# Prediction of Transportation Index for Urban Patterns in Small and Medium-
sized Indian Cities using Hybrid RidgeGAN Model

Rahisha Thottolil  Spatial Computing Laboratory, Center for Data Sciences,
International Institute of Information Technology, Bangalore, 560100, India.
Uttam Kumar  Spatial Computing Laboratory, Center for Data Sciences,
International Institute of Information Technology, Bangalore, 560100, India.
Tanujit Chakraborty  Spatial Computing Laboratory, Center for Data Sciences,
International Institute of Information Technology, Bangalore, 560100, India.

###### Abstract

The rapid urbanization trend in most developing countries including India is
creating a plethora of civic concerns such as loss of green space, degradation
of environmental health, clean water availability, air pollution, traffic
congestion leading to delays in vehicular transportation, etc. Transportation
and network modeling through transportation indices have been widely used to
understand transportation problems in the recent past. This necessitates
predicting transportation indices to facilitate sustainable urban planning and
traffic management. Recent advancements in deep learning research, in
particular, Generative Adversarial Networks (GANs), and their modifications in
spatial data analysis such as CityGAN, Conditional GAN, and MetroGAN have
enabled urban planners to simulate hyper-realistic urban patterns. These
synthetic urban universes mimic global urban patterns and evaluating their
landscape structures through spatial pattern analysis can aid in comprehending
landscape dynamics, thereby enhancing sustainable urban planning. This
research addresses several challenges in predicting the urban transportation
index for small and medium-sized Indian cities. A hybrid framework based on
Kernel Ridge Regression (KRR) and CityGAN is introduced to predict
transportation index using spatial indicators of human settlement patterns.
This paper establishes a relationship between the transportation index and
human settlement indicators and models it using KRR for the selected 503
Indian cities. This nonlinear KRR model helps in deriving the transportation
network for GAN-generated human settlements through the settlement indicators.
Our approach leverages human settlement indices, which capture information
about demographics and urban land use to predict the transportation index. The
proposed hybrid pipeline, we call it RidgeGAN model, can evaluate the
sustainability of urban sprawl associated with infrastructure development and
transportation systems in sprawling cities. Experimental results show that the
two-step pipeline approach outperforms existing benchmarks based on spatial
and statistical measures. By predicting future urban patterns, this study can
help in the creation of more livable and sustainable cities, particularly by
improving transportation infrastructure in small and medium-sized Indian
cities.

###### keywords:

Generative adversarial networks, kernel ridge regression, hybrid model, deep
learning, World Settlement Footprint

## Introduction

Mapping urban land use dynamics has been valuable research in urban studies
over several decades. The advancement in remote sensing technology makes it
possible to track the spatiotemporal changes in urban landscape structures
with relatively high accuracy and on a required scale [1]. The spatial
distribution of land use activities (residential, commercial, industrial,
etc.) including the transportation system is important for understanding the
current urban centers and for planning future city development [2]. Land use
and land cover maps become a starting point for modeling urban patterns and
they can infer the future urban growth and the direction of land expansion of
cities to inform urban planners and government policymakers towards
sustainable urban planning [3, 4, 5]. While urban areas continue to experience
rapid growth, they pose new challenges to the nation, especially for
developing and underdeveloped countries [6]. Hence, urban growth prediction
models and related studies have become a hot topic that has been extensively
and deeply investigated. The existing urban growth models [7, 8, 9, 10]
include the driving factors which affect urban expansion. These factors
influencing urban expansion include population growth, economic development,
urbanization, transportation infrastructure, topography, and land use
regulations [11]. However, in developing and underdeveloped nations, where
urban expansion is more likely to occur, data on driving forces are hard to
obtain and are often expensive to collect.

According to the UN report [12], India is the most populous country in the
world. From 1901 to 2011, the country’s urban population expanded by around 14
times [13]. Although largely unequal, its increase is not skewed and is not
limited to one region across the nation. The skyrocketing living costs in
metropolitan areas and increasing house rents discourage enterprises from
investing in major cities. Therefore, it is essential to assess the settlement
pattern and infrastructure facilities of small and medium towns as an
alternate option to larger metropolitan cities [14]. These towns sometimes
called the “next billion” markets, will be important in propelling the
expansion of the national economy in India [15]. Further to the intricacy of
urban settlement, more basic infrastructure and facilities are required for
these regions.

Various reports in recent years have estimated a massive demand for funding
urban infrastructures in developing countries. The World Bank estimates that
nearly 70000 Billion (INR) of investment in urban India will be required to
meet the growing population demands in the next 15 years until 2036 (in 2020
prices) [16]. For example, the Indian Government introduced a scheme called
the Integrated Development of Small and Medium Towns (IDSMT) project that aims
to encourage the planned and sustainable growth of the nation’s small and
medium-sized towns or cities [15]. The Ministry of Urban Development,
Government of India introduced this scheme in 2005, and it offers financial
and technical assistance to local governments in order to help them develop
their towns’ infrastructure and fundamental services. This scheme focuses on
the expansion of small and medium-sized towns (the population size is up to
500K), which may act as growth hubs for the nearby rural regions, in order to
promote inclusive growth and balanced regional development. By providing
funding for the construction of fundamental utilities including water supply,
sanitation, solid waste management, and urban transportation, the program
seeks to solve the infrastructure deficit and service shortages in these
communities. The overall goal of the IDSMT program is to support sustainable
urban growth and raise the standard of living in India’s small and medium-
sized towns. As a result, it is important to examine the small and medium
towns (Tier 3 and above cities with populations up to 500K) in India. Adopting
cutting-edge technologies can have a significant impact on enhancing
Government’s effectiveness in improving planning and decision-making, problem-
solving, accelerating development, and deployment [17].

To mitigate this urban planning challenge, recent developments in machine
learning and deep learning have become handy tools for urban planners and
geoscience practitioners. Deep learning models such as Generative Adversarial
Networks (GAN) can approximate complex, high-dimensional probability
distributions [18]. GANs have achieved numerous state-of-the-art breakthroughs
in the fields of computer vision [19], natural language processing [20], and
more recently in urban science and geospatial domain [21, 22]. Several GAN-
based models have been proposed to simulate hyper-realistic urban land use
maps and generate synthetic urban universe without considering the driving
factors, see for example CityGAN [23] and MetroGAN [24]. Among these, CityGAN
[23] simulates urban patterns using global urban land-use inventory and builds
an “urban universe” to reproduce the complex spatial patterns observed in
global cities. An extension to CityGAN by incorporating geographical knowledge
is called Metropolitan GAN (MetroGAN) [24] which learns hierarchical features
for urban morphology simulation. Another deep learning method, namely U-Net
[25], is also applied to generate future urban cities using water bodies,
digital elevation models, and nighttime lights as inputs [22]. The application
of previous GAN-based urban models was limited to the generation of urban
patterns. There are limited works on quantifying the urban pattern of GAN-
generated images and predicting the transportation metric (representing urban
infrastructure) for these new urban regions. Thus, quantification and modeling
of landscape patterns of those GAN-simulated cities remain an unattempted
problem. The structure of a landscape emerges from the characteristics of the
individual elements of an ecosystem and their spatial configuration [26, 27,
28, 29]. Human Settlement Indices (HSI), e.g., Class Area (CA), Number of
Patches (NP), Largest Patch Index (LPI), Clumpiness Index (CLUMPY),
Aggregation Index (AI), and Normalized Landscape Shape Index (NLSI) [30, 31,
32] provide some concrete information about the landscape structures and
therefore contributes in the prediction of Transportation Index (TI). This
paper makes an attempt to answer the following challenging questions:

  1. (a)

How to generate an urban universe for India based on spatial patterns via
learning urban morphology?

  2. (b)

Is there a relationship between HSI and TI in small and medium cities in
India?

  3. (c)

How to predict (forecast) TI for synthetic urban cities generated by CityGAN
for developing countries like India?

To generate small and medium-sized Indian cities with CityGAN, we collected
the World Settlement Footprints (WSF 2019) maps which are publicly available
and the best representations of urban patterns as input features [33, 34].
Then, we build a city image database of 503 small and medium Indian cities
whose populations range between 20K and 500K. Each city image represents
$10.5\times 10.5$ km covering the urban center and surrounding regions. We
also explored existing spatial and statistical measures to evaluate the
performance of CityGAN in Indian cities due to the complex nature of
individual cities with varying structural and hierarchical properties [23].
Assessing the spatial relationship between urban patterns (human settlement)
and the transportation index of actual cities can help to build a model for
predicting the transportation index for generated cities. We used different
linear and nonlinear measures of statistical correlations to establish this
spatial relationship. Furthermore, we propose a hybrid model (namely,
RidgeGAN) to predict the transportation index for simulated urban patterns.
Fig. 2 depicts the methodological framework. In RidgeGAN, a supervised
learning model (KRR) builds a relationship between the human settlement
patterns and the characteristics of the urban road transportation system and
implements this to predict TI for the GAN-simulated urban universe for India.
Our proposal has numerous applications, ranging from understanding urban land
patterns to predicting relevant urban infrastructure facilities to guiding
policymakers toward a better and more inclusive planning process.

## Background and related work

### Applications of GANs in geospatial field

Deep learning has reached a significant milestone in geospatial research,
computer vision and other cutting-edge technologies [35]. GAN [18], an
essential subfield of unsupervised deep learning, has opened a new vista for
geoscience research in recent years. GANs are utilized to generate data that
is close to a given training set which can be images, texts and tabular data
[36]. Geoscientists and urban planners have adopted this new deep learning
methodology for handling geophysical and remote sensing data. In remote
sensing, MARTA GANs were proposed for producing fake satellite images of urban
environments [37]. It consists of a discriminator network that receives both
real and synthetic images as input and predicts whether each image is genuine
or synthetic, as well as a generation network that uses random noise as input
to create synthetic images. Further, Spatial Generative Adversarial Networks
(SpaGANs) [38] were introduced for synthesizing textures by incorporating
spatial information (such as the position and orientation of the texture) into
the generator and discriminator networks. A comprehensive review of GANs
demonstrates promising performance in the built environment, from processing
large-scale urban mobility data and remote sensing images at the regional
level to performance analysis and design generation at the building level
[22].

In addition, GANs were also applied to modeling global urban patterns. For
example, CityGANs [23], conditional GANs [39], and MetroGANs [24] was built to
generate urban land patterns by training the generator networks to generate
synthetic images of urban areas that closely resemble real urban areas and it
will be useful for analyzing urban human settlement data from space-based
sensors. For more accurate urbanization parameters or spatial indices
estimates in locations where local data is unavailable or impossible to
collect, these models are very effective in simulating urban land use
patterns. GANs are used to model hyper-realistic settlement patterns since
they do not make any assumptions about the data distribution and can generate
real-like samples from the latent space in a straightforward manner. This
unique property lends GANs to a variety of geospatial applications, including
image synthesis, image attribute editing, image translation, domain
adaptation, and other computing fields [40].

### Transportation and urban landscape structures

The spatial structure of a city is extremely complex and is constantly
evolving. Therefore, there are significant attempts to analyze cities, and
thus to link urban policy to shape cities. Delineating
homogeneous/heterogeneous human settlements, quantifying them, and analyzing
their diversity and spatial organization are necessary to assess their
structures and spatial patterns. Due to this, urban researchers utilized
landscape metrics to quantify the qualities of the landscape related to shape,
pattern, and area by measuring the structure and spatial distribution of
settlements. Landscape metrics were originally introduced in ecological
studies that reflected social, cultural, and ecological richness and
heterogeneity [41]. Also, progressive and well-functioning urban planning
departments can use spatial indicators to regularly monitor urban development
and, when necessary, propose regulatory or public investment action [42].
These indicators can also evaluate the geometrical characteristics of
ecological processes and landscape elements, as well as their relative
locations and distribution [43]. The effect of landscape metrics on spatial
patterns was studied to quantify landscape structures and these metrics can
statistically determine the outcome [31]. Spatial patterns of urban growth and
landscape metrics were studied for various cities in India [44, 30]. The
integration of efficient urban structures and comprehensive transportation
metrics plays a vital role in fostering sustainable development and improving
the overall livability of cities.

Understanding the interaction between transportation infrastructures and urban
pattern areas is always critical for driving smooth urban services. The
investigation into the development of mathematical models for studying the
relationship between transportation metrics and urban land use began in the
early 1960s and technological advancements brought us to an era of integrated
land use transportation modeling [45]. Several road network models have been
developed to solve transportation problems. Most of the existing
transportation models for prediction now in use are based on simple linear
regression models. An inverse relationship between urban growth and
transportation was found for the middle east regions [46]. Their analysis
suggested that urban population growth has increased urban trips and increased
travel demand due to transportation infrastructure.

In a recent study, the link between population and the characteristics of the
road network in the Lebanese Republic was investigated using a multivariate
regression model to estimate the population count based on various data
sources and statistical modeling techniques [47]. However, linear regression
models have the drawback of excluding all variables which are not linearly
connected, and multicollinear variables adversely affect the model. Besides,
it is proved that the relationship between transportation features and their
influencing factors is not always linear in nature. Predicting the
transportation index is an important step towards minimizing traffic
congestion and providing critical information to individual travelers as well
as various Government sectors to plan the city in a sustainable way. A support
vector regression (SVR) approach was used to predict traffic flow from
California highways using different types of kernels [48]. A road network
density (one of the transportation indices) prediction model was proposed
using highway capacity, and turning probabilities manual methods were used to
determine the shortest cycling time in metropolitan areas [49]. The model
could aid in vehicle distribution and congestion relief in urban areas.
Further, the concept of graph theory was used to analyze the topology of road
networks in an Indian city to better understand the connectivity and coverage
of the existing road transportation system [50]. Their findings indicate that
there is a strong relationship between road connectivity and coverage and that
improving the road network is essential for a reliable and safe road
transportation system. To accurately estimate the connectivity index, the
paper [50] proposed a model based on the relationship between the Eta index
and Network Density (ND), Edge Graph Density (EGD) and Nodal Graph Density
(NGD).

## Results

The scholarly literature on urban challenges primarily focuses on megacities
and large urban centers, but there are a great number of small and medium-
sized cities in developing countries that should be prioritized. There is a
pressing need to address the challenges of developing transportation networks
and settlement patterns in these cities. Previous literature on urban studies
does not adequately address the transportation, unplanned city growth and
socioeconomic and environmental challenges of small and medium-sized towns
[51]. In this study, we utilize global training WSF data across India, and we
demonstrate a simple and unconstrained GAN model to generate realistic
settlement patterns that encompass the diversity of urban forms. We are
primarily interested in how small and medium-sized cities are simulated using
unsupervised CityGANs. Subsequently, an effective data-driven hybrid model is
developed to predict road network density for a given urban settlement
pattern.

### Study area

Our study focuses on small and medium-sized Indian cities (South Asia), one of
the world’s fastest-urbanizing regions. The selection of the study area
involved the identification of the geographical location and corresponding
demographic data for which the population data from the World Cities database
( https://simplemaps.com/data/world-cities) were used. Approximately, 503
cities out of 1600 were selected for our study where the population size
ranges between 20k to 500k. The geographical location of study areas marked in
the map of India is depicted in Fig. 1(b) showing visualization of human
settlement patterns and corresponding transportation networks (also see Fig.
1(a) and 1(c)).

Figure 1: (b) Geographical distribution of 503 small and medium-sized Indian
cities included in the study (red colored square grids indicate the selected
cities); (a) and (c) are examples of human settlement and transportation maps
of two random cities, namely Calicut from the state of Kerala and Panihati
from the state of West Bengal.

### Data collection and preprocessing

Settlement footprints and transportation network datasets of all the selected
cities were collated from various sources over 2019. Settlement maps were
procured from the global inventory built-up database called WSF, published by
the German Aerospace Center (DLR). These are binary maps (urban area pixels
have a value of 1 and non-urban area pixels have a value of 0) derived from
multi-temporal space-borne satellites namely Sentinel-1 and Sentinel-2 data
that aided in estimating the human settlement pattern of an urban area
($10.5\times 10.5$ km) with a resolution of around 10m/px. Open source GIS
software (QGIS) was used to pre-process (rectify, project, and crop) the
images and build a city database. To measure Human Settlement Indices (HSI),
existing landscape metrics were selected and computed using Fragstat software
[52]. It includes the packages to compute popular landscape metrics using
spatial pattern analysis. We use six settlement indices: Total class area
(CA), number of patches (NP), largest patch index (LPI), clumpiness index
(CLUMPY), aggregation index (AI) and normalized landscape shape index (NLSI)
to estimate the characteristics of human settlement [30, 31].

CA is a useful metric to depict the spatial extent of the settlements. It is a
composition that specifies the extent of landscape that is made up of a
specific class type (e.g., built-up area). The total class area, which is the
sum of the areas (${m}^{2}$) of all the patches of the relevant patch type
divided by 10,000 (converted to hectares) and CA $>0$ indefinitely. NP in each
landscape indicates the degree of fragmentation that counts the number of
human settlements or urban patches. The higher the value of NP, the higher is
the fragmentation with no limit. At the class level, LPI estimates the
percentage of the total landscape area occupied by the largest patch as an
indicator of dominance. LPI is calculated by dividing the area (${m}^{2}$) of
the largest patch of the relevant patch type by the entire landscape area
(${m}^{2}$) and multiplying the result by 100 (converted to a percentage),
i.e., LPI is the percentage of the landscape comprised by the largest patch.
LPI values (0 < LPI < 100) decrease from the city center to the outskirts.
Another human settlement metric CLUMPY deals with aggregation and
disaggregation for adjacent settlements. It shows the frequency with which
different pairs of patch types appear side by side. The value ranges from -1
to 1; -1 indicates maximally disaggregated patch type, 0 when the patch type
is randomly distributed, and 1 when the patch type is maximally aggregated
[52]. Another metric AI is calculated using an adjacency matrix, which
indicates how frequently distinct pairs of patch types (including adjacencies
between the same patch type) appear on the map side by side in the settlement
map. Its values range from 0 to 100; AI values are less indicating maximum
disaggregation and the high AI shows the maximally aggregated single and
compact patch. Finally, NLSI provides a measure of class aggregation for which
the values ranges from 0 to 1, where 0 means the landscape consists of a
single square or maximally compact (i.e., almost square) patch. NLSI increases
as the patch type becomes increasingly disaggregated and reaches 1 when the
patch type is maximally disaggregated [30].

To compute the Transportation Index (TI), a layer of the road network that has
been topologically cleaned and converted into polylines is a prerequisite. The
application software used here is integrated with QGIS 3.30 for this purpose.
Individual cities and their corresponding road networks were extracted for
assessing the spatial patterns of the road systems corresponding to the
respective cities. As transportation measures need to be calculated in a
metric system, a projected coordinate system was used. Instead of common WGS84
- EPSG:4326, which uses degrees as a unit for distance, the Coordinate
Reference System WGS84/UTM-EPSG was used here, to measure road length in
meters. All categories of roads such as National highways, State highways,
major roads, street roads, residential paths, footways, and service roads were
included in this study. To measure the development of the urban road network,
the network density of the respective cities was computed as follows:

$\text{Network Density}\;(ND)=\frac{L}{A}=\frac{\text{Total length of the road
network}}{\text{City area}};$

where $L$ is determined from road maps and it has been calculated using an
open field calculator in QGIS software. Network length specifies the total
span of the road network and network density is measured according to the area
occupied by road networks (city area), denoted as $A$. Fig. 2 shows the
overall workflow of the proposed hybrid framework used in this study to
predict the transportation index for any kind of urban pattern in Indian
cities.

Figure 2: Prediction framework of the proposed hybrid RidgeGAN model: (a)
Implementing an unsupervised learning model (CityGAN) to generate small and
medium-sized Indian cities; (b) Landscape structures of generated cities are
measured in terms of human settlement indices (HSI) using spatial landscape
metrics; (c) Characteristics of the road network and landscape structures of
real cities are measured in terms of HSI and transportation index (TI); (d)
Assessing the relations between the settlement patterns and transportation
system and building a supervised learning model to predict the transportation
index for GAN-generated urban universe.

### Validation metrics

In the subsequent section, we estimate the Average Radial Profile (ARP) for
real and generated urban patterns to assess the accuracy of CityGAN
quantitatively. An example of computing the ARP of a city is illustrated in
Fig. 7 and using a peak search algorithm, we determined the polycentricity of
actual and simulated scenes from the radial profiles. ARP ($h(d)$ or $x(d)$)
represents how much the human settlement area changes as we go out from the
city center. As indicated in Fig. 7 (b), we draw rings at a distance of $d$
from the center and a width $\Delta$ of $d$. By averaging the entire
settlement area inside rings of width $\Delta d$ at a distance $d$ from the
city center, we can compute $ARP$ ($h(d)$). The region inside the ring with
radius $d$ is denoted as $R(d)$ and each pixel inside the ring has some build-
up area, that is the amount of urbanized area denoted as $H(u,v)$, where
$(u,v)$ is a point inside the ring $H(u,v)\in R(d)$, with

$\begin{split}R(d)\equiv(u,v)\mid(u-u_{0})^{2}+(v-v_{0})^{2}>d^{2}\;\;\text{and}\;\;(u-u_{0})^{2}+(v-v_{0})^{2}\leq
d^{2};\end{split}$ (1) $h(d)=\frac{1}{|R(d)|}\sum_{(u,v)\in R(d)}{h(u,v)};$
(2)

where $R(d)$ can be defined as the collection of all the two-dimensional
points included within the ring, $|R(d)|$ indicates the size of set $R(d)$,
and $h(d)$ is the average radial profile of a city.

There are several statistical measures that are used to assess the supervised
regression models, for e.g., mean squared error (MSE), mean absolute error
(MAE), R-squared ($R^{2}$), and Adjusted R-squared (Adj $R^{2}$). MSE is the
average squared difference between the predicted and actual values. It is a
widely used metric that measures the quality of a regression model whereas MAE
is the average absolute difference between the predicted and actual values. It
is a robust metric that is less sensitive to outliers than MSE. R-squared
measures the proportion of variance in the target variable that is explained
by the model. It ranges from 0 to 1, with higher values indicating a higher
correlation. Adjusted R-squared is a modified version of R-squared that takes
into account the number of predictors in the model. It penalizes the model for
adding unnecessary variables and is a better measure of a model’s goodness of
fit [53].

### Generating human settlement area from WSF 2019

A dataset of real-time human settlement images was collected and pre-processed
before training the GAN. We utilized squared shape settlement maps of cities
from the WSF 2019 database. We clipped them representing 10.5km × 10.5km
spatial extent and resized each image to 256× 256 (43m/px) for optimization
purposes and to avoid overfitting. The final input dataset contains 503 binary
images and can be formulated as $H_{i}={h_{1},….,h_{n}}$, with $H\in R^{WXW}$
and $W=256$ and $n=503$. The source of $H_{i}$ is an urban binary map (1 and 0
represent urban and non-urban areas respectively). The generator network is
trained to generate synthetic urban settlement images by generating random
noise and transforming it into an urban image whose distribution matches the
real urban images. The discriminator network is trained to distinguish between
real and synthetic binary images. Here, generator $G$ takes a random noise
vector $Z_{noise}$ as input, which deterministically changes (e.g., by passing
it through successive deconvolutional layers if $G$ is a deep CNN) to generate
a sample fake human settlement image $H_{fake}=G(z)$. Then the discriminator
($D$) accepts an input image $H$ (which can be an actual human settlement
image ($H_{real}$) from an empirical dataset or generated image ($H_{fake}$)
synthetically by a generator and outputs the source probability that $H$ is
either sampled from the real distribution ($H_{real}$) or produced by
generator ($H_{fake}$). Having trained a generator ($G$) (refer Fig. 2 (a)),
we generated synthetic Indian urban settlement patterns of 500 binary images
using the CityGAN model. Fig. 3 illustrates randomly selected real cities
(Fig. 3(a)) and simulated urban patterns (in Fig. 3(b)). On a visual
inspection, simulations are practically indistinguishable from the actual
urban patterns, with realistic densities and complexity of settlement
patterns. Input images and generated images are exhibiting realistic
concentration at the center and distribution of settlement in the surrounding
regions. Various quantitative metrics as discussed earlier are used to
evaluate the performance of the Indian CityGAN model [42].

Figure 3: Comparison of real urban built land use maps (a) and synthetic maps
(b) generated by a CityGAN. The pixel values in each case are in the range [0,
1], where 1 represents the portion of land occupied by buildings. Names of the
cities are reported in (a) using yellow color text.

Among various spatial statistical measures, ARP [23] is used to compare the
real and simulated urban patterns. We utilize Eq. 2 to compile the polycentric
nature of real and generated images via the peak search algorithm illustrated
in Fig. 7. The peak search algorithm finds points in univariate profiles whose
value (peak height) is a fraction of the maximum height $h$ and at a distance
from the previously identified peak of at least $d$. We set an acceptable
value of $h=80\%$ and $d=430m$ via the cross-validation method. Graphical
representations of peak search outcomes are illustrated in Figs. 4 (a) and
(b).

Figure 4: (a) Average radial profile map of Bhagalpur city; (b) Human
settlement maps of two example cities (top row) along with their average
radial profiles (bottom row), where the blue dots represent the peaks found by
the peak-search algorithm; (c) Clustered radial profiles of real and synthetic
settlement patterns for determining the number of clusters. Figure 5: (a)
Comparison of the distribution of the number of peaks of real and generated
cities; (b) Comparison of the distribution of average radial profile classes
of real and generated cities; (c) The typical radial profiles for real and
generated Indian cities (similar profile)

The distribution of the number of peaks for real and fake cities is compared
(refer to Fig. 5(a)) and similarities between the distributions are found.
Further, we cluster the radial profiles of real cities using K-means algorithm
[54, 55] and compare it to the typical profile of generated cities. Fig. 5
presents a summary of our findings from the CityGAN model. Our analysis
suggests that $K^{*}=10$ (refer Fig. 4(c)) gives the optimal number of
clusters for both actual and synthetic scenes using a straightforward fraction
of the sum-of-squares argument [55]. In Fig. 5(c), the distribution of scenes
by class is given and they have a similar shape and are more comparable. But
in Fig. 5(b), we find more disparities for classes 1 and 4 (monocentric), 6,
8, and 11 (sprawled patterns). These discrepancies may result from a sampling
technique that would have favored the abundance of mono-centric urban patterns
while the simulation was produced regardless of the location of the urban
center. Experimental results show that using the WSF dataset, CityGAN
generates precise urban patterns for Indian cities.

### Relationship between human settlement and transportation network of real
cities

HSIs and TI are computed for the selected cities (workflow is illustrated in
Figs. 2 (b) and (c)). The outcomes of the analysis of human settlements using
selected spatial indices are displayed in Table 1. Table 2 provides examples
of the calculation of the transportation index (network density) and Table 3
shows descriptive statistics of network density. The result shows the spatial
distributions of network density vary among cities. Once the metrics are
derived, correlation coefficients (CC) are calculated to determine the
relationship between the human settlement indices (CA, NP, CLUMPY, LPI, AI,
and NLSI) and the transportation index (RL, ND). The heat maps of the
correlations between transportation indices and human settlement indices are
illustrated in Fig. 6.

Grid number | City name | CA | NP | LPI | CLUMPY | AI | NLSI
---|---|---|---|---|---|---|---
G1 | New Delhi | 4054.11 | 5299 | 3.782 | 0.680 | 79.607 | 0.203
G2 | Belgaum | 1534.05 | 5999 | 0.234 | 0.637 | 68.421 | 0.315
G3 | Gulbarga | 2377.14 | 5722 | 0.844 | 0.652 | 72.184 | 0.278
G4 | Jamnagar | 2141.93 | 3003 | 1.857 | 0.733 | 78.272 | 0.217
G5 | Dhulia | 1608.7 | 4145 | 0.629 | 0.692 | 73.565 | 0.264

Table 1: Human settlement indices of small and medium-sized towns/cities in India calculated for the year 2019 SI No | City name | n | L (km) | A (sq. km) | ND
---|---|---|---|---|---
1 | New Delhi | G1 | 1898.33 | 108.4 | 17.513
2 | Belgaum | G2 | 1313.71 | 108.4 | 11.084
3 | Gulbarga | G3 | 1714.51 | 108.4 | 14.574
4 | Jamnagar | G4 | 1454.75 | 108.4 | 12.764
5 | Dhulia | G5 | 1164.13 | 108.4 | 10.106
Table 2: City number (n), the total length of the road network (L), City buffer area (A) and network density (ND) Transportation metrics | Min | Max | Mean | std. deviation
---|---|---|---|---
RL | 15.7 | 2791.51 | 434.514 | 392.389
Table 3: Descriptive statistics of transportation metrics (namely road length)
Figure 6: Heat map of the correlation between transportation indices and human
settlement indices, the (a) PCC, and (b) CCC based on the input data.

Fig. 6(a) demonstrates the value matrix of Pearson’s correlation coefficient
(PCC) as a measure of a linear relationship (ranges between $-1$ to $1$). Its
value reflects the strength of the link between metrics. Positive numbers
demonstrate the beneficial influence of variables on each other, and negative
values represent the negative connection between variables. Here, the
correlation index is displayed by the color intensity as well. The correlation
increases as the color bar rises, light yellow color denotes a lower
correlation. As shown in Fig. 6(a), the PCC values of coverage measures RL and
ND are highly related to each other; therefore we choose ND as the response
variable of TI. Settlement metrics such as CLUMPY and NLSI have the minimum
correlation with transportation metrics (light blue color), while CA
demonstrates the maximum value of correlation coefficient with transportation
variables. The correlation coefficients of RL and ND with CA are 0.7 and 0.80
respectively. According to PCC, the highest correlation exists between CA and
RL, CA and ND. Hence, CA is an inevitable variable in our regression model.
Nonlinear relationships between HSIs and TIs are explored using Chatterjee
correlation coefficients (CCC) and reported in Fig. 6(b). In the case of CCC,
values reflect that most variables have positive correlations and CA has the
highest rank followed by NP and LPI.

### Prediction of transportation index

A supervised machine learning approach (Kernel Ridge Regression) was
implemented to predict road network density for given settlement patterns
(refer to Fig. 2 (d)). To train and evaluate the prediction model, the raw
dataset (database of 503 real cities) was divided into two parts: training
(80%) and testing (20%). We compare the performance of various other
supervised regression models such as support vector regression (SVR), decision
tree (DT), gradient boosting (GB), multilayer perceptron regression (MLP),
XGboost (XGB), linear regression (LR), random forest (RF) and simple ridge
regression (RR) to select the best-fit model. To validate the models, four
statistical scores: Mean Squared Error (MSE), Mean Absolute Error (MAE),
R-Squared and Adjusted R-Squared were used. The results of our model and
comparison with other models are summarized in Table 4. Experimental result
shows that KRR outperforms all other eight state-of-the-art regression models,
in terms of the highest $R^{2}$ and Adjusted $R^{2}$ and lowest error metrics
(MSE and MAE values). Because of the ability to handle nonlinearity and
multicollinearity difficulties within datasets, the KRR regression model
performs best. Validation metrics indicate that our model is good at
predicting network density for urban patterns. This implies that the
supervised KRR model can be applied to predict TI for newly generated cities
by CityGAN.

Accuracy metrics | SVR | DT | GB | MLP | XGB | LR | RF | RR | KRR
---|---|---|---|---|---|---|---|---|---
MSE | 6.439 | 5.792 | 5.265 | 4.505 | 4.448 | 4.343 | 4.133 | 3.998 | 3.661
MAE | 1.832 | 1.716 | 1.688 | 1.582 | 1.535 | 1.576 | 1.475 | 1.511 | 1.397
$R^{2}$ Score | 0.490 | 0.541 | 0.583 | 0.643 | 0.648 | 0.656 | 0.673 | 0.683 | 0.710
Adj $R^{2}$ Score | 0.463 | 0.517 | 0.561 | 0.624 | 0.629 | 0.638 | 0.655 | 0.667 | 0.695

Table 4: Performance metrics for the test set of real dataset. Best model’s
values are highlighted in bold.

## Discussion

India is now the most populous country in the world [12] with more than 30% of
the population residing in the urban area. Government of India recently came
up with a scheme called IDSMT [15] to improve urban planning and road networks
for the development of small and medium-sized cities (population size up to
500k). The Ministry of Urban Development offers financial and technical
assistance to local bodies in developing their region’s infrastructure and
basic services to promote inclusive growth and balanced regional development.
One of the objectives of this scheme is to address the transportation
infrastructural deficits and service shortfalls of the eligible cities.
However, Central Government finds difficulty in making a correct decision to
allocate funds for transportation infrastructure development.

This study proposes a hybrid model to predict road network density for small
and medium-sized settlement patterns in India. We used the publicly available
WSF datasets and CityGAN model to build an unsupervised model to simulate
realistic Indian urban patterns. The average radial profile was used to
compare real against simulated cities to validate the performance of CityGAN.
Also, we used the K-means technique to cluster the radial profiles with the
optimal number of clusters to be equal to 10 for both actual and synthetic
scenes using a straightforward fraction of sum-of-squares reasoning. Landscape
structures of these generated cities were measured in terms of human
settlement indices using spatial landscape metrics. Then, various supervised
machine learning models were implemented for predicting transportation indices
from human settlement indices based on real city datasets. All the regression
models were compared based on error measurement metrics. The performance of
the Kernel Ridge Regression (KRR) model outperformed the benchmark regression
methods. The transportation index estimated from the KRR model is compared
with actual test data (from real imagery). KRR has comparatively less MAE of
1.39 and a higher $R^{2}$ value of 0.71. Thus, the proposed hybrid model can
be used to predict the transportation index in terms of road network density
for CityGAN-generated towns and cities. Our proposal can be treated as a
versatile decision-support system for sustainable planning and development of
new small and medium-sized towns and cities in terms of transportation
infrastructure. However, the proposed method is useful to establish a
relationship between coverage measures of transportation variables with HSIs,
but the current work doesn’t consider any connectivity measure. As a future
scope of work, making interconnections between connectivity measures with HSIs
will be worth exploring.

## Methods

In this section, we introduce the components of the model used in the hybrid
framework are demonstrated. First, we discuss various correlation measures
that are used in this study. Further, our proposed two-step pipeline approach
utilizes the popularly used GAN model (CityGAN) in this case and the KRR
model, a nonlinear shrinkage method for regression modeling. After this, we go
over the suggested RidgeGAN method.

### Correlation analysis

Correlation coefficients (CC) are popular statistical measures used to
determine the strength of a relationship between two or more variables (can be
numerical or categorical). Pearson’s correlation coefficient (PCC) is the most
commonly used classical method of measuring linear associations, and its ease
of use is advantageous [56]. However, their efficiency may be limited when
dealing with non-normal, noisy, closed, or open data (even after applying log
ratios to the data). Chatterjee Correlation Coefficient (CCC) [57], a recently
developed method based on cross-correlation between ranked increments, is a
reliable alternative to traditional correlation methods. CCC can deal with
data that contains outliers or has non-normal distributions and it does not
make any assumptions about the data distribution [56]. A Python implementation
of CCC can be done using the “TripleCpy” package in Python. We can define CCC
mathematically as follows: Given a pair of random variables $(X,Y)$ and
suppose the realizations $X_{i}$’s and $Y_{i}$’s have no tie. A rearrangement
of the pairs as
$\left(X_{(1)},Y_{(1)}\right),\ldots,\left(X_{(n)},Y_{(n)}\right)$ is done
such that $X_{(1)}\leq\cdots\leq X_{(n)}$. Let $r_{i}$ be the rank of
$Y_{(i)}$ then CCC is defined using the formula:

$\xi_{n}(X,Y):=1-\frac{3\sum_{i=1}^{n-1}\left|r_{i+1}-r_{i}\right|}{n^{2}-1},$

where $n$ is the number of observations. Once the relationships are assessed
between TI and HSIs, selecting the “best” regression model is easier so that
the model explains the variability in the response variables with possibly
lower prediction error. However, the ridge regression (RR) method can directly
handle multicollinearity structures in the data along with the instability of
least square estimators [58]. A more effective nonlinear regularized
regression technique in machine learning is kernel ridge regression (KRR). The
creation of the ridge regression method addresses some of the shortcomings of
the least square method (over-fitting and multicollinearity) [59]. One of
their advantages is that the kernel implementation allows to handle
nonlinearity of the data [60, 61, 62].

### CityGAN: Generative Adversarial Networks for modeling urban patterns

GAN is a powerful unsupervised deep learning model that learns representations
of input data to fit high dimensional complex distributions [18]. GANs are
revolutionary in that they can produce very high-quality (i.e., extremely
realistic) samples compared to predecessor models at similar computational
costs. In general, GAN is a system that consists of two neural networks
competing against each other in a zero-sum game context [63]. The two neural
network architectures are a generator ($G$) and a discriminator ($D$) and they
can generate new data that conforms to learned patterns through both
generative and adversarial processes. GANs demonstrate promising performance
in modeling complex geospatial data having spatial dependence [22]. Whilst the
core application of GANs has been computer vision and image processing [18];
however, their use in geoscience has provided urban planners with novel ways
of generating “new” samples that can easily outperform state-of-the-art
geostatistical tools. In this study, we deploy CityGAN [23] to learn the urban
patterns from real settlement images and generate hyper-realistic urban
settlement images. $G$ and $D$ are both deep convolutional neural networks
with weight vectors $\theta_{G}$ and $\theta_{D}$. Back-propagation is used to
learn these weights by alternatively reducing the following loss functions

$\theta_{D}:\mathcal{L}_{D}=E_{h\sim p_{h}}[\log D(H)]+E_{z\sim
p_{z}}[\log(1-D(G(z)))]$ (3)

$\theta_{G}:\mathcal{L}_{G}=E_{z\sim p_{z}}[\log(1-D(G(z)))]$ (4)

Here, the generator is made up of numerous convolutional blocks, including
inverse-convolutional, batch normalization, and rectified linear unit (ReLU)
layers, and ends with a hyperbolic tangent layer (which applies tanh ($\cdot$)
nonlinearity to each element of the produced map). Recent modifications of
GANs have allowed performing conditional generation as domain transformation.
In the GAN training phase, it is worth noting that the generator network is
usually able to create realistic samples whereas the discriminator is an
auxiliary network that gets discarded after training. Once GAN is trained, the
CityGAN [23] can be used to generate new synthetic urban images that can be
used for a variety of applications such as urban planning, disaster response,
and simulations. Iteratively optimizing the $G$ and $D$ networks is part of
the training process. The generator network attempts to deceive the
discriminator by generating images that resemble real urban images, whereas
the discriminator network attempts to correctly classify whether an image is
real or fake. The networks are updated based on classification and generation
errors until the generator produces images that are indistinguishable from
real-world human settlement scenes. $H_{fake}$ is implicitly sampled from the
data distribution that the generator tries to imitate when G is at its
optimum. However, the GAN-generated images may not be representative of all
possible urbanization patterns because they are based on the training dataset
and the GAN architecture used. As a result, before using GAN-generated images
for any practical application, it is critical to carefully evaluate them and
compare them to real-world urban areas.

### Kernel Ridge Regression (KRR)

Regression modeling is a fundamental area of machine learning where the target
variable is quantitative (real numbers) in nature. The most classical approach
is linear regression using the ordinary least square method. However, it has
salient disadvantages, e.g., overfitting and multicollinearity which can be
addressed via ridge regression. Ridge regression “shrinks” the least square
coefficients using regularization parameter via minimizing the objective
function given below:

$\text{Ridge}(\beta)=\frac{1}{2}(Y-X\beta)^{T}(Y-X\beta)+\frac{\lambda}{2}\beta^{T}\beta,$
(5)

where $X\in R^{N\times D}$ is the feature matrix with $N$ being the number of
training samples, $D$ is the number of features $Y\in R^{1}$ is the real-
valued target vector, $\beta$ is the regression coefficients, and $\lambda\geq
0$ is the regularizer that helps in dealing multicollinearity problem.
However, the Ridge regression model still has troubles when dealing with
nonlinear data data [64]. A more general framework can be achieved by using a
nonlinear mapping function $\phi(\cdot)$ that maps low dimension feature to
high dimension (helps in learning nonlinear patterns). Now, a kernel function
in the form of the dot product is used to avoid the cause of dimensionality of
the nonlinear transformation. Mathematically, Kernel between two points, say
$x_{m}$ and $x_{n}$ is given by

$K(x_{m},x_{n})=\phi(x_{m})^{T}\phi(x_{n}),$ (6)

which satisfies Mercer’s condition [65]. The major impact of Kernel is ridge
regression that allows the identification of nonlinear functional
relationships between one variable with remaining features. In this study, we
use radial basis kernel function (RBF) [62] which is defined by:

$K(x_{m},x_{n})=e^{-\gamma\|x_{m}-x_{n}\|^{2}},$ (7)

where $\gamma$ is the width of the kernel. Predictions in KRR model for a new
test input $x_{*}$ is given by,

$\beta^{T}\phi(x_{*})=\sum_{n=1}^{N}(XX^{T}+\lambda
I_{N})^{-1}YK(x_{n},x_{*}).$ (8)

We use KRR to establish the relationship between HSIs and TI as shown in Fig.
2 (d).

### Hybrid model: RidgeGAN

RidgeGAN is a hybrid approach based on unsupervised CityGAN and supervised KRR
models. KRR [62] has a built-in mechanism to perform nonlinear regularization
analysis in the presence of multicollinearity. CityGAN [23] became popular to
generate fake city images (a.k.a possible future cities) that look like real
cities from the visual inspection and are statistically significant via
learning the urban morphology. After implementation, we evaluated the
performance of CityGAN, by comparing the real and simulated cities using the
most widely used spatial summary statistics in an urban analysis called
average radial profile and peak search algorithm. Each city is represented as
a $10.5\times 10.5$ km image covering the urban center and surrounding
regions. Although, the quantifying transportation index has a vital role in
the development of sustainable city planning and management. Here, we built a
supervised KRR model to predict the transportation index by learning the
relationship between urban patterns and the road transportation index. The KRR
prediction model is integrated with the CityGAN model to predict the
transportation index of newly generated cities using CityGAN. To build our
hybrid model, we mainly use two models: an unsupervised learning model for
generating urban patterns and a supervised learning model to predict the
transportation index. To sum up, the workflow of the proposed RidgeGAN is
detailed as follows (also see Fig. 2 for a schematic workflow):

  * •

First, we apply CityGAN, an unsupervised learning model to generate small and
medium-sized Indian cities using the available urban morphological features.

  * •

Landscape structures of real and generated cities are measured in terms of
Human Settlement Indices (HSI) using spatial landscape metrics.

  * •

We assess the relations between two important features of urban forms (human
settlement and transportation system) and build a KRR model to predict the
transportation index, namely network density.

  * •

The proposed hybrid model framework can predict the road network density on a
given urban pattern for the urban universes generated in the first step.

Figure 7: (a) Google satellite view of Bhagalpur city (randomly selected city
to explain) in Bihar state (b) human settlement map with the method of
computing their average radial profiles.

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## Data and Code availability statement

The datasets and the codes for implementing the methods are made available at
https://github.com/Rahisha-Thottolil/RidgeGAN.

## Author contributions

R.T. conceived the experiment(s) and collected the data, T.C. build the
framework and R.T. analyzed the results, and R.T., T.C., and U.K. wrote and
revised the manuscript.

## Additional information

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.