A new fuzzy rule-based model to partition a complex urban system in homogeneous urban contexts

We present a new unsupervised method aimed to obtain a partition of a complex urban system in homogenous urban areas, called urban contexts. The area of study is initially partitioned in microzones, homogeneous portion of the urban system, that are the atomic reference elements for the census data. With the contribution of domain experts, we identify the physical, morphological, environmental and socio-economic indicators need to identify synthetic characteristics of urban contexts and create the fuzzy rule set necessary to determine the type of urban context. We implement the set of spatial analysis processes necessary to calculate the indicators for microzone and apply a Mamdani fuzzy rule system to classify the microzones. Finally, the partition of the area of study in urban contexts is obtained by dissolving continuous microzones belonging to the same type of urban context. Tests are performed on the Municipality of Pozzuoli (Naples Italy); the reliability of out model is measured by comparing the results with the ones obtained by detailed analysis.


Introduction
An urban system is a complex entity, composed of various elements with physical, morphological, environmental and socio-economic characteristics, related to each other.Often, in order to analyze the area of study related to urban analysis problems, is useful partition it in a set of areas homogeneous with respect to specific characteristics.In literature there are various studies in which unsupervised methods are proposed to segment the area of study in homogeneous zones in order to analyze specific problems.Various authors propose automatic classification methods to partition urban areas and elements from raster remote sensing data.In [19] a genetic algorithm is applied in order to extract automatically classification rules of urban areas from remote sensing data.In [9] a is applied a framework modeling the expert knowledge in order to segment coastal areas in raster remote sensing data.In [12] a new method based on unsupervised change detection focused on individual buildings is applied to very-high resolution remote sensing imageres to extract elements in urban systems.In [4] a hierarchical object-oriented model is proposed to classify objects in an urban area from high resolution satellite images.In [8] a multiple-kernel learning model is proposed to classify urban areas from spectral and LiDAR raster data.A review of classification methods proposed to classify urban land cover by using raster LiDAR remote sensing images is presented in [19].
Recently, the aviability of various thematic data at different scales from different institutional sources together with the use of socio-demographic census data, allows to implement methods for the unsupervised classification of urban systems that take into consideration the knowledge of the urban system and the expert knowledge of the analyzed problem.In [5] the area of study is partitioned in homogeneous zones based to morphological and soil characteristics in order to analyze the vulnerability of aquifer to pollution; a fuzzy algebraic structure is applied in order to assess the aquifer vulnerability in any zone.In [15] a multiple level association rule mining method is applied on spatiotemporal socio-economic and land cover datasets based on a hierarchical classification scheme to extract relations between objects in the area of study and classify them.
In [3] a simulated annealing method is applied to partition an area of study in homogeneous zones based on socioeconomic characteristics.In [6] a partition of the urban system in census zones is performed in order to study the spatial distribution of socioeconomic characteristics.In [1] a multiobjective approach is applied in order to partition into microregions the municipalities of the region of Parana in Brazil; this approach maximize the population homogeneity and the medical procedure used in any microregion and minimize inter-microregion traveling.
In this research we propose a novel model based on a Mamdani fuzzy rule system [13,14] aimed to partition an urban system in homogeneous zones, called urban contexts; each urban context is labeled with a specific urban class based on a specific taxonomy related to the studied problem.
Our approach is independent of the analyzed problem; initially we partition the area of study in homogeneous zones given by census atomic elements called microzones.We follow the Italian Presidential Decree n. 138 of 1998 that in the Article 1 defines a microzone as a homogeneous portion of the urban system, which may include one municipality, a portion thereof, or groups of municipalities, characterized by similar environmental and socio-economic characteristics.The microzone represents a portion of the municipality or, in the case of areas consisting of groups of municipalities, an entire municipal territory homogeneous in terms of urban, historicalenvironmental and socio-economic characteristics, as well as in the provision of urban services and infrastructure.For example, in each microzone buildings are predominantly uniform for construction features, construction period and residential/industrial/commercial use.
The first step of our method concerns the acquisition of different not normalized thematic data from various institutional sources, including of the last microzone census database.
Subsequently, a homogeneous knowledge base of the analyzed urban system is created, in order to extract a set of synthetic indicators representing characteristics of the urban system related to the analyzed problem.These indicators express the input variables of a fuzzy rule set extracted by domain experts in which the output variable expresses an urban class.
A Mamdani fuzzy rule system is applied to classify the microzones assigning them a specific class; finally, a dissolve spatial operator is used to aggregate microzones spatially contiguous classified in the same urban class in urban contexts; in addition, we assess a membership degree of each urban context to its class, given by a weighted average of the membership degrees to this category calculated in any microzone include in the urban context.This membership degree represents the uncertainty in the attribution of the urban context to its urban class and provides an evaluation of the reliability of the classification.
The main advantages of the proposed model are the independence of it from the analyzed problem and its usability.In fact, our framework can be applied to any type of problems involved analysis of urban systems and streamlines and make more efficient the construction of the knowledge transferred by the domain experts.Finally, the assessment of the membership degree of the urban contexts to their urban classes allows the analyst to evaluate the reliability of the resultant partition.
In next section is described in detail the proposed model; in order to show the ways in which the components of our model are applied, a case study concerned with partitioning an urban system in contexts in which urban classes are typified by different residential density is explored.
In section 3 are described the area of study and the institutional datasets used in our experiments; in section 4 are shown the results of our experiments.Final considerations are reported in section 5.

The proposed model
Our model is composed by a set of 5 phases, as in fig. 1.The phases 1a and 1b are executable in parallel.The phase 1a (Data acquisition) concerns with the acquisition of the datasets from Institutional sources.A set of staging procedures are necessary to provide the reconciliation of these inhomogeneous data (for example, to carry out the transformation and conversions of spatial data in a unique coordinate system and to correct spatial topological errors) and the creations of relations between the various datasets.Output of this phase is given by the homogeneous spatial database of the area od study.
In the phase 1b (Indicators and fuzzy rule set creation) are defined the various physical, environmental and socio-economic indicators and is created the fuzzy rule set; this phase is executed with the contribution of domain experts.To model the expert knowledge and construct the fuzzy rules, we create a fuzzy partition of the domain of each indicator in which any fuzzy set is assigned by using a triangular or semi-trapezoidal fuzzy number and is titled with a linguistic label assigned by the domain expert.
In the phase 2 (Calculus of the microzone indicators) are implemented the spatial analysis processes need to calculate the indicators.Each indicator represents a summarize of specific characteristics of the microzone; it is calculated by applying the formulas created in the phase 1b and by using a set of geoprocessing and statistical operators applied on entities and characteristics in the spatial database.
In the phase 3 (Fuzzy rule system execution) for each microzone is executed the Mamdani fuzzy rule system in order to assign the microzone to a specific urban class.The indicators are fuzzified by a fuzzification component; then the fuzzy inference component is applied by using the Mamdani min and max operators; the urban class assigned to the microzone is given by the consequent of the fuzzy rule with greatest strength.
In the phase 4 (Homogeneous urban contexts creation) the adjoining microzones belonging to the same urban class are dissolved and is created the thematic map of the urban contexts of the area of study.

Phase 1.a -Data acquisition
In this phase the data on the area of study are acquired from various institutional sources.Output of this phase is a spatial database implementing the homogenous knowledge base of the area of study.A spatial dataset to acquire is given by the microzone census data, including the polygon spatial data corresponding to the microzones.Other datasets are need to extract the synthetic indicators, related to different information layers as population, buildings, roads, urban green, schools, infrastructures.
A set of geo-processing activities are necessary in order to normalize the spatial datasets; all datasets must be converted in a unique coordinate system and a topological check it needs to verify the integrity of the dataset.Other geoprocessing activities could be carried out to extract and normalize the thematic data, as, for examples: -extracting themes from a dataset in various format; -merge of datasets correspondent to a theme and distributed per tiles and clipping it on the area of study; -apply spatial operators to relate to any feature of the theme information inserted as annotation texts (for example the road name to assign to any polyline of a road network).A data cleaning activity on the data fields it needs in order to verify their integrity and accuracy, to delete outliers and correct inconsistent data and redundancies.Finally, all themes and tables are imported in a spatial database and the relation between them are created.

Phase 1b. -Indicators and fuzzy rule set creation
The indicators need to classify the microzones are evaluated by domain experts.In our experimentation the experts consider 14 indicators related to various thematic layers that characterize the area of study and are necessary to evaluate to which urban class the microzone belongs.In Tab. 1 are described all the indicators; to each indicator is assigned an identify and are reported the type of indicator, i.e. the thematic layer to whom it is referred, a brief description and its unit of measure.After defining the indicators, the domain experts create a fuzzy partition of any indicator by using triangular and semi-trapezoidal fuzzy numbers to create the fuzzy sets.The fuzzy partitions of the indicators in Tab.1 are shown in Tab.2. in which are reported the identifier of the indicator, a label assigned to any fuzzy sets, the inf, mean and sup values of the fuzzy number and the type of fuzzy set (ST = Semi-Trapezoidal, TR = Triangular).In order to extract the fuzzy rules, the experts define the taxonomy of the urban area classes.In our experimentation are considered the following set of urban area classes in which any class characterize a type of residential or rural zone of the urban system.Each class in Tab. 3 is correspondent to a fuzzy set of an output linguistic variable Z defined in the domain [0,1] and representing, following an increasing order from 0 to 1, the impact of residential settlements to the area.The first fuzzy set is a semi-trapezoidal fuzzy set representing a predominantly rural or wooded area; the last fuzzy set is a semi-trapezoidal fuzzy set representing a compact residential old town.The intermediate fuzzy sets are triangular.These fuzzy sets are defined in tab 4 and are graphically shown in fig. 2. Based on their knowledges, the experts extract the set of fuzzy rules need to evaluate the urban class to whom belongs any microzone.In our experimentation the 14 indicators are used as input variables in the antecedent of each rule and the output variable Z is used in the consequent, labeled as in tab. 3. The fuzzy rule set is composed by fuzzy rules extracted by the experts written in the form: where I1, I2, In, are input variables given by the linguistic labels of the fuzzy sets of the indicators and Z is the output variable.The operator Δi (i=1,…,n) is given by an AND or an OR connectives.We construct the fuzzy rule set considering only AND connectives, splitting rules in which there are OR connectives in the antecedent.To show the splitting process of the rules, we take into consideration the following subset of fuzzy rules created by the experts.

-Calculus of the microzone indicators
To calculate the indicators in any microzone are applied specific spatial analysis functions.For example, the indicator I1 in Tab. 1 is calculated by selecting the residential buildings in the area of study and extracting the total surface area covered by residential buildings and the number of residents per microzone.Finally, for any microzone the ratio between this total surface area and the number of residents is calculated.
A hierarchy of spatial analysis processes could be need in order to calculate the value of an indicator.In our experiment, to calculate the indicators I11, I12, I13 and I14 is necessary to calculate further parameters, labeled II level indicators, described in the following table.The indicator I11 is obtained as a weighted mean of the indicators I11a, I11b and I11b where the weights, are, respectively, the residents with age between 5 and 9 years, the residents with age between 10 and 14 years and the residents with age between 15 and 19 years.
Formally, let n5-9 be the number of residents in the microzone with age in the range 5-9 years, n10- The indicator I12 is obtained as a weighted mean of the indicators I12a and I12b.
where w12a and w12b are the weights assigned, respectively to the indicators I11a and I11b.The experts set w12a = 3 and w12b = 7 considering the influence of railway/subway station services to be greater than the bus services one.
The indicator I13 is calculated as: The indicator I14 is calculated as:

Phase 3. -Fuzzy rule system execution
In this phase a Mamdani fuzzy rule-based system is used to classify the microzones.In Fig. 2 is schematized the fuzzy rule-based system used.From the spatial database constructed in the previous phase is extracted the microzone dataset containing the crisp values of the indicators calculated for any microzone.The Fuzzifier component imports these indicator values and assign to any indicator the membership degrees to its fuzzy sets.Then, the Fuzzy Inference Engine component reads the membership degree of the fuzzy sets related to any indicator and performs the inference process calculating the strength of any fuzzy rule in the fuzzy rule set.
The min operator is applied to the AND connectives in the antecedent of the fuzzy rule to calculate its strength.The Fuzzy Inference Engine realizes the aggregation process to construct the output final fuzzy set.Aggregation is the process by which the truncated output fuzzy sets in each rule are combined into a single fuzzy set that represents the output aggregated fuzzy set.
In order to show the aggregation process, we consider a system formed by two fuzzy rules in the form: where A1 and A2 are two fuzzy sets of the linguistic input variable I1, B1 and B2 are two fuzzy sets of the input linguistic variable I2 and C1 and C2 are two Fuzzy sets of the output variable Z. Now suppose that, after the fuzzification process, we obtain the following membership degree for the input variables: A1 = 0.3, B1 = 0.5, A2 = 0.7, B1 = 0.8.
The strength of the two rules are given by: S(R1) = min(0.3,0.5) = 0.3 S(R2) = min(0.7,0.8) = 0.7.In the aggregation process we construct the output fuzzy set given by: In Fig. 4 is shown the output fuzzy set constructed in this example.The defuzzification process of the output fuzzy set is carried out via the discrete Center of Gravity (CoG) method by the formula: where the two integrals are extended in the range [0,1] which is the domain of the output variable Z.
We classify the microzone assigning it to urban class label of the output variable fuzzy set with greater membership degree in the point Ẑ ; the membership degree of the microzone to this class is given by the membership degree of the output variable to C in the point Ẑ .
In Fig. 5 is show the result of the defuzzification process.As assign the microzone to the class C1 with a membership degree given by   Ĉ Z .In this phase the area of study is partitioned in urban contexts.Each urban context is obtained dissolving adjoining microzones belonging to the same urban class; then, is realized the thematic map of the urban contexts of the area of study.
A weighted mean of the membership degree of the microzones forming an urban context is calculated, to extract the reliability of the urban context; the weight is given by the area of the microzone as the greater the surface of a micro-zone included in a context greater is its impact on the reliability of the classification of the context.

Application on an area of study
We test our model applying it on an urban system in order to partition the area of study in urban contexts by considering the taxonomy of the urban area classes in Tab. 3.

The area of study
The area of study is given by the Municipality of Pozzuoli (Naples -Italy).The municipality of Pozzuoli shows a multiplicity of urban area classes; it contains industrial areas, modern residential zones, a dense hold town and high uncultivated/wooded green areas.In [7] historical land use, photogrammetric and airborne LiDAR data are used to detect buried landfill sites in the area of Campi Flegrei, that contains the municipality of Pozzuoli; this study shows that in this area are present modifications of the landscape associated with the urban development and quarrying activity.The presence of volcanic hills within the municipal area has allowed an urban development mainly below them and towards the coastal areas.A survey on the seismic activities produced by the Campi Flegrei caldera in densely inhabited areas and the consequent risk for the population was carried out in [11] and recently in [17].A study of all the different cultural resources presents in the Municipality of Pozzuoli performed by using GIS technologies is presented in [10].It is interesting to study how are distributed the various contexts in the municipality in relation to its different natural, social and urban characteristics.We apply our model to obtain a partition of the municipality in these different contexts.In fig.6 is show the area of study; the microzones are outlined in yellow.The satellite base map is extracted by the ESRI satellite World Imagery database.

Spatial data sources
The microzone dataset collected for the study were provided by the ISTAT Italian National Statistical Institute, the Italian public research body that deals with censuses and surveys their social and economic characteristics.
The geo-topographic dataset used to extract the base theme of the municipality is the topographical database provided by the Campania Region in 1: 5000 scale, from which it was possible to extract information on buildings and their intended use, presence of urban green, presence of infrastructure such as hospitals, schools.The under study is a municipality bordering the sea, it was necessary, to make some indicators of our set, to identify the coastal microzones.
The datasets necessary to calculate the 14 indicators are extracted from four institutional data source: the regional geo-topographic database in scale 1:5000, the census database provided with the last Italian census data per microzone, the aero-photogrammetric spatial database provided by the Municipality of Pozzuoli and the free spatial database provided by the Open StreetMap community.
The datasets are extracted limited to the extension of the municipality of Pozzuoli.
In the following table are described all the data sources used in our tests.The polygonal census tracts dataset provided from the ISTAT institute was used as base dataset to calculate the indicators; the census tracts corresponds to the microzones used in our model.The municipality of Pozzuoli is partitioned in 283 microzones.For each microzone we extract the population dataset, composed of data concerning with various sections of residents as the number of residents in a specific age range, and the building dataset composed of data related to the number of buildings and dwellings with specific characteristics, as the number of buildings built in a period, the mean number of housings in any residential buildings, etc. polygonal buildings theme was acquired from the 2011 geo-topographic database in scale 1:5000, distributed by the Campania Region in an Italian National geo-topographic structure following the InSpire GeoUML data model [2,16].
Other dataset concerning streets, infrastructures and schools, where extracted from the aerophotogrammetric municipality data in scale 1:4000 provided from the municipality of Pozzuoli and from the Open StreetMap community spatial database.
All the datasets were converted in the plane coordinate system UTM WGS84 zone 33N.The same data layers providing from different data source were normalized and integrated.

Test results
We test our framework on a Pentium I7 dual core platform by using the tool GIS ESRI ArcGIS 10.5; all the spatial analysis processes are implemented as functions in the tool GIS; the fuzzy inference system is implemented in C++ language and incapsulated in the tool GIS.
In order to calculate the indicators needed to test our model a set of spatial operators as spatial intersects and spatial joins were used to summarize per census tract data assigned to features belonging to the various spatial datasets.Next are synthetized the processes applied to extract the indicators.
To calculate the indicators I1 and I2 the polygonal buildings dataset was partitioned in residential and industrial buildings in order to extract, respectively the area covered by residential and industrial building per microzone.
The indicator I3, given by the mean square meters of green areas for resident, is calculated by selecting the urban green areas and calculating the sum of urban green areas covering any microzone.Finally, this area is divided by the number of residents in the microzone.
The indicator I4 is calculated by dividing the sum of green areas in the microzone by the area of the microzone.
To calculate the indicators I5 the district urban roads are selected from the road network layer and the sum of the lengths of the selected arcs falling in every microzone is calculated; finally, this value is divided by the sum of the length of all the road arcs falling in the microzone.The indicator I6 is calculated by selecting the district urban roads with a width less than 7 m and dividing the sum of the selected arcs fallings in any microzone by the sum of the district urban road arcs falling in the microzone.
The indicator I7 is calculated by dividing the number of residents in any microzone by the area of the microzone in square kilometers.To calculate the indicators I8, I9 and I10 the Buildings and dwellings census dataset is used, extracting for any microzone, respectively, the number of residential buildings built before 1945, the number of dwellings with at least one resident and the number of residential buildings with at least 16 dwellings, and dividing them, respectively by the number of residential buildings, the number of dwellings and the number of residential buildings in the microzone.
The II level indicators I11a, I11b and I11c are calculated extracting from the point school layer, respectively, the primary, low secondary and secondary schools and constructing circular buffer areas with a radius of 500 meters centered in any school.Then, for any type of school, the area of the microzone covered by the buffer areas is extracted and divided by the area of the microzone.
The II level indicators I12a and I12b are calculated extracting from the point Transport facilitiy layers, respectively, the bus stops and the railway's stops and constructing circular buffer areas with a radius of, respectively, 100 and 300 centered in any stop.Then, for any type of stop, the area of the microzone covered by the calculated buffer areas is extracted and divided by the area of the microzone.
The II level indicators I13a and I13b are calculated selecting, respectively, microzones including coastal areas, and containing a maritime terminal.
The II level indicators I14a and I14b are calculated extracting respectively, the polygon Hospitals and Sports facilities layers and selecting the microzones including the selected elements.
For brevity we show the thematic maps obtained for the indicators I2 (Fig. 7) and I4 (Fig. 8) in which an equal interval classification method of the indicator is applied.In Fig. 9 and 10 are shown two thematic maps of, respectively, the indicators I2 and I4 in which to any microzone is assigned the label of the fuzzy set to whom the microzone belongs with the highest membership degree.After the fuzzification process the fuzzy inference engine component is started; a set of about 100 fuzzy rules created by the domain experts is used.Finally, the defuzzification process is executed and the appropriated urban area class is assigned to any microzone.
The thematic map in fig.11 show the classification results.In this map the urban area classification of the microzone is shown.In order to evaluate the performance of the classification we compare the results with the supervised urban area classification of the microzones performed by the experts.For each class we  These results show that the classification of the microzones obtained by applying our model is almost similar to that supervised one attributed by the experts.The only deviations are present in the class Fragmented rural/wooded zone and Sprawl; two of the 18 microzones classified by the experts as Fragmented rural/wooded zone by using our model are classified as Sprawl.
Finally adjoining microzones belonging to the same class are dissolved forming urban contexts.The municipality of Pozzuoli is partitioned in 60 urban contexts, shown in the map in Fig. 12.The only urban context classified as Residential old town (in magenta) is an area including the historical center of Pozzuoli.The urban contexts classified as Coastal residential zone (in light blue) area residential coastal areas.The other coastal areas are, respectively, the maritime industrial area, classified as Industrial zone, and an area given by a maritime not residential microzone, classified as Fragmented rural/wooded zone since it is not a residential zone and a high percentage of this zone is covered by vegetation.All the contexts classified as Industrial zone (in red) are areas where most of the buildings are industrial buildings or warehouses.The contexts classified as Downtrodden residential zone (in orange) are residential areas with a high density of residential real estates for building and with a high population density.The other on average residential contexts are classified as Comfortable residential zone (in light green); in these zones the population density and the number of dwellings per residential building are not high; in addition, these zones are almost covered by transportation services and schools and in them there are public green areas.The contexts classified as Sprawl (in brown) are areas where the density of residential buildings is sparse; they are probably urban agglomerations in recent, slow and unplanned expansion.Finally, the contexts classified as Fragmented rural/wooded zone (in green) are areas predominantly or completely covered with vegetation.
In fig.13 is shown a thematic map with the reliability of the results.The reliability is calculated as a weighted average of the membership degree to their urban area class of the microzones included in the context where the weight is given by the area of the microzone.There are four contexts with a low reliability, in the range 0.2-0.4:three of these contexts are classified as Sprawl and the last as Downtrodden residential zone.In all these contexts are included microzones with a not high membership degree to their urban area class, meanly under the value 0.4.
These results suggest the need of a finer classification of urban areas that for the urban contexts with a low reliability.In fact, in microzones classified as a specified urban area with a low membership degree probably there are different types of urban areas; a finer classification could also take into account classes of urban area to which microzones belong to a slightly lower degree of membership.For example, the context with low reliability classified as Downtrodden residential zone is given by a microzone classified as Downtrodden residential zone with a membership degree 0.36 and belonging to the class Industrial zone with a membership degree 0.31; this microzone are included a densely populated residential area and a non-residential areas with industrial premises; a finer classification of this microzone could consider both this class in order to characterize in greater detail the type of urban area that it represents.

Final considerations
We present a new model based on a Mamdani fuzzy rule system to partition an urban system in homogeneous urban contexts.We implement our model in a GIS platform and construct the urban contexts by considering initially the urban system partitioned in microzones.A set of indicators are defined to characterize urban areas; these indicators are fuzzified and used as variables in a fuzzy rule set used to classify the microzones; the urban contexts are obtained dissolving adjoining microzones belonging to the same urban area class.We assess the reliability of our classification assigning to any urban context the weighted average of the membership degree of the microzones within in it where the weight is given by the area of the microzone.
We test our model applying it to the Municipality of Pozzuoli (Italy) in order to partition the municipality in context classified based to the type of residential or rural area.
A comparison of the results with the results of a supervised classification obtained by expert show that our model has high classification performances in terms of accuracy, precision and recall.The results show that the contexts were the reliability is low include microzones in which are present zones with different characteristics; in the future we intend improve this model in order to obtain a finer partition of the urban system by considering all the more relevant class of urban area characterizing the microzones.

Figure 1 .
Figure 1.Scheme of the phases of the model.

Figure 3 .
Figure 3. Scheme of the fuzzy rule based system

PreprintsFigure 4 .
Figure 4. Example of construction of the output fuzzy set in the aggregation process

Figure 5 .
Figure 5. Results of the defuzzification process

Figure 6 .
Figure 6.The microzones of the municipality of Pozzuoli.

Figure 7 .Figure 8 .
Figure 7. Thematic map of the indicator I2 -Percent of industrial areas with respect to total built areas

Figure 9 .Figure 10 .
Figure 9. Thematic map of the indicator I2 in which any microzone is classified assigning it the label of the fuzzy sets to whom it belongs with highest membership degree

Figure 11 .
Figure 11.Thematic map of the microzones classified by urban area.

Figure 12 .
Figure 12.Thematic map of the urban contexts.

PreprintsFigure 13 .
Figure 13.Thematic map of the reliability of the urban contexts.

Table 1 .
Indicators used to classify the microzones of the area of study

Table 3 .
Urban area classes

Table 5 .
II level Indicators used to classify the microzones of the area of study

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 4 October 2018 doi:10.20944/preprints201810.0069.v1
Peer-reviewed version available at Geosciences 2018, 8, 440; doi:10.3390/geosciences8120440 14 the number of residents in the microzone with age in the range 10-14 years and n15-19 the number of residents in the microzone with age in the range 15-19 years.The indicator I11 is given by the formula:

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 4 October 2018 doi:10.20944/preprints201810.0069.v1
Peer-reviewed version available at Geosciences 2018, 8, 440; doi:10.3390/geosciences8120440calculate the accuracy, precision and recall (or sensitivity) indexes.This calculus is performed by extracting from the confusion matrix the TP, TN, FP and FN parameters, where: TP (True Positive) is the number of microzones correctly assigned to the class; TN (True Negative) is the number of microzones correctly not assigned to the class; FP (False Positive) is the number of microzones wrongly assigned to the class; FN (False Negative) is the number of microzones wrongly not assigned to the class.

Table 7
show the classification results; the three indexes are calculated for any class.

Table 7 .
Classification results obtained comparing the urban area classifications of the microzone obtained by applying or method with the supervised classification performed by the experts.