EDMeasure (version 1.2.0)

mdm_ica: Independent Component Analysis via Mutual Dependence Measures

Description

mdm_ica performs independent component analysis by minimizing mutual dependence measures of all univariate components in X.

Usage

mdm_ica(X, num_lhs = NULL, type = "comp", num_bo = NULL, kernel = "exp",
  algo = "par")

Arguments

X

A matrix or data frame, where rows represent samples, and columns represent components.

num_lhs

The number of points generated by Latin hypercube sampling. If omitted, an adaptive number is used.

type

The type of mutual dependence measures, including

• asym: asymmetric measure \(\mathcal{R}_n\) based on distance covariance \(\mathcal{V}_n\);

• sym: symmetric measure \(\mathcal{S}_n\) based on distance covariance \(\mathcal{V}_n\);

• comp: simplified complete measure \(\mathcal{Q}_n^\star\) based on incomplete V-statistics;

• dhsic: d-variable Hilbert--Schmidt independence criterion dHSIC\(_n\) based on Hilbert--Schmidt independence criterion HSIC\(_n\).

num_bo

The number of points evaluated by Bayesian optimization.

kernel

The kernel of the underlying Gaussian process in Bayesian optimization, including

• exp: squared exponential kernel;

• mat: Matern 5/2 kernel.

algo

The algorithm of optimization, including

• def: deflation algorithm, where the components are extracted one at a time;

• par: parallel algorithm, where the components are extracted simultaneously.

Value

mdm_ica returns a list including the following components:

theta

The rotation angles of the estimated unmixing matrix.

W

The estimated unmixing matrix.

obj

The objective value of the estimated independence components.

S

The estimated independence components.

References

Jin, Z., and Matteson, D. S. (2017). Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence. arXiv preprint arXiv:1709.02532. https://arxiv.org/abs/1709.02532.

Pfister, N., et al. (2018). Kernel-based tests for joint independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80(1), 5-31. http://dx.doi.org/10.1111/rssb.12235.

Examples

# NOT RUN {
# X is a 10 x 3 matrix with 10 samples and 3 components
X <- matrix(rnorm(10 * 3), 10, 3)

# deflation algorithm
mdm_ica(X, type = "asym", algo = "def")
# parallel algorithm
mdm_ica(X, type = "asym", algo = "par")

# }
# NOT RUN {
# bayesian optimization with exponential kernel
mdm_ica(X, type = "sym", num_bo = 1, kernel = "exp", algo = "par")
# bayesian optimization with matern kernel
mdm_ica(X, type = "comp", num_bo = 1, kernel = "mat", algo = "par")
# }