Adaptive histograms can reveal patterns in data more effectively than regular (equal-bin-width) histograms. The "discontinuous" style adaptive histogram is recommended because it adapts to the data without attempting to assign a non-zero density to every bin. When bins are not equal with, the vertical axis of the histogram is density instead of frequencies.

Plot an adaptive histogram from data generated by a Gaussian mixture model with three components:

require("Ckmeans.1d.dp") x <- c(rnorm(40, mean=-2, sd=0.3), rnorm(45, mean=1, sd=0.1), rnorm(70, mean=3, sd=0.2)) ahist(x, col="lightblue", sub=paste("n =", length(x)), col.stick="darkblue", lwd=2, xlim=c(-4,4), main="Example 1. Gaussian mixture model with 3 components\n(one bin per component)\nAdaptive histogram")

When breaks is specified, ahist will call hist (regular histogram function in R).

ahist(x, breaks=3, col="lightgreen", sub=paste("n =", length(x)), col.stick="forestgreen", lwd=2, main="Example 1. Regular histogram")

Plot an adaptive histogram from data generated by a Gaussian mixture model with three components using a given number of bins

ahist(x, k=9, col="lavender", col.stick="navy", sub=paste("n =", length(x)), lwd=2, main="Example 2. Gaussian mixture model with 3 components\n(on average 3 bins per component)\nAdaptive histogram")

When breaks is specified, ahist will call hist (regular histogram function in R).

ahist(x, breaks=9, col="lightgreen", col.stick="forestgreen", sub=paste("n =", length(x)), lwd=2, main="Example 2. Regular histogram")

The DNase data frame has 176 rows and 3 columns of data obtained during development of an ELISA assay for the recombinant protein DNase in rat serum:

data(DNase) res <- Ckmeans.1d.dp(DNase$density) kopt <- length(res$size) ahist(res, data=DNase$density, col=rainbow(kopt), col.stick=rainbow(kopt)[res$cluster], sub=paste("n =", length(x)), border="transparent", xlab="Optical density of protein DNase", main="Example 3. Elisa assay of DNase in rat serum\nAdaptive histogram")

Using the same data with Example 3, this example demonstrates the inadequacy of equal-bin-width histograms. The third bin gives a false sense of sample distribution.

We can specifiy breaks="Sturges" in ahist() function to use equal-bin-width histograms. The difference is that sticks are added to the histogram by ahist(), but not by the R provided hist() function.

ahist(DNase$density, breaks="Sturges", col="palegreen", add.sticks=TRUE, col.stick="darkgreen", main="Example 3. Elisa assay of DNase in rat serum\nRegular histogram (equal bin width)", xlab="Optical density of protein DNase")

Cluster data with repetitive elements:

x <- c(1,1,1,1, 3,4,4, 6,6,6) ahist(x, k=c(2,4), col="gray", lwd=2, lwd.stick=6, col.stick="chocolate", main="Example 4. Adaptive histogram of repetitive elements") ahist(x, breaks=3, col="lightgreen", lwd=2, lwd.stick=6, col.stick="forestgreen", main="Example 4. Regular histogram")

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