Prediction Power of Logistic Regression (LR) and Multi-Layer Perceptron (MLP) Models in Exploring Driving Forces of Urban Expansion to Be Sustainable in Estonia

: Estonia mainly experienced urban expansion after regaining independence in 1991. Employing the CORINE Land Cover dataset to analyze the dynamic changes in land use/land cover (LULC) in Estonia over 28 years revealed that urban land increased by 33.96% in Harju County and by 19.50% in Tartu County. Therefore, after three decades of LULC changes, the large number of shifts from agricultural and forest land to urban ones in an unplanned manner have become of great concern. To this end, understanding how LULC change contributes to urban expansion will provide helpful information for policy-making in LULC and help make better decisions for future transitions in urban expansion orientation and plan for more sustainable cities. Many different factors govern urban expansion; however, physical and proximity factors play a signiﬁcant role in explaining the spatial complexity of this phenomenon in Estonia. In this research, it was claimed that urban expansion was affected by the 12 proximity driving forces. In this regard, we applied LR and MLP neural network models to investigate the prediction power of these models and ﬁnd the inﬂuential factors driving urban expansion in two Estonian counties. Using LR determined that the independent variables “distance from main roads (X7)”, “distance from the core of main cities of Tallinn and Tartu land (X2)”, and “distance from water land (X11)” had a higher negative correlation with urban expansion in both counties. Indeed, this investigation requires thinking towards constructing a balance between urban expansion and its driving forces in the long term in the way of sustainability. Using the MLP model determined that the “distance from existing residential areas (X10)” in Harju County and the “distance from the core of Tartu (X2)” in Tartu County were the most inﬂuential driving forces. The LR model showed the prediction power of these variables to be 37% for Harju County and 45% for Tartu County. In comparison, the MLP model predicted nearly 80% of variability by independent variables for Harju County and approximately 50% for Tartu County, expressing the greater power of independent variables. Therefore, applying these two models helped us better understand the causative nature of urban expansion in Harju County and Tartu County in Estonia, which requires more spatial planning regulation to ensure sustainability.


Introduction
Urban expansion is a complex and dynamic process that comprises built-up land, extends to the suburbs [1] and transforms non-urban land into urban land. It can occur through considerably distinctive forms, including the redevelopment of built-up areas with higher densities or infilling urban and suburban areas [2,3]. From the standpoint of sustainability, urban expansion results from unplanned changes in LULC. While it causes economic growth, agglomeration and increases property prices [4], urban expansion brings conversions in the landscape [5][6][7], shifts agricultural land and increases trips between the city and its periphery [6]. Hence, it plays a significant role in reshaping LULC. A Accordingly, the implementation of LR and MLP models in this study leads to better determining and investigating the causative factors of urban expansion with their weights of influence. At the same time, this research presents the prediction power of these models in urban expansion in two Estonian counties.
The CORINE (Coordination of Information on the Environment) Land Cover dataset was used in this study. The CORINE Land Cover dataset is the most essential and integrated land monitoring dataset for Europe prepared by the European Commission [65]. It is the central database for spatial-temporal analysis of urban expansion on different territorial levels, from cities at the regional level to the European continent level. Cieślak et al. [66] used the CORINE Land Cover database to monitor urbanization processes and urban sprawl in Polish cities. Garcia-López [67] studied highway effects on the expansion of 579 European cities in 1990, 2000, and 2012 using CORINE Land Cover. Grigorescu et al. [68] represented a LULC change simulation in Romania using the CORINE Land Cover database. Moreover, Mozaffaree Pour and Oja [69] examined the urban expansion and built-up densities in Estonia using the CORINE Land Cover dataset and one other database. Using CORINE Land Cover, Cole et al. [65] monitored the land cover transition in the United Kingdom for 2012 and depicted their changes from 2006 to 2012. Besides, Oueslati et al. [70] adopted a heuristic approach to measuring the urban sprawl in the level of cities based on the CORINE Land Cover dataset for 1990, 2000, and 2006 for 282 European cities.
It is noticeable that crucial steps in this research include analyzing the dynamic changes in LULC and the spatial surface trends in two main counties in Estonia over 28 years, visualizing the LULC maps in five timestamps using the CORINE Land Cover dataset, exploring drivers of urban expansion employing prediction power of the LR and MLP models, and sustainable urban expansion. Consequently, this paper has two aims. One is methodological, to study the suitability of the LR and MLP models and dataset implied; the other is practical, to analyze the changes in LULC as related to urban expansion.

Study Area
Estonia is located between 57 • 30 00" N to 59 • 50 00" N latitudes and 21 • 50 00" E to 28 • 10 00" E longitudes on the eastern shores of the Baltic Sea. Its water neighbors are Finland and Sweden and its terrestrial neighbors are Latvia and Russia. In this study, two counties in Estonia were selected: Harju County, containing the nation's capital, Tallinn, and Tartu County, where the country's second major city, Tartu, is located. The area of these two counties covers approximately 767,544.04 ha of Estonia ( Figure 1).

Data and Data Processing
This research utilized the time-series CORINE Land Cover dataset to analyze the LULC change between 1990 and 2018, plus employed geostatistical methods to determine LULC changes and urban expansion in two major counties of Estonia. The European Commission [65] prepared CORINE Land Cover maps with geometry accuracy less than 50 m Tallinn, the nation's political, cultural, educational, and transportation center, is located in the northern part of the country. Additionally, Tallinn and its surrounding area are the regions with the highest economic activities in Estonia. Tartu is situated in the southeast and because of the popularity of the University of Tartu, it is the main center of education in Estonia.

Data and Data Processing
This research utilized the time-series CORINE Land Cover dataset to analyze the LULC change between 1990 and 2018, plus employed geostatistical methods to determine LULC changes and urban expansion in two major counties of Estonia. The European Commission [65] prepared CORINE Land Cover maps with geometry accuracy less than 50 m for 1990, 25 m for 2000, 2006, and 2012, and less than 10 m for 2018. The coordinate system of CORINE Land Cover was the projection of Lambert Azimuthal Equal Area (GCS_ETRS_1989, EPSG 3035), which were reprojected to Lambert Conformal Conic (Estonia_1997_Estonia_National_Grid, EPSG 3301), the primary Estonian projection system. The ArcMap 10.6 (Esri, CA, USA) and IDRISI Selva 17.0 (Clark Labs, Worcester, MA, USA) software were used to generate, analyze, and model LULC changes and urban expansion.
There were 12 independent variables selected in this study. Accordingly, the raster layers of green urban areas, industrial or commercial units, sport and leisure facilities, agricultural and forest land, existing residential areas, and wetlands were extracted from the CORINE Land Cover database. Vector data of near cities, the core of main cities, the airport, and main roads were downloaded from Estonian land board geoportal-Estonian Topographic Database (ETAK) and converted to raster capable of the analysis purposes. All variables were resized to 100 m resolution in the exact resolution as the CORINE Land Cover dataset and the equivalent extent to the study area for the reference years of 1990 and 2018. The extent of Harju County consisted of 1395 columns and 1066 rows, while Tartu County included 1131 columns and 864 rows.

LULC Dynamics Model
In this study, the LULC dynamics model proposed by Liu et al. [72] is used to determine the number of LULC changes over time. LULC dynamics were calculated using the following formula:

Data and Data Processing
This research utilized the time-series CORINE Land Cover dataset to LULC change between 1990 and 2018, plus employed geostatistical methods t LULC changes and urban expansion in two major counties of Estonia. The Eur mission [65] prepared CORINE Land Cover maps with geometry accuracy le for 1990, 25 m for 2000, 2006, and 2012, and less than 10 m for 2018. The coord of CORINE Land Cover was the projection of Lambert Azimuthal (GCS_ETRS_1989, EPSG 3035), which were reprojected to Lambert Conforma tonia_1997_Estonia_National_Grid, EPSG 3301), the primary Estonian projec The ArcMap 10.6 (Esri, CA, USA) and IDRISI Selva 17.0 (Clark Labs, Worceste software were used to generate, analyze, and model LULC changes and urban There were 12 independent variables selected in this study. Accordingl layers of green urban areas, industrial or commercial units, sport and leisu agricultural and forest land, existing residential areas, and wetlands were ex the CORINE Land Cover database. Vector data of near cities, the core of ma airport, and main roads were downloaded from Estonian land board geoport Topographic Database (ETAK) and converted to raster capable of the analys All variables were resized to 100 m resolution in the exact resolution as the CO Cover dataset and the equivalent extent to the study area for the reference y and 2018. The extent of Harju County consisted of 1395 columns and 1066 Tartu County included 1131 columns and 864 rows.

LULC Dynamics Model
In this study, the LULC dynamics model proposed by Liu et al. [72] is us mine the number of LULC changes over time. LULC dynamics were calculat following formula: where ∆ ℓ is the variation of a LULC type ℓ over the period 2 1 and represent the area of the LULC type ℓ at time 2 and 1, respectively. In th area covered by each LULC class was calculated and, subsequently, the tran compared in five periods of 1990-2000, 2000-2006, 2006-2012, 2012-2018, and The dynamic LULC changes were analyzed from the perspective of urban exp prints. A map comparison matrix was applied using the Cross-Tabulation com alyze LULC change dynamics. Cross-Tabulation is a helpful tool in represent

Data and Data Processing
This research utilized the time-series CORINE Land Cover dat LULC change between 1990 and 2018, plus employed geostatistical m LULC changes and urban expansion in two major counties of Estonia. T mission [65] prepared CORINE Land Cover maps with geometry accu for 1990, 25 m for 2000, 2006, and 2012, and less than 10 m for 2018. Th of CORINE Land Cover was the projection of Lambert Azim (GCS_ETRS_1989, EPSG 3035), which were reprojected to Lambert Co tonia_1997_Estonia_National_Grid, EPSG 3301), the primary Estonian The ArcMap 10.6 (Esri, CA, USA) and IDRISI Selva 17.0 (Clark Labs, W software were used to generate, analyze, and model LULC changes an There were 12 independent variables selected in this study. Acc layers of green urban areas, industrial or commercial units, sport a agricultural and forest land, existing residential areas, and wetlands w the CORINE Land Cover database. Vector data of near cities, the cor airport, and main roads were downloaded from Estonian land board g Topographic Database (ETAK) and converted to raster capable of the All variables were resized to 100 m resolution in the exact resolution a Cover dataset and the equivalent extent to the study area for the refe and 2018. The extent of Harju County consisted of 1395 columns an Tartu County included 1131 columns and 864 rows.

LULC Dynamics Model
In this study, the LULC dynamics model proposed by Liu

Data and Data Processing
This research utilized the time-series CORINE Land Cover datase LULC change between 1990 and 2018, plus employed geostatistical metho LULC changes and urban expansion in two major counties of Estonia. The mission [65] prepared CORINE Land Cover maps with geometry accurac for 1990, 25 m for 2000, 2006, and 2012, and less than 10 m for 2018. The co of CORINE Land Cover was the projection of Lambert Azimuth (GCS_ETRS_1989, EPSG 3035), which were reprojected to Lambert Confo tonia_1997_Estonia_National_Grid, EPSG 3301), the primary Estonian pr The ArcMap 10.6 (Esri, CA, USA) and IDRISI Selva 17.0 (Clark Labs, Worc software were used to generate, analyze, and model LULC changes and u There were 12 independent variables selected in this study. Accord layers of green urban areas, industrial or commercial units, sport and agricultural and forest land, existing residential areas, and wetlands wer the CORINE Land Cover database. Vector data of near cities, the core of airport, and main roads were downloaded from Estonian land board geo Topographic Database (ETAK) and converted to raster capable of the an All variables were resized to 100 m resolution in the exact resolution as th Cover dataset and the equivalent extent to the study area for the referen and 2018. The extent of Harju County consisted of 1395 columns and 1 Tartu County included 1131 columns and 864 rows.

LULC Dynamics Model
In this study, the LULC dynamics model proposed by Liu et al. [72] mine the number of LULC changes over time. LULC dynamics were calc following formula: where ∆ ℓ is the variation of a LULC type ℓ over the period 2 1 a represent the area of the LULC type ℓ at time 2 and 1, respectively. I area covered by each LULC class was calculated and, subsequently, the compared in five periods of 1990-2000, 2000-2006, 2006-2012, 2012-2018 The dynamic LULC changes were analyzed from the perspective of urban prints. A map comparison matrix was applied using the Cross-Tabulation alyze LULC change dynamics. Cross-Tabulation is a helpful tool in repre where ∆L is the variation of a LULC type over the period

Data and Data Processing
This research utilized the time-series CORINE L LULC change between 1990 and 2018, plus employed g LULC changes and urban expansion in two major count mission [65] prepared CORINE Land Cover maps with for 1990, 25 m for 2000, 2006, and 2012, and less than 10 of CORINE Land Cover was the projection of L (GCS_ETRS_1989, EPSG 3035), which were reprojected tonia_1997_Estonia_National_Grid, EPSG 3301), the pr The ArcMap 10.6 (Esri, CA, USA) and IDRISI Selva 17.0 software were used to generate, analyze, and model LU There were 12 independent variables selected in t layers of green urban areas, industrial or commercial agricultural and forest land, existing residential areas, a the CORINE Land Cover database. Vector data of near airport, and main roads were downloaded from Estonia Topographic Database (ETAK) and converted to raster All variables were resized to 100 m resolution in the exa Cover dataset and the equivalent extent to the study a and 2018. The extent of Harju County consisted of 13 Tartu County included 1131 columns and 864 rows.

LULC Dynamics Model
In this study, the LULC dynamics model proposed mine the number of LULC changes over time. LULC dy following formula: where ∆ ℓ is the variation of a LULC type ℓ over the represent the area of the LULC type ℓ at time 2 and area covered by each LULC class was calculated and, s compared in five periods of 1990-2000, 2000-2006, 2006 The dynamic LULC changes were analyzed from the pe prints.
A map comparison matrix was applied using the C alyze LULC change dynamics. Cross-Tabulation is a he

Data and Data Processing
This research utilized the time-series CORIN LULC change between 1990 and 2018, plus employ LULC changes and urban expansion in two major c mission [65] prepared CORINE Land Cover maps for 1990, 25 m for 2000, 2006, and 2012, and less tha of CORINE Land Cover was the projection (GCS_ETRS_1989, EPSG 3035), which were reproj tonia_1997_Estonia_National_Grid, EPSG 3301), t The ArcMap 10.6 (Esri, CA, USA) and IDRISI Selva software were used to generate, analyze, and mod There were 12 independent variables selecte layers of green urban areas, industrial or comme agricultural and forest land, existing residential ar the CORINE Land Cover database. Vector data o airport, and main roads were downloaded from E Topographic Database (ETAK) and converted to All variables were resized to 100 m resolution in th Cover dataset and the equivalent extent to the stu and 2018. The extent of Harju County consisted Tartu County included 1131 columns and 864 row
A map comparison matrix was applied using alyze LULC change dynamics. Cross-Tabulation i

Data and Data Processing
This research utilized the time-seri LULC change between 1990 and 2018, plu LULC changes and urban expansion in tw mission [65] prepared CORINE Land Co for 1990, 25 m for 2000, 2006, and 2012, an of CORINE Land Cover was the p (GCS_ETRS_1989, EPSG 3035), which we tonia_1997_Estonia_National_Grid, EPSG The ArcMap 10.6 (Esri, CA, USA) and IDR software were used to generate, analyze, There were 12 independent variabl layers of green urban areas, industrial o agricultural and forest land, existing resi the CORINE Land Cover database. Vect airport, and main roads were downloade Topographic Database (ETAK) and conv All variables were resized to 100 m resolu Cover dataset and the equivalent extent and 2018. The extent of Harju County c Tartu County included 1131 columns an

LULC Dynamics Model
In this study, the LULC dynamics m mine the number of LULC changes over following formula:

∆ ℓ
where ∆ ℓ is the variation of a LULC ty represent the area of the LULC type ℓ a area covered by each LULC class was ca compared in five periods of 1990-2000, 2 The dynamic LULC changes were analyz prints.
A map comparison matrix was app alyze LULC change dynamics. Cross-Tab

Data and Data Processing
This research utilized the LULC change between 1990 and LULC changes and urban expan mission [65] prepared CORINE for 1990, 25 m for 2000, 2006, an of CORINE Land Cover wa (GCS_ETRS_1989, EPSG 3035), tonia_1997_Estonia_National_G The ArcMap 10.6 (Esri, CA, USA software were used to generate, There were 12 independen layers of green urban areas, in agricultural and forest land, exi the CORINE Land Cover datab airport, and main roads were do Topographic Database (ETAK) All variables were resized to 100 Cover dataset and the equivale and 2018. The extent of Harju Tartu County included 1131 col

LULC Dynamics Model
In this study, the LULC dy mine the number of LULC chan following formula: where ∆ ℓ is the variation of a represent the area of the LULC area covered by each LULC cla compared in five periods of 199 The dynamic LULC changes we prints.
A map comparison matrix alyze LULC change dynamics. C

Data and Data Processing
This research utilized the time-series CORINE Land Cover datas LULC change between 1990 and 2018, plus employed geostatistical meth LULC changes and urban expansion in two major counties of Estonia. Th mission [65] prepared CORINE Land Cover maps with geometry accura for 1990, 25 m for 2000, 2006, and 2012, and less than 10 m for 2018. The c of CORINE Land Cover was the projection of Lambert Azimu (GCS_ETRS_1989, EPSG 3035), which were reprojected to Lambert Con tonia_1997_Estonia_National_Grid, EPSG 3301), the primary Estonian p The ArcMap 10.6 (Esri, CA, USA) and IDRISI Selva 17.0 (Clark Labs, Wor software were used to generate, analyze, and model LULC changes and There were 12 independent variables selected in this study. Accor layers of green urban areas, industrial or commercial units, sport and agricultural and forest land, existing residential areas, and wetlands we the CORINE Land Cover database. Vector data of near cities, the core o airport, and main roads were downloaded from Estonian land board ge Topographic Database (ETAK) and converted to raster capable of the a All variables were resized to 100 m resolution in the exact resolution as t Cover dataset and the equivalent extent to the study area for the refere and 2018. The extent of Harju County consisted of 1395 columns and Tartu County included 1131 columns and 864 rows.

LULC Dynamics Model
In this study, the LULC dynamics model proposed by Liu

Data and Data Processing
This research utilized the time-series CORINE Land Cove LULC change between 1990 and 2018, plus employed geostatistic LULC changes and urban expansion in two major counties of Esto mission [65] prepared CORINE Land Cover maps with geometry for 1990, 25 m for 2000, 2006, and 2012, and less than 10 m for 201 of CORINE Land Cover was the projection of Lambert (GCS_ETRS_1989, EPSG 3035), which were reprojected to Lamb tonia_1997_Estonia_National_Grid, EPSG 3301), the primary Est The ArcMap 10.6 (Esri, CA, USA) and IDRISI Selva 17.0 (Clark La software were used to generate, analyze, and model LULC chang There were 12 independent variables selected in this study layers of green urban areas, industrial or commercial units, sp agricultural and forest land, existing residential areas, and wetla the CORINE Land Cover database. Vector data of near cities, th airport, and main roads were downloaded from Estonian land bo Topographic Database (ETAK) and converted to raster capable All variables were resized to 100 m resolution in the exact resolut Cover dataset and the equivalent extent to the study area for th and 2018. The extent of Harju County consisted of 1395 colum Tartu County included 1131 columns and 864 rows.

LULC Dynamics Model
In this study, the LULC dynamics model proposed by Liu e mine the number of LULC changes over time. LULC dynamics w following formula: where ∆ ℓ is the variation of a LULC type ℓ over the period represent the area of the LULC type ℓ at time 2 and 1, respe area covered by each LULC class was calculated and, subsequen compared in five periods of 1990-2000, 2000-2006, 2006-2012, 20 The dynamic LULC changes were analyzed from the perspective prints.
A map comparison matrix was applied using the Cross-Tab alyze LULC change dynamics. Cross-Tabulation is a helpful too 1 , respectively. In this study, the area covered by each LULC class was calculated and, subsequently, the transforms were compared in five periods of 1990-2000, 2000-2006, 2006-2012, 2012-2018, and 1990-2018. The dynamic LULC changes were analyzed from the perspective of urban expansion footprints.
A map comparison matrix was applied using the Cross-Tabulation command to analyze LULC change dynamics. Cross-Tabulation is a helpful tool in representing changes in LULC classes [73]. Hence, LULC classes in 1990 (in columns) that shifted to other land were compared with 2018 (rows) in a comparison matrix.
Due to the complexity of LULC modification patterns and the necessity of the trend interpretations, the spatial surface trends from all LULC classes to urban land were analyzed using the third-order polynomial trend surface.

LR Model
In this research, the LR model was employed to distinguish the relationship between the independent categorical variables and the urban expansion as the binary dependent variable [74]. "LOGISTICREG" is an analytical tool in IDRISI software that generates the LR model. A binary (0 and 1) dependent variable is the model input, with its value estimated by the following formula [75,76]: where P represents the probability of the dependent variable being 1; X is the independent variable (X = (x 0 , x 1 , x 2 , . . . , x k ), x 0 = 1); and B is the estimated parameter,

MLP Neural Network Analysis
The MLP neural network model, often called a "back-propagation" network model [64], is an approach that performs a non-parametric regression analysis. The MLP comprises one input layer, some hidden layers, and one output layer [77]. The model results are a neuron and predicted membership map, representing the predicted urban expansion map based on the defined independent variables [75]. Furthermore, it is possible to use an automatic training option through a random process in the model implementation. This study adopted 50% of samples for training the algorithm and 50% for validation using 10,000 iterations, as generated via research [78,79].
The MLP function has two crucial forward and backward propagation steps to complete the adjustments in neurons connection weights [75,76]. The input of a single node is weighted according to Equation (3): where W ij represents the weights between nodes i and j, and O i is the output from node i. The output from node j is calculated by Equation (4): As function f in our research is a sigmoidal function, the weights will be applied earlier than the signal reaches the subsequent layer. When the forward pass is finished, the comparison will be made between the output nodes and the expected activities.

Driving Factors Analysis
In this research, a single dependent variable and 12 independent variables were determined to explore the prediction power of the LR and MLP models and analyze the urban expansion as follows:

Dependent Variable
In this study, the urban transitions between 1990 and 2018 were taken as the dependent variable (Y) for the LR and MLP models. The binary dependent variable was defined as the urban and non-urban/no changes. When land is converted from non-urban into urban between 1990 and 2018, its value is set as Y = 1; otherwise, Y = 0 and the results of these shifts are shown in Figure 2.

Independent Variables
Different physical drivers played roles in the urban expansion and transitioning from non-urban areas to urban land. The physical driving forces of the urban expansion were normalized to range from 0 to 1; they are represented in Figures 3 and 4 and explained in Table 1.

Independent Variables
Different physical drivers played roles in the urban expansion and transitioning from non-urban areas to urban land. The physical driving forces of the urban expansion were normalized to range from 0 to 1; they are represented in Figures 3 and 4 and explained in Table 1. Table 1. Independent variables and their explanation were used in models.

Independent Variables
Explanation Independent variable 1 (X1) distance from near cities Independent variable 2 (X2) distance from the core of cities: Tallinn and Tartu Independent variable 3 (X3) distance from green urban areas Independent variable 4 (X4) distance from industrial or commercial units Independent variable 5 (X5) distance from airport Independent variable 6 (X6) distance from sport and leisure facilities Independent variable 7 (X7) distance from main roads Independent variable 8 (X8) distance from agricultural land Independent variable 9 (X9) distance from forest land Independent variable 10 (X10) distance from existing residential areas Independent variable 11 (X11) distance from water land Independent variable 12 (X12) distance from wetlands  Table 1. Independent variables and their explanation were used in models.

Independent Variables Explanation
Independent variable 1 (X1) distance from near cities Independent variable 2 (X2) distance from the core of cities: Tallinn and Tartu Independent variable 3 (X3) distance from green urban areas Independent variable 4 (X4) distance from industrial or commercial units Independent variable 5 (X5) distance from airport Independent variable 6 (X6) distance from sport and leisure facilities Independent variable 7 (X7) distance from main roads Independent variable 8 (X8) distance from agricultural land Independent variable 9 (X9) distance from forest land Independent variable 10 (X10) distance from existing residential areas Independent variable 11 (X11) distance from water land Independent variable 12 (X12) distance from wetlands

Correlation Matrix
To determine the relationship between independent variables and reduce multicollinearity, Pearson correlation analysis was performed. Figure 5 shows the correlation matrix, colored blue for positive correlations and red for negative correlations. Pearson correlation is efficient for exploring the linear relationship between interval variables. While coefficients close to 1 or −1 show the stronger correlations, 0 indicates no correlation [80]. The maximum values (±0.68) represent no collinearity [14] and determine the implication of that variable into the models.
In this regard, Tartu County and Harju County's correlation matrix indicates an acceptable range of correlation among the independent variables applicable for the LR and MLP models. In both counties, X9, X11, and X12 variables negatively correlated with other variables, while a positive correlation existed between the other distance variables.

Correlation Matrix
To determine the relationship between independent variables and reduce multicollinearity, Pearson correlation analysis was performed. Figure 5 shows the correlation matrix, colored blue for positive correlations and red for negative correlations. Pearson correlation is efficient for exploring the linear relationship between interval variables. While coefficients close to 1 or −1 show the stronger correlations, 0 indicates no correlation [80]. The maximum values (±0.68) represent no collinearity [14] and determine the implication of that variable into the models.
In this regard, Tartu County and Harju County's correlation matrix indicates an acceptable range of correlation among the independent variables applicable for the LR and MLP models. In both counties, X9, X11, and X12 variables negatively correlated with other variables, while a positive correlation existed between the other distance variables.

LULC Dynamics Model Analysis
LULC changes in Harju and Tartu counties during the study period are presented in Figures 6 and 7, with the statistics summarized in Table 2. Some significant trends were evident in the transitions of LULC over the approximate 28 years. From Table 2, it is evi- Figure 5. The correlation matrix represents relationships between independent variables for Tartu County and Harju County.

LULC Dynamics Model Analysis
LULC changes in Harju and Tartu counties during the study period are presented in Figures 6 and 7, with the statistics summarized in Table 2. Some significant trends were evident in the transitions of LULC over the approximate 28 years. From Table 2, it is evident that enormous shifts from 1990 to 2018 in Harju County were associated with urban land, with a 33.96% increase and an increase of 8.94% in the wetland area. The significant trends evident in Tartu County were related to the transformations in the suburban areas surrounding Tartu, which experienced moderate increases of about 19.50%. The most significant decrease was related to agricultural land, which showed a 5.95% decline in Harju County and a 2.31% decline in Tartu County.    Tartu Table 3 shows the area of LULC in the study period in 1990 (columns) against LULC in 2018 (rows), while a map containing different combinations of "from-to" change classes is presented in Figure 8. In Harju County, the significant transformation was related to agricultural land; out of the 129,773 ha in 1990, 6836 ha was converted to urban land, with 118,614 ha still agricultural area by 2018. In comparison, 568 ha of urban land, 2856 ha of forest, 21 ha of wetlands, and 1 ha of water were converted to agricultural land by 2018. This trend is also the most notable shift in Tartu County. From 149,645 ha of agricultural land in 1990, 4034 ha were converted to forest and 1638 ha to urban land by 2018. In contrast, 1770 ha of forest land, 440 ha urban land, and 10 ha of wetlands were converted to agriculture by 2018. In Harju County, of 22,804 ha of land that was urban in 1990, 20,930 ha remained urban in 2018.   Table 3 shows the area of LULC in the study period in 1990 (columns) against LULC in 2018 (rows), while a map containing different combinations of "from-to" change classes is presented in Figure 8   The wetlands in Harju County covered 15,213 ha in 1990, with 668 ha converted to forest, 21 ha to agricultural land, 12 ha to the urban area, and 8 ha to water, meaning 14,504 ha had remained wetlands by 2018. However, 1963 ha of the forest, 70 ha of agricultural, and 37 ha of water land had transited to wetlands by 2018. In Tartu County, most of the wetlands' shifts were related to the forest (120 ha), 34 ha to water, and 10 ha to agricultural land. In contrast, 692 ha of forest and 2 ha of water were added to wetlands by 2018.

Forest land in
Less transition was related to the water class. Out of 4052 ha of water in 1990, 3900 ha was still water in 2018; 89 ha had changed to urban, 37 ha to wetlands, 24 ha to forest, and 1 ha to agricultural land in Harju County, with just 2 ha to wetlands in Tartu County.
From Figure 9, it is notable that the transition to urban land in Harju County was primarily concentrated to the west and in Tartu County to the southwest of the image. To The wetlands in Harju County covered 15,213 ha in 1990, with 668 ha converted to forest, 21 ha to agricultural land, 12 ha to the urban area, and 8 ha to water, meaning 14,504 ha had remained wetlands by 2018. However, 1963 ha of the forest, 70 ha of agricultural, and 37 ha of water land had transited to wetlands by 2018. In Tartu County, most of the wetlands' shifts were related to the forest (120 ha), 34 ha to water, and 10 ha to agricultural land. In contrast, 692 ha of forest and 2 ha of water were added to wetlands by 2018.
Less transition was related to the water class. Out of 4052 ha of water in 1990, 3900 ha was still water in 2018; 89 ha had changed to urban, 37 ha to wetlands, 24 ha to forest, and 1 ha to agricultural land in Harju County, with just 2 ha to wetlands in Tartu County.
From Figure 9, it is notable that the transition to urban land in Harju County was primarily concentrated to the west and in Tartu County to the southwest of the image. To investigate the spatial trends of the surface, urban expansion from 1990 to 2018 based on the dynamic LULC being shifted to urban areas was put into action.

LR Model Results
The LR analysis results are presented in Table 4. The coefficient values define the importance and the degree of relationship between dependent and independent variables as drivers of urban expansion. The sign of the coefficient (±) indicates a positive or negative correlation to the response of the dependent variable [76]. The values with positive coefficients indicate positive impacts, while negative values determine negative impacts [81]. From the results of the LR, it can be explained that the distance factors from near cities (X1), the core of main cities of Tallinn and Tartu (X2), sport and leisure facilities (X6), main roads (X7), forest land (X9), and water land (X11) in both counties had a negative correlation with urban expansion. This means that where the distance from these variables

LR Model Results
The LR analysis results are presented in Table 4. The coefficient values define the importance and the degree of relationship between dependent and independent variables as drivers of urban expansion. The sign of the coefficient (±) indicates a positive or negative correlation to the response of the dependent variable [76]. The values with positive coefficients indicate positive impacts, while negative values determine negative impacts [81]. From the results of the LR, it can be explained that the distance factors from near cities (X1), the core of main cities of Tallinn and Tartu (X2), sport and leisure facilities (X6), main roads (X7), forest land (X9), and water land (X11) in both counties had a negative correlation with urban expansion. This means that where the distance from these variables increases, the urban expansion decreases. In other words, the greater the distance from these factors, the tendency for urban expansion decreases.
A 10% sampling rate was applied based on stratified random sampling to reduce the impact of spatial dependency between observations, namely spatial autocorrelation [19].
Model validation was calculated with ROC (Relative Operating Characteristic Curve) values presented in Figure 10, comparing the predicted map of urban expansion for 2018 with the actual map of 2018. Its range is between 0 and 1 [29,51], with a higher value indicating a better fit of the model. As observed from Table 4, the ROC values for Harju County and Tartu County were 0.95 and 0.97, respectively, indicating that LR models were a good fit. Another indicator of fitting the model for LR results is the Pseudo R 2 parameter. While a perfect fit is 1, 0 indicates no relationship. It is assumed by Saeedi Razavi et al. [77] that a Pseudo R 2 larger than 0.2 is a relatively good fit. This parameter was 0.36 for Harju County and 0.43 for Tartu County, indicating a good fit for the LR model. The results showed that using these variables provides prediction values of 37% in Harju County and 45% in Tartu County.
The LR prediction maps verified where urban expansion occurred in 2018 when the coefficients of proximity factors were employed in the study area. Additionally, the overlay was conducted to visualize the predicted maps with the actual urban expansion maps of 2018 in both counties. A 10% sampling rate was applied based on stratified random sampling to reduce the impact of spatial dependency between observations, namely spatial autocorrelation [19].
Model validation was calculated with ROC (Relative Operating Characteristic Curve) values presented in Figure 10, comparing the predicted map of urban expansion for 2018 with the actual map of 2018. Its range is between 0 and 1 [29,51], with a higher value indicating a better fit of the model. As observed from Table 4, the ROC values for Harju County and Tartu County were 0.95 and 0.97, respectively, indicating that LR models were a good fit. Another indicator of fitting the model for LR results is the Pseudo R 2 parameter. While a perfect fit is 1, 0 indicates no relationship. It is assumed by Saeedi Razavi et al. [77] that a Pseudo R 2 larger than 0.2 is a relatively good fit. This parameter was 0.36 for Harju County and 0.43 for Tartu County, indicating a good fit for the LR model. The results showed that using these variables provides prediction values of 37% in Harju County and 45% in Tartu County.
The LR prediction maps verified where urban expansion occurred in 2018 when the coefficients of proximity factors were employed in the study area. Additionally, the overlay was conducted to visualize the predicted maps with the actual urban expansion maps of 2018 in both counties.

MLP Neural Network Model Results
Running the process of MLP in IDRISI, the outputs provided a detailed statistical analysis and a predicted map based on the strength of the independent variables. Table 5 presents the statistical information for both counties in two categories, including (1) model sensitivity when a single variable is constant. After training the whole variables to check the strength of independent variables, it holds the input values of a selected variable constant to remove its variability. (2) Except one variable, all variables are held constant. It shows complementary information about the existence of intercorrelation between independent variables. The results will prepare the most and least influential driving forces [76].
In the case of Harju County, the most influential independent variable was "distance from existing residential areas (X10)" and the least influential was "distance from sports and leisure facilities (X6)". The variables "distance from the core of Tallinn (X2)", "distance from green urban areas (X3)", and "distance from main roads (X7)" were the most influential among the other variables in Harju County.

MLP Neural Network Model Results
Running the process of MLP in IDRISI, the outputs provided a detailed statistical analysis and a predicted map based on the strength of the independent variables. Table 5 presents the statistical information for both counties in two categories, including (1) model sensitivity when a single variable is constant. After training the whole variables to check the strength of independent variables, it holds the input values of a selected variable constant to remove its variability. (2) Except one variable, all variables are held constant. It shows complementary information about the existence of intercorrelation between independent variables. The results will prepare the most and least influential driving forces [76].
In the case of Harju County, the most influential independent variable was "distance from existing residential areas (X10)" and the least influential was "distance from sports and leisure facilities (X6)". The variables "distance from the core of Tallinn (X2)", "distance from green urban areas (X3)", and "distance from main roads (X7)" were the most influential among the other variables in Harju County.
The most influential driving force in Tartu County was "distance from the core of Tartu (X2)" and the least influential was "distance from the airport (X5)".

LULC Changes for 28 Years in the Study Area
From the standpoint of urban expansion, LULC change has a substantial effect. A fundamental core for urban expansion research is the quantitative characterization of its dynamic LULC changes. This study provided evidence that "urban" land was the most dynamic class and "forest" was the least dynamic LULC in both counties. As the forest was the largest LULC unit, perceptual change cannot be high. In terms of change analysis, the results demonstrated two things. First, urban areas have increased by almost 33.96% in Harju County and 19.50% in Tartu County. Second, there was a significant loss of agricultural land from 2006 to 2012. About 6836 ha of agricultural land in 1990 were converted to urban by 2018 in Harju County and 1638 ha in Tartu County. It should be noted that agricultural land was an essential resource in the Soviet era and could not be used for residential development. So, from the late 1990s, these areas became especially attractive plots for housing development [30].
The spatial surface trends showed that the change to urban land in Harju County was primarily concentrated in the west and the spatial trends of change to urban in Tartu County were to the southwest of the image.

LR Model and Impacts of Proximity Factors on Urban Expansion
Using LR to analyze the urban expansion, it was claimed that urban expansion is affected by the 12 driving forces, including "distance from near cities (X1)", "distance from the core of main cities of Tallinn and Tartu (X2)", "distance from the green urban areas (X3)", "distance from industrial or commercial units (X4)", "distance from airports (X5)", "distance from sport and leisure facilities (X6)", "distance from main roads (X7)", "distance from agriculture land (X8)", "distance from forest land (X9)", "distance from existing residential areas (X10)", "distance from water land (X11)", and "distance from wet-

LULC Changes for 28 Years in the Study Area
From the standpoint of urban expansion, LULC change has a substantial effect. A fundamental core for urban expansion research is the quantitative characterization of its dynamic LULC changes. This study provided evidence that "urban" land was the most dynamic class and "forest" was the least dynamic LULC in both counties. As the forest was the largest LULC unit, perceptual change cannot be high. In terms of change analysis, the results demonstrated two things. First, urban areas have increased by almost 33.96% in Harju County and 19.50% in Tartu County. Second, there was a significant loss of agricultural land from 2006 to 2012. About 6836 ha of agricultural land in 1990 were converted to urban by 2018 in Harju County and 1638 ha in Tartu County. It should be noted that agricultural land was an essential resource in the Soviet era and could not be used for residential development. So, from the late 1990s, these areas became especially attractive plots for housing development [30].
The spatial surface trends showed that the change to urban land in Harju County was primarily concentrated in the west and the spatial trends of change to urban in Tartu County were to the southwest of the image.

LR Model and Impacts of Proximity Factors on Urban Expansion
Using LR to analyze the urban expansion, it was claimed that urban expansion is affected by the 12 driving forces, including "distance from near cities (X1)", "distance from the core of main cities of Tallinn and Tartu (X2)", "distance from the green urban areas (X3)", "distance from industrial or commercial units (X4)", "distance from airports (X5)", "distance from sport and leisure facilities (X6)", "distance from main roads (X7)", "distance from agriculture land (X8)", "distance from forest land (X9)", "distance from existing residential areas (X10)", "distance from water land (X11)", and "distance from wetlands (X12)".
The LR model determined that distance from main roads (X7) had a very high impact on urban expansion in Harju County with a lower coefficient in Tartu County, meaning that urban expansion is more likely to occur close to the main roads. Sarkar and Chouhan [29] assessed the distance from roads as an influential factor of urban settlements scattering. Our finding is broadly in line with the argument made by Reimets et al. [30], who mentioned that the distance from the main cities in Estonia appeared to be a less important factor than the distance from the main roads. Roads make it possible to commute between work and home easily.
The distance from near cities (X1) had a negative impact on urban expansion in both counties. Sarkar and Chouhan [29] found that the negative proximity means that further away from near cities, the tendency of urban expansion declines. One possible reason for this could be the willingness of people to live in distanced areas and make even daily commutes to Tallinn in Harju County and Tartu in Tartu County. Additionally, the west direction of the trend surface in Harju County could impact these smaller towns located in the west.
Distance from water land (X11) in both counties was negatively correlated with urban expansion. This finding is in line with the experiments of Tammaru et al. [17], which indicated urban expansion along the water bodies showed the attraction of this land for housing development.
Distance from the forest (X9) also had a negative impact on urban expansion, indicating the importance of forest land in trade-offs of urban expansion in both counties. It is also evident from the LULC analysis that in Harju County, 2680 ha of forest land were under construction from 1990 to 2018, indicating the importance of this land for urban expansion.
It is imperative to mention that the distance from the core of Tartu (X2) has the highest negative impact on urban expansion in Tartu County, while the distance from the airport (X5) has the highest positive impact on urban expansion.
Distance from agricultural land (X2) ranked amongst the most influential factors of urban expansion in Tartu County. Furthermore, based on the LULC analysis, agricultural land decreased 2.31% from 1990 to 2018, highlighting the importance of this land in people's lives and the tendency for conversion to urban expansion.
Distance from sport and leisure facilities (X6) had a fragile relationship with the transformation from non-urban to urban land in both counties. Tammaru et al. [17] argued environmental preferences were also more critical in the new suburban areas despite the significant distance from Tallinn, as proved truly significant in our case studies.
In addition, the LR results demonstrated that the ROC values for Harju County and Tartu County were 0.95 and 0.97, respectively, and the Pseudo R 2 parameter was 0.36 for Harju County and 0.43 for Tartu County, indicating that the LR models were a good fit.

MLP Neural Network Model and Impacts of Proximity Factors on Urban Expansion
In this research, the MLP model was employed to investigate the power of each independent variable on the dependent variable. In Harju County, the most influential independent variable was "distance from existing residential areas (X10)", which influences new construction and urban expansion in the long term. This finding supports the conclusion reached by Samarüütel et al. [82] that suburbs of Tallinn are transforming from non-urban to urban areas mainly by people who want a cheaper settlement or better living conditions. The most influential driving force in Tartu County was "distance from the core of Tartu (X2)". It was also the most influential factor in the LR model, indicating the importance of proximity to the core in Tartu County. These two factors significantly showed that although transforming suburban land into urban was a prominent factor outside Tallinn and Tartu cities, people tend to settle in proximate with existing residential areas while taking advantage of environmental attractions in the suburbs.
Access to the main roads (X10) in both counties was the most influential factor using the MLP model. Reimets et al. [30] noted that single houses, especially in rural areas, were located along Estonia's main roads. Rungskunroch et al. [4] determined that providing a cycle of planned destinations and transportation infrastructure, while encouraging people to travel or commute, affects the rapid development of a city.
Distance from green urban areas (X3) ranked amongst the most influential factors of urban expansion. Muhamad Nor et al. [83] indicated the importance of urban greenery despite its reduction under the expansion of urban areas.
The MLP model revealed that distance from the airport (X5) is essential in Tallinn, while it is least influential in Tartu County. In line with the results of the LR model, it is important to point out that the Tallinn international airport (Lennart Meri) is located inside the city of Tallinn's boundary, with many residential settlements shaped in the periphery of the airport area during recent decades. In Tartu County, the Tartu airport (Ülenurme) is situated outside Tartu's boundaries with local services.

Towards Sustainable Urban Expansion
As illustrated in the LULC maps and the LR and MLP models, our results demonstrated that mainly scattering patterns of urban expansion in these counties occurred proximate to main cities and existing residential areas, taking advantage of main roads accessibility.
The proximity relationships are challenging because other factors, such as socioeconomic or governmental policies, influence urban expansion. These primary findings are consistent with research showing that in Estonia, it is more likely that the development of new housing areas around cities has been influenced by the lack of planning policy [30,82]. This is particularly important when investigating dynamic LULC changes as the physical driving forces of urban expansion in Estonia.
While the distances from near cities, core, and existing residential areas were ranked amongst the most influential factors of urban expansion around Tallinn and Tartu, enhancing public awareness and efficient regulations by the local government seems necessary to reduce the negative effects of urban expansion on the environment. Roads influenced the scattering of settlements in recent decades in Estonia. Therefore, effective land policies should be formulated.
Hence, to reach sustainability, local governments should consider policies to maintain biodiversity and reduce the continued agricultural and forest land conversion to builtup areas around Tallinn and Tartu. To this end, establishing more land regulations in master plans, protecting urban green areas surrounding Tallinn and Tartu, employing infrastructure expansion restrictions and implementing coordinated mechanisms covering the interests of natural and legal actors of urban expansion seems to be applicable.

Conclusions
Urban expansion is associated with dynamic LULC change. Understanding how LULC change contributes to urban expansion will provide helpful information for policymaking in LULC, help achieve better decisions for future transitions in urban expansion orientation and plan for more sustainable cities.
This research explored and analyzed the dynamic changes in LULC over 28 years in Estonia. In summary, geospatial analysis of urban expansion leads to the following conclusions: In Harju County, the most significant shifts in LULC from 1990 to 2018 were associated with urban land with a 33.96% increase and an increase of 8.94% in the wetland's areas. The significant trends evident in Tartu County were related to the transforms in the suburban areas surrounding Tartu, which experienced a moderate increase of about 19.50%. The most significant decrease is the agricultural LULC class, with a 5.95% decline in Harju County and a 2.31% drop in Tartu County.
Applying LR and MLP neural network models, the prediction power of these models was investigated and the influential driving factors of urban expansion in two Estonian counties were found.
The LR model was an essential indicator that explained the relationships between urban expansion and potential driving forces. The dependent variable (Y) was defined as converted land from non-urban into urban LULC between 1990 and 2018, with 12 independent variables as proximity factors. The independent variables of "distance from main roads (X7)", "distance from the core of main cities of Tallinn and Tartu land (X2)", and "distance from water land (X11)" in both counties had a higher negative correlation with urban expansion, showing their influence on urban expansion. The ROC values for Harju County and Tartu County of 0.95 and 0.97, respectively, and the Pseudo R 2 parameter of 0.36 for Harju County and 0.43 for Tartu County indicated that the LR model was a good fit.
Further, the MLP model showed that "distance from existing residential areas (X10)" in Harju County and "distance from the core of Tartu (X2)" had more power than the other variables. It indicated urban expansion extended outside Tallinn and Tartu and transformed suburban land into urban mostly along main roads. Indeed, it is crucial to investigate the long-term effects of urban expansion and roads construction balances in the way of sustainability.
The LR and MLP models assisted us in exploring the prediction power of independent variables on urban expansion. The MLP model computed the correlation between independent variables with urban expansion using hidden nodes. It was found that using these variables in the LR model provided a prediction of independent variables, with a value of 37% in Harju County and 45% in Tartu County. Using the MLP model predicted nearly 80% of variability by independent variables for Harju County and approximately 50% for Tartu County. It explained the power of using hidden nodes and experimenting with all possible interactions among variables in the MLP model.
It is also essential to notice that the socioeconomic aspects of Estonian life were driven by a fragmented urban expansion and rapid transformations of LULC during the study period. These created preconditions for the scattered spatial distribution of new existing residential areas in Estonia, providing new insight into assessing the impacts of macrolevel factors on urban expansion and encouraging us to conduct further research through these factors.