-
Classification of the techniques of spatial analysis is difficult because of the large number of different fields of research involved, the different fundamental approaches
which can be chosen, and the many forms the data can take. -
The graphic also shows the three celestial objects that are related to the units of time.The Modified Temporal Unit Problem (MTUP) is a source of statistical bias that occurs
in time series and spatial analysis when using temporal data that has been aggregated into temporal units. -
Spatial heterogeneity means that overall parameters estimated for the entire system may not adequately describe the process at any given location.
-
[citation needed] Common errors often arise in spatial analysis, some due to the mathematics of space, some due to the particular ways data are presented spatially, some due
to the tools which are available. -
The fundamental tenet is Tobler’s First Law of Geography: if the interrelation between entities increases with proximity in the real world, then representation in geographic
space and assessment using spatial analysis techniques are appropriate. -
[citation needed] Fundamental issues Spatial analysis confronts many fundamental issues in the definition of its objects of study, in the construction of the analytic operations
to be used, in the use of computers for analysis, in the limitations and particularities of the analyses which are known, and in the presentation of analytic results. -
[16][21] It is particularly important to consider the UGCoP within the discipline of time geography, where phenomena under investigation can move between spatial enumeration
units during the study period. -
However, in spatial analysis, we are concerned with specific types of mathematical spaces, namely, geographic space.
-
Spatial autocorrelation that is more positive than expected from random indicate the clustering of similar values across geographic space, while significant negative spatial
autocorrelation indicates that neighboring values are more dissimilar than expected by chance, suggesting a spatial pattern similar to a chess board. -
Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research.
-
SDA effectively uses the missing geographical information outside sample locations in methods of the first dimension of spatial association (FDA), which explore spatial association
using observations at sample locations. -
After specifying the functional forms of these relationships, the analyst can estimate model parameters using observed flow data and standard estimation techniques such as
ordinary least squares or maximum likelihood. -
Statistical techniques favor the spatial definition of objects as points because there are very few statistical techniques which operate directly on line, area, or volume
elements. -
These statistics require measuring a spatial weights matrix that reflects the intensity of the geographic relationship between observations in a neighborhood, e.g., the distances
between neighbors, the lengths of shared border, or whether they fall into a specified directional class such as “west”. -
A better solution, proposed by psychometricians,[49] groups the data in a « cubic matrix », with three entries (for instance, locations, variables, time periods).
-
For example, the spatial analysis of crime data has recently become popular but these studies can only describe the particular kinds of crime which can be described spatially.
-
While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed
around the data. -
Furthermore, census district boundaries are also subject to change over time,[6] meaning the MAUP must be considered when comparing past data to current data.
-
[citation needed] Dependency suggests that since one location can predict the value of another location, we do not need observations in both places.
-
[36] In more general terms, no scale independent method of analysis is widely agreed upon for spatial statistics.
-
It is also possible to exploit ancillary data, for example, using property values as a guide in a spatial sampling scheme to measure educational attainment and income.
-
Local spatial autocorrelation statistics provide estimates disaggregated to the level of the spatial analysis units, allowing assessment of the dependency relationships across
space. -
[13][14] It relates to the boundary problem, in that delineated neighborhoods used for analysis may not fully account for an individuals activity space if the borders are
permeable, and individual mobility crosses the boundaries. -
Spatial dependence is of importance in applications where it is reasonable to postulate the existence of corresponding set of random variables at locations that have not been
included in a sample. -
Studies of humans often reduce the spatial existence of humans to a single point, for instance their home address.
-
[43] Using multivariate methods in spatial analysis began really in the 1950s (although some examples go back to the beginning of the century) and culminated in the 1970s,
with the increasing power and accessibility of computers. -
[30] Traditional spatial analysis, by necessity, treats each discrete areal unit as a self-contained neighborhood and does not consider the daily activity of crossing the
boundaries. -
The locations in a spatial measurement framework often represent locations on the surface of the Earth, but this is not strictly necessary.
-
In addition, the topological, or connective, relationships between areas must be identified, particularly considering the often conflicting relationship between distance and
topology; for example, two spatially close neighborhoods may not display any significant interaction if they are separated by a highway. -
[38] • Britain measured using a 200 km linear measurement • Britain measured using a 100 km linear measurement • Britain measured using a 50 km linear measurement Locational
fallacy[edit] The locational fallacy refers to error due to the particular spatial characterization chosen for the elements of study, in particular choice of placement for the spatial presence of the element. -
[citation needed] Spatial auto-correlation[edit] Spatial dependency is the co-variation of properties within geographic space: characteristics at proximal locations appear
to be correlated, either positively or negatively. -
[50] This method, which exhibits data evolution over time, has not been widely used in geography.
-
Since information is concentrated on the first new factors, it is possible to keep only a few of them while losing only a small amount of information; mapping them produces
fewer and more significant maps 2. -
But heterogeneity suggests that this relation can change across space, and therefore we cannot trust an observed degree of dependency beyond a region that may be small.
-
In a more restricted sense, spatial analysis is geospatial analysis, the technique applied to structures at the human scale, most notably in the analysis of geographic data.
-
[31] As with other types of statistical dependence, the presence of spatial dependence generally leads to estimates of an average value from a sample being less accurate than
had the samples been independent, although if negative dependence exists a sample average can be better than in the independent case. -
[32] Spatial dependency leads to the spatial autocorrelation problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques that
assume independence among observations. -
Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics.
-
It is also appropriate to view spatial dependency as a source of information rather than something to be corrected.
-
[citation needed] Sampling[edit] Spatial sampling involves determining a limited number of locations in geographic space for faithfully measuring phenomena that are subject
to dependency and heterogeneity. -
This, however, assumes that the definition of the variables has not changed over time and produces very large tables, difficult to manage.
-
Factors can include origin propulsive variables such as the number of commuters in residential areas, destination attractiveness variables such as the amount of office space
in employment areas, and proximity relationships between the locations measured in terms such as driving distance or travel time. -
Mathematics continues to provide the fundamental tools for analysis and to reveal the complexity of the spatial realm, for example, with recent work on fractals and scale
invariance. -
Spatial interaction[edit] Spatial interaction or “gravity models” estimate the flow of people, material or information between locations in geographic space.
-
While this property is fundamentally true of all analysis, it is particularly important in spatial analysis because the tools to define and study entities favor specific characterizations
of the entities being studied. -
[citation needed] These problems represent a challenge in spatial analysis because of the power of maps as media of presentation.
-
[edit] The uncertain geographic context problem or UGCoP is a source of statistical bias that can significantly impact the results of spatial analysis when dealing with aggregate
data. -
[19][20] It is caused by the difficulty, or impossibility, of understanding how phenomena under investigation (such as people within a census tract) in different enumeration
units interact between enumeration units, and outside of a study area over time. -
The definition of the spatial presence of an entity constrains the possible analysis which can be applied to that entity and influences the final conclusions that can be reached.
-
Analysis of the distribution patterns of two phenomena is done by map overlay.
-
-
For example, we can represent individuals’ incomes or years of education within a coordinate system where the location of each individual can be specified with respect to
both dimensions. -
A Three-Way Factor Analysis produces then three groups of factors related by a small cubic « core matrix ».
-
The possibility of spatial heterogeneity suggests that the estimated degree of autocorrelation may vary significantly across geographic space.
-
— G. Upton & B. Fingelton[41] Spatial data analysis[edit] Urban and Regional Studies deal with large tables of spatial data obtained from censuses and surveys.
-
MAUP affects results when point-based measures of spatial phenomena are aggregated into spatial partitions or areal units (such as regions or districts) as in, for example,
population density or illness rates. -
A spatial measurement framework can also capture proximity with respect to, say, interstellar space or within a biological entity such as a liver.
-
Types Spatial data comes in many varieties and it is not easy to arrive at a system of classification that is simultaneously exclusive, exhaustive, imaginative, and satisfying.
-
Computer tools favor the spatial definition of objects as homogeneous and separate elements because of the limited number of database elements and computational structures
available, and the ease with which these primitive structures can be created. -
[16][17] The problem is highly related to the ecological fallacy, edge effect, and Modifiable areal unit problem (MAUP) in that, it relates to aggregate units as they apply
to individuals. -
The second dimension of spatial association[edit] The second dimension of spatial association (SDA) reveals the association between spatial variables through extracting geographical
information at locations outside samples. -
[21][27][28] Different individuals, or groups may have completely different activity spaces, making an enumeration unit that is relevant for one person meaningless to another.
-
[22][23] Schematic and example of a space-time prism using transit network data: On the right is a schematic diagram of a space-time prism, and on the left is a map of the
potential path area for two different time budgets. -
In spatial modeling, the concept of spatial association allows the use of covariates in a regression equation to predict the geographic field and thus produce a map.
-
[citation needed] Spatial dependence[edit] Spatial dependence is the spatial relationship of variable values (for themes defined over space, such as rainfall) or locations
(for themes defined as objects, such as cities). -
In geographic space, the observations correspond to locations in a spatial measurement framework that capture their proximity in the real world.
Works Cited
[‘o The History of Land Surveying. Accessed Dec 17 2020. https://info.courthousedirect.com/blog/history-of-land-surveying
o ^ Mark Monmonier How to Lie with Maps University of Chicago Press, 1996.
o ^ Openshaw, Stan (1983). The Modifiable Areal
Unit Problem (PDF). ISBN 0-86094-134-5.
o ^ Chen, Xiang; Ye, Xinyue; Widener, Michael J.; Delmelle, Eric; Kwan, Mei-Po; Shannon, Jerry; Racine, Racine F.; Adams, Aaron; Liang, Lu; Peng, Jia (27 December 2022). “A systematic review of the modifiable
areal unit problem (MAUP) in community food environmental research”. Urban Informatics. 1. doi:10.1007/s44212-022-00021-1. S2CID 255206315.
o ^ “MAUP | Definition – Esri Support GIS Dictionary”. support.esri.com. Retrieved 2017-03-09.
o ^ Geography,
US Census Bureau. “Geographic Boundary Change Notes”. www.census.gov. Retrieved 2017-02-24.
o ^ Cheng, Tao; Adepeju, Monsuru; Preis, Tobias (27 June 2014). “Modifiable Temporal Unit Problem (MTUP) and Its Effect on Space-Time Cluster Detection”.
PLOS ONE. 9 (6): e100465. doi:10.1371/journal.pone.0100465. PMC 4074055. PMID 24971885.
o ^ Jong, R. de; Bruin, S. de (5 January 2012). “Linear trends in seasonal vegetation time series and the modifiable temporal unit problem”. Biogeosciences.
9: 71–77. doi:10.5194/bg-9-71-2012.
o ^ Deckard, Mica; Schnell, Cory (22 October 2022). “The Temporal (In)Stability of Violent Crime Hot Spots Between Months and The Modifiable Temporal Unit Problem”. Crime & Delinquency. 69 (6–7): 1312–1335. doi:10.1177/00111287221128483.
o ^
Jump up to:a b Kwan, Mei-Po (2018). “The Neighborhood Effect Averaging Problem (NEAP): An Elusive Confounder of the Neighborhood Effect”. Int J Environ Res Public Health. 15 (9). doi:10.3390/ijerph15091841. PMC 6163400. PMID 30150510.
o ^ Jump up
to:a b Kwan, Mei-Po (2023). “Human Mobility and the Neighborhood Effect Averaging Problem (NEAP)”. In Li, Bin; Xun, Shi; A-Xing, Zhu; Wang, Cuizhen; Lin, Hui (eds.). New Thinking in GIScience. Springer. ISBN 978-981-19-3818-4. Retrieved 7 October
2023.
o ^ Xu, Tiantian; Wang, Shiyi; Liu, Qing; Kim, Junghwan; Zhang, Jingyi; Ren, Yiwen; Ta, Na; Wang, Xiaoliang; Wu, Jiayu (August 2023). “Vegetation color exposure differences at the community and individual levels: An explanatory framework based
on the neighborhood effect averaging problem”. Urban Forestry & Urban Greening. 86. doi:10.1016/j.ufug.2023.128001.
o ^ Ham, Maarten van; Manley, David (2012). “Neighbourhood Effects Research at a Crossroads. Ten Challenges for Future Research Introduction”.
Environment and Planning A: Economy and Space. 44 (12): 2787–2793. doi:10.1068/a4543.
o ^ Parry, Marc (5 November 2012). “The Neighborhood Effect”. THE CHRONICLE REVIEW. The Chronical of Higher Education. Retrieved 7 October 2023.
o ^ See the
TSP world tour problem which has already been solved to within 0.05% of the optimal solution. [1]
o ^ Jump up to:a b c d Kwan, Mei-Po (2012). “The Uncertain Geographic Context Problem”. Annals of the Association of American Geographers. 102 (5):
958–968. doi:10.1080/00045608.2012.687349. S2CID 52024592.
o ^ Jump up to:a b c d Kwan, Mei-Po (2012). “How GIS can help address the uncertain geographic context problem in social science research”. Annals of GIS. 18 (4): 245–255. doi:10.1080/19475683.2012.727867.
S2CID 13215965. Retrieved 4 January 2023.
o ^ Matthews, Stephen A. (2017). International Encyclopedia of Geography: People, the Earth, Environment and Technology: Uncertain Geographic Context Problem. doi:10.1002/9781118786352.wbieg0599.
o ^ Jump
up to:a b Openshaw, Stan (1983). The Modifiable Aerial Unit Problem (PDF). GeoBooks. ISBN 0-86094-134-5.
o ^ Jump up to:a b c Chen, Xiang; Ye, Xinyue; Widener, Michael J.; Delmelle, Eric; Kwan, Mei-Po; Shannon, Jerry; Racine, Racine F.; Adams, Aaron;
Liang, Lu; Peng, Jia (27 December 2022). “A systematic review of the modifiable areal unit problem (MAUP) in community food environmental research”. Urban Informatics. 1. doi:10.1007/s44212-022-00021-1. S2CID 255206315.
o ^ Jump up to:a b Gao, Fei;
Kihal, Wahida; Meur, Nolwenn Le; Souris, Marc; Deguen, Séverine (2017). “Does the edge effect impact on the measure of spatial accessibility to healthcare providers?”. International Journal of Health Geographics. 16 (1): 46. doi:10.1186/s12942-017-0119-3.
PMC 5725922. PMID 29228961.
o ^ Jump up to:a b Chen, Xiang; Kwan, Mei-Po (2015). “Contextual Uncertainties, Human Mobility, and Perceived Food Environment: The Uncertain Geographic Context Problem in Food Access Research”. American Journal of Public
Health. 105 (9): 1734–1737. doi:10.2105/AJPH.2015.302792. PMC 4539815. PMID 26180982.
o ^ Zhou, Xingang; Liu, Jianzheng; Gar On Yeh, Anthony; Yue, Yang; Li, Weifeng (2015). “The Uncertain Geographic Context Problem in Identifying Activity Centers
Using Mobile Phone Positioning Data and Point of Interest Data”. Advances in Spatial Data Handling and Analysis. Advances in Geographic Information Science. pp. 107–119. doi:10.1007/978-3-319-19950-4_7. ISBN 978-3-319-19949-8.
o ^ Allen, Jeff (2019).
“Using Network Segments in the Visualization of Urban Isochrones”. Cartographica: The International Journal for Geographic Information and Geovisualization. 53 (4): 262–270. doi:10.3138/cart.53.4.2018-0013. S2CID 133986477.
o ^ Zhao, Pengxiang;
Kwan, Mei-Po; Zhou, Suhong (2018). “The Uncertain Geographic Context Problem in the Analysis of the Relationships between Obesity and the Built Environment in Guangzhou”. International Journal of Environmental Research and Public Health. 15 (2): 308.
doi:10.3390/ijerph15020308. PMC 5858377. PMID 29439392.
o ^ Zhou, Xingang; Liu, Jianzheng; Yeh, Anthony Gar On; Yue, Yang; Li, Weifeng (2015). “The Uncertain Geographic Context Problem in Identifying Activity Centers Using Mobile Phone Positioning
Data and Point of Interest Data”. Advances in Spatial Data Handling and Analysis. Advances in Geographic Information Science. pp. 107–119. doi:10.1007/978-3-319-19950-4_7. ISBN 978-3-319-19949-8. Retrieved 22 January 2023.
o ^ Tobler, Waldo (2004).
“On the First Law of Geography: A Reply”. Annals of the Association of American Geographers. 94 (2): 304–310. doi:10.1111/j.1467-8306.2004.09402009.x. S2CID 33201684. Retrieved 10 March 2022.
o ^ Salvo, Deborah; Durand, Casey P.; Dooley, Erin E.;
Johnson, Ashleigh M.; Oluyomi, Abiodun; Gabriel, Kelley P.; Van Dan Berg, Alexandra; Perez, Adriana; Kohl, Harold W. (June 2019). “Reducing the Uncertain Geographic Context Problem in Physical Activity Research: The Houston TRAIN Study”. Medicine
& Science in Sports & Exercise. 51 (6S): 437. doi:10.1249/01.mss.0000561808.49993.53. S2CID 198375226.
o ^ Thrift, Nigel (1977). An Introduction to Time-Geography (PDF). Geo Abstracts, University of East Anglia. ISBN 0-90224667-4.
o ^ Shmool,
Jessie L.; Johnson, Isaac L.; Dodson, Zan M.; Keene, Robert; Gradeck, Robert; Beach, Scott R.; Clougherty, Jane E. (2018). “Developing a GIS-Based Online Survey Instrument to Elicit Perceived Neighborhood Geographies to Address the Uncertain Geographic
Context Problem”. The Professional Geographer. 70 (3): 423–433. doi:10.1080/00330124.2017.1416299. S2CID 135366460. Retrieved 22 January 2023.
o ^ Journel, A G and Huijbregts, C J, Mining Geostatistics, Academic Press Inc, London.
o ^ von Csefalvay,
Chris (2023), “Spatial dynamics of epidemics”, Computational Modeling of Infectious Disease, Elsevier, pp. 257–303, doi:10.1016/b978-0-32-395389-4.00017-7, ISBN 978-0-323-95389-4, retrieved 2023-03-05
o ^ Knegt, De; Coughenour, M.B.; Skidmore, A.K.;
Heitkönig, I.M.A.; Knox, N.M.; Slotow, R.; Prins, H.H.T. (2010). “Spatial autocorrelation and the scaling of species–environment relationships”. Ecology. 91 (8): 2455–2465. doi:10.1890/09-1359.1. PMID 20836467.
o ^ “Spatial Association” (PDF). Geography
Teachers’ Association of Victoria. Retrieved 17 November 2014.
o ^ Song, Yongze (July 2022). “The second dimension of spatial association”. International Journal of Applied Earth Observation and Geoinformation. 111: 102834. doi:10.1016/j.jag.2022.102834.
hdl:20.500.11937/88649. S2CID 249166886.
o ^ Halley, J. M.; Hartley, S.; Kallimanis, A. S.; Kunin, W. E.; Lennon, J. J.; Sgardelis, S. P. (2004-03-01). “Uses and abuses of fractal methodology in ecology”. Ecology Letters. 7 (3): 254–271. doi:10.1111/j.1461-0248.2004.00568.x.
ISSN 1461-0248.
o ^ Ocaña-Riola, R (2010). “Common errors in disease mapping”. Geospatial Health. 4 (2): 139–154. doi:10.4081/gh.2010.196. PMID 20503184.
o ^ Jump up to:a b c d e f “Understanding Spatial Fallacies”. The Learner’s Guide to Geospatial
Analysis. Penn State Department of Geography. Retrieved 27 April 2018.
o ^ Quattrochi, Dale A (2016-02-01). Integrating scale in remote sensing and GIS. Taylor & Francis. ISBN 9781482218268. OCLC 973767077.
o ^ Robinson, Ws (April 2009). “Ecological
Correlations and the Behavior of Individuals*”. International Journal of Epidemiology. 38 (2): 337–341. doi:10.1093/ije/dyn357. PMID 19179346.
o ^ Graham J. Upton & Bernard Fingelton: Spatial Data Analysis by Example Volume 1: Point Pattern and
Quantitative Data John Wiley & Sons, New York. 1985.
o ^ Harman H H (1960) Modern Factor Analysis, University of Chicago Press
o ^ Rummel R J (1970) Applied Factor Analysis. Evanston, ILL: Northwestern University Press.
o ^ Bell W & E Shevky
(1955) Social Area Analysis, Stanford University Press
o ^ Moser C A & W Scott (1961) British Towns; A Statistical Study of their Social and Economic Differences, Oliver & Boyd, London.
o ^ Berry B J & F Horton (1971) Geographic Perspectives on
Urban Systems, John Wiley, N-Y.
o ^ Berry B J & K B Smith eds (1972) City Classification Handbook : Methods and Applications, John Wiley, N-Y.
o ^ Ciceri M-F (1974) Méthodes d’analyse multivariée dans la géographie anglo-saxonne, Université de
Paris-1; free download on http://www-ohp.univ-paris1.fr
o ^ Tucker L R (1964) « The extension of Factor Analysis to three-dimensional matrices », in Frederiksen N & H Gulliksen eds, Contributions to Mathematical Psychology, Holt, Rinehart and Winston,
NY.
o ^ R. Coppi & S. Bolasco, eds. (1989), Multiway data analysis, Elsevier, Amsterdam.
o ^ Cant, R.G. (1971). “Changes in the location of manufacturing in New Zealand 1957-1968: An application of three-mode factor analysis”. New Zealand Geographer.
27: 38–55. doi:10.1111/j.1745-7939.1971.tb00636.x.
o ^ Marchand B (1986) The Emergence of Los Angeles, 1940-1970, Pion Ltd, London
o ^ Brunsdon, C.; Fotheringham, A.S.; Charlton, M.E. (1996). “Geographically Weighted Regression: A Method for Exploring
Spatial Nonstationarity”. Geographical Analysis. 28 (4): 281–298. doi:10.1111/j.1538-4632.1996.tb00936.x.
o ^ Jump up to:a b Banerjee, Sudipto; Carlin, Bradley P.; Gelfand, Alan E. (2014), Hierarchical Modeling and Analysis for Spatial Data, Second
Edition, Monographs on Statistics and Applied Probability (2nd ed.), Chapman and Hall/CRC, ISBN 9781439819173
o ^ Bivand, Roger (20 January 2021). “CRAN Task View: Analysis of Spatial Data”. Retrieved 21 January 2021.
o ^ Banerjee, Sudipto; Gelfand,
Alan E.; Finley, Andrew O.; Sang, Huiyan (2008). “Gaussian predictive process models for large spatial datasets”. Journal of the Royal Statistical Society, Series B. 70 (4): 825–848. doi:10.1111/j.1467-9868.2008.00663.x. PMC 2741335. PMID 19750209.
o ^
Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O.; Gelfand, Alan E. (2016). “Hierarchical Nearest Neighbor Gaussian Process Models for Large Geostatistical Datasets”. Journal of the American Statistical Association. 111 (514): 800–812. arXiv:1406.7343.
doi:10.1080/01621459.2015.1044091. PMC 5927603. PMID 29720777.
o ^ Morer I, Cardillo A, Díaz-Guilera A, Prignano L, Lozano S (2020). “Comparing spatial networks: a one-size-fits-all efficiency-driven approach”. Physical Review. 101 (4): 042301.
doi:10.1103/PhysRevE.101.042301. hdl:2445/161417. PMID 32422764. S2CID 49564277.
o ^ Gupta J, Molnar C, Xie Y, Knight J, Shekhar S (2021). “Spatial variability aware deep neural networks (SVANN): a general approach”. ACM Transactions on Intelligent
Systems and Technology. 12 (6): 1–21. doi:10.1145/3466688. S2CID 244786699.
o ^ Hagenauer J, Helbich M (2022). “A geographically weighted artificial neural network”. International Journal of Geographical Information Science. 36 (2): 215–235. doi:10.1080/13658816.2021.1871618.
S2CID 233883395.
o ^ Silva, E. A.; Clarke, K.C. (2002). “Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal”. Computers, Environment and Urban Systems. 26 (6): 525–552. doi:10.1016/S0198-9715(01)00014-X.
o ^ Silva, E A
(2003). “Complexity, emergence and cellular urban models: lessons learned from applying SLEUTH to two Portuguese metropolitan areas”. European Planning Studies. 13 (1): 93–115. doi:10.1080/0965431042000312424. S2CID 197257.
o ^ Liu and Silva (2017).
“Examining the dynamics of the interaction between the development of creative industries and urban spatial structure by agent-based modelling: A case study of Nanjing, China”. Urban Studies. 65 (5): 113–125. doi:10.1177/0042098016686493. S2CID 157318972.
o ^
Liu, Lun; Silva, Elisabete A.; Wu, Chunyang; Wang, Hui (2017). “A machine learning-based method for the large-scale evaluation of the qualities of the urban environment” (PDF). Computers Environment and Urban Systems. 65: 113–125. doi:10.1016/j.compenvurbsys.2017.06.003.
o ^
Honarkhah, M; Caers, J (2010). “Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling”. Mathematical Geosciences. 42 (5): 487–517. Bibcode:2010MaGeo..42..487H. doi:10.1007/s11004-010-9276-7. S2CID 73657847.
o ^ Tahmasebi, P.; Hezarkhani,
A.; Sahimi, M. (2012). “Multiple-point geostatistical modeling based on the cross-correlation functions”. Computational Geosciences. 16 (3): 779–79742. doi:10.1007/s10596-012-9287-1. S2CID 62710397.
o ^ Tahmasebi, P.; Sahimi, M. (2015). “Reconstruction
of nonstationary disordered materials and media: Watershed transform and cross-correlation function”. Physical Review E. 91 (3): 032401. Bibcode:2015PhRvE..91c2401T. doi:10.1103/PhysRevE.91.032401. PMID 25871117.
o ^ Tahmasebi, P.; Sahimi, M. (2015).
“Geostatistical Simulation and Reconstruction of Porous Media by a Cross-Correlation Function and Integration of Hard and Soft Data”. Transport in Porous Media. 107 (3): 871–905. doi:10.1007/s11242-015-0471-3. S2CID 123432975.
o ^ “Graduate Program
in Spatial Analysis”. Ryerson University. Retrieved 17 December 2015.
o ^ geospatial. Collins English Dictionary – Complete & Unabridged 11th Edition. Retrieved 5tth August 2012 from CollinsDictionary.com website: http://www.collinsdictionary.com/dictionary/english/geospatial
o ^
Dictionary.com’s 21st Century Lexicon Copyright © 2003-2010 Dictionary.com, LLC http://dictionary.reference.com/browse/geospatial
o ^ The geospatial web – blending physical and virtual spaces. Archived 2011-10-02 at the Wayback Machine, Arno Scharl
in receiver magazine, Autumn 2008
o ^ Chen, Ruizhi; Guinness, Robert E. (2014). Geospatial Computing in Mobile Devices (1st ed.). Norwood, MA: Artech House. p. 228. ISBN 978-1-60807-565-2. Retrieved 1 July 2014.
o ^ González, Ainhoa; Donnelly,
Alison; Jones, Mike; Chrysoulakis, Nektarios; Lopes, Myriam (2012). “A decision-support system for sustainable urban metabolism in Europe”. Environmental Impact Assessment Review. 38: 109–119. doi:10.1016/j.eiar.2012.06.007.
Photo credit: https://www.flickr.com/photos/hieulavoce/5705695593/’]