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Represent how to use SpatPCA for two-dimensional data for capturing the most dominant spatial pattern
library(SpatPCA)
library(ggplot2)
base_theme <- theme_minimal(base_size = 10, base_family = "Times") +
theme(legend.position = "bottom")
fill_bar <- guides(fill = guide_colourbar(
barwidth = 10,
barheight = 0.5,
label.position = "bottom")
)
coltab <- with(
list(),
colorRampPalette(c("#3b4cc0", "#f7f7f7", "#b40426"))(128)
)
color_scale_limit <- c(-.8, .8)
Selected realizations are displayed as static images below. #### True spatial pattern (eigenfunction) - The underlying spatial pattern below indicates realizations will vary dramatically at the center and be almost unchanged at the both ends of the curve.
set.seed(1024)
p <- 25
n <- 8
location <-
matrix(rep(seq(-5, 5, length = p), 2), nrow = p, ncol = 2)
expanded_location <- expand.grid(location[, 1], location[, 2])
unnormalized_eigen_fn <-
as.vector(exp(-location[, 1] ^ 2) %*% t(exp(-location[, 2] ^ 2)))
true_eigen_fn <-
unnormalized_eigen_fn / norm(t(unnormalized_eigen_fn), "F")
plot_df <- data.frame(
location_dim1 = expanded_location[, 1],
location_dim2 = expanded_location[, 2],
eigenfunction = true_eigen_fn
)
ggplot(plot_df, aes(location_dim1, location_dim2)) +
geom_tile(aes(fill = eigenfunction)) +
scale_fill_gradientn(colours = coltab, limits = color_scale_limit) +
base_theme +
labs(title = "True Eigenfunction", fill = "") +
fill_bar
realization_df <- data.frame(
location_dim1 = expanded_location[, 1],
location_dim2 = expanded_location[, 2],
value = realizations[1, ]
)
ggplot(realization_df, aes(location_dim1, location_dim2)) +
geom_tile(aes(fill = value)) +
scale_fill_gradientn(colours = coltab, limits = c(-10, 10)) +
base_theme +
labs(title = "1st realization", fill = "") +
fill_bar
SpatPCA::spatpca
We add a candidate set of tau2
to see how
SpatPCA obtain a localized smooth pattern.
The following figure shows that SpatPCA can find sparser pattern than PCA, which is close to the true pattern.
plot_df <- data.frame(
location_dim1 = expanded_location[, 1],
location_dim2 = expanded_location[, 2],
spatpca = eigen_est[, 1],
pca = svd(realizations)$v[, 1]
)
plot_df_long <- rbind(
data.frame(location_dim1 = plot_df$location_dim1,
location_dim2 = plot_df$location_dim2,
estimate = "spatpca",
eigenfunction = plot_df$spatpca),
data.frame(location_dim1 = plot_df$location_dim1,
location_dim2 = plot_df$location_dim2,
estimate = "pca",
eigenfunction = plot_df$pca)
)
ggplot(plot_df_long, aes(location_dim1, location_dim2)) +
geom_tile(aes(fill = eigenfunction)) +
scale_fill_gradientn(colours = coltab, limits = color_scale_limit) +
base_theme +
facet_wrap(~estimate) +
labs(fill = "") +
fill_bar
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They may not be fully stable and should be used with caution. We make no claims about them.
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