9:30 AM - 9:45 AM
[MGI29-03] Principal Geodesic Analysis applied to climate time series
Keywords:Principal Geodesic Analysis, signature, climate time series
Principal Geodesic Analysis (PGA; e.g., Fletcher et al., 2004) is applied to a climate time series. First, we transform each multidimensional sequence into the path signature (e.g., Lyons et al., 2007). Since the signature lives in a curved space, usual principal component analysis (PCA) is not applicable. Instead, we treat the signature space as a geodesic manifold (e.g., Pennec and Lorenzi, 2020). By replacing the notion of straight lines with that of geodesics, the domain of PCA can be extended to the curved space. Then, the first principal component is derived as the geodesic that minimizes the unexplained variance in the data. As an application, we computed the leading modes for one-year NINO SST time series, which are divided into segments that represent annual variations of monthly averages. It is interesting that some months in a year reveal characteristic undulations that could indicate the early signs of upcoming El Nino events.