A0152
Title: Spatial smoothing using graph Laplacian penalized filter
Authors: Hiroshi Yamada - Hiroshima University (Japan) [presenting]
Abstract: A filter is considered for smoothing spatial data. Since smoothing coincides with detrending, spatial detrending is also considered. The filter consists of a quantity analogous to Geary's c, which is one of the most prominent measures of spatial autocorrelation. In addition, the quantity can be represented by a matrix called the graph Laplacian in the spectral graph theory/linear algebraic graph theory. We show mathematically how spatial data become smoother as a parameter called the smoothing parameter increases from 0 and fully smoothed as the parameter goes to infinity, except for the case where spatial data are originally fully smoothed. We also illustrate the results numerically. In the numerical illustration, we demonstrate how the generalized cross-validation criterion works for specifying the smoothing parameter. Finally, as supplementary investigations, we examine how the sum of squared residuals and effective degrees of freedom vary with the smoothing parameter.
