SpatialBSS-package {SpatialBSS}

Blind Source Separation for Multivariate Spatial Data

Description

Blind source separation for multivariate spatial data based on simultaneous/joint diagonalization of local covariance matrices. This package is an implementation of the methods described in Nordhausen, Oja, Filzmoser and Reimann (2015) <doi:10.1007/s11004-014-9559-5>, Bachoc, Genton, Nordhausen, Ruiz-Gazen and Virta (2020) <doi:10.1093/biomet/asz079> and Muehlmann, Bachoc and Nordhausen (2022) <doi:10.1016/j.spasta.2021.100574> as well as some related methods.

Details

Package:	SpatialBSS
Type:	Package
Version:	0.14-0
Date:	2023-07-20
License:	GPL (>= 2)

This package provides functions to solve the Blind Source Separation problem for multivariate spatial data. These methods are designed to work with random fields that are observed on irregular locations. Moreover, the random field is assumed to show weak second order stationarity. The main functions of this package are:

• sbss This function derives a set of local scatter matrices that are based on spatial kernel functions, where the spatial kernel functions can be chosen. Then this set of local covariance matrices as well as the sample covariance matrix are simultaneously/jointly diagonalized. Local covariance matrices as well as local difference matrices are implemented.

• sbss_asymp, sbss_boot These functions test for white noise components in the estimated latent field estimated by the sbss function based on asymptotic results or bootstrap inference principles.

• snss_sd, snss_jd and snss_sjd These functions estimate the latent random field assuming a spatial non-stationary source separation model. This is done by splitting the domain into a number of sub-domains and diagonalizing the corresponding covariance and/or local covariance matrices for each sub-domain.

• robsbss Uses robust estimates of local covariance matrices to solve the SBSS problem.

Joint diagonalization is computed with the frjd (fast real joint diagonalization) algorithm from the package JADE.

The random field can be either a pair of numeric matrices giving the coordinates and field values or an object of class SpatialPointsDataFrame or sf.

Author(s)

Christoph Muehlmann, Mika Sipila, Klaus Nordhausen, Sara Taskinen, Joni Virta

Maintainer: Klaus Nordhausen [e-mail]

References

Muehlmann, C., Filzmoser, P. and Nordhausen, K. (2021), Spatial Blind Source Separation in the Presence of a Drift, Submitted for publication. Preprint available at https://arxiv.org/abs/2108.13813.

Bachoc, F., Genton, M. G, Nordhausen, K., Ruiz-Gazen, A. and Virta, J. (2020), Spatial Blind Source Separation, Biometrika, 107, 627-646, doi:10.1093/biomet/asz079.

Nordhausen, K., Oja, H., Filzmoser, P., Reimann, C. (2015), Blind Source Separation for Spatial Compositional Data, Mathematical Geosciences 47, 753-770, doi:10.1007/s11004-014-9559-5.

Muehlmann, C., Bachoc, F. and Nordhausen, K. (2022), Blind Source Separation for Non-Stationary Random Fields, Spatial Statistics, 47, 100574, doi:10.1016/j.spasta.2021.100574.

Muehlmann, C., Bachoc, F., Nordhausen, K. and Yi, M. (2022), Test of the Latent Dimension of a Spatial Blind Source Separation Model, to appear in Statistica Sinica, doi:10.5705/ss.202021.0326.