Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring

Statistical Atmospheric Parameter Retrieval Largely Benefits from Spatial-Spectral Image Compression

The Infrared Atmospheric Sounding Interferometer (IASI) is flying on board of the Metop satellite series, which is part of the EUMETSAT Polar System (EPS). Products obtained from IASI data represent a significant improvement in the accuracy and quality of the measurements used for meteorological models. Notably, IASI collects rich spectral information to derive temperature and moisture profiles –among other relevant trace gases–, essential for atmospheric forecasts and for the understanding of weather. Here, we investigate the impact of near-lossless and lossy compression on IASI L1C data when statistical retrieval algorithms are later applied. We search for those compression ratios that yield a positive impact on the accuracy of the statistical retrievals. The compression techniques help reduce certain amount of noise on the original data and, at the same time, incorporate spatial-spectral feature relations in an indirect way without increasing the computational complexity. We observed that compressing images, at relatively low bitrates, improves results in predicting temperature and dew point temperature, and we advocate that some amount of compression prior to model inversion is beneficial. This research can benefit the development of current and upcoming retrieval chains in infrared sounding and hyperspectral sensors

Characterization of the Earth\u27s surface and atmosphere for multispectral and hyperspectral thermal imagery

The goal of this research was to develop a new approach to solve the inverse problem of thermal remote sensing of the Earth. This problem falls under a large class of inverse problems that are ill-conditioned because there are many more unknowns than observations. The approach is based on a multivariate analysis technique known as Canonical Correlation Analysis (CCA). By collecting two ensembles of observations, it is possible to find the latent dimensionality where the data are maximally correlated. This produces a reduced and orthogonal space where the problem is not ill-conditioned. In this research, CCA was used to extract atmospheric physical parameters such as temperature and water vapor profiles from multispectral and hyperspectral thermal imagery. CCA was also used to infer atmospheric optical properties such as spectral transmission, upwelled radiance, and downwelled radiance. These properties were used to compensate images for atmospheric effects and retrieve surface temperature and emissivity. Results obtained from MODTRAN simulations, the MODerate resolution Imaging Spectrometer (MODIS) Airborne Sensor (MAS), and the MODIS and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) (MASTER) airborne sensor show that it is feasible to retrieve land surface temperature and emissivity with 1.0 K and 0.01 accuracies, respectively

Deep Gaussian processes for biogeophysical parameter retrieval and model inversion

Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel based methods, and Gaussian Processes (GPs) in particular, have provided useful and informative solutions to such RTM inversion problems. This is in large part due to the confidence intervals they provide, and their predictive accuracy. However, RTMs are very complex, highly nonlinear, and typically hierarchical models, so that very often a single (shallow) GP model cannot capture complex feature relations for inversion. This motivates the use of deeper hierarchical architectures, while still preserving the desirable properties of GPs. This paper introduces the use of deep Gaussian Processes (DGPs) for bio-geo-physical model inversion. Unlike shallow GP models, DGPs account for complicated (modular, hierarchical) processes, provide an efficient solution that scales well to big datasets, and improve prediction accuracy over their single layer counterpart. In the experimental section, we provide empirical evidence of performance for the estimation of surface temperature and dew point temperature from infrared sounding data, as well as for the prediction of chlorophyll content, inorganic suspended matter, and coloured dissolved matter from multispectral data acquired by the Sentinel-3 OLCI sensor. The presented methodology allows for more expressive forms of GPs in big remote sensing model inversion problems.European Research Council (ERC) 647423Spanish Ministry of Economy and Competitiveness TIN2015-64210-R DPI2016-77869-C2-2-RSpanish Excellence Network TEC2016-81900-REDTLa Caixa Banking Foundation (Barcelona, Spain) 100010434 LCF-BQ-ES17-1160001