Exploring non-linear relationships among redundant variables through non-parametric principal component analysis: An empirical analysis with land-use data
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F86652079%3A_____%2F21%3A00542554" target="_blank" >RIV/86652079:_____/21:00542554 - isvavai.cz</a>
Result on the web
<a href="https://www.academia.edu/44560921/Exploring_non_linear_relationships_among_redundant_variables_through_non_parametric_principal_component_analysis_An_empirical_analysis_with_land_use_data" target="_blank" >https://www.academia.edu/44560921/Exploring_non_linear_relationships_among_redundant_variables_through_non_parametric_principal_component_analysis_An_empirical_analysis_with_land_use_data</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.15196/RS110105" target="_blank" >10.15196/RS110105</a>
Alternative languages
Result language
angličtina
Original language name
Exploring non-linear relationships among redundant variables through non-parametric principal component analysis: An empirical analysis with land-use data
Original language description
Principal Component Analysis (PCA) is a widely applied statistical technique aimed at summarising a multidimensional set of input (partly redundant) variables into a restricted number of independent components that are linear combinations of the inputs. PCA transforms the original data matrix by performing a spectral decomposition of the related variance/covariance (or correlation) matrix. When decomposing a correlation matrix, Pearson product-moment correlation coefficients are traditionally used in the correlation matrix. The statistical properties of Pearson correlation coefficients (being insensitive to non-linear, high-order correlations) represent an intrinsic limitation of PCA, restricting its applicability to linear relationships among inputs. However, working with variables displaying (more or less intense) deviations from linearity is common in both socioeconomic research and environmental studies. Following the theoretical assumptions of earlier studies, a generalisation of PCA aimed at exploring non-linear multivariate relationships among inputs is illustrated in the present article by using non-parametric Spearman and Kendall coefficients to replace linear Pearson coefficients in the correlation matrix. The per cent share of 19 land-use classes in the total landscape in a given study area (the Athens metropolitan region, Greece), obtained from a high-resolution map at the local scale, were used as inputs. The results of the standard PCA (via decomposition of a Pearson linear correlation matrix) and a generalised approach (via decomposition of a non-parametric correlation matrix based on Spearman or Kendall rank coefficients) were compared using traditional diagnostics. The PCA performed by decomposing a Spearman correlation matrix exhibited the highest variance extracted by the principal components, giving refined loadings and scores that allow recognition of latent land-use patterns. Contributing to a recent debate on the use of multidimensional techniques in regional studies, non-parametric approaches are promising tools for analysis of large datasets displaying complex, almost non-linear relationships among inputs.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10508 - Physical geography
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Regional Statistics
ISSN
2063-9538
e-ISSN
2064-8243
Volume of the periodical
11
Issue of the periodical within the volume
1
Country of publishing house
HU - HUNGARY
Number of pages
16
Pages from-to
25-41
UT code for WoS article
000613906400002
EID of the result in the Scopus database
2-s2.0-85101932836