Statistics on cluster member relationships over several days - r

Question

Assume, I have hourly data corresponding to 5 categories for consective 10 days, created as:
library(xts)
set.seed(123)
timestamp <- seq(as.POSIXct("2016-10-01"),as.POSIXct("2016-10-10 23:59:59"), by = "hour")
data <- data.frame(cat1 = rnorm(length(timestamp),150,5),
cat2 = rnorm(length(timestamp),130,3),
cat3 = rnorm(length(timestamp),150,5),
cat4 = rnorm(length(timestamp),100,8),
cat5 = rnorm(length(timestamp),200,15))
data_obj <- xts(data,timestamp) # creat time-series object
head(data_obj,2)
Now, for each day separately, I perform clustering and see how these categories behave with respect to each other using simple kmeans as:
daywise_data <- split.xts(data_obj,f="days",k=1) # split data day wise
clus_obj <- lapply(daywise_data, function(x){ # clustering day wise
return (kmeans(t(x), 2))
})
Once clustering is over, I visualize the cluster relationships over different 10 days with
sapply(clus_obj,function(x) x$cluster) # clustering results
and I found the results as
On visual inspection, it is clear that cat1 and cat3 always remained in the same cluster. Similarly cat4 and cat5 are mostly in different clusters on 10 different days.
Apart from visual inspection, is there any automatic approach to gather this type of statistic from such clustering tables?
Note: This is a dummy example. I have a data frame containing such 80 categories over continuous 100 days. An automatic summary like above one will reduce the effort.

Answer 1

Pair-counting cluster evaluation measures show an easy way to tackle this problem.
Rather than looking at object-cluster assignments, which are unstable, these methods look at whether or not two objects are in the same cluster (that is called a "pair").
So you could check if these pairs change much over time, or not.
Since k-means is randomized, you may also want to run it several times for every time slice, as they may return different clusterings!
You could then say that e.g. series 1 is in the same cluster as series 2 in 90% of the results. etc.