Leveraging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants
LLeveraging Artificial Intelligence to Analyze the COVID-19Distribution Pattern based on Socio-economic Determinants
Mohammadhossein Ghahramani a , Francesco Pilla a a Spatial Dynamics Lab, University College Dublin, Ireland
A R T I C L E I N F O
Keywords :Geodemographic analysisBig DataDimensionality ReductionNeural Network
A B S T R A C T
The spatialization of socioeconomic data can be used and integrated with other sources of informationto reveal valuable insights. Such data can be utilized to infer different variations, such as the dynamicsof city dwellers and their spatial and temporal variability. This work focuses on such applications toexplore the underlying association between socioeconomic characteristics of different geographicalregions in Dublin, Ireland, and the number of confirmed COVID cases in each area. Our aim is toimplement a machine learning approach to identify demographic characteristics and spatial patterns.Spatial analysis was used to describe the pattern of interest in Electoral Divisions (ED), which arethe legally defined administrative areas in the Republic of Ireland for which population statistics arepublished from the census data. We used the most informative variables of the census data to modelthe number of infected people in different regions at ED level.
1. Introduction
In March 11th, 2020, the Republic of Ireland’s govern-ment launched a national action plan in response to COVID-19, a widespread lock-down in order to minimize the riskof illness. The impacts of pandemics such as the currentCOVID-19 should be explored extensively. To mitigate andrecover from the negative repercussions, it is of paramountimportance to study the effects on the social tissue in cities.It seems that various research is needed to thoroughly in-vestigate, understand, mitigate and recover from the effectof this pandemic. Some studies have been focused on pro-viding risk assessment frameworks based on artificial intel-ligence and leveraging data generated from heterogeneoussources such as disease-related data, demographic, mobil-ity, and social media data [29, 33, 12, 3, 32]. The exposurerisk of the pandemic in different environments has been as-sessed. Many researchers are exploring the dynamics of thepandemic in urban areas to mitigate effects and understandthe impacts of COVID-19 on cities [26, 33, 7]. In this areaof research, four distinctive categories have received signif-icant attention: environmental quality, socio-economic im-pacts, management and governance, and transportation andurban design [30]. As far as the socio-economic impactsare concerned, pandemics can substantially negatively af-fect people at the bottom of the socio-economic hierarchy,those with low education, low income, and low-status jobs.For instance, it has been discussed that the Black and Latinopeople’s mortality rate is twice that of the Whites in the US[38]. The pandemics can also hit vulnerable groups of peo-ple in poor sanitary conditions. Moreover, various factorssuch as high density, inadequate access to health services andinfrastructure facilities can exacerbate the situation [9, 25].Different inequality issues can also make it difficult to main- ⋆ [email protected] (M. Ghahramani); [email protected] (F. Pilla) ORCID (s): tain social distancing [35]. Hence, it is essential to under-stand the existed relation between socio-economic inequal-ities and the pandemic. As discussed, such inequalities canthreaten public health by making it difficult to enforce pro-tective measures such as social distancing.Artificial Intelligence technologies such as Neural Net-works and Deep learning can play a significant role during apandemic. They can be used to provide different platformsfor social distance tracking [1, 23], monitor and control thespread of COVID-19 [4, 44]. Such technology has beenused in this study. We assess the association between thedemographic features and the number of confirmed casesat Electoral Divisions (i.e., ED) in Dublin, Ireland basedon an optimized self-organizing neural network. It shouldbe mentioned that the number of cases until September 10,2020, have been considered in this work. Our aim is to un-derstand the impacts of the pandemic on Dublin city givenassociated characteristics and study the related patterns indifferent clusters obtaining from demographic information,i.e., census data. We used a machine learning method basedon an unsupervised learning approach to group spatial datainto meaningful clusters. In doing so, the similarities amongspatial objects were taken into account. Given the imple-mented model, the implicit information about different EDswere extracted, and all associated relations were examined.Such data exploration can help us extract demographic infor-mation related to various clusters. First, a feature selectionmethod was used to extract the most relevant variables sincethe census data includes over 700 features, and redundantfeatures can significantly affect the model accuracy. Fea-ture extraction aims to project high-dimensional data setsinto lower-dimensional ones in which relevant features canbe preserved. These features, then, were used to distinguishpatterns. Dimensionality reduction and feature selection/extractionmethods [13], e.g., principal component analysis (PCA), lin-ear discriminant analysis (LDA), and canonical correlationanalysis (CCA), play a critical role in dealing with noiseand redundant features. These methods were used as a pre-
M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 1 of 12 a r X i v : . [ c s . S I] F e b everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants processing phase of data analysis and helped us obtain betterinsights and robust decisions.Broadly speaking, dimensionality reduction is consid-ered as a method to remove redundant variables. This tech-nique can be regarded as two distinctive approaches, i.e.,feature extraction and feature selection. Feature extractionrefers to those techniques that project original variables toa new latent space with lower dimensionality, while featureselection methods aim to choose a subset of variables suchthat a trained model minimizes redundancy and maximizesrelevance to the target feature. In this work, we deal with aclustering problem and high-dimensionality issue; hence, afeature extraction technique was used. Since interpreting as-sociated patterns in feature extraction methods can be a sub-jective process, different tests were implemented to deal withrelated issues such as readability and interpretability. PCAis a classic approach to dimensionality reduction (feature ex-traction) and has been implemented in various research stud-ies. However, it suffers from a global linearity issue. Thus,to address this concern, a nonlinear technique (i.e., kernelPCA [19]) was used in this work.Then, the extracted features from the census data werefed into a clustering model, and different clusters were iden-tified. The goal in this phase is to cluster EDs (includingvarious demographic variables) such that similarities amongthem within each group are maximized. The model is basedon an advanced spatial clustering technique and can dealwith non-linear relationships between features of a high di-mensional data set. To do so, we implemented an unsu-pervised approach based on an Artificial Neural Network(ANN) that can properly transform geo-referenced data intoinformation. The main property of ANNs is their ability tolearn and model nonlinear and complex relationships. Themodel employ a competition-based learning mechanism togenerate insights from unlabelled data. It leverages a multi-layer clustering approach, i.e., a self-organizing neural net-work [8, 43], to transform a complex high-dimensional in-put space into low dimensional output space while preserv-ing the topology of the data. Given a set of EDs, the modelgroups together different spatial objects that are similar withother (i.e., the distance among observations is minimized ina given cluster). Different validity measures were also ap-plied and the results are illustrated. For visualization, weuse the shapefile of Dublin. Fig. 1 demonstrates the Dublinshapefile, including different districts.The contributions of this work are as follows:1. The link between the number of confirmed Covid casesand socio-economic determinants at Electoral Divi-sion level in Dublin, Ireland is analyzed based on anAI-based spatial clustering method.2. A topology-preserving model is implemented to ex-plore nonlinear relationship among Electoral Divisionsgiven the census data to characterize the spatial distri-bution of city dwellers.The remainder of this paper is organized as follows: somerelated work on application of machine learning and arti- Figure 1:
Dublin shapefile including different polygons of theadministrative boundary and attributes of geographic features. ficial intelligence to deal with concerns related to the pan-demic is described in Section 2; data pre-processing oper-ations including feature extraction is explained in Section3; the proposed approach with its associated discussions ispresented in Section 4; Section 5 shows the experimentalsettings and the clustering results; and the future work andconclusions are presented in Section 6.
2. Related Work
Due to the global spread of coronavirus, many researchersacross the world are working to understand the underlyingpatterns of the pandemic from different perspectives. Theyare looking for effective ways to manage the flow of peo-ple and prevent new viral infections. As expected, numer-ous research has been undertaken as to medical concerns(e.g., diagnosis and treatment of the disease like lung dis-ease, lung nodules, chronic inflammation, chronic obstruc-tive pulmonary diseases) to ensure all required measures arein place. Different strategies, such as chest computed to-mography imaging [42] and polymerase chain reaction [18],have been discussed for detecting and classifying COVID-19infections. Artificial Intelligence (AI) approaches have alsobeen used in the field of medical data analysis [4], and dif-ferent algorithms have been implemented for such analysisand patients’ classification. Different neural network tech-niques have been utilized for diagnosis based on identifiedclinical characteristics such as cough, fever, sputum devel-opment, and pleuritic chest pain [20, 24]. Various impacts
M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 2 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants of the pandemic on urban areas have also attracted the at-tention of researchers. In [2], the authors have introduceda novel method to identify regions with high human den-sity and mobility, which are at risk for spreading COVID-19by exploiting cellular-network functionalities. In doing so,they have used the frequency of handover and cell selectionevents to identify the density of congestion. Several visu-alization techniques like Class Activation Mapping (CAM)[37], Class-specific Saliency Map, and Gradient-weightedClass Activation Mapping (Grad-CAM) [17] has been usedto generate localization heatmaps in order to highlight cru-cial areas that are closely associated with the pandemic. Rus-tam et al., have implemented four Machine Learning mod-els, such as linear regression, least absolute shrinkage, andselection operator, support vector machine, and exponentialsmoothing to understand the threatening factors of COVID-19 [27]. Different features, such as the number of newly in-fected cases, the number of deaths, and the number of recov-eries have been taken into account in their model.Network analysis, as a set of integrated techniques, canbe used to provide direct visualization of the pandemic risk.By illustrating the degree of similarity among various ar-eas given confirmed cases, So et al. have demonstrated thatnetwork analysis can provide a relatively simple yet power-ful way to estimate the pandemic risk [34]. Such analysiscan also supplement traditional modelling techniques to im-prove global control and prevention of the disease and pro-vide more timely evidence to inform decision-making in cri-sis zones. In [22], the authors have presented a methodologyto identify spreaders using the analysis of the relationship be-tween socio-cultural and economic characteristics with thenumber of infections and deaths caused by the virus in dif-ferent countries. The authors have explored the effect of so-cioeconomics, population, gross domestic product, health,and air connections by solving a vertex separator problem inmultiplex complex networks.Targeting policy responses to crises such as the currentpandemic and interventions exclusively on people who livein deprived areas requires insights such as which clusters insociety are most affected. In this work, we explore demo-graphic and socioeconomic factors and investigate the roleof socioeconomic factors in the spread of COVID-19. Ouraim is to analyze underlying features obtained from censusdata and describe such demographic information concerningthe geolocation of patients. We study the link of the pan-demic with such factors. Fig. 2 illustrates different phasesof the proposed model.
3. Data Processing
Geodemographic is referred to as the study of spatial pat-terns and socio-economic characteristics of different areas.Associated demographic databases, such as census data, canbe used to understand population diversity better since theyinclude characteristics of a country’s inhabitants. Generallyspeaking, Spatio-temporal datasets can be divided into dif-ferent categories, such as geo-referenced data points, geo-
Figure 2:
Different phases of the analysis model used in thiswork. referenced time series, moving objects, and trajectories. Theestimation of a region’s population has been a critical appli-cation of geospatial science in demography. In this sense,geodemographic clustering can be considered as a tool tounderstand spatially dependent datasets. This kind of clus-tering is unsupervised learning that groups spatial data intomeaningful clusters based on similarities among various ar-eas. The learning procedure is correlated to the tendency ofpeople to associate themselves with others who have com-mon characteristics. Census data can be considered as areference for overall population estimation. It includes in-formation about individuals who have been counted withinhouseholds in different regions. Such data sets have somespecial characteristics such as geospatial features. They con-sist of measurements or observations taken at specific loca-tions, referenced by latitude and longitude coordinates and/orassociated within specific regions (in this work Electoral Di-visions). Census data for the population living in the Repub-lic of Ireland are available at a different level, i.e., Small Areaand Electoral Division (ED), from a survey taken in 2016.However, since the number of confirmed cases are availableat EDs, the census data at such administrative areas were in-corporated.
Demographic information is available at the local popu-lation level via censuses carried out by countries. In Ireland,a census is conducted at five-year periods by the government,with the most recent census prior to this work occurring in
M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 3 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants
Table 1
Some observations of the census data at electoral divisions level consisting of variables.
GEOGID GEOGDESC T1-1AGE0M T1-1AGE1M T1-1AGE2M T1-1AGE3M T1-1AGE4M ... T15-3-N T15-3-NS Covid casesE02008 Ayrfield 33 33 34 31 37 ... 341 43 133E02012 Ballygall B 10 10 5 8 11 ... 266 27 109E02022 Beaumont B 29 26 35 24 21 ... 270 38 75E02006 Ashtown A 100 84 70 66 49 ... 626 111 99E02093 Whitehall D 11 15 12 11 5 ... 258 16 150 m -tuple ( 𝑚 is the number offeatures).Let matrix 𝑋 ∈ 𝐑 𝑛 × 𝑚 as: 𝑋 = ⎡⎢⎢⎢⎣ 𝑋 𝑋 ⋮ 𝑋 𝑛 ⎤⎥⎥⎥⎦ = ⎡⎢⎢⎢⎣ 𝑥 𝑥 ⋯ 𝑥 𝑚 𝑥 𝑥 ⋯ 𝑥 𝑚 ⋮ ⋮ ⋱ ⋮ 𝑥 𝑛 𝑥 𝑛 ⋯ 𝑥 𝑛𝑚 ⎤⎥⎥⎥⎦ (1)where 𝐑 is the real number set, 𝑋 𝑖 is the 𝑖 th region and itscorresponding variables ( m -tuple), and 𝑛 is the number ofall areas. As stated earlier, we deal with high dimensional-ity in this work. Such datasets can pose serious challenges,such as model overfitting. The more the number of variablesincreases, the more the chance of overfitting. Dimensionality reduction is the process of eliminatingredundant variables. To handle such concerns, different ap-proaches have been considered in the literature. Generallyspeaking, feature extraction and feature selection techniquesare applied to reduce data dimensionality. In the former ap-proach, original features are mapped to a new feature spacewith lower dimensionality. The latter refers to those meth-ods that identify and select a subset of features such thatthe trained model (based on the selected features) minimizesredundancy and maximizes relevance to the target feature.PCA is the most common dimensionality reduction approach;however, the transformation applied is linear. But when datafollow a nonlinear structure, as in our case, approximatingthe model by a linear method like PCA will not perform wellon the original data. Likewise, Multidimensional Scaling[28] and Independent Component Analysis (ICA) [11, 31]suffer from the linearity issue. To address this shortcoming,nonlinear techniques such as Kernel PCA, Laplacian Eigen-maps [36], and Semidefinite Embedding [40] can be used.The two first-mentioned methods have been applied in thiswork. The result of the Kernel PCA is illustrated to savespace. We can define the variance-covariance matrix as 𝑆 = 1 𝑛 𝑛 ∑ 𝑖 =1 ( 𝑋 𝑖 − ̄𝑋 ) 𝑇 ( 𝑋 𝑖 − ̄𝑋 ) (2)The aim is to maximize the trace of the covariance ma-trix (i.e., 𝐴 ∗ = arg max 𝐴 𝑡𝑟 ( 𝑆 ) ) given a weighted covariance M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 4 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants
StatisticsFeatures
Mean Std deviation Median Absolute Deviation IQR MedianPercentage of population aged 0-4 7.298 2.168 1.425 [5.797, 8.638] 7.238Percentage of population aged 5-14 14.053 3.379 1.964 [12.272, 16.228] 14.313Percentage of population aged 65 and over 13.580 4.413 2.620 [10.721, 16.071] 13.243Percentage of single population 56.157 4.881 2.432 [53.146, 58.103] 55.468Percentage of house-share household 4.254 4.147 1.389 [3.112, 5.984] 4.347Percentage with higher education degrees 20.471 9.131 4.292 [14.908, 23.724] 18.501Percentage of professional social class 4.981 3.816 1.863 [2.511, 6.417] 4.098Percentage of unemployed population 11.015 3.938 2.436 [8.241, 13.249] 10.526
Table 2
Summary information on a subset of summarized variables from the Irish census data acrossall EDs
Figure 3:
Result of the dimensinlity reduction phase implemented for feature extraction based on Kernel PCA. eigendecomposition approach [5], where 𝐴 is a set of eigen-vectors (unitary matrices that can represent rotations of thespace). A nonlinear transformation 𝜙 ( 𝑋 ) from the original 𝑚 -dimensional space has been considered, and the covari-ance matrix of the projected features has been measure as 𝑆 = 1 𝑛 𝑛 ∑ 𝑖 =1 𝜙 ( 𝑋 𝑖 ) 𝜙 ( 𝑋 𝑖 ) 𝑇 (3)The eigenvalues and eigenvectors are given by 𝑆𝜈 𝑘 = 𝜆𝜈 𝑘 (4)The eigenvectors have been measured ( 𝜈 𝑘 = ∑ 𝑛𝑖 =1 𝑎 𝑘𝑖 𝜙 ( 𝑋 𝑖 ) ),where 𝑘 is the new number of dimensions. 𝑛 𝑛 ∑ 𝑖 =1 𝜙 ( 𝑋 𝑖 ){ 𝜙 ( 𝑋 𝑖 ) 𝑇 𝜈 𝑘 } = 𝜆 𝑘 𝜈 𝑘 (5) By substituting 𝜈 𝑘 in above equation 𝑛 𝑛 ∑ 𝑖 =1 𝜙 ( 𝑋 𝑖 ) 𝜙 ( 𝑋 𝑖 ) 𝑇 𝑛 ∑ 𝑗 =1 𝑎 𝑘𝑖 𝜙 ( 𝑋 𝑗 ) = 𝜆 𝑘 𝑛 ∑ 𝑖 =1 𝑎 𝑘𝑖 𝜙 ( 𝑋 𝑖 ) (6)The kernel function ( Ψ( 𝑋 𝑖 , 𝑋 𝑗 ) = 𝜙 ( 𝑋 𝑖 ) 𝑇 𝜙 ( 𝑋 𝑗 ) ) is, then,multiply both sides of Eq. 6 and the kernel principal com-ponents can be calculated as: 𝜙 ( 𝑋 ) 𝑇 𝜈 𝑘 = 𝑛 ∑ 𝑖 =1 𝑎 𝑘𝑖 Ψ( 𝑋, 𝑋 𝑖 ) (7)It should be mentioned that we have constructed the kernelmatrix from the census data. To that end, a Gaussian ker-nel ( Ψ( 𝑋 𝑖 , 𝑋 𝑗 ) = 𝑒𝑥𝑝 (− || 𝑋 𝑖 − 𝑋 𝑗 || ∕2 𝜎 ) ) has been used,where 𝑐 is a constant. Given the measured variance for each M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 5 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants feature, the associated weight can be measured 𝜎 𝑋 = ∑ 𝑛𝑖 =1 𝜔 𝑖 ( 𝑋 𝑖 − 𝑋 ) ∑ 𝑛𝑖 =1 𝜔 𝑖 (8)We have also examined the relevance of all features usingthe coefficient of determination. In doing so, the proportionof the variances have been tested. A supervised learner hasbeen used, and iteratively one feature of the dataset has beenconsidered as the dependent variable and others as the in-dependent variables. The Hopkins statistic, which is a wayof measuring the clustering tendency of a data set, has beencalculated for both scenarios with the value of . beforedimensionality reduction and . after that phase. A valueclose to indicates that the data is highly clustered. Fig. 3 il-lustrates the result of the dimensionality reduction given theKernel PCA approach. Given the fraction of variances mea-sured in this phase and also given all the weights associatedto each feature, features, such as percentage of popula-tion aged 65 and over, percentage of house-share household,and percentage of the unemployed population, have been se-lected. All these features have been integrated with two ad-ditional variables, i.e., the population of each ED and thenumber of confirmed covid cases in each of those areas. Thefinal dataset is then used in the second phase (i.e., clustering)of the model.
4. Clustering Approach
After performing all the data preprocessing operationsexplained above, a clustering method can be implemented tofind underlying patterns. Due to characteristics of this work,i.e., non-linear dynamics, an unsupervised learning mecha-nism based on a vector quantization technique [41] has beenconsidered. It should be mentioned that most neural net-work approaches operate based on the non-linear optimiza-tion of a criterion, which may result in the local minimumissue and/or the convergence may take a long time. It hasbeen discussed that self-organizing maps are less sensitive tosuch concerns. This approach is motivated by retina-cortexmapping and considered as an optimal technique for vectorquantization problems. The topographic mechanism used inthis method can enable us to study relationships among spa-tial and non-spatial features and identify associated patterns.The model is self-organized and operates based on learningrules and neuron interactions. The learning process is basedon cooperation and competition among neurons. Moreover,neurons maintain proximity relationships during the learn-ing process. The idea is to quantize the input space intoa finite number of vectors. All observations in the inputspace (census vectors, together with the number of Covidcases in each spatial area) are projected to post-synaptic neu-rons in the latent space. The implemented model can trans-form all the census features in the input space into a low-dimensional discrete output space while preserving the rela-tionships among variables. To do so, all vectors are mappedto neurons based on synaptic connections, each of which is assigned with weights. These weights are updated such thatadjacent neurons on the lattice have similar values. The clus-tering procedures consists of different phases, i.e., competi-tion, collaboration, and weight updating.In the competition phase of the algorithm, a predefinednumber of neurons are initialized by randomly setting theirweights using census features. Neurons compete for each in-put vector’s ownership, and the most similar neuron (giventhe distance measure between an ED object together with allrelevant features and all neurons) to a given observation isdetected. The winning neuron is called the Best MatchingUnit (BMU). There are different distance measures to findthe similarity between neurons and an input vector, such asthe Euclidian distance, Correlation tests, and Cosine similar-ity. However, the squared Euclidean distance is often used ina real application. Let 𝑋 𝑖 be the 𝑖 th input vector (i.e., 𝑖 th ED’sfeatures) and 𝑊 𝑗 the associated weights of the 𝑗 th neuron.Then, the distance matrix 𝐷 𝑖𝑗 = 𝑛 ∑ 𝑛𝑖 =1 ∑ 𝑘𝑗 =1 ( 𝑋 𝑖 − 𝑊 𝑗 ) can be defined as: 𝐷 𝑖𝑗 = ⎡⎢⎢⎢⎣ 𝑑 𝑑 𝑑 … 𝑑 𝑘 𝑑 𝑑 𝑑 … 𝑑 𝑘 ⋮ ⋮ ⋮ ⋱ ⋮ 𝑑 𝑛 𝑑 𝑛 𝑑 𝑛 … 𝑑 𝑛𝑘 ⎤⎥⎥⎥⎦ (9)The BMU can be measured according to Ψ = arg min 𝑗 || 𝑋 𝑖 − 𝑊 𝑗 || (10)In the collaboration phase, the adjacent neurons of a givenBMU are updated. The aim is to find out which of the non-winning neurons are within the BMU’s neighbourhood de-tected in the previous phase. To do so, the spatial loca-tion of a topological neighbourhood of the excited neuronis detected. Several neighbourhood functions can be used tocalculate the neighbourhood radius, i.e., Rectangular, Mex-ican hat, and Gaussian functions. The latter (i.e., Gaussianfunction) is the most commonly used one and has been uti-lized in this work. The cooperative process in this phasestarts with defining an initial neighbourhood radius, whichshrinks throughout different iterations based on the neigh-bourhood function. For each neuron 𝑗 ( 𝑁 𝑗 ) in the neigh-borhood of the 𝑖 th winning neuron ( 𝑁 𝑖 ), the algorithm up-dates all the weights associated with the 𝑗 th neuron based ona learning rate. It should be mentioned that the weights ofother neurons outside of 𝑁 𝑖 neighbourhood are not adjusted(in a given iteration). The procedure can be defined by thefunction below: 𝜆 ( 𝜉 𝑖𝑗 ) = 𝑒𝑥𝑝 (− 𝜉 𝑖𝑗 𝜎 ) (11)where 𝜆 ( 𝜉 𝑖𝑗 ) is the topological neighborhood value of the 𝑖 th winning neuron ( 𝑁 𝑖 ), 𝜉 𝑖𝑗 is a lateral distance (the dis-tance between Ψ 𝑖 and its adjacent neurons 𝑁 𝑗 ), and 𝜎 is a M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 6 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants function of the number of iterations and starts with an ini-tial value ( 𝜎 𝑜 ). A decay function ( − 𝑛𝑇 ) is also employed, 𝜎 ( 𝑛 ) = 𝜎 𝑜 .𝑒𝑥𝑝 (− 𝑛𝐺 ) , where 𝑛 is the number of iterations, and 𝐺 is a constant. By defining the distance function formulatedabove, the neighbourhood territory for updating all adjacentneurons is explored. Two different connections, i.e., short-range excitatory connections and long-range inhibitory in-terconnections, are used during the projection process. Theformer is utilized at the presynaptic layer and the latter at thepostsynaptic one. The process can be expressed as: 𝜕𝑌 𝑗 ( 𝑛 ) 𝜕𝑛 + 𝜏𝑌 𝑗 ( 𝑛 ) = ∑ 𝑗 𝑊 𝑖𝑗 ( 𝑛 ) 𝑋 𝑖 ( 𝑛 ) + ∑ 𝑘 𝜂 𝑘 𝑌 ∗ 𝑘 ( 𝑛 ) − ∑ 𝑘 ′ 𝛾 𝑘 ′ 𝑌 ∗ 𝑘 ′ ( 𝑛 ) where 𝜏 is a constant, 𝑊 𝑖𝑗 ( 𝑛 ) is the synaptic strength be-tween input vectors at the presynaptic layer and neurons atthe postsynaptic layer, 𝜂 𝑘 and 𝛾 𝑘 are connection weights atthe presynaptic and postsynaptic layers, respectively, and 𝑌 ∗ is an active neuron at the postsynaptic layer.In the third phase, two methods (i.e., Hebb’s rule [39, 21]and Forgetting rule [6]) for adjusting weights of neurons areconsidered. Based on the Hebb’s rule, the change of thesynaptic weight ( Δ 𝑊 ) is a function of relative neuron spiketiming and is proportional to the correlation between an in-put ( 𝑋 ) and an output ( 𝑌 ) of a network, i.e., Δ 𝑊 = 𝜕𝑊 𝑖𝑗 ( 𝑛 ) 𝜕𝑡 = Θ 𝑌 𝑗 ( 𝑛 ) 𝑋 𝑖 ( 𝑛 ) (12)where Θ is the learning rate ( < Θ < ). A sigmoid func-tion has been applied during the learning process on the out-puts to make sure that they are not negative. 𝑌 𝑗 ( 𝑛 + 1) = Φ [ 𝑊 𝑇𝑗 𝑋 ( 𝑛 ) + ∑ 𝑗 𝜂𝑌 𝑗 ( 𝑛 ) ] (13)where Φ means a sigmoid function. Since adopting Hebbe’srule for weight updating can make weights saturated, theForgetting rule ( 𝛽𝑌 𝑗 ( 𝑛 ) 𝑊 𝑖𝑗 ( 𝑛 ) ) is also used in the model.Given (12) and the Gaussian neighborhood function definedby (11), let Θ = 𝛽 , then 𝛽𝑌 𝑗 ( 𝑛 ) = Θ 𝑌 𝑗 ( 𝑛 ) = Θ 𝜆 ( 𝜉 𝑖𝑗 ) we can formulate the synaptic learning rule as: 𝜕𝑊 𝑖𝑗 ( 𝑛 ) 𝜕𝑡 = Θ 𝑌 𝑗 ( 𝑛 ) 𝑋 𝑖 ( 𝑛 ) − 𝛽𝑌 𝑗 ( 𝑛 ) 𝑊 𝑖𝑗 ( 𝑛 )= Θ [ 𝑋 𝑖 ( 𝑛 ) − 𝑊 𝑖𝑗 ( 𝑛 ) ] 𝑌 𝑗 ( 𝑛 ) (14)With the above discussions, the weight updating processcan be defined as 𝑊 𝑗 ( 𝑛 + 1) = 𝑊 𝑗 ( 𝑛 ) + Δ 𝑊 𝑗 = 𝑊 𝑗 ( 𝑛 ) + Θ( 𝑛 ) 𝜆 ( 𝜉 𝑖𝑗 )[ 𝑋 ( 𝑛 ) − 𝑊 𝑗 ( 𝑛 )] (15) where Θ( 𝑛 ) is the learning rate for the 𝑛 th iteration, 𝑊 𝑗 ( 𝑡 ) isthe weight vector of the 𝑗 th neuron, and 𝜆 is a neighborhoodfunction. The learning rate is also a function of time anddecreases monotonically, i.e., Θ( 𝑛 ) = Θ 𝑒𝑥𝑝 ( 𝑛 − 𝐺 ) where Θ is an initial value, 𝐺 is a constant, and 𝑛 is thenumber of iterations.After the weights for all the input vectors are calculated,both the learning rate and the radius are diminished. Thepostsynaptic weights are adjusted to resemble the census fea-tures and reflect its properties as closely as possible. To sumup the procedures, the pseudo-code of the implemented Self-organizing map is presented in Algorithm 1. The summaryof notations used is also given in Table 3. Two quantizationand organization criteria have been utilized to measure thereliability of the model. Given such validity measures, thesensitive parameters of the algorithm have been adjusted. Adiscussion regarding the settings of the algorithm such as thelearning rate, the size of lattice (the number of neurons), andlevel of similarities among neurons are presented next. Algorithm 1:
Pseudo-code for the SOM model
Input : 𝑋 ← Census features, 𝑝 ← | 𝑋 | , 𝑘 ← 𝑘 , 𝜎 ← 𝜎 , Θ ← Θ { 𝑁 , 𝑁 , ⋯ , 𝑁 𝑘 } : 𝑘 neurons; { 𝑙 𝑁 , 𝑙 𝑁 , ⋯ , 𝑙 𝑁 𝑘 } : position set; { 𝑤 𝑁 , 𝑤 𝑁 , ⋯ , 𝑤 𝑁 𝑘 } : initial weights; Output: neurons’ weight vectors Set N = { 𝑁 , 𝑁 , ⋯ , 𝑁 𝑘 } ; for 𝑖 ← , ⋯ , 𝑝 do 𝜎 ( 𝑖 ) = 𝜎 . 𝑒𝑥𝑝 (− 𝑖𝑇 ) Θ( 𝑖 ) = Θ . 𝑒𝑥𝑝 (− 𝑖𝑇 ) Select the 𝑖 th observation (ED) 𝑥 𝑖 ∈ 𝑋 ; Ψ = arg min 𝑛 ∈ 𝑁 || 𝑥 𝑖 − 𝑤 𝑁 || ; for 𝑗 ← , ⋯ , 𝑘 do 𝜉 = || 𝑙 𝑥 𝑗 − 𝑙 Ψ || ; if 𝜉 < 𝜎 then 𝑤 𝑁 𝑗 = 𝑤 𝑁 𝑗 + Θ . 𝜆 ( 𝜉, 𝜎, 𝑛 ) . ( 𝑥 𝑖 − 𝑤 𝑁 𝑗 ); end end end Output the result.
The learning rate and the number of units needed shouldbe set in the algorithm, while the level of similarities amongunits and the proper number of clusters are designated there-after. Different techniques can be utilized to explore theconvergence of the algorithm, such as Quantisation Error(QE) [10], Topographic Error, Weight-value Convergence,
M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 7 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants
Table 3
Summary of the notations
Symbol Meaning 𝑋 Census features 𝑝 = | 𝑋 | The number of observations 𝑘 Size of the lattice 𝜎 The neighborhood parameter Θ The learning rate Ψ The lateral distance 𝜉 Best Matching Unit 𝑙𝑁𝑖
Position of the 𝑖 th neuron on the lattice and probabilistic models. It should be noted that there is noexact cost function that a self-organizing map (SOM) followsprecisely. As explained before, two criteria (i.e., QE andtopology preservation metric) have been taken into accountto ensure that the output of the model is reliable. The quanti-zation metric was used to assess the required number of neu-rons. The squared distance between an observation 𝑋 𝑖 andits corresponding neuron was calculated. In other words, anoptimization problem was solved based on the similarity be-tween vectors at presynaptic and postsynaptic layers. The ul-timate synaptic weights of neurons were achieved after run-ning Algorithm 1. The metric calculates the variance associ-ated with neurons’ synaptic weights by measuring the aver-age distance between each observation and its correspondingBMU, i.e., 𝑄 𝐸 = 1 𝑝 𝑝 ∑ 𝑖 =1 || 𝑋 𝑖 − Ψ( 𝑖 ) || (16)where 𝑝 is the number of observations at the presynapticlayer, summing all the errors can be expressed as: Ω = 𝑘 ∑ 𝑖 =1 ∑ 𝑋 𝑗 ∈ 𝑉 𝑖 𝜉 ( 𝑋 𝑗 , Ψ 𝑖 )= arg min 𝑋 𝑗 𝜉 ( 𝑋 𝑗 , Ψ 𝑖 ) (17)where 𝑘 is the size of the lattice (the number of neurons at thepostsynaptic layer) and 𝑉 𝑖 is the Voronoi areas associatedwith the 𝑖 th BMU ( Ψ 𝑖 ). Therefore, by using such a metricfor determining the convergence of the algorithm, the propernumber of neurons was detected. The learning rate of thealgorithm is a value between and . Different initial valuesfor the learning rate of the algorithm were tested, and theresults are illustrated in Fig. 4. The initial learning rate hasbeen set to . , and neurons have been considered.
5. Results
Given the implemented model, the algorithm leads toan organized representation of activation patterns and pro-totypes that well represent the census features are obtained.
Figure 4:
Comparing the Quantization Error given differentlattice size
The next step is determining the level of similarity amongneurons. We have performed different validity measures todivide neurons at the postsynaptic layer into clusters whereinter-cluster similarities are minimized while the intraclus-ter similarities are maximized. Let 𝐶 = { 𝐶 , 𝐶 , ..., 𝐶 𝑚 } bea set 𝑚 clusters’ centroids, 𝑁 = ( 𝑁 , 𝑁 , … , 𝑁 𝑘 ) be 𝑘 neu-rons at the postsynaptic layer and 𝜑 ( 𝑥 𝑖 , 𝑥 𝑗 ) be the similaritymeasure between two EDs 𝑥 𝑖 and 𝑥 𝑗 . | 𝑁 𝑖 | { 𝑚 } is the numberof neurons in the 𝑚 th cluster. The first validity measure usedin this work, Davies-Bouldin index (DBI), operates based onthe inter-cluster and intra-cluster variance. The similaritiesamong all ED’s features projected into neurons are consid-ered. Let denote the mean distance of all neurons belongingto cluster 𝐶 𝑚 to their centroid as: 𝛿 𝑚 = 1 | 𝑁 | { 𝑚 } ∑ 𝑁 𝑖 ∈ 𝐶𝑙 { 𝑚 } || 𝑁 { 𝑚 } 𝑖 − 𝐶 𝑚 || (18)Let Δ 𝑖𝑗 be the distance between two centroids ( 𝐶 𝑖 and 𝐶 𝑗 ). The Davies-Bouldin index can be formulated as: 𝐷𝐵𝐼 ( 𝑝 ) = 1 𝑝 𝑝 ∑ 𝑖 =1 𝑚𝑎𝑥 ( 𝛿 𝑖 + 𝛿 𝑗 Δ 𝑖𝑗 ) (19)The number of clusters, i.e., 𝑝 in (19) which minimizes theindex can be considered as an optimal value.For the second validity metric (i.e., Silhouette index), thewithin-cluster distance (Eq. 20), the mean distance amongneurons in each cluster ( 𝐶𝑙 𝑖 ), and the intra-cluster similarity(Eq. 21) between the cluster to which 𝑁 𝑖 belongs and itsnearest cluster are calculated. 𝛼 ( 𝑖 ) = 1 | 𝑁 | { 𝑚 } − 1 ∑ 𝑁 𝑖 ,𝑁 𝑗 ∈ 𝐶𝑙 { 𝑚 } 𝑑 ( 𝑁 𝑖 , 𝑁 𝑗 ) (20) Λ( 𝑁 𝑖 , 𝐶 𝑝 ) = 1 | 𝑁 | { 𝑝 } ∑ 𝑁 𝑗 ∈ 𝐶𝑙 { 𝑝 } 𝑑 ( 𝑁 𝑖 , 𝑁 𝑗 ) (21) M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 8 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants
Table 4
Two validity measures tested for selecting an appropriate num-ber of clusters.
Number of clusters Silhouette index Davies-Bouldin index3 0.4212 0.17214 0.4961 0.12815 0.5007 0.09986 0.6741 0.09547 0.8311 0.07048 0.8019 0.07319 0.7702 0.0782
The smallest intra-cluster distance is then calculated, 𝛽 ( 𝑖 ) =arg min 𝑚 ≠ 𝑝 Λ( 𝑁 𝑖 , 𝐶 𝑝 ) . The Silhouette index ( ̌𝑆 ) for each neuron( 𝑁 𝑖 ) at the postsynaptic layer can be defined as ̌𝑆 = 𝛽 ( 𝑖 ) − 𝛼 ( 𝑖 ) 𝑚𝑎𝑥 ( 𝛼 ( 𝑖 ) , 𝛽 ( 𝑖 )) (22)The mean of the index defined above for a given cluster isthen calculated. Silhouette values fall between −1 and , anda value close to indicates that the corresponding numberof clusters is optimal. Considering the DBI measure, the av-erage distance among clusters should be minimized. Hence,the minimum values for this validity index are considered.According to the results achieved from the validity measurespresented in Table 4, we choose seven as the optimal numberof clusters. The results achieved in this work show that thealgorithm converges appropriately, and the generated neu-ral network units have been decently grouped into super-clusters. Finally, the results of the clustering method areillustrated in Fig. 5.We have aggregated the number of confirmed COVIDcases in each Electoral Division given the identified clusters,and the results are demonstrated in Table 5. As shown, thenumber of confirmed COVID cases in Clusters 5, 6, and 7 arehigher comparing with others. Given the result of the clus-tering model and the visualizations in Fig. 5, we can identifydifferent characteristics of each cluster. The detailed featuresare presented in Table 6. We have found that those clusterswith a high number of cases have the lowest proportions ofthe population with age over 65, high percentage of employ-ment, high percentage of private rent, and high percentageof the population aged 25-44 (young professionals). At thesame time, they have the highest proportion of house shares.The boxplots illustrated in Fig. 6 correspond to the clustercharacteristics in the seven detected clusters.
6. Conclusions and Future Work
In this work, we have proposed a multiple-level approachto study the association between geodemographic clusteringand the number of confirmed Covid cases in Dublin, Ireland.This work suggests that by incorporating and clustering thepublicly available census data, we can obtain valuable in-sights regarding the spatial variations of people who havecontracted the virus. The proposed method includes vari-ous phases. As the census data used in this work consists
Figure 5:
Clustering result of the implemented method forElectoral Divisions based on the census data, in which 7 clus-ters are detected.
Clusters
Number of casesCluster 1 788Cluster 2 1534Cluster 3 901Cluster 4 1077Cluster 5 2040Cluster 6 1824Cluster 7 3635
Table 5
The number of confirmed Covid cases across seven clusters of numerous features, and such characteristics can make apredictive modelling task challenging, a feature selection ap-proach has been implemented based on a non-linear method.Different tests have also been applied to make sure the mostrelevant features are selected. Then, an advanced geodemo-graphic clustering algorithm has been implemented based ona self-organizing feature map to extract clusters given the se-lected features. The quality of the generated map has beenanalyzed. It should be noted that there is no universal defi-nition of what is good clustering, and this notion is relative.As discussed throughout the paper, an SOM has been con-sidered in this work due to the inherent non-linear character-
M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 9 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants
Clusters
Some characteristics of three clusters with high number of casesCluster 5 ∙ High percentage of house share ∙ High number of couples with no child ∙ High proportion of aged 25-44Cluster 6 ∙ High percentage of house share ∙ High proportion of dink family ∙ High employment rateCluster 7 ∙ High percentage of house share ∙ High employment rate ∙ High proportion of aged 0-14
Table 6
Some characteristics of clusters
Figure 6:
Boxplots of census data on percentage of different variables given 7 detected clusters. istics of the spatial dataset. Different validity measures havealso been employed to make sure the results of the methodused are reliable. We have demonstrated that the algorithmhas converged properly.According to the analysis, we have detected seven clus-ters based on the census data and the spatial distributionof the people were explored using the unsupervised neural network method. The distribution of people who have con-tracted the virus was studied. The use of the proposed geode-mographic approach incorporating spatial data of a geode-mographic nature means that clusters can be interpreted interms of real-life infected people attributes.
M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 10 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants
References [1] Ahmed, I., Ahmad, M., Rodrigues, J.J., Jeon, G., Din, S., 2021.A deep learning-based social distance monitoring framework forcovid-19. Sustainable Cities and Society 65, 102571. URL: ,doi: https://doi.org/10.1016/j.scs.2020.102571 .[2] Alsaeedy, A.A.R., Chong, E.K.P., 2020. Detecting regions at risk forspreading covid-19 using existing cellular wireless network function-alities. IEEE Open Journal of Engineering in Medicine and Biology1, 187–189. doi: .[3] Beria, P., Lunkar, V., 2021. Presence and mobility of the popula-tion during the first wave of covid-19 outbreak and lockdown initaly. Sustainable Cities and Society 65, 102616. URL: ,doi: https://doi.org/10.1016/j.scs.2020.102616 .[4] Bhattacharya, S., Reddy Maddikunta, P.K., Pham, Q.V., Gadekallu,T.R., Krishnan S, S.R., Chowdhary, C.L., Alazab, M., Jalil Piran, M.,2021. Deep learning and medical image processing for coronavirus(covid-19) pandemic: A survey. Sustainable Cities and Society 65,102589. doi: https://doi.org/10.1016/j.scs.2020.102589 .[5] Chan, S.C., Wu, H.C., Tsui, K.M., 2012. Robust recursive eigende-composition and subspace-based algorithms with application to faultdetection in wireless sensor networks. IEEE Transactions on Instru-mentation and Measurement 61, 1703–1718. doi: .[6] Chushig-Muzo, D., Soguero-Ruiz, C., Engelbrecht, A.P., De MiguelBohoyo, P., Mora-Jiménez, I., 2020. Data-driven visual character-ization of patient health-status using electronic health records andself-organizing maps. IEEE Access 8, 137019–137031. doi: .[7] Das, A., Ghosh, S., Das, K., Basu, T., Dutta, I., Das, M., 2021. Livingenvironment matters: Unravelling the spatial clustering of covid-19hotspots in kolkata megacity, india. Sustainable Cities and Society 65,102577. URL: , doi: https://doi.org/10.1016/j.scs.2020.102577 .[8] Díaz Ramos, A., López-Rubio, E., Palomo, E.J., 2020. The forbiddenregion self-organizing map neural network. IEEE Transactions onNeural Networks and Learning Systems 31, 201–211. doi: .[9] Duffey, R.B., Zio, E., 2020. Analysing recovery from pandemicsby learning theory: The case of covid-19. IEEE Access 8, 110789–110795. doi: .[10] Fan, Q., Yang, G., Ye, D., 2018. Quantization-based adaptive actor-critic tracking control with tracking error constraints. IEEE Trans-actions on Neural Networks and Learning Systems 29, 970–980.doi: .[11] Feng, Y., Li, H., 2020. Dynamic spatial-independent-component-analysis-based abnormality localization for distributed parameter sys-tems. IEEE Transactions on Industrial Informatics 16, 2929–2936.doi: .[12] Ge, X.Y., Pu, Y., Liao, C.H., Huang, W.F., Zeng, Q., Zhou, H., Yi,B., Wang, A.M., Dou, Q.Y., Zhou, P.C., Chen, H.L., Liu, H.X.,Xu, D.M., Chen, X., Huang, X., 2020. Evaluation of the expo-sure risk of sars-cov-2 in different hospital environment. Sustain-able Cities and Society 61, 102413. URL: , doi: https://doi.org/10.1016/j.scs.2020.102413 .[13] Ghahramani, M., Qiao, Y., Zhou, M.C., O’Hagan, A., Sweeney, J.,2020a. Ai-based modeling and data-driven evaluation for smart man-ufacturing processes. IEEE/CAA Journal of Automatica Sinica 7,1026–1037. doi: .[14] Ghahramani, M., Zhou, M., Hon, C.T., 2019a. Extracting signifi-cant mobile phone interaction patterns based on community struc-tures. IEEE Transactions on Intelligent Transportation Systems 20,1031–1041. doi: .[15] Ghahramani, M., Zhou, M., Hon, C.T., 2019b. Mobile phone dataanalysis: A spatial exploration toward hotspot detection. IEEETransactions on Automation Science and Engineering 16, 351–362. doi: .[16] Ghahramani, M., Zhou, M., Wang, G., 2020b. Urban sensing basedon mobile phone data: approaches, applications, and challenges.IEEE/CAA Journal of Automatica Sinica 7, 627–637. doi: .[17] He, T., Guo, J., Chen, N., Xu, X., Wang, Z., Fu, K., Liu, L., Yi,Z., 2020. Medimlp: Using grad-cam to extract crucial variables forlung cancer postoperative complication prediction. IEEE Journal ofBiomedical and Health Informatics 24, 1762–1771. doi: .[18] Hu, S., Gao, Y., Niu, Z., Jiang, Y., Li, L., Xiao, X., Wang, M.,Fang, E.F., Menpes-Smith, W., Xia, J., Ye, H., Yang, G., 2020.Weakly supervised deep learning for covid-19 infection detectionand classification from ct images. IEEE Access 8, 118869–118883.doi: .[19] Kim, C., Klabjan, D., 2020. A simple and fast algorithm for l1-normkernel pca. IEEE Transactions on Pattern Analysis and Machine In-telligence 42, 1842–1855. doi: .[20] Li, L., Qin, L., Xu, Z., Yin, Y., Wang, X., Kong, B., et al., 2020. Ar-tificial intelligence distinguishes covid-19 from community acquiredpneumonia on chest ct. Radiology 19.[21] Martins, D.M.L., de Lima Neto, F.B., 2020. Hybrid intelligentdecision support using a semiotic case-based reasoning and self-organizing maps. IEEE Transactions on Systems, Man, and Cyber-netics: Systems 50, 863–870. doi: .[22] Montes-Orozco, E., Mora-Gutiérrez, R., De-Los-Cobos-Silva, S.,Rincón-García, E., Torres-Cockrell, G., Juárez-Gómez, J., Obregón-Quintana, B., Lara-Velázquez, P., Gutierrez-Andrade, M., 2020. Iden-tification of covid-19 spreaders using multiplex networks approach.IEEE Access 8, 122874–122883. doi: .[23] Nagrath, P., Jain, R., Madan, A., Arora, R., Kataria, P., Hemanth,J., 2021. Ssdmnv2: A real time dnn-based face mask detection sys-tem using single shot multibox detector and mobilenetv2. Sustain-able Cities and Society 66, 102692. URL: , doi: https://doi.org/10.1016/j.scs.2020.102692 .[24] Ouyang, X., Huo, J., Xia, L., Shan, F., Liu, J., Mo, Z., Yan, F., Ding,Z., Yang, Q., Song, B., Shi, F., Yuan, H., Wei, Y., Cao, X., Gao, Y.,Wu, D., Wang, Q., Shen, D., 2020. Dual-sampling attention networkfor diagnosis of covid-19 from community acquired pneumonia. IEEETransactions on Medical Imaging 39, 2595–2605. doi: .[25] Rahman, M.A., Zaman, N., Asyhari, A.T., Al-Turjman, F., AlamBhuiyan, M.Z., Zolkipli, M., 2020. Data-driven dynamic clus-tering framework for mitigating the adverse economic impact ofcovid-19 lockdown practices. Sustainable Cities and Society 62,102372. URL: , doi: https://doi.org/10.1016/j.scs.2020.102372 .[26] Rumpler, R., Venkataraman, S., Göransson, P., 2020. An observa-tion of the impact of covid-19 recommendation measures monitoredthrough urban noise levels in central stockholm, sweden. Sustain-able Cities and Society 63, 102469. URL: , doi: https://doi.org/10.1016/j.scs.2020.102469 .[27] Rustam, F., Reshi, A.A., Mehmood, A., Ullah, S., On, B., Aslam,W., Choi, G.S., 2020. Covid-19 future forecasting using supervisedmachine learning models. IEEE Access 8, 101489–101499. doi: .[28] Saeed, N., Nam, H., Al-Naffouri, T.Y., Alouini, M., 2019. A state-of-the-art survey on multidimensional scaling-based localization tech-niques. IEEE Communications Surveys Tutorials 21, 3565–3583.doi: .[29] Sannigrahi, S., Pilla, F., Basu, B., Basu, A.S., Molter, A., 2020.Examining the association between socio-demographic compositionand covid-19 fatalities in the european region using spatial regres-sion approach. Sustainable Cities and Society 62, 102418. doi: https://doi.org/10.1016/j.scs.2020.102418 .[30] Sharifi, A., Khavarian-Garmsir, A.R., 2020. The covid-19 pandemic:
M. Ghahramani et al.:
Preprint submitted to Elsevier
Page 11 of 12everaging Artificial Intelligence to Analyze the COVID-19 Distribution Pattern based on Socio-economic Determinants
Impacts on cities and major lessons for urban planning, design, andmanagement. Science of The Total Environment , 142391doi: .[31] Shi, X., Yang, H., Xu, Z., Zhang, X., Farahani, M.R., 2019. An in-dependent component analysis classification for complex power qual-ity disturbances with sparse auto encoder features. IEEE Access 7,20961–20966. doi: .[32] Shokouhyar, S., Shokoohyar, S., Sobhani, A., Gorizi, A.J., 2021.Shared mobility in post-covid era: New challenges and opportu-nities. Sustainable Cities and Society 67, 102714. URL: ,doi: https://doi.org/10.1016/j.scs.2021.102714 .[33] Silva, J.C.S., de Lima Silva, D.F., de Sá Delgado Neto, A., Ferraz, A.,Melo, J.L., Ferreira Júnior, N.R., de Almeida Filho, A.T., 2021. Acity cluster risk-based approach for sars-cov-2 and isolation barriersbased on anonymized mobile phone users’ location data. SustainableCities and Society 65, 102574. doi: https://doi.org/10.1016/j.scs.2020.102574 .[34] So, M., Tiwari, A., Chu, A., Tsang, J., Chan, J., 2020. Visualizingcovid-19 pandemic risk through network connectedness. InternationalJournal of Infectious Diseases 96, 558–561.[35] Sun, C., Zhai, Z., 2020. The efficacy of social distance and ventila-tion effectiveness in preventing covid-19 transmission. SustainableCities and Society 62, 102390. URL: , doi: https://doi.org/10.1016/j.scs.2020.102390 .[36] Sun, G., et al., 2019. Effective dimensionality reduction for visual-izing neural dynamics by laplacian eigenmaps. Neural Computation31, 1356–1379.[37] Sun, K.H., Huh, H., Tama, B.A., Lee, S.Y., Jung, J.H., Lee, S., 2020.Vision-based fault diagnostics using explainable deep learning withclass activation maps. IEEE Access 8, 129169–129179. doi: .[38] Wade, L., Khavarian-Garmsir, A.R., 2020. An unequal blow. Science, 700–70.[39] Wickramasinghe, C.S., Amarasinghe, K., Manic, M., 2019. Deepself-organizing maps for unsupervised image classification. IEEETransactions on Industrial Informatics 15, 5837–5845. doi: .[40] Xiang, S., Nie, F., Zhang, C., Zhang, C., 2009. Nonlinear dimension-ality reduction with local spline embedding. IEEE Transactions onKnowledge and Data Engineering 21, 1285–1298. doi: .[41] Xie, K., Chen, C., Lewis, F.L., Xie, S., 2018. Adaptive asymptoticneural network control of nonlinear systems with unknown actuatorquantization. IEEE Transactions on Neural Networks and LearningSystems 29, 6303–6312. doi: .[42] Xie, X., Zhong, Z., Zhao, W., Zheng, C., Wang, F., Liu, J., 2020.Chest ct for typical 2019-ncov pneumonia: Relationship to negativert-pcr testing. Radiology 12.[43] Yu, H., Lu, J., Zhang, G., 2020. Online topology learning by a gaus-sian membership-based self-organizing incremental neural network.IEEE Transactions on Neural Networks and Learning Systems 31,3947–3961. doi: .[44] Zivkovic, M., Bacanin, N., Venkatachalam, K., Nayyar, A., Djord-jevic, A., Strumberger, I., Al-Turjman, F., 2021. Covid-19cases prediction by using hybrid machine learning and beetleantennae search approach. Sustainable Cities and Society 66,102669. URL: , doi: https://doi.org/10.1016/j.scs.2020.102669 . M. Ghahramani et al.: