# Cluster Data in Blocks of Similar x Values and Summarize y Values per Block

Cluster Data in Blocks of Similar x Values and Summarize y Values per Block

clusterX(
x,
y = NULL,
groupsize = 5,
resolution = 0.1,
lambda = 1,
iterlim = 100,
log = FALSE
)

statXY(x, y = NULL, ..., quantiles = c(0.05, 0.95))

## Arguments

x

x values or data.frame of x and y values

y

y values or NULL, if x is a data.frame of x and y values

groupsize

smallest expected group size

resolution

gaps between groups of data points greater than resolution lead to separation of groups.

lambda

penalization of intra-group variance, set to 1 to have more groups and set to 0 to get less but larger groups.

iterlim

maximum number of iterations the algorithm takes.

log

cluster on log(x) or on x. Does not change the value of resolution.

...

arguments going to clusterX().

quantiles

the requested quantiles, usually 0.05 and 0.95. Quantiles are returned in columns named PX.VALUE, where X = round(100*quantiles).

## Value

clusterX() returns a data.frame with x, y and group values. Group is returned as a factor with numerically sorted levels. statXY() returns summary information as a data frame. The output of clusterX()is returned in the attribute "clusterOut".

## Details

Data points are sorted by increasing x value and assigned into groups of size groupsize. Next, groups separated by less than resolution are merged. In the following iterative algorithm, the L1-distance of each data point to each of the groups is computed and wheighted by the groups geometric standard deviation. Data points are then reassigned to the closest group. The procedure is repeated until group membership does not change any more.

statXY() computes a data.frame with the following columns

• GROUP = group, group identifier

• TIME = mean(x), mean group x value, usually time

• MEAN.VALUE = mean(y), mean group y value

• MEDIAN.VALUE = median(y), median of group y values

• SD.VALUE = sd(y), standard deviation of group y values

• SE.VALUE = sd(y)/sqrt(length(y)), standard error of group y values

• GEOMMEAN.VALUE = exp(mean(log(y))), geometrical mean of y values

• GEOMSD.VALUE = exp(sd(log(y))), geometrical standard deviation of y values

• PX.VALUE = quantile(y, probs = X/100), X\

## Examples

if (FALSE) {

# Center timers for simulation and function to produce nice curve
timesD <- c(2, 10, 15, 30, 60, 120)
myfn <- function(x) 100*(1-exp(-.03*x))*exp(-.1*x)
# Randomly sampled times around center times with variable sample size
times <- unlist(lapply(timesD, function(x) stats::rnorm(runif(1, 2, 10), x, 0.2*x)))
# Simulate noisy data
x <- data.frame(
TIME = times,
VALUE = stats::rnorm(length(times), myfn(times), 0.1*myfn(times) + 1)
)
x <- subset(x, TIME > 0)

# Run cluster algorithm and get statistics
stat <- statXY(x, groupsize = 5, resolution = .01)
out <- attr(stat, "clusterOut")

# Plot result
P <- ggplot(out, aes(x = TIME, y = VALUE, color = block, pch = block)) + geom_point() +
annotate("line", x = stat$TIME, y = stat$MEDIAN.VALUE) +
annotate("line", x = stat$TIME, y = c(stat$P5.VALUE), lty = 2) +
annotate("line", x = stat$TIME, y = c(stat$P95.VALUE), lty = 2)
print(P)
print(P + scale_x_log10())

}