Change detection in circular data

Question

Suppose I have a data set that represents circular data measured in degrees:

x <- c(rnorm(1000, 0, 10), rnorm(700, 110, 3), rnorm(1100, 230, 5)) %% 360

The R package circular provides a very nice way to represent that data, and a basic tool for detecting change points in it:

library(circular)
x <- circular(x, units='degrees')
cp <- change.point(x)

However, this particular algorithm is limited, because it's (in my experience) relatively inefficient, and it's limited to finding one change point at a time, so if multiple change points are present, a recursive approach is needed. This causes some difficulty in deciding when to terminate.

If a linear change point algorithm is used, it will have difficulty with x[1:1000] because some values will be close to 0 and some close to 360.

For linear data, I like the 'PELT' algorithm of Killick, Fearnhead, and Eckley (2011) implemented by the R package changepoint's cpt.mean() function. It's fast and seems to be pretty reliable. Has anyone looked at adapting this method to circular data?

Or other recommendations?

Answer 1

I'm not aware of any multiple changepoint algorithms for circular data available within R.

PELT can be applied to any test statistic which satisfies the assumptions in the paper. The PELT code is the same regardless of the cost function. The existing changepoint package implementation is in C. It is simply a case of coding up a new cost function that can be plugged into the existing PELT code instead of e.g.mll.mean for the PELT.mean.norm function in C.

Which test statistic from the change.point function were you interested in? I can then check if it satisfies the assumptions for PELT. If it does then it isn't a large job to code it up.