Developing a Complex Independent Component Analysis (CICA) Technique to Extract Non-stationary Patterns from Geophysical Time Series

In recent decades, decomposition techniques have enabled increasingly more applications for dimension reduction, as well as extraction of additional information from geophysical time series. Traditionally, the principal component analysis (PCA)/empirical orthogonal function (EOF) method and more recently the independent component analysis (ICA) have been applied to extract, statistical orthogonal (uncorrelated), and independent modes that represent the maximum variance of time series, respectively. PCA and ICA can be classified as stationary signal decomposition techniques since they are based on decomposing the autocovariance matrix and diagonalizing higher (than two) order statistical tensors from centered time series, respectively. However, the stationarity assumption in these techniques is not justified for many geophysical and climate variables even after removing cyclic components, e.g., the commonly removed dominant seasonal cycles. In this paper, we present a novel decomposition method, the complex independent component analysis (CICA), which can be applied to extract non-stationary (changing in space and time) patterns from geophysical time series. Here, CICA is derived as an extension of realvalued ICA, where (a) we first define a new complex dataset that contains the observed time series in its real part, and their Hilbert transformed series as its imaginary part, (b) an & Ehsan Forootan [email protected] 1 School of Earth and Ocean Sciences, Cardiff University, Main Building, Park Pl, Cardiff CF10 3AT, UK 2 Institute of Geodesy and Geoinformation, University of Bonn, Nußallee 17, 53115 Bonn, Germany 3 Aerospace Engineering Sciences, University of Colorado Boulder, 2598 Colorado Ave, Boulder, CO 80302, USA 4 Division of Geodetic Science, School of Earth Sciences, Ohio State University, 275 Mendenhall Lab, 125 South Oval Mall, Columbus, OH 43210, USA 5 State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China 6 German Geodetic Research Institute, Technical University of Munich, Arcisstraße 21, 80333 Munich, Germany 123 Surv Geophys https://doi.org/10.1007/s10712-017-9451-1