| Title: | Blind Source Separation for Multivariate Spatial Data using Eigen Analysis |
|---|---|
| Description: | Provides functions for blind source separation over multivariate spatial data, and useful statistics for evaluating performance of estimation on mixing matrix. 'BSSoverSpace' is based on an eigen analysis of a positive definite matrix defined in terms of multiple normalized spatial local covariance matrices, and thus can handle moderately high-dimensional random fields. This package is an implementation of the method described in Zhang, Hao and Yao (2022)<arXiv:2201.02023>. |
| Authors: | Sixing Hao [aut, cre] |
| Maintainer: | Sixing Hao <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2024-10-31 06:49:30 UTC |
| Source: | CRAN |
BSSS estimates the mixing matrix of blind source separation model for multivariate spatial data.
BSSS(x, coord, kernel_type, kernel_parameter, kernel_list = NULL)BSSS(x, coord, kernel_type, kernel_parameter, kernel_list = NULL)
x |
A numeric matrix of dimension c(n, p), where the p columns correspond to the entries of the random field and the n rows are the observations. |
coord |
A numeric matrix of dimension c(n,2) where each row represents the coordinates of a point in the spatial domain. Only needed if the argument kernel_list is NULL. |
kernel_type |
A string indicating which kernel function to use. Either 'ring', 'ball' or 'gauss'. |
kernel_parameter |
A numeric vector that gives the parameters for the kernel function. At least length of one for 'ball' and 'gauss' or two for 'ring' kernel. |
kernel_list |
List of spatial kernel matrices with dimension c(n,n). Can be computed by the function |
BSSS estimates the mixing matrix by combining the information of all local covariance matrices together and conduct eigenanalysis.
BSSS returns a list, including the estimation of maxing matrix, the estimated latent field, and eigenvalues of matrix W for validating the estimation. Larger gaps among first few eigenvalues of matrix W strengthens the validity of estimation. See Zhang, Hao and Yao (2022) <arXiv:2201.02023> for details.
sample_size <- 500 coords <- runif(sample_size * 2) * 50 dim(coords) <- c(sample_size, 2) dim <- 5 # specify the dimensionality of random variable nu <- runif(dim, 0, 6) # parameter for matern covariance function kappa <- runif(dim, 0, 2) # parameter for matern covariance function zs <- gen_matern_gaussian_rf(coords=coords, dim=dim, nu=nu, kappa=kappa) mix_mat <- diag(dim) # create a diagonal matrix as the mixing matrix xs <- t(mix_mat %*% t(zs)) example <- BSSS(xs, coords, 'ring', c(0,0.5,0.5,1,1,8)) d_score(example$mix_mat_est, mix_mat)sample_size <- 500 coords <- runif(sample_size * 2) * 50 dim(coords) <- c(sample_size, 2) dim <- 5 # specify the dimensionality of random variable nu <- runif(dim, 0, 6) # parameter for matern covariance function kappa <- runif(dim, 0, 2) # parameter for matern covariance function zs <- gen_matern_gaussian_rf(coords=coords, dim=dim, nu=nu, kappa=kappa) mix_mat <- diag(dim) # create a diagonal matrix as the mixing matrix xs <- t(mix_mat %*% t(zs)) example <- BSSS(xs, coords, 'ring', c(0,0.5,0.5,1,1,8)) d_score(example$mix_mat_est, mix_mat)
d score measures the similarity of two square matrix with same dimension. d_score equals 0 if the estimator is a column permutation of true value.
d_score(estimator, true_value)d_score(estimator, true_value)
estimator |
A square matrix, usually an estimator of the |
true_value |
A square matrix, which the estimator is compared to. |
A numeric value in [0,1].
d_score(diag(3), diag(3))d_score(diag(3), diag(3))
Generate Gaussian random fields with Matern covariance function
gen_matern_gaussian_rf(coords, dim, nu, kappa)gen_matern_gaussian_rf(coords, dim, nu, kappa)
coords |
coordinate of target randon field to be generated |
dim |
dimension of target randon field to be generated |
nu |
parameter of matern covariance function |
kappa |
parameter of matern covariance function |
A data matrix with number of rows equal to 'coords', and number of columns equal to 'dim'.