2023/03/30 by Nozomi Sugiura, Sugiura, Nozomi
Computer Science · Environmental Science · Mathematics · #Atmospheric and Oceanic Physics (physics.ao-ph) #Computer science #Data Analysis #Domain (mathematical analysis) #FOS: Physical sciences #Geochemistry and Geologic Mapping #Geodesic #Geology #Geometry #Geophysics (physics.geo-ph) #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Paleontology #Principal component analysis #Science and Climate Studies #Sequence (biology) #Series (stratigraphy) #Signature (topology) #Space (punctuation) #Statistics #Statistics and Probability (physics.data-an) #Time series
paper · pdf · doi:10.48550/arxiv.2303.17613
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Principal Geodesic Analysis (PGA) is applied to a climate time series. First, we transform each multidimensional sequence into the path signature. 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. 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 Ninõ events.