Let's consider more general nonlinear approaches to study teleconnections of climate variables

The recent work by (Rieger et al 2021) is concerned with the problem of extracting features from spatio-temporal geophysical signals. The authors introduce the complex rotated MCA (xMCA) to deal with lagged effects and non-orthogonality of the feature representation. This method essentially (1) transforms the signals to a complex plane with the Hilbert transform; (2) applies an oblique (Varimax and Promax) rotation to remove the orthogonality constraint; and (3) performs the eigendecomposition in this complex space (Horel et al, 1984). We argue that this method is essentially a particular case of the method called rotated complex kernel principal component analysis (ROCK-PCA) introduced in (Bueso et al., 2019, 2020), where we proposed the same approach: first transform the data to the complex plane with the Hilbert transform and then apply the varimax rotation, with the only difference that the eigendecomposition is performed in the dual (kernel) Hilbert space. The latter allows us to generalize the xMCA solution by extracting nonlinear (curvilinear) features when nonlinear kernel functions are used. Hence, the solution of xMCA boils down to ROCK-PCA when the inner product is computed in the input data space instead of in the high-dimensional (possibly infinite) kernel Hilbert space to which data has been mapped. In this short correspondence we show theoretical proof that xMCA is a special case of ROCK-PCA and provide quantitative evidence that more expressive and informative features can be extracted when working with kernels; results of the decomposition of global sea surface temperature (SST) fields are shown to illustrate the capabilities of ROCK-PCA to cope with nonlinear processes, unlike xMCA.

Machine Learning Information Fusion in Earth Observation: A Comprehensive Review of Methods, Applications and Data Sources

This paper reviews the most important information fusion data-driven algorithms based on Machine Learning (ML) techniques for problems in Earth observation. Nowadays we observe and model the Earth with a wealth of observations, from a plethora of different sensors, measuring states, fluxes, processes and variables, at unprecedented spatial and temporal resolutions. Earth observation is well equipped with remote sensing systems, mounted on satellites and airborne platforms, but it also involves in-situ observations, numerical models and social media data streams, among other data sources. Data-driven approaches, and ML techniques in particular, are the natural choice to extract significant information from this data deluge. This paper produces a thorough review of the latest work on information fusion for Earth observation, with a practical intention, not only focusing on describing the most relevant previous works in the field, but also the most important Earth observation applications where ML information fusion has obtained significant results. We also review some of the most currently used data sets, models and sources for Earth observation problems, describing their importance and how to obtain the data when needed. Finally, we illustrate the application of ML data fusion with a representative set of case studies, as well as we discuss and outlook the near future of the field.