A toy example
This is a basic example which shows you how to solve a common problem.
First we load the package and generate simulated images with a probabilistic ICA model:
library(BSPBSS)
set.seed(612)
sim = sim_2Dimage(length = 30, sigma = 5e-4, n = 30, smooth = 6)The true source signals are three 2D geometric patterns (set
smooth=0 to generate patterns with sharp edges).
levelplot2D(sim$S,lim = c(-0.04,0.04), sim$coords)
#> Warning: Removed 177 rows containing missing values or values outside the scale range
#> (`geom_tile()`).
which generate observed images such as
levelplot2D(sim$X[1:3,], lim = c(-0.12,0.12), sim$coords)
#> Warning: Removed 177 rows containing missing values or values outside the scale range
#> (`geom_tile()`).
Then we generate initial values for mcmc,
ini = init_bspbss(sim$X, sim$coords, q = 3, ker_par = c(0.1,50), num_eigen = 50)and run!
res = mcmc_bspbss(ini$X,ini$init,ini$prior,ini$kernel,n.iter=2000,n.burn_in=1000,thin=10,show_step=100)
#> iter 100 Thu Oct 16 17:04:03 2025
#>
#> zeta0.154297 stepsize_zeta 0.00712258 accp_rate_zeta 0.45
#> iter 200 Thu Oct 16 17:04:03 2025
#>
#> zeta0.182201 stepsize_zeta 0.00783484 accp_rate_zeta 0.35
#> iter 300 Thu Oct 16 17:04:04 2025
#>
#> zeta0.205042 stepsize_zeta 0.00861832 accp_rate_zeta 0.45
#> iter 400 Thu Oct 16 17:04:04 2025
#>
#> zeta0.189928 stepsize_zeta 0.00948015 accp_rate_zeta 0.42
#> iter 500 Thu Oct 16 17:04:04 2025
#>
#> zeta0.199043 stepsize_zeta 0.0104282 accp_rate_zeta 0.39
#> iter 600 Thu Oct 16 17:04:04 2025
#>
#> zeta0.197815 stepsize_zeta 0.011471 accp_rate_zeta 0.39
#> iter 700 Thu Oct 16 17:04:05 2025
#>
#> zeta0.22763 stepsize_zeta 0.0126181 accp_rate_zeta 0.34
#> iter 800 Thu Oct 16 17:04:05 2025
#>
#> zeta0.166707 stepsize_zeta 0.0138799 accp_rate_zeta 0.31
#> iter 900 Thu Oct 16 17:04:05 2025
#>
#> zeta0.188473 stepsize_zeta 0.0152679 accp_rate_zeta 0.22
#> iter 1000 Thu Oct 16 17:04:05 2025
#>
#> zeta0.208003 stepsize_zeta 0.0152679 accp_rate_zeta 0.27
#> iter 1100 Thu Oct 16 17:04:06 2025
#>
#> zeta0.176799 stepsize_zeta 0.0152679 accp_rate_zeta 0.24
#> iter 1200 Thu Oct 16 17:04:06 2025
#>
#> zeta0.180526 stepsize_zeta 0.0152679 accp_rate_zeta 0.28
#> iter 1300 Thu Oct 16 17:04:06 2025
#>
#> zeta0.158511 stepsize_zeta 0.0152679 accp_rate_zeta 0.31
#> iter 1400 Thu Oct 16 17:04:06 2025
#>
#> zeta0.127507 stepsize_zeta 0.0152679 accp_rate_zeta 0.28
#> iter 1500 Thu Oct 16 17:04:07 2025
#>
#> zeta0.18967 stepsize_zeta 0.0152679 accp_rate_zeta 0.23
#> iter 1600 Thu Oct 16 17:04:07 2025
#>
#> zeta0.198324 stepsize_zeta 0.0152679 accp_rate_zeta 0.3
#> iter 1700 Thu Oct 16 17:04:07 2025
#>
#> zeta0.183634 stepsize_zeta 0.0152679 accp_rate_zeta 0.3
#> iter 1800 Thu Oct 16 17:04:07 2025
#>
#> zeta0.140081 stepsize_zeta 0.0152679 accp_rate_zeta 0.26
#> iter 1900 Thu Oct 16 17:04:08 2025
#>
#> zeta0.244967 stepsize_zeta 0.0152679 accp_rate_zeta 0.29
#> iter 2000 Thu Oct 16 17:04:08 2025
#>
#> zeta0.226313 stepsize_zeta 0.0152679 accp_rate_zeta 0.27Then the results can be summarized by
res_sum = sum_mcmc_bspbss(res, ini$X, ini$kernel, start = 101, end = 200, select_p = 0.5)and shown by
levelplot2D(res_sum$S, lim = c(-1.3,1.3), sim$coords)
#> Warning: Removed 177 rows containing missing values or values outside the scale range
#> (`geom_tile()`).
For comparison, we show the estimated sources provided by informax ICA here.
levelplot2D(ini$init$ICA_S, lim = c(-1.7,1.7), sim$coords)
#> Warning: Removed 177 rows containing missing values or values outside the scale range
#> (`geom_tile()`).