Histogram with “negative” logarithmic scale in R

Question

I have a dataset with some outliers, such as the following

x <- rnorm(1000,0,20)
x <- c(x, 500, -500)

If we plot this on a linear x axis scale at this we see

histogram(x)

I worked out a nice way to put it on a log scale using this useful thread: how to use a log scale for y-axis of histogram in R? :

mat <- data.frame(x)
ggplot(ee, aes(x = xx)) + geom_histogram(colour="darkblue", size=1, fill="blue") + scale_x_log10()

However, I would like the x axis labels from this 2nd example to match that of the first example, except with a kind of "negative log" - ie first tick (moving from the centre to the left) could be -1, then the next could be -10, the next -100, but all equidistant. Does that make sense?

Answer 1

I am not sure I understand your goal, but when you want a log-like transformation yet have zeroes or negative values, the inverse hyperbolic sine transformation asinh() is often a good option. It is log-like for large values and is defined for all real values. See Rob Hyndman's blog and this question on stats.stackexchange.com for discussion, details, and other options.

If this is an acceptable approach, you can create a custom scale for ggplot. The code below demonstrates how to create and use a custom scale (with custom breaks), along with a visualization of the asinh() transformation.

library(ggplot2)
library(scales)

limits <- 100
step <- 0.005
demo <- data.frame(x=seq(from=-1*limits,to=limits,by=step))

asinh_trans <- function(){
  trans_new(name = 'asinh', transform = function(x) asinh(x), 
            inverse = function(x) sinh(x))
}

ggplot(demo,aes(x,x))+geom_point(size=2)+
     scale_y_continuous(trans = 'asinh',breaks=c(-100,-50,-10,-1,0,1,10,50,100))+
     theme_bw()

ggplot(demo,aes(x,x))+geom_point(size=2)+
     scale_x_continuous(trans = 'asinh',breaks=c(0,1,10,50,100))+
     scale_y_log10(breaks=c(0,1,10,50,100))+ # zero won't plot
     xlab("asinh() scale")+ylab("log10 scale")+
     theme_bw()

Answer 2

Realizing that the question is fairly old, I decided to answer it anyway since I ran into exactly the same problem.

I see that some answers above misunderstood your original question. I think it is a valid visualization question and I outline below my solution that will hopefully be useful for others as well.

My approach was to use ggplot and create custom log transform for x and y axis (as well as custom break generators)

library(ggplot2)
library(scales)

# Create custom log-style x axis transformer (...,-10,-3,-1,0,1,3,10,...)
custom_log_x_trans <- function()
  trans_new("custom_log_x",
            transform = function (x) ( sign(x)*log(abs(x)+1) ),
            inverse = function (y) ( sign(y)*( exp(abs(y))-1) ),
            domain = c(-Inf,Inf))

# Custom log x breaker (...,-10,-3,-1,0,1,3,10,...)
custom_x_breaks <- function(x)
{ 
  range <- max(abs(x), na.rm=TRUE)

  return (sort( c(0,
                  sapply(0:log10(range), function(z) (10^z) ),
                  sapply(0:log10(range/3), function(z) (3*10^z) ),
                  sapply(0:log10(range), function(z) (-10^z) ),
                  sapply(0:log10(range/3), function(z) (-3*10^z) )
  )))
}

# Create custom log-style y axis transformer (0,1,3,10,...)
custom_log_y_trans <- function()
  trans_new("custom_log_y",
            transform = function (x) ( log(abs(x)+1) ),
            inverse = function (y) ( exp(abs(y))-1 ),
            domain = c(0,Inf))

# Custom log y breaker (0,1,3,10,...)
custom_y_breaks <- function(x)
{ 
  max_y <- length(x)

  range <- max(abs(max_y), na.rm=TRUE)

  return (sort( c(0,
                  sapply(0:log10(range), function(z) (10^z) ),
                  sapply(0:log10(range/3), function(z) (3*10^z) )
  )))
}

ggplot(data=mat) +
  geom_histogram(aes(x=x,fill=..count..), 
                 binwidth = 1, color="black", size=0.1) +
  scale_fill_gradient("Count", low = "steelblue", high = "red") +
  coord_trans(x="custom_log_x",y="custom_log_y") +
  scale_x_continuous(breaks = custom_x_breaks(mat$x)) +
  scale_y_continuous(breaks = custom_y_breaks(mat$x)) +
  theme(axis.text.x=element_text(angle=90,hjust=1,vjust=0.5))  + 
  theme_bw()

which gives me the following plot.

Note that:

• the plot also includes coloring scheme to show visually the absolute value of each bar.
• the bins become increasingly thinner as x increases (side effect of log-transform)

In either case, the two outliers are clearly visible .

Answer 3

I found a way to cheat on it. I say "cheat", because it actually plot negative and positive parts of the data separately. Thus you can not compare the negative and positive data. But only can show the distribution of negative and positive parts separately.

And one of the problem is if there is zero values in your data, it will not be shown in the plot.

reverselog_trans <- function(base = exp(1)) {
  trans <- function(x) -log(x, base)
  inv <- function(x) base^(-x)
  trans_new(paste0("reverselog-", format(base)), trans, inv, 
            log_breaks(base = base), 
            domain = c(1e-100, Inf))
}

quartz();


dist1 <- ggplot(data=df.meltFUAC) +
  geom_point(alpha=1,aes(x=deltaU.deltaUltrasensitivity,y=deltaF.deltaFitness, 
                         colour=deltaF.w_c)) + 
  scale_x_continuous(name = expression(Delta * S[ult]), 
                     limits=c(1e-7,1),trans = "log10",breaks=c(1e-01,1e-03,1e-05),
                     labels=c("1e-01","1e-03","1e-05")) + 
  scale_y_continuous(name = expression(paste(Delta, " Fitness")),trans = "log10", 
                     limits = c(1e-7,1), breaks=c(1e-01,1e-03,1e-05),
                     labels=c("1e-01","1e-03","1e-05")) +
  theme_bw() +
  theme(legend.position = "none", axis.title.x=element_blank(),strip.background=element_blank(),
        panel.border=element_rect(colour = "black"),panel.grid.major=element_blank(),
        panel.grid.minor=element_blank(),plot.background=element_blank(),
        plot.margin=unit(c(0,0,0,-11),"mm"))

dist2 <- ggplot(data=df.meltFUAC, aes(x=-deltaU.deltaUltrasensitivity,y=deltaF.deltaFitness, 
                                      colour=deltaF.w_c)) +
  geom_point(alpha=1) + 
  scale_x_continuous(name = expression(Delta * sqrt(S[ult] %.% S[amp])),limits=c(1,1e-7),
                     trans = reverselog_trans(10),breaks=c(1e-01,1e-03,1e-05),
                     labels=c("-1e-01","-1e-03","-1e-05")) +
  scale_y_continuous(name = expression(paste(Delta, " Fitness")),trans = "log10", 
                     limits = c(1e-7,1), breaks=c(1e-01,1e-03,1e-05),
                     labels=c("1e-01","1e-03","1e-05")) +
  theme_bw() +
  theme(legend.position = "none",strip.background=element_blank(),panel.border=element_rect(colour = "black"),
        axis.text.y=element_blank(), axis.ticks.y=element_blank(), axis.title.y=element_blank(),
        axis.line.y=element_line(colour="black",size=1,linetype="solid"),axis.title.x=element_blank(),
        panel.grid.major=element_blank(),panel.grid.minor=element_blank(),plot.background=element_blank(),
        plot.margin=unit(c(0,-8,0,2.5),"mm"))

hist0 <- ggplot(data=df.meltFUAC, aes(deltaF.deltaFitness,fill=deltaF.w_c)) +
  #geom_histogram(alpha = 0.5, aes(y=..density..),position = 'identity') +
  geom_density(alpha = 0.5, aes(colour=deltaF.w_c)) +
  scale_x_continuous(name = expression(paste(Delta, " Fitness")), 
                     limits=c(1e-7,1),trans = "log10",breaks=c(1e-01,1e-03,1e-05),
                     labels=c("1e-01","1e-03","1e-05")) + 
  scale_y_continuous(name = "Density", limits=c(0,0.6)) + 
  theme_bw() +
  theme(legend.position = "none", axis.title.x=element_blank(),strip.background=element_blank(),
        axis.text.y=element_blank(), axis.ticks.y=element_blank(), axis.title.y=element_blank(),
        axis.text.x=element_blank(), axis.ticks.x=element_blank(), axis.title.x=element_blank(),
        panel.border=element_rect(colour = "black"),panel.grid.major=element_blank(),
        panel.grid.minor=element_blank(),plot.background=element_blank(),
        plot.margin=unit(c(0,5,2.5,-2.5),"mm")) +
  coord_flip()

hist1 <- ggplot(data=df.meltFUAC, aes(deltaU.deltaUltrasensitivity,fill=deltaF.w_c)) +
  #geom_histogram(alpha = 0.5, aes(y=..density..),position = 'identity') +
  geom_density(alpha = 0.5, aes(colour=deltaF.w_c)) +
  scale_x_continuous(name = expression(Delta * S[ult]), 
                     limits=c(1e-7,1),trans = "log10",breaks=c(1e-01,1e-03,1e-05),
                     labels=c("1e-01","1e-03","1e-05")) + 
  scale_y_continuous(name = "Density", limits=c(0,0.6)) + 
  theme_bw() +
  theme(legend.position = "none", axis.title.x=element_blank(),strip.background=element_blank(),
        axis.text.y=element_blank(), axis.ticks.y=element_blank(), axis.title.y=element_blank(),
        axis.text.x=element_blank(), axis.ticks.x=element_blank(), axis.title.x=element_blank(),
        axis.line.x=element_line(colour="black",size=1,linetype="solid"),
        panel.border=element_rect(colour = "black"),panel.grid.major=element_blank(),
        panel.grid.minor=element_blank(),plot.background=element_blank(),
        plot.margin=unit(c(5,0,-2.5,2),"mm"))

hist2 <- ggplot(data=df.meltFUAC, aes(-deltaU.deltaUltrasensitivity,fill=deltaF.w_c)) +
  #geom_histogram(alpha = 0.5, aes(y=..density..),position = 'identity') +
  geom_density(alpha = 0.5, aes(colour=deltaF.w_c)) +
  scale_x_continuous(name = expression(Delta * S[ult]),limits=c(1,1e-7),
                     trans = reverselog_trans(10),breaks=c(1e-01,1e-03,1e-05),
                     labels=c("-1e-01","-1e-03","-1e-05")) +
  scale_y_continuous(name = "Density", limits=c(0,0.6)) + 
  theme_bw() +
  theme(legend.position = "none",strip.background=element_blank(),panel.border=element_rect(colour = "black"),
        axis.text.y=element_blank(), axis.ticks.y=element_blank(), axis.title.y=element_blank(),
        axis.text.x=element_blank(), axis.ticks.x=element_blank(), axis.title.x=element_blank(),
        axis.line.y=element_line(colour="black",size=1,linetype="solid"),
        axis.line.x=element_line(colour="black",size=1,linetype="solid"),
        panel.grid.major=element_blank(),panel.grid.minor=element_blank(),plot.background=element_blank(),
        plot.margin=unit(c(5,-8,-2.5,2.5),"mm"))



grid.newpage();
pushViewport(viewport(layout = grid.layout(3, 3, widths = unit(c(4,4,2),"null"),
                                           heights=unit(c(2,7.5,0.5),"null"))));
vplayout <- function(x, y) viewport(layout.pos.row = x, layout.pos.col = y);

print(dist2, vp = vplayout(2, 1));
print(dist1, vp = vplayout(2, 2));
print(hist2, vp = vplayout(1, 1));
print(hist1, vp = vplayout(1, 2));
print(hist0, vp = vplayout(2, 3));
grid.text(expression(Delta * Ultrasensitivity),vp = vplayout(3,1:2),x = unit(0.55, "npc"), 
          y = unit(0.9, "npc"),gp=gpar(fontsize=12, col="black"));

dev.copy2pdf(file=sprintf("%s/_dist/dist_hist_deltaF_deltaU_wc_01vs10.pdf", resultDir));
dev.off();

Here is the graph it got (but you need to manually to put the legend on):

Or a simpler one:

reverselog_trans <- function(base = exp(1)) {
  trans <- function(x) -log(x, base)
  inv <- function(x) base^(-x)
  trans_new(paste0("reverselog-", format(base)), trans, inv, 
            log_breaks(base = base), 
            domain = c(1e-100, Inf))
}

quartz();

hist1 <- ggplot(deltaF, aes(deltaFitness,fill=w_c)) + guides(fill=guide_legend(title=expression(omega[c]))) + geom_histogram(alpha = 0.5, aes(y=..density..),position = 'identity') + geom_density(alpha = 0.05, aes(colour=w_c)) + scale_x_continuous(name = expression(paste(Delta, " Fitness")),trans = "log10");
hist1 <- hist1 + scale_y_continuous(name = "Density", limits=c(0,1));
#hist1 <- hist1 + theme(panel.background=element_blank(),panel.border=element_blank(),axis.line.x=element_blank(),axis.line.y=element_line(colour="black",linetype="solid",size=1),axis.title.x=element_blank(),panel.grid.major=element_blank(),panel.grid.minor=element_blank(),plot.background=element_blank(),plot.margin=unit(c(5,5,0,5),"mm"));
hist1 <- hist1 + theme_bw();
hist1 <- hist1 + theme(strip.background=element_blank(),panel.border=element_rect(colour = "black"),axis.title.x=element_blank(),panel.grid.major=element_blank(),panel.grid.minor=element_blank(),plot.background=element_blank(),plot.margin=unit(c(5,5,0,5),"mm"));
hist1 <- hist1 + scale_color_discrete(name=expression(omega[c]));# + geom_vline(xintercept=0, colour="grey", size = 1);# + geom_hline(yintercept=0, colour="grey", size = 0.5);

hist2 <- ggplot(deltaU, aes(deltaUltrasensitivity,fill=w_c)) + geom_histogram(alpha = 0.5, aes(y=..density..),position = 'identity') + geom_density(alpha = 0.05, aes(colour=w_c))  + scale_x_continuous(name = expression(paste(Delta, " Ultrasensitivity")), limits=c(1e-7,1),trans = "log10",breaks=c(1e-01,1e-03,1e-05),labels=c("1e-01","1e-03","1e-05"));
hist2 <- hist2 + scale_y_continuous(name = "Density",limits=c(0,1)) ;#+ geom_vline(xintercept=0, colour="grey", size = 1);# + geom_hline(yintercept=0, colour="grey", size = 0.5);
#hist2 <- hist2 + theme(legend.position = "none", axis.title.x=element_blank(),panel.background=element_blank(),panel.border=element_blank(),panel.grid.major=element_blank(),panel.grid.minor=element_blank(),plot.background=element_blank(),plot.margin=unit(c(0,5,0,-7.5),"mm"));
hist2 <- hist2 + theme_bw();
hist2 <- hist2 + theme(legend.position = "none", axis.title.x=element_blank(),strip.background=element_blank(),panel.border=element_rect(colour = "black"),panel.grid.major=element_blank(),panel.grid.minor=element_blank(),plot.background=element_blank(),plot.margin=unit(c(0,5,0,-7.5),"mm"));
# + ggtitle("Positive part")

hist3 <- ggplot(deltaU, aes(-deltaUltrasensitivity,fill=w_c)) + geom_histogram(alpha = 0.5, aes(y=..density..),position = 'identity') + geom_density(alpha = 0.05, aes(colour=w_c)) + scale_x_continuous(name = expression(paste(Delta, " Ultrasensitivity")), limits=c(1,1e-7),trans = reverselog_trans(10),breaks=c(1e-01,1e-03,1e-05),labels=c("-1e-01","-1e-03","-1e-05"));
hist3 <- hist3 + scale_y_continuous(name = "Density", limits=c(0,1));# + geom_hline(yintercept=0, colour="black", size = 0.5);
#hist3 <- hist3 + theme(legend.position = "none",panel.background=element_blank(),axis.text.y=element_blank(), axis.ticks.y=element_blank(), axis.title.y=element_blank(),axis.line.y=element_line(colour="black",size=1,linetype="solid"),axis.title.x=element_blank(),panel.grid.major=element_blank(),panel.grid.minor=element_blank(),plot.background=element_blank(),plot.margin=unit(c(0,-7.5,0,5),"mm"));
hist3 <- hist3 + theme_bw();
hist3 <- hist3 + theme(legend.position = "none",strip.background=element_blank(),panel.border=element_rect(colour = "black"),axis.text.y=element_blank(), axis.ticks.y=element_blank(), axis.title.y=element_blank(),axis.line.y=element_line(colour="black",size=1,linetype="solid"),axis.title.x=element_blank(),panel.grid.major=element_blank(),panel.grid.minor=element_blank(),plot.background=element_blank(),plot.margin=unit(c(0,-7.5,0,5),"mm"));
# + ggtitle("Negative part")

grid.newpage();
pushViewport(viewport(layout = grid.layout(4, 2, widths = unit(c(5,5),"null"),heights=unit(c(4.6,0.4,4.6,0.4),"null"))));
vplayout <- function(x, y) viewport(layout.pos.row = x, layout.pos.col = y);
print(hist1, vp = vplayout(1, 1:2));  # key is to define vplayout
grid.text(expression(paste(Delta, " Fitness")),vp = vplayout(2,1:2),x = unit(0.5, "npc"), y = unit(0.9, "npc"),gp=gpar(fontsize=12, col="black"));
print(hist3, vp = vplayout(3, 1));
print(hist2, vp = vplayout(3, 2));
grid.text(expression(paste(Delta, " Ultrasensitivity")),vp = vplayout(4,1:2),x = unit(0.5, "npc"), y = unit(0.9, "npc"),gp=gpar(fontsize=12, col="black"));


dev.copy2pdf(file=sprintf("%s/deltaF_deltaU_wc_01vs10.pdf", resultDir));
dev.off();

Here is the graph I got:

Answer 4

Why suffer with ggplot2 solution? Your first plot was done with lattice histogram function, and this is where you should stay. Just apply logarithmic transformation directly within histogram function, use nint argument to specify the number of histogram bins, and type argument to choose between "count", or "density". I think that you got everything you need there, but maybe I'm missing some crucial detail of your question...

library(lattice)
histogram(log10(x), nint=50, type="count")