Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids

2021 ◽  
pp. 107165
Author(s):  
Jian Cao ◽  
Marc G. Genton ◽  
David E. Keyes ◽  
George M. Turkiyyah
Keyword(s):  
Covariance Matrices ◽  
Cholesky Factorization ◽  
Kronecker Products ◽  
Spatial Covariance

scholarly journals Embedding Tangent Space Extreme Learning Machine for EEG Decoding in Brain Computer Interface Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mingwei Zhang ◽  
Yao Hou ◽  
Rongnian Tang ◽  
Youjun Li
Keyword(s):  
Extreme Learning Machine ◽  
Motor Imagery ◽  
Tangent Space ◽  
Brain Computer Interface ◽  
Covariance Matrices ◽  
Computer Interface ◽  
Spatial Covariance ◽  
Learning Machine ◽  
Low Dimensional ◽  
Bci System

In motor imagery brain computer interface system, the spatial covariance matrices of EEG signals which carried important discriminative information have been well used to improve the decoding performance of motor imagery. However, the covariance matrices often suffer from the problem of high dimensionality, which leads to a high computational cost and overfitting. These problems directly limit the application ability and work efficiency of the BCI system. To improve these problems and enhance the performance of the BCI system, in this study, we propose a novel semisupervised locality-preserving graph embedding model to learn a low-dimensional embedding. This approach enables a low-dimensional embedding to capture more discriminant information for classification by efficiently incorporating information from testing and training data into a Riemannian graph. Furthermore, we obtain an efficient classification algorithm using an extreme learning machine (ELM) classifier developed on the tangent space of a learned embedding. Experimental results show that our proposed approach achieves higher classification performance than benchmark methods on various datasets, including the BCI Competition IIa dataset and in-house BCI datasets.

Uncertainties of TWS Time Series for Arbitrary Regions - Modelled vs. Formal Covariances

2021 ◽  
Author(s):  
Eva Boergens ◽  
Andreas Kvas ◽  
Henryk Dobslaw ◽  
Annette Eicker ◽  
Christoph Dahle ◽  
...  
Keyword(s):  
Time Series ◽  
Covariance Matrices ◽  
Gobi Desert ◽  
Covariance Model ◽  
Spatial Covariance ◽  
Formal Approach ◽  
Data Set ◽  
Terrestrial Water ◽  
Spherical Harmonic Synthesis ◽  
Processing Steps

<p>Knowledge of the variances and covariances of gridded terrestrial water storage anomalies (TWS) as observed with GRACE and GRACE-FO is crucial for many applications thereof. For example, data assimilation into different models, trend estimations, or combinations with other data set require reliable estimations of the variances and covariances. Today, the Level-2 Stokes coefficients are provided with formal variance-covariance matrices which can yield variance-covariance matrices of the gridded data after a labourious variance propagation through all post-processing steps, including filtering and spherical harmonic synthesis. Unfortunately, this is beyond the capabilities of many, if not most, users.</p><p><br>This is why, we developed a spatial covariance model for gridded TWS data. The covariance model results in non-homogeneous, non-stationary, and anisotropic covariances. This model also accommodates a wave-like behaviour in latitudinal-directed correlations caused by residual striping errors. The model is applied to both VDK3 filtered GFZ RL06 and ITSG-Grace2018 TWS data. </p><p><br>With thus derived covariances it is possible to estimate the uncertainties of mean TWS time series for any arbitrary region such as river basins. On the other hand, such time series uncertainties can also be derived from the afore mentioned formal covariance matrices. Here, only the formal covariance matrices of ITSG-Grace2018 are used which are also filtered with the VDK3 filter. All together, we are able to compare globally the time series uncertainties of both the modelled and formal approach. Further, the modelled uncertainties are compared to empirical standard deviations in arid regions in the Arabian, Sahara, and Gobi desert where residual hydrological signal can be neglected. Both in the temporal and spatial domain they show a very satisfying agreement proving the usefulness of the covariance model for the users. </p>

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