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.

require(Ckmeans.1d.dp) x <- c(rnorm(50, sd=0.3), rnorm(50, mean=1, sd=0.3), rnorm(50, mean=2, sd=0.3)) # Divide x into 3 clusters k <- 3 result <- Ckmeans.1d.dp(x, k) plot(result) plot(x, col=result$cluster, pch=result$cluster, cex=1.5, main="Optimal univariate clustering given k", sub=paste("Number of clusters given:", k)) abline(h=result$centers, col=1:k, lty="dashed", lwd=2) legend("bottomright", paste("Cluster", 1:k), col=1:k, pch=1:k, cex=1.5, bty="n")

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.

x <- c(7, 4, 1, 8, 15, 22, -1) k <- 3 ckm <- Ckmeans.1d.dp(x, k=k) midpoints <- ahist(ckm, style="midpoints", data=x, plot=FALSE)$breaks[2:k] plot(ckm, main="Midpoints as cluster boundaries") abline(v=midpoints, col="RoyalBlue", lwd=3) legend("topright", "Midpoints", lwd=3, col="RoyalBlue")

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