Results for “multilinear statistics”

DOE OSTI2024

Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2017

Evaluating Soil Moisture Retrievals from ESA's SMOS and NASA's SMAP Brightness Temperature Datasets

Two satellites are currently monitoring surface soil moisture (SM) using L-band observations: SMOS (Soil Moisture and Ocean Salinity), a joint ESA (European Space Agency), CNES (Centre national d'tudes spatiales), and CDTI (the Spanish government agency with responsibility for space) satellite launched on November 2, 2009 and SMAP (Soil Moisture Active Passive), a National Aeronautics and Space Administration (NASA) satellite successfully launched in January 2015. In this study, we used a multilinear regression approach to retrieve SM from SMAP data to create a global dataset of SM, which is consistent with SM data retrieved from SMOS. This was achieved by calibrating coefficients of the regression model using the CATDS (Centre Aval de Traitement des Donnes) SMOS Level 3 SM and the horizontally and vertically polarized brightness temperatures (TB) at 40 deg incidence angle, over the 2013 - 2014 period. Next, this model was applied to SMAP L3 TB data from Apr 2015 to Jul 2016. The retrieved SM from SMAP (referred to here as SMAP_Reg) was compared to: (i) the operational SMAP L3 SM (SMAP_SCA), retrieved using the baseline Single Channel retrieval Algorithm (SCA); and (ii) the operational SMOSL3 SM, derived from the multiangular inversion of the L-MEB model (L-MEB algorithm) (SMOSL3). This inter-comparison was made against in situ soil moisture measurements from more than 400 sites spread over the globe, which are used here as a reference soil moisture dataset. The in situ observations were obtained from the International Soil Moisture Network (ISMN; https:ismn.geo.tuwien.ac.at) in North of America (PBO_H2O, SCAN, SNOTEL, iRON, and USCRN), in Australia (Oznet), Africa (DAHRA), and in Europe (REMEDHUS, SMOSMANIA, FMI, and RSMN). The agreement was analyzed in terms of four classical statistical criteria: Root Mean Squared Error (RMSE),Bias, Unbiased RMSE (UnbRMSE), and correlation coefficient (R). Results of the comparison of these various products with in situ observations show that the performance of both SMAP products i.e. SMAP_SCA and SMAP_Reg is 48 similar and marginally better to that of the SMOSL3 product particularly over the PBO_H2O, SCAN, and USCRN sites. However, SMOSL3 SM was closer to the in situ observations over the DAHRA and Oznet sites. We found that the correlation between all three datasets and in situ measurements is best (R 0.80) over the Oznet sites and worst (R 0.58) over the SNOTEL sites for SMAP_SCA and over the DAHRA and SMOSMANIA sites (R 0.51 and R 0.45 for SMAP_Reg and SMOSL3, respectively). The Bias values showed that all products are generally dry, except over RSMN, DAHRA, and Oznet (and FMI for SMAP_SCA). Finally, our analysis provided interesting insights that can be useful to improve the consistency between SMAP and SMOS datasets.

SMOS↗