Plots and tables summarizing results of Poisson simulations

Analysis settings

We will extract the results from these methods:

methods <- c("ash","BMSM","haarfisz_R")

Specify the row and column names for the tables:

table.row.names <- c("SMASH","BMSM","Haar-Fisz")
table.col.names <- c("intensity (0.01,3)","intensity (1/8,8)",
                     "intensity (1/128,128)")

These are settings used in plotting the test functions:

n <- 1024
t <- 1:n/n

Set up environment

Add text here.

library(ggplot2)
library(cowplot)
library(xtable)

Some of the test functions are defined in signals.R:

source("../code/signals.R")

Load results

Load the results of the simulation experiments.

load("../output/pois.RData")

Spikes data

This is the function used to simulate the “Spikes” data sets at different ranges of intensities:

mu.s <- spike.f(t)
plot(t,mu.s,xlab = "",ylab = "",type = "l",
     main = "Spikes intensity function")

Summarize the results from the Spikes simulations in a table.

Comparison of methods for denoising Poisson data for the “Spikes” test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.

mise.s.table   <- cbind(mise.s.1[methods],
                        mise.s.8[methods],
                        mise.s.128[methods])
rownames(mise.s.table) <- table.row.names
colnames(mise.s.table) <- table.col.names
print(xtable(mise.s.table),type = "html")

Summarize the results from the Spikes simulations in combined violin and boxplots.

mise.hf.ti.r.s.1   <- colMeans(rbind(mise.hf.ti.r.4.s.1,
                                     mise.hf.ti.r.5.s.1,
                                     mise.hf.ti.r.6.s.1,
                                     mise.hf.ti.r.7.s.1))
mise.hf.ti.r.s.8   <- colMeans(rbind(mise.hf.ti.r.4.s.8,
                                     mise.hf.ti.r.5.s.8,
                                     mise.hf.ti.r.6.s.8,
                                     mise.hf.ti.r.7.s.8))
mise.hf.ti.r.s.128 <- colMeans(rbind(mise.hf.ti.r.4.s.128,
                                     mise.hf.ti.r.5.s.128,
                                     mise.hf.ti.r.6.s.128,
                                     mise.hf.ti.r.7.s.128))
m     <- length(mise.ash.s.1)
pdat1 <- data.frame(method = rep(c("SMASH","BMSM","HF"),each = m),
                    mise   = c(mise.ash.s.1,mise.BMSM.s.1,mise.hf.ti.r.s.1))
p1 <- ggplot(pdat1,aes(x = method,y = mise)) +
      geom_violin(fill = "skyblue",color = "skyblue") +
      geom_boxplot(width = 0.15,outlier.shape = NA) +
      coord_flip()
      labs(x = "",y = "MISE") +
     theme(axis.line = element_blank(),
           axis.ticks.y = element_blank())
# NULL

Combine the results of the simulation experiments into several larger tables.

mise.ang.table <- cbind(mise.ang.1[methods],
                        mise.ang.8[methods],
                        mise.ang.128[methods])
mise.bur.table <- cbind(mise.bur.1[methods],
                        mise.bur.8[methods],
                        mise.bur.128[methods])
mise.cb.table  <- cbind(mise.cb.1[methods],
                        mise.cb.8[methods],
                        mise.cb.128[methods])
mise.b.table   <- cbind(mise.b.1[methods],
                        mise.b.8[methods],
                        mise.b.128[methods])
mise.hs.table  <- cbind(mise.hs.1[methods],
                        mise.hs.8[methods],
                        mise.hs.128[methods])
rownames(mise.ang.table) <- table.row.names
rownames(mise.b.table)   <- table.row.names
rownames(mise.cb.table)  <- table.row.names
rownames(mise.hs.table)  <- table.row.names
rownames(mise.bur.table) <- table.row.names
colnames(mise.ang.table) <- table.col.names
colnames(mise.b.table)   <- table.col.names
colnames(mise.cb.table)  <- table.col.names
colnames(mise.hs.table)  <- table.col.names
colnames(mise.bur.table) <- table.col.names

Angles data

This is the function used to simulate the “Angles” data sets at different ranges of intensities:

mu.ang <- dop.f(t)
sig <- ((2 * t + 0.5) * (t <= 0.15)) +
  ((-12 * (t - 0.15) + 0.8) * (t > 0.15 & t <= 0.2)) +
  0.2 * (t > 0.2 & t <= 0.5) + 
  ((6 * (t - 0.5) + 0.2) * (t > 0.5 & t <= 0.6)) +
  ((-10 * (t - 0.6) + 0.8) * (t > 0.6 & t <= 0.65)) +
  ((-0.5 * (t - 0.65) + 0.3) * (t > 0.65 & t <= 0.85)) +
  ((2 * (t - 0.85) + 0.2) * (t > 0.85))
mu.ang <- 3/5 * ((5/(max(sig) - min(sig))) * sig - 1.6) - 0.0419569
plot(t,mu.ang,xlab = "",ylab = "",type = "l",
     main = "Angles intensity function")

print(xtable(mise.ang.table,caption="Comparison of methods for denoising Poisson data for the ``Angles'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_ang",digits=2),type = "html")

Heavisine data

This is the function used to simulate the “Heavisine” data sets at different ranges of intensities:

heavi <- 4 * sin(4 * pi * t) - sign(t - 0.3) - sign(0.72 - t)
mu.hs <- heavi/sqrt(var(heavi)) * 1 * 2.99/3.366185
mu.hs <- mu.hs - min(mu.hs)
plot(t,mu.hs,xlab = "",ylab = "",type = "l",
     main = "Heavisine intensity function")

print(xtable(mise.hs.table,caption="Comparison of methods for denoising Poisson data for the ``Heavisine'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_hs",digits=2),type = "html")

Bursts data

This is the function used to simulate the “Bursts” data sets at different ranges of intensities:

I_1 <- exp(-(abs(t - 0.2)/0.01)^1.2) * (t <= 0.2) +
       exp(-(abs(t - 0.2)/0.03)^1.2) * (t > 0.2)
I_2 <- exp(-(abs(t - 0.3)/0.01)^1.2) * (t <= 0.3) +
       exp(-(abs(t - 0.3)/0.03)^1.2) * (t > 0.3)
I_3 <- exp(-(abs(t - 0.4)/0.01)^1.2) * (t <= 0.4) +
       exp(-(abs(t - 0.4)/0.03)^1.2) * (t > 0.4)
mu.bur <- 2.99/4.51804 * (4 * I_1 + 3 * I_2 + 4.5 * I_3)
plot(t,mu.bur,xlab = "",ylab = "",type = "l",
     main = "Bursts intensity function")

print(xtable(mise.bur.table,caption="Comparison of methods for denoising Poisson data for the ``Bursts'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_bur",digits=2),type = "html")

Clipped Blocks data

This is the function used to simulate the “Clipped Blocks” data sets at different ranges of intensities:

pos   <- c(0.1,0.13,0.15,0.23,0.25,0.4,0.44,0.65,0.76,0.78,0.81)
hgt   <- 2.88/5 * c(4,-5,3,-4,5,-4.2,2.1,4.3,-3.1,2.1,-4.2)
mu.cb <- rep(0,n)
for (j in 1:length(pos))
  mu.cb <- mu.cb + (1 + sign(t - pos[j])) * (hgt[j]/2)
mu.cb[mu.cb < 0] <- 0
plot(t,mu.cb,xlab = "",ylab = "",type = "l",
     main = "Clipped Blocks intensity function")

print(xtable(mise.cb.table,caption="Comparison of methods for denoising Poisson data for the ``Clipped Blocks'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_cb",digits=2),type = "html")

Bumps data

This is the function used to simulate the “Bumps” data sets at different ranges of intensities:

pos  <- c(0.1,0.13,0.15,0.23,0.25,0.4,0.44,0.65,0.76,0.78,0.81)
hgt  <- 2.97/5 * c(4,5,3,4,5,4.2,2.1,4.3,3.1,5.1,4.2)
wth  <- c(0.005,0.005,0.006,0.01,0.01,0.03,0.01,0.01,0.005,0.008,0.005)
mu.b <- rep(0, n)
for (j in 1:length(pos))
  mu.b <- mu.b + hgt[j]/((1 + (abs(t - pos[j])/wth[j]))^4)
plot(t,mu.b,xlab = "",ylab = "",type = "l",
     main = "Bumps intensity function")

print(xtable(mise.b.table,caption="Comparison of methods for denoising Poisson data for the ``Bumps'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_b",digits=2),type = "html")

Session information

sessionInfo()
# R version 3.4.3 (2017-11-30)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS High Sierra 10.13.6
# 
# Matrix products: default
# BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
# 
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] xtable_1.8-2  cowplot_0.9.3 ggplot2_3.1.0
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_1.0.0        compiler_3.4.3    pillar_1.2.1     
#  [4] git2r_0.23.0      plyr_1.8.4        workflowr_1.1.1  
#  [7] bindr_0.1.1       R.methodsS3_1.7.1 R.utils_2.6.0    
# [10] tools_3.4.3       digest_0.6.17     evaluate_0.11    
# [13] tibble_1.4.2      gtable_0.2.0      pkgconfig_2.0.2  
# [16] rlang_0.2.2       yaml_2.2.0        bindrcpp_0.2.2   
# [19] withr_2.1.2       stringr_1.3.1     dplyr_0.7.6      
# [22] knitr_1.20        rprojroot_1.3-2   grid_3.4.3       
# [25] tidyselect_0.2.4  glue_1.3.0        R6_2.2.2         
# [28] rmarkdown_1.10    purrr_0.2.5       magrittr_1.5     
# [31] whisker_0.3-2     backports_1.1.2   scales_0.5.0     
# [34] htmltools_0.3.6   assertthat_0.2.0  colorspace_1.4-0 
# [37] stringi_1.2.4     lazyeval_0.2.1    munsell_0.4.3    
# [40] R.oo_1.21.0