The ocean is warm and calm, but at some point its currents shift dramatically. Temperature maps recorded over many years will also change their character at that moment. A new algorithm FSBS can find such moments even when data are sparse or noisy.
The algorithm works as follows. First, for each point in time, it reconstructs the average temperature across all measurement points. Then it compares the average values before and after each possible moment. If the difference is large, a jump has occurred there. To find all jumps, the algorithm tests different time intervals and splits them in half when it finds a suspicious spot.
On real data of sea surface temperature in the southern Pacific Ocean, the algorithm found two changes: in 1981 and 1996. These years coincide with strong climate events such as El Niño and the Indian Ocean Dipole. The ocean indeed changed its character, and the algorithm saw it.
The algorithm can detect a change point even if each curve is measured at just one point (n=1). This is equivalent to detecting a change in the mean over time for scalar observations, but with guarantees that account for the functional nature of the data.
In Isaac Asimov's novel 'Foundation', psychohistorians predict crises in the development of a galactic empire by analyzing vast arrays of social data. FSBS does something similar, but for continuous functions: it finds moments when a system's behavior shifts abruptly, which may herald a crisis.