with the Central region. They have the largest average values of street density, street intersection density degree, closeness and information centrality which is consistent with the findings of Figure 2. A similar argumentation holds for the land use at the planning area level, shown in the left-hand side Figure 5(a). It is observed that profile 4 matches the special use areas which are the ones that have the largest proportion of land allocated to street but they also have poor street density and street intersection density. The result is consistent with Figure 1(a). 6. Discussion and conclusions This paper studies the relationship between street-connectivity indicators, street-centrality indicators, and major land use-types in Singapore. Different from previous studies, these relationships

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Acknowledgments

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are addressed using two levels of spatial aggregation as shown in Figure 1. The findings from Section 5, in particular Table 6, confirm that both type of indicators can be used to classify the urban patterns of the city in terms of land use and geographical regions but the results are mixed. On the one hand, if the combination of indicators is not taken into account, land use is better explained by street-connectivity whereas regions are better explained by street-centrality. This study supports the view that connectivity indicators are more suitable than centrality metrics for investigating the associations between street layouts and land use. Notwithstanding, the evidence suggests that at least in the case of Singapore, the combination of both type of indicators improves classification’s accuracy. On the other hand, the level of spatial aggregation plays an important role during the statistical analysis phase. For example, the study of larger spatial units, e.g., planning areas, results in larger variation of indicators’ values as displayed by Figure 2. This yields poor correlations between the street-connectivity/centrality with other socio-economic and demographic information, see Figure 4. If the analysis is performed by smaller spatial units, e.g., subzones, the interactions of street-connectivity/centrality with other variables is stronger and closer to the evidence suggested in previous studies (positive associations with rental housing prices and number of companies). Clearly, the key seems to reside in the indicators used to measure connectivity/centrality. An example of this is seen in the behavior of the land allocated to street (extremely high in areas of special use, see Figure 3(a)) or the closeness and information centrality (showing a power law statistical distribution, see 3(b)). The main aim of the study is not to offer a full account of the land use and regional patterns of a city by means of its street connectivity/centrality, but to strengthen the claim that both type of indicators exercise an important role describing the urban structure for urban planning and design. Additionally, the methodology adopted can guide local governments in relocating and retrofitting existing land use patterns without the need for costly socioeconomic data and by taking advantage of the existing road street network. Namely, local planning authorities may consider the methodology as an inexpensive evaluation mechanism that would allow them to more accurately assess changes and trends in land use. But does these results hold in different cities? Up to which level of spatial detail should urban planners do the analysis? The proposed methodology is applicable as it is to any other city, in particular the large metropolis of Asia such as Hong Kong, Taipei, Seoul or Tokyo. For instance, the equivalent of planning areas (subzones) in Singapore are the municipalities (sub-municipalities) in Seoul. Whereas the empirical results of this work indicate the merits of the proposed method, its efficiency needs to be tested by using data from different cities world-wide in order to examine the universality of the observed relationship between street-centrality/connectivity and the developments of different land uses.

The authors would like to express their gratitude to the anonymous referees, whose valuable comments and recommendations greatly helped improve the paper’s quality. Author contributions

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Francisco Benita conceived and designed the analysis. Georgios Piliouras supervised development of work, helped in data interpretation and manuscript evaluation.

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Appendix A. Appendix A.1. Centrality indicators

CiC = P

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Let the road street network be represented as an undirected edge-weighted graph (G, w) where G = (N , E) is a graph and w : E → R is a weight function (i.e., distance). Here N is the set of nodes (with |N | = N ) and E is the set of edges (with |E| = E). Moreover, N (G) and E(G) represent the nodes and edges of G, respectively. The graph G is described by the adjacency matrix A ∈ RN ×N , whose entry aij is equal to 1(0) when there is (there is no) edge between nodes i and j. The degree centrality of node i is defined as (Wasserman and Faust, 1994): P ki j∈N aij CiD = = , (A.1) N −1 N −1 where ki is the degree of node i, this is, the number of nodes adjacent to i. The closeness centrality of node i is computed by (Wasserman and Faust, 1994): N −1

j∈N (G) j6=i

dij

,

(A.2)

CiB =

Pr e-

where d is the shortest path length between node i and j. The betweenness centrality of node i is computed by (Freeman, 1978): 1 (N − 1)(N − 2))

X

j,k∈N (G) j6=k6=i

sjk (i) , sjk

(A.3)

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where sjk is the number of shortest paths between nodes j and k, and sjk (i) is the number of shortest paths between j and k that pass node i. Note that equation (A.3) is normalized such that Cib ∈ [0, 1]. One can define a variety of different shortest paths depending on how the weights are established (speed-limits of each edge, Euclidean distances, route preferences, etc.) (Kirkley et al., 2018). In this work the shortest paths are computed by minimizing of the sum of the weights of links, which is the length of the street segments. The information centrality takes into account the performance before and after a node is deactivated measured by the efficiency, Ef f , of the graph G. The information centrality of node i is given by (Latora and Marchiori, 2007):

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CiI =

Ef f [G] − Ef f [Gi ] , Ef f [G]

(A.4)

where Ef f [Gi ] is the decreased efficiency of the graph G i that the node i is removed. The graph G i has N i nodes and K − ki edges by deleting the edges incident in node i from the original graph G. The efficiency of the graph G can be computed by: 1 N −1

X

i,j∈G,j6=i

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Ef f [G] =

dstraight ij , dij

where dstraight is the Euclidean distance between nodes i and j along a straight line. ij

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Figure A1: Centrality measures. Five groups of intensity according to the Jenks natural breaks classification method

Appendix A.2. Power law A power law distribution is a special type of probability distribution described by a parameter α > 1. The probability that the centrality is drawn from a distribution with a given α can be described by a likelihood function L(α, x). Then it is used the maximum likelihood estimation to obtain α (denoted α ˆ ). For a given power law of the form f (x) ∝ x−α ,

(A.5)

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the most likely estimate of α is given by:

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α ˆ = 1 + ntail

n tail X i=1

ln



xi xmin

!

,

(A.6)

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where xmin corresponds no to the smallest value of x measured but to the smallest for which the centrality obey a power law, and ntail is the number of data points in the subsample xi , i = 1, . . . , ntail . To get a handle on the uncertainty in the parameter estimates, α ˆ , it is used the bootstrapping procedure of Clauset et al. (2009) based on maximum likelihood to estimate this parameter as well as check all possible values of xmin . Next, it is performed an hypothesis test using a goodness-of-fit test such that H0 : the centrality indicator is generated from a power law distribution. If the p − value is small (p < 0.1), then the power law model does not provide a plausible fit. The goodness of fit of the power-law distributions need to be carefully assessed to determine if they are better models compared to rival distributions. In doing so, alternative models are estimated to explore whether they fit better the centrality indicators. As detailed in Clauset et al. (2009), there are considered the following rival models: log-normal, exponential, stretched exponential and powerlaw with exponential cut-off. Vuong’s likelihood ratio test is then implemented to determine which 18

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model is most favored by the data. This is a directional test, so it can be positive or negative, if positive (negative) then the power-law model gives a better (worse) fit compared to the alternative distribution. Additionally, the p − value of the test tells us whether the observed sign is statistically significant. If the p − value for the likelihood ratio test is small (p ≤ 0.1 by convention), then the model which gives a worse fit to the data is rejected. Alternatively, if the p − value is large (p > 0.1) then one is not able to choose between the two compared models.

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Appendix A.3. Connectivity/centrality index based on Principal Component Analysis

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For each version of the index, the data matrix, X, has m(m = 4) indicators and n(n = 52 for planning areas, and n = 302 for subzones) observations. First, each indicator is centered to have mean 0 and scaled standard deviation 1. For convenience, the normalized matrix would be still denoted by X. Second, let λ1 ≥ λ2 ≥ · · · ≥ λm ≥ 0 be the eigenvalues of the covariance matrix, S, of X with corresponding eigenvectors e1 , e2 , · · · , em . Third, the contribution rate of the k-th principal component is given by Pmλk λi and the cumulative contribution rate of the first k principal i=1 Pk i=1 λi Pm . Third, i=1 λi

according to the Kaiser (1970) criterion one should retain components is denoted by the first k principal components whose λk ≥ 0, and in practice its cumulative contribution rate is higher than the 65%. The Principal Component Analysis solves the eigenvalue problem i = 1, . . . , m.

Pr e-

λi ei = Sei ,

Based on the estimated ei , the components Hi are then calculated from an orthogonal transformation of X. Finally, the connectivity/centrality index of each geographical area a(a = 1, . . . , n) can be computed by:  k  X λi Pm hai , CIa = (A.7) i=1

i=1

where hai are the elements of component Hi . Note that the index of equation (A.7) is a weighted sum using the contribution rate of the k-th principal component. Appendix A.4. Latent Profile Analysis

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In LPA the latent profile membership of observation a(a = 1, . . . , n) is estimated as a probability conditional on observation’s response indicator scores. The data is expressed by m (being m = 4 or 6 depending on the configuration) continuous indicators observed on the geographical units. The indicators need to be standardized as in the Principal Component Analysis so that they can be denoted by X1 , . . . , Xm , where xja is the observed response to indicator j for observation a. LPA finds the P (p = 1, . . . , P ) optimal number of profiles. The representation of the LPA model is given by (Hagenaars and McCutcheon, 2002): f (xa | θ) =

P X p=1

πp fp (xa | θp ),

(A.8)

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where xa := (xa1 , xa,2 , . . . , xam )> is the vector of observation responses on the set of observed streetconnectivity/centrality indicators. P is the total number of profiles, and the parameters πp and θp are estimated by maximum likelihood.

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Appendix A.5. Normalized Mutual Information The NMI between two profiles P1 and P2 can be expressed by (Danon et al., 2005):   PnP 1 PnP 2 Nij N −2 i=1 j=1 Nij · log Ni. N,j    , NMI(P1 , P2 ) = PnP1 PnP2 Ni. N.j + j=1 N.j · log i=1 Ni. · log N N

(A.9)

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where nP1 , nP2 ∈ N denote the number of real communities (i.e., the ground truth labels) in P1 and P2 , respectively. N is a confusion matrix where the rows correspond to the real communities, and the columns correspond to the found communities. Nij is the number of nodes in the real community i that appear in the found community j. On the other hand, Ni. (N.j ) corresponds to the sum over row (column) i (j) of matrix N .

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