Randomized kernels for large scale Earth observation applications

Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in the last years to develop statistical retrieval and classification models that can ingest large amounts of Earth observation data. Kernel methods constitute a family of powerful machine learning algorithms, which have found wide use in remote sensing and geosciences. However, kernel methods are still not widely adopted because of the high computational cost when dealing with large scale problems, such as the inversion of radiative transfer models or the classification of high spatial-spectral-temporal resolution data. This paper introduces an efficient kernel method for fast statistical retrieval of bio-geo-physical parameters and image classification problems. The method allows to approximate a kernel matrix with a set of projections on random bases sampled from the Fourier domain. The method is simple, computationally very efficient in both memory and processing costs, and easily parallelizable. We show that kernel regression and classification is now possible for datasets with millions of examples and high dimensionality. Examples on atmospheric parameter retrieval from hyperspectral infrared sounders like IASI/Metop; large scale emulation and inversion of the familiar PROSAIL radiative transfer model on Sentinel-2 data; and the identification of clouds over landmarks in time series of MSG/Seviri images show the efficiency and effectiveness of the proposed technique.