caa a22 4500 469064498 CHVBK 20180323132904.0 cr unu---uuuuu 170328e19920801xx s 000 0 eng 10.1007/BF00894238 doi (NATIONALLICENCE)springer-10.1007/BF00894238 Spatial relationships of multivariate data [Elektronische Daten] [E. Grunsky, F. Agterberg] Spatial factor analysis (SFA) is a multivariate method that determines linear combinations of variables with maximum autocorrelation at a given lag. This is achieved by deriving estimates of auto-/cross-correlations of the variables and calculating the corresponding eigenvectors of the covariance quotient matrix. A two-point spatial factor analysis model derives factors by the formation of transition matrixU comparing auto-/cross-correlations at lag "0,”R 0, with those at a specified lag "d,”R d, expressed asU d=R 0 −1 Rd. The matrixU d can be decomposed into its spectral components which represent the spatial factors. The technique has been extended to include three points of reference. Spatial factors can be derived from the relationship: $$\left[ {\begin{array}{*{20}c} {U_{d1} } \\ {} \\ {\begin{array}{*{20}c} {} \\ {} \\ \end{array} } \\ {U_{d2} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {R_0 R_{d3} } \\ {} \\ {\begin{array}{*{20}c} {} \\ {} \\ \end{array} } \\ {R_{d3} R_0 } \\ \end{array} } \right]^{ - 1} \left[ {\begin{array}{*{20}c} {R_{d1} } \\ {} \\ {\begin{array}{*{20}c} {} \\ {} \\ \end{array} } \\ {R_{d2} } \\ \end{array} } \right]$$ where the factors ofU d1 andU d2 predict the relationships of the variables over three lag distances and orientations from matricesR d1,R d2, andR d3. Estimates of auto-/cross-correlation can be achieved using irregularly spaced or gridded data from experimental correlograms or function estimates determined from the experimental correlograms. The technique has applications in studies where several variables have different spatial ranges or zones of influence. International Association for Mathematical Geology, 1992 spatial factors nationallicence autocorrelation nationallicence crosscorrelation nationallicence correlogram nationallicence gridded data nationallicence irregularly spaced data nationallicence Grunsky E. CSIRO, 6014, Perth, Western Australia, Australia aut Agterberg F. Geological Survey of Canada, 601 Booth St., K1A OE8, Ottawa, Canada aut Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/6(1992-08-01), 731-758 0882-8121 24:6<731 1992 24 11004 https://doi.org/10.1007/BF00894238 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00894238 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grunsky E. CSIRO, 6014, Perth, Western Australia, Australia aut NATIONALLICENCE 700 1- Agterberg F. Geological Survey of Canada, 601 Booth St., K1A OE8, Ottawa, Canada aut NATIONALLICENCE 773 0- Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/6(1992-08-01), 731-758 0882-8121 24:6<731 1992 24 11004 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer