This tutorial illustrates applications of optimal univariate clustering function `Ckmeans.1d.dp`

. It clusters univariate data given the number of clusters \(k\). It can estimate \(k\) if not provided. It can also perform optimal weighted clustering when a weight vector is provided with the input univariate data. Weighted clustering can be used to analyze 1-D signals such as time series data. The corresponding clusters obtained from weighted clustering can be the basis for optimal time course segmentation or optimal peak calling.

Cluster data generated from a Gaussian mixture model of three components.

The number of clusters is provided.

`## Loading required package: Ckmeans.1d.dp`

Cluster data generated from a Gaussian mixture model of three components. The number of clusters is determined by Bayesian information criterion:

```
require(Ckmeans.1d.dp)
x <- c(rnorm(50, mean=-1, sd=0.3), rnorm(50, mean=1, sd=1), rnorm(50, mean=2, sd=0.4))
# Divide x into k clusters, k automatically selected (default: 1~9)
result <- Ckmeans.1d.dp(x)
plot(result)
```

```
k <- max(result$cluster)
plot(x, col=result$cluster, pch=result$cluster, cex=1.5,
main="Optimal univariate clustering with k estimated",
sub=paste("Number of clusters is estimated to be", k))
abline(h=result$centers, col=1:k, lty="dashed", lwd=2)
legend("topleft", paste("Cluster", 1:k), col=1:k, pch=1:k, cex=1.5, bty="n")
```

We segment a time course to identify peaks using weighted clustering. The input data is the time stamp of obtaining each intensity measurement; the weight is the signal intensity.

```
require(Ckmeans.1d.dp)
n <- 160
t <- seq(0, 2*pi*2, length=n)
n1 <- 1:(n/2)
n2 <- (max(n1)+1):n
y1 <- abs(sin(1.5*t[n1]) + 0.1*rnorm(length(n1)))
y2 <- abs(sin(0.5*t[n2]) + 0.1*rnorm(length(n2)))
y <- c(y1, y2)
w <- y^8 # stress the peaks
res <- Ckmeans.1d.dp(t, k=c(1:10), w)
plot(res)
```

```
plot(t, w, main = "Time course clustering / peak calling",
col=res$cluster, pch=res$cluster, type="h",
xlab="Time t", ylab="Transformed intensity w")
abline(v=res$centers, col="chocolate", lty="dashed")
text(res$centers, max(w) * .95, cex=0.75, font=2,
paste(round(res$size / sum(res$size) * 100), "/ 100"))
```

It is often desirable to visualize boundaries between consecutive clusters. The `ahist()`

function offers several ways to estimate cluster boundaries. The simplest is to use the midpoint between the two closest points in two consecutive clusters, as illustrated in the code below.