A novel measure of time series data pattern based on persistent homology that can detect the trend change of the daily all-cause mortality in Tokyo after the temperature rise
Haruhisa Oda, Chris Fook Sheng Ng, Masahiro Hashizume · Research Square · 2024
Abstract Background: Evaluating the effect of temperature rise on mortality has been an important theme in environmental epidemiology. However, few studies examine the problem: ''Are there any differences in the mortality data pattern between recent years and former years that can be linked to climate change?" We might think we can investigate peak patterns. However, we do not have a complete list of peak types relevant to our problem. We can still try to take into account as many types of peaks as possible, but this microscopic method should not be the most straightforward way, given that our problem deals with macroscopic trends in data patterns. We will construct a new measure of data pattern based on persistent homology. With this measure, we will see the change in the mortality trends in Tokyo that took place after the climate change. Methods: We circularly plot the time series data and apply persistent homology to this point cloud. The main output of our analysis is the hole structures represented by triangles connecting points in our data. We define our measure of data pattern to be whether multiple holes are detected. This single measure can behave like simplified versions of various peak analysis methods without the information on what peaks to focus on. Results: With our measure, we succeed in detecting the change in the mortality trends preceded by the temperature rise in Tokyo. Conclusions: We propose that we should regard the holes detected by our novel methodology as a fundamental characteristic of time series data. Trial registration: Not applicable.