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Time–Space Analysis of Multidimensional Phenomena: A Composite Indicator of Social Exclusion Through k-Means

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Abstract

Composite Indicators are one-dimensional measurements that simplify the interpretation of multidimensional phenomena that facilitate public policies' elaboration. The literature on composite indicators is abundant, diversified, and inserted in practically all knowledge areas. Part of this literature aims to reduce uncertainties that propagate through the structure of the composite indicator during the process of normalization, weighting, and aggregation of indicators. Even if no composite indicator is exempt from criticism, the current literature is already sufficiently large and deep to guide researchers in constructing reliable composite indicators. However, most related works are concerned with representing multidimensional phenomena in time or space. Although some studies are interested in representing multidimensional phenomena that co-occur in time–space, the portion of the literature that addresses composite indicators is still not comprehensive, therefore leaving several open questions: What are the additional challenges in representing multidimensional phenomena in time–space? What methods can be used? Which method is most appropriate for this type of representation? What are the shortcomings of this method? How to reduce these shortcomings? This research aims at answering these questions in order to advance the time–space analysis of multidimensional phenomena. As a general contribution, the work presents a scheme of procedures that reduce subjectivities and uncertainties in the representations of multidimensional phenomena in time–space. As a specific contribution, it provides accurate and reliable information on the trajectory of social exclusion in the analyzed region.

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References

  • Abello, A., Cassells, R., Daly, A., D’Souza, G., & Miranti, R. (2016). Youth social exclusion in Australian communities: A new index. Social Indicators Research, 128(2), 635–660.

    Article  Google Scholar 

  • Alabi, T. R., Adebola, P. O., Asfaw, A., De Koeyer, D., Lopez-Montes, A., & Asiedu, R. (2019). Spatial multivariate cluster analysis for defining target population of environments in West Africa for yam breeding. International Journal of Applied Geospatial Research (IJAGR), 10(3), 1–30.

    Article  Google Scholar 

  • Alkire, S., & Foster, J. (2011). Counting and multidimensional poverty measurement. Journal of Public Economics, 95(7–8), 476–487.

    Article  Google Scholar 

  • Andrienko, G., Andrienko, N., Bremm, S., Schreck, T., Von Landesberger, T., Bak, P., & Keim, D. (2010). Space-in-time and time-in-space self-organizing maps for exploring spatiotemporal patterns. Computer Graphics Forum, 29(3), 913–922.

    Article  Google Scholar 

  • Andrienko, N., Andrienko, G., & Gatalsky, P. (2003). Exploratory spatio-temporal visualization: An analytical review. Journal of Visual Languages & Computing, 14(6), 503–541.

    Article  Google Scholar 

  • Apparicio, P., Riva, M., & Séguin, A. M. (2015). A comparison of two methods for classifying trajectories: a case study on neighborhood poverty at the intra-metropolitan level in Montreal. Cybergeo: European journal of geography. https://doi.org/10.4000/cybergeo.27035

    Article  Google Scholar 

  • Bárcena-Martín, E., Pérez-Moreno, S., & Rodríguez-Díaz, B. (2020). Rethinking multidimensional poverty through a multi-criteria analysis. Economic Modelling, 91, 313–325.

    Article  Google Scholar 

  • Becker, W., Saisana, M., Paruolo, P., & Vandecasteele, I. (2017). Weights and importance in composite indicators: Closing the gap. Ecological Indicators, 80, 12–22.

    Article  Google Scholar 

  • Bueno, M. D. C. D., & Alvaro de Oliveira, D. A. (2017). A geografia do censo no Brasil: Potencialidades e limites dos dados censitários em análises espaciais. Geographia, 19(39), 16–28.

    Article  Google Scholar 

  • Carroll, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika, 35(3), 283–319.

    Article  Google Scholar 

  • Charrad, M., Ghazzali, N., Boiteux, V., & Niknafs, A. (2014). NbClust: An r package for determining the relevant number of clusters in a data set. Journal of Statistical Software, 61(6), 1–36.

    Article  Google Scholar 

  • Chehreghan, A., & Ali Abbaspour, R. (2018). An assessment of the efficiency of spatial distances in linear object matching on multi-scale, multi-source maps. International Journal of Image and Data Fusion, 9(2), 95–114.

    Article  Google Scholar 

  • Chu, K., Liu, W., She, Y., Hua, Z., Tan, M., Liu, X., & Jia, Y. (2018). Modified principal component analysis for identifying key environmental indicators and application to a large-scale tidal flat reclamation. Water, 10(1), 69.

    Article  Google Scholar 

  • Cinelli, M., Spada, M., Kim, W., Zhang, Y., & Burgherr, P. (2021). MCDA Index Tool: An interactive software to develop indices and rankings. Environment Systems and Decisions, 41(1), 82–109.

    Article  Google Scholar 

  • Davidescu, A. A., Apostu, S. A., Pantilie, A. M., & Amzuica, B. F. (2020). Romania’s South-Muntenia region, towards sustainable regional development. Implications for Regional Development Strategies. Sustainability, 12(14), 5799.

    Article  Google Scholar 

  • Delmelle, E. C. (2015). Five decades of neighborhood classifications and their transitions: A comparison of four US cities, 1970–2010. Applied Geography, 57, 1–11. https://doi.org/10.1016/j.apgeog.2014.12.002

    Article  Google Scholar 

  • Delmelle, E. C. (2016). Mapping the DNA of urban neighborhoods: Clustering longitudinal sequences of neighborhood socioeconomic change. Annals of the American Association of Geographers, 106(1), 36–56.

    Article  Google Scholar 

  • Dialga, I. (2017). Highlighting methodological limitations in the steps of composite indicators construction. Social Indicators Research, 131(2), 441–465.

    Article  Google Scholar 

  • Dias, F., & Silver, D. (2018). Visualizing demographic evolution using geographically inconsistent census data. UT Sociology Working Paper No. 2018–03, 24, 1–12.

  • Dinh, H., Freyens, B., Daly, A., & Vidyattama, Y. (2017). Measuring community economic resilience in Australia: Estimates of recent levels and trends. Social Indicators Research, 132(3), 1217–1236.

    Article  Google Scholar 

  • El Gibari, S., Gómez, T., & Ruiz, F. (2019). Building composite indicators using multicriteria methods: A review. Journal of Business Economics, 89(1), 1–24.

    Article  Google Scholar 

  • Exeter, D. J., Feng, Z., Zhao, J., Cavadino, A., & Norman, P. (2019). The geographic harmonisation of Scotland’s small area census data, 1981 to 2011. Health & Place, 57, 22–26.

    Article  Google Scholar 

  • Fanaee-T, H., & Gama, J. (2016). Tensor-based anomaly detection: An interdisciplinary survey. Knowledge-Based Systems, 98, 130–147.

    Article  Google Scholar 

  • Foote, N. S. (2017). Beyond studentification in United States College Towns: Neighborhood change in the knowledge nodes, 1980–2010. Environment and Planning A, 49(6), 1341–1360.

    Article  Google Scholar 

  • Foote, N., & Walter, R. (2017). Neighborhood and socioeconomic change in emerging megapolitan nodes: Tracking shifting social geographies in three rapidly growing United States metropolitan areas, 1980–2010. Urban Geography, 38(8), 1203–1230.

    Article  Google Scholar 

  • Franklin, J. B., Sathish, T., Vinithkumar, N. V., & Kirubagaran, R. (2020). A novel approach to predict chlorophyll-a in coastal-marine ecosystems using multiple linear regression and principal component scores. Marine pollution bulletin, 152, 110902.

    Article  Google Scholar 

  • Giambona, F., & Vassallo, E. (2014). Composite indicator of social inclusion for European countries. Social Indicators Research, 116(1), 269–293.

    Article  Google Scholar 

  • Greco, S., Ishizaka, A., Tasiou, M., & Torrisi, G. (2019). On the methodological framework of composite indices: A review of the issues of weighting, aggregation, and robustness. Social Indicators Research, 141(1), 61–94.

    Article  Google Scholar 

  • Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2019). Multivariate Data Analysis (8th ed.). Cengage.

    Google Scholar 

  • Hartigan, J. A., & Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the Royal Statistical Society Series C (Applied Statistics), 28(1), 100–108.

    Google Scholar 

  • IBGE - Brazilian Institute of Geography and Statistics (2020). Estimativas da população [Population estimates]. https://www.ibge.gov.br/estatisticas/sociais/9103-estimativas-de-populacao.html. Accessed 23 March 2021.

  • IBGE - Brazilian Institute of Geography and Statistics (2000). Censo demográfico. [Demographic census] www.ibge.gov.br Accessed 23 March 2021.

  • IBGE - Brazilian Institute of Geography and Statistics (2010). Censo demográfico. [Demographic census] www.ibge.gov.br Accessed 23 March 2021.

  • Kassambara, A. (2017). Practical guide to cluster analysis in R: Unsupervised machine learning (Vol. 1). STHDA.

  • Kaufman, L., & Rousseeuw, P. J. (2009). Finding groups in data an introduction to cluster analysis (Vol. 344). John Wiley & Sons.

    Google Scholar 

  • Keogh, S., O’Neill, S., & Walsh, K. (2021). Composite measures for assessing multidimensional social exclusion in later life: Conceptual and methodological challenges. Social Indicators Research, 155(2), 389–410. https://doi.org/10.1007/s11205-021-02617-7

  • Kim, S. S. (2015). Variable selection and outlier detection for automated K-means clustering. Communications for Statistical Applications and Methods, 22(1), 55–67.

    Article  Google Scholar 

  • Kneale, D. (2012). Is social exclusion still important for older people? London, UK: The International Longevity Centre.

    Google Scholar 

  • Krishna, T. S., Babu, A. Y., & Kumar, R. K. (2018). Determination of optimal clusters for a Non-hierarchical clustering paradigm K-Means algorithm. In Proceedings of International Conference on Computational Intelligence and Data Engineering (pp. 301–316). Springer, Singapore.

  • Landi, S., Ivaldi, E., & Testi, A. (2018). Measuring change over time in socio-economic deprivation and health in an urban context: The case study of Genoa. Social Indicators Research, 139(2), 745–785.

    Article  Google Scholar 

  • Li, Y., & Xie, Y. (2018). A new urban typology model adapting data mining analytics to examine dominant trajectories of neighborhood change: A case of Metro Detroit. Annals of the American Association of Geographers, 108(5), 1313–1337.

    Article  Google Scholar 

  • Li, Z., & Wang, P. (2013). Comprehensive evaluation of the objective quality of life of Chinese residents: 2006 to 2009. Social Indicators Research, 113(3), 1075–1090.

    Article  Google Scholar 

  • Libório, M. P., Machado-Coelho, T. M., Bernardes, P., Machado, A. M. C., Ekel, P. Y., & Soares, G. L. (2018). Forecasting Internet demand using public data: A case study in brazil. IEEE Access, 6, 65974–65980.

    Article  Google Scholar 

  • Libório, M. P., Martinuci, O. D. S., Machado, A. M. C., Hadad, R. M., Bernardes, P., & Camacho, V. A. L. (2021). Adequacy and consistency of an intraurban inequality indicator constructed through principal component analysis. The Professional Geographer, 72(2), 282–296.

    Article  Google Scholar 

  • Libório, M. P., Martinuci, O. S., Machado, A. M. C., Machado-Coelho, T. M., Laudares, S., & Bernardes, P. (2020a). Principal component analysis applied to multidimensional social indicators longitudinal studies: Limitations and possibilities. GeoJournal. https://doi.org/10.1007/s10708-020-10322-0

    Article  Google Scholar 

  • Libório, M. P., da Silva Martinuci, O., Hadad, R. M., & de Melo Silva, J. F. (2020). Procedimento para compatibilizar mapas em diferentes escalas e o problema da mudanca de suporte espacial. Caminhos de Geografia, 21(74). https://doi.org/10.14393/RCG217449943

  • Ling, C., & Delmelle, E. C. (2016). Classifying multidimensional trajectories of neighbourhood change: A self-organizing map and k-means approach. Annals of GIS, 22(3), 173–186.

    Google Scholar 

  • Liu, L., Peng, Z., Wu, H., Jiao, H., Yu, Y., & Zhao, J. (2018). Fast identification of urban sprawl based on K-means clustering with population density and local spatial entropy. Sustainability, 10(8), 2683.

    Article  Google Scholar 

  • Liu, Y., Singleton, A., & Arribas-Bel, D. (2019). A principal component analysis (PCA)-based framework for automated variable selection in geodemographic classification. Geo-Spatial Information Science, 22(4), 1–14.

    Article  Google Scholar 

  • MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability (Vol. 1, No. 14, pp. 281–297).

  • Martinuci, O. S., Machado, A. M. C., Libório, M. P. (2021). Data for: Time-in-space analysis of multidimensional phenomena. Mendeley Data, V3, doi.org/https://doi.org/10.17632/m3y4jncvch.4

  • Mazziotta, M., & Pareto, A. (2017). Synthesis of indicators: The composite indicators approach. In F. Maggino (Ed.), Complexity in society: From indicators construction to their synthesis. Social indicators research series (Vol. 70). Cham: Springer. https://doi.org/10.1007/978-3-319-60595-1_7

    Google Scholar 

  • Mazziotta, M., & Pareto, A. (2015). Comparing two non-compensatory composite indices to measure changes over time: A case study. Statistika-Statistics and Economy Journal, 95(2), 44–53.

    Google Scholar 

  • Mazziotta, M., & Pareto, A. (2017). Synthesis of indicators: The composite indicators approach. In Complexity in society: From indicators construction to their synthesis (pp. 159–191). Springer, Cham.

  • Mazziotta, M., & Pareto, A. (2018). Measuring well-being over time: The adjusted Mazziotta-Pareto index versus other non-compensatory indices. Social Indicators Research, 136(3), 967–976.

    Article  Google Scholar 

  • McLachlan, G., & Norman, P. (2021). Analysing socio-economic change using a time comparable geodemographic classification: England and Wales, 1991–2011. Applied Spatial Analysis and Policy, 14(1), 89–111.

    Article  Google Scholar 

  • Monmonier, M. (1990). Strategies for the visualization of geographic time-series data. Cartographica. The International Journal for Geographic Information and Geovisualization, 27(1), 30–45.

    Article  Google Scholar 

  • Nardo M., Saisana, M., Saltelli, A., Tarantola, S., Hoffmann, A., Giovannini, E. (2005). Handbook on Constructing Composite Indicators: Methodology and User Guide, OECD Statistics Working Papers, No. 2005/03, OECD Publishing, Paris. www.oecd.org/publishing, http://213.253.134.43/oecd/pdfs/browseit/3008251E.PDF Accessed 14 February 2020.

  • Nilsson, I., & Delmelle, E. (2018). Transit investments and neighborhood change: On the likelihood of change. Journal of Transport Geography, 66, 167–179.

    Article  Google Scholar 

  • Nomikos, P., & MacGregor, J. F. (1995). Multivariate SPC charts for monitoring batch processes. Technometrics, 37(1), 41–59.

    Article  Google Scholar 

  • Norman, P. (2010). Identifying change over time in small area socio-economic deprivation. Applied Spatial Analysis and Policy, 3(2), 107–138.

    Article  Google Scholar 

  • Norman, P., & Darlington-Pollock, F. (2017). The changing geography of deprivation in Great Britain. The Routledge Handbook of Census Resources, Methods and Applications: Unlocking the UK 2011 Census, 404.

  • Norman, P., Rees, P., & Boyle, P. (2003). Achieving data compatibility over space and time: Creating consistent geographical zones. International Journal of Population Geography, 9(5), 365–386.

    Article  Google Scholar 

  • Oliveira, S. D., Sousa, R. D., Davis JR, C. A., & Amaral, F. D. (1996). Adequação da delimitação dos setores censitários a outras unidades espaciais urbanas. In: Encontro nacional de produtores e usuários de informações sociais, econômicas e territoriais do IBGE, Rio de Janeiro (RJ).

  • Ortegren, J. T., Weatherall, A., & Maxwell, J. T. (2014). Subregionalization of low-frequency summer drought variability in the southeastern United States. The Professional Geographer, 66(2), 323–332.

    Article  Google Scholar 

  • Otoiu, A., Pareto, A., Grimaccia, E., Mazziotta, M., & Terzi, S. (2021). Open issues in composite indicators A starting point and a reference on some state-of-the-art issues (Vol. 3). Roma TrE-Press.

    Google Scholar 

  • Otoiu, A., Titan, E., & Dumitrescu, R. (2014). Are the variables used in building composite indicators of well-being relevant? Validating composite indexes of well-being. Ecological Indicators, 46, 575–585.

    Article  Google Scholar 

  • Pearson, K. (1901). LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559–572.

    Article  Google Scholar 

  • Pozo, F., Vidal, Y., & Salgado, Ó. (2018). Wind turbine condition monitoring strategy through multiway PCA and multivariate inference. Energies, 11(4), 749.

    Article  Google Scholar 

  • Qiang, Y., & Van de Weghe, N. (2019). Re-arranging space, time and scales in GIS: Alternative models for multi-scale spatio-temporal modeling and analyses. ISPRS International Journal of Geo-Information, 8(2), 72.

    Article  Google Scholar 

  • Quagli, A., Lagazio, C., & Ramassa, P. (2021). Correction to: From enforcement to financial reporting controls (FRCs): A country‑level composite indicator. Journal of Management and Governance, 25(2), 429–432. https://doi.org/10.1007/s10997-020-09556-4

  • Renahy, E., Alvarado-Llano, B., Koh, M., & Quesnel-Vallée, A. (2012). Income and economic exclusion: Do they measure the same concept? International Journal for Equity in Health, 11(1), 1–11.

    Article  Google Scholar 

  • Room, G. (Ed.). (1995). Beyond the threshold: the measurement and analysis of social exclusion. Policy Press.

    Google Scholar 

  • Royuela, V., Suriñach, J., & Reyes, M. (2003). Measuring quality of life in small areas over different periods of time. Social Indicators Research, 64(1), 51–74.

    Article  Google Scholar 

  • Ruiz, F., Cabello, J. M., & Pérez-Gladish, B. (2018). Building Ease-of-Doing-Business synthetic indicators using a double reference point approach. Technological Forecasting and Social Change, 131, 130–140.

    Article  Google Scholar 

  • Russolillo, M., Giordano, G., & Haberman, S. (2011). Extending the lee-carter model: A three-way decomposition. Scandinavian Actuarial Journal, 2011(2), 96–117.

    Article  Google Scholar 

  • Saito, M., Kondo, N., Kondo, K., Ojima, T., & Hirai, H. (2012). Gender differences on the impacts of social exclusion on mortality among older Japanese: AGES cohort study. Social Science & Medicine, 75(5), 940–945.

    Article  Google Scholar 

  • Schwirian, K. P. (1983). Models of neighborhood change. Annual Review of Sociology, 9(1), 83–102.

    Article  Google Scholar 

  • Serra, A. S., Yalonetzky, G. I., & Maia, A. G. (2021). Multidimensional poverty in Brazil in the Early 21st Century: Evidence from the demographic census. Social Indicators Research, 154(1), 79–114.

    Article  Google Scholar 

  • Singh, K., Malik, D., & Sharma, N. (2011). Evolving limitations in K-means algorithm in data mining and their removal. International Journal of Computational Engineering & Management, 12, 105–109.

    Google Scholar 

  • Singleton, A., Pavlis, M., & Longley, P. A. (2016). The stability of geodemographic cluster assignments over an intercensal period. Journal of Geographical Systems, 18(2), 97–123.

    Article  Google Scholar 

  • Sulaiman, M. S., Abood, M. M., Sinnakaudan, S. K., Shukor, M. R., You, G. Q., & Chung, X. Z. (2019). Assessing and solving multicollinearity in sediment transport prediction models using principal component analysis. ISH Journal of Hydraulic Engineering. https://doi.org/10.1080/09715010.2019.1653799

    Article  Google Scholar 

  • Swiercz, M., & Mroczkowska, H. (2020). Multiway PCA for early leak detection in a pipeline system of a steam boiler—selected case studies. Sensors, 20(6), 1561.

    Article  Google Scholar 

  • Thomas, G. D., & Jesse, N. G. (2012). Social well-being in Northern Ireland: A longitudinal study 1958–1998. Social Indicators Research, 106(2), 199–212.

    Article  Google Scholar 

  • Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (statistical Methodology), 63(2), 411–423.

    Article  Google Scholar 

  • Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31(3), 279–311.

    Article  Google Scholar 

  • Umbelino, G. & Barbieri, A. (2008). Metodologia para a compatibilização de setores censitários e perímetros urbanos entre os censos de 1991, 2000 e 2010. XVI Encontro Nacional de Estudos Populacionais, ABEP, pp. 1–18,.

  • Van Regenmortel, S., De Donder, L., Smetcoren, A. S., Lambotte, D., De Witte, N., & Verté, D. (2018). Accumulation of disadvantages: Prevalence and categories of old-age social exclusion in Belgium. Social Indicators Research, 140(3), 1173–1194.

    Article  Google Scholar 

  • Vickers, D. (2010). England’s changing social geology. In J. Stillwell, P. Norman, C. Thomas, & P. Surridge (Eds.), Spatial and social disparities (pp. 37–51). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Vickers, D., & Rees, P. (2007). Creating the UK national statistics 2001 output area classification. Journal of the Royal Statistical Society: Series A (statistics in Society), 170(2), 379–403.

    Article  Google Scholar 

  • Von Landesberger, T., Brodkorb, F., Roskosch, P., Andrienko, N., Andrienko, G., & Kerren, A. (2015). Mobilitygraphs: Visual analysis of mass mobility dynamics via spatio-temporal graphs and clustering. IEEE Transactions on Visualization and Computer Graphics, 22(1), 11–20.

    Article  Google Scholar 

  • Wang, Y., Yan, W., Guo, H., Mahmood, Q., Guo, J., Liu, C., & Liu, D. (2017). Trace element analysis and associated risk assessment in mining area soils from Zhexi river plain, Zhejiang China. Environmental Forensics, 18(4), 318–330.

    Article  Google Scholar 

  • Ward, M. O., Grinstein, G., & Keim, D. (2015). Interactive data visualization: foundations, techniques, and applications. AK Peters/CRC Press.

    Book  Google Scholar 

  • Wątróbski, J., Jankowski, J., Ziemba, P., Karczmarczyk, A., & Zioło, M. (2019). Generalised framework for multi-criteria method selection. Omega, 86, 107–124.

    Article  Google Scholar 

  • Xavier, A., Freitas, M. D. B. C., Fragoso, R., & do SocorroRosário, M. (2018). A regional composite indicator for analysing agricultural sustainability in Portugal: A goal programming approach. Ecological Indicators, 89, 84–100.

    Article  Google Scholar 

  • Xie, Y. (1996). A generalized model for cellular urban dynamics. Geographical Analysis, 28(4), 350–373.

    Article  Google Scholar 

  • Yuan, C., & Yang, H. (2019). Research on K-value selection method of K-means clustering algorithm. J—Multidisciplinary Scientific Journal, 2(2), 226–235.

    Article  Google Scholar 

  • Zheng, Y., Wu, W., Chen, Y., Qu, H., & Ni, L. M. (2016). Visual analytics in urban computing: An overview. IEEE Transactions on Big Data, 2(3), 276–296.

    Article  Google Scholar 

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Authors and Affiliations

  1. Pontifical Catholic University of Minas Gerais, Belo Horizonte, 30535-012, Brazil

    Matheus Pereira Libório, Alexei Manso Correa Machado & Patrícia Bernardes

  2. Universidade Estadual de Maringá, Maringá, 87020-900, Brazil

    Oseias da Silva Martinuci

  3. Federal University of Minas Gerais, Belo Horizonte, 31270-901, Brazil

    Alexei Manso Correa Machado & Renata de Mello Lyrio

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Appendix Basic Statistics of the 2000 Data

Appendix Basic Statistics of the 2000 Data

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Table 3 Descriptive statistics given for the year 2000
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Correlation matrix for indicators

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Libório, M.P., Martinuci, O.d., Machado, A.M.C. et al. Time–Space Analysis of Multidimensional Phenomena: A Composite Indicator of Social Exclusion Through k-Means. Soc Indic Res 159, 569–591 (2022). https://doi.org/10.1007/s11205-021-02763-y

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