fastIVA {ivaBSS}

Fast Fixed-point IVA Algorithm

Description

The algorithm estimates the sources from multiple dependent datasets jointly using their observed mixtures. The estimation is done by maximizing the independence between the sources, when the estimated unmixing matrices are restricted to be orthogonal. The options for different source densities are provided.

Usage

fastIVA(X, source_density="laplace_diag", student_df=1,
max_iter = 1024, eps = 1e-6, W_init = NA, verbose = FALSE)

Arguments

X

numeric data array containing the observed mixtures with dimension [P, N, D], where P is the dimension of the observed dataset, N is the number of the observations and D is the number of the datasets. The number of datasets D should be at least 2. Missing values are not allowed.

source_density

string to determine which source density model should be used. The options are "laplace_diag", "student" or "entropic". For more information see the details section.

student_df

integer. The degree of freedom for multivariate Student's distribution. Used only if source_denisty = "student".

max_iter

positive integer, used to define the maximum number of iterations for algorithm to run. If max_iter is reached, the unmixing matrices of the last iteration are used.

eps

convergence tolerance, when the convergence measure is smaller than eps, the algorithm stops.

W_init

numeric array of dimension [P, P, D] containing initial unmixing matrices. If not set, initialized with identity matrices.

verbose

logical. If TRUE the convergence measure is printed during the learning process.

Details

The algorithm uses fixed-point iteration to estimate to estimate the multivariate source signals from their observed mixtures. The elements of the source signals, or the datasets, should be dependent of each other to achieve the estimates where the sources are aligned in same order for each dataset. If the datasets are not dependent, the sources can still be separated but not necessarily aligned. This algorithm restricts the estimates unmixing matrices to be orthogonal. For more of the fast fixed-point IVA algorithm, see Lee, I. et al (2007).

The source density model should be selected to match the density of the true source signals. When source_density = "laplace_diag", the multivariate Laplace source density model with diagonal covariance structure is used. When source_density = "entropic", the approximated entropy based source density model is used. For more about multivariate Laplace and entropic source density models, see Lee, I. et al (2007). When source_density = "student" the multivariate Student's source density model is used, for more see Liang, Y. et al (2013).

The algorithm assumes that observed signals are multivariate, i.e. the number of datasets D >= 2. The estimated signals are zero mean and scaled to unit variance.

Value

An object of class "iva".

S

The estimated source signals with dimension [P, N, D]. The estimated source signals are zero mean with unit variance.

W

The estimated unmixing matrices with dimension [P, P, D].

W_whitened

The estimated unmixing matrices with dimension [P, P, D] for whitened data.

V

The whitening matrices with dimension [P, P, D].

X_means

The means for each observed mixture with dimension [P, D].

niter

The number of iterations that the algorithm did run.

converged

Logical value which tells if the algorithm converged.

source_density

The source density model used.

N

The number of observations.

D

The number of datasets.

P

The number of sources.

student_df

The degree of freedom for Student's source density model.

call

The function call.

DNAME

The name of the variable containing the observed mixtures.

Author(s)

Mika Sipilä

References

Lee, I., Kim, T., & Lee, T.-W. (2007). Fast fixed-point independent vector analysis algorithms for convolutive blind source separation. Signal Processing, 87, 1859–1871. <doi:10.1016/j.sigpro.2007.01.010>

Liang, Y., Chen, G., Naqvi, S., & Chambers, J. A. (2013). Independent vector analysis with multivariate Student’s t-distribution source prior for speech separation. Electronics Letters, 49, 1035–1036. <doi:10.1049/el.2013.1999>

See Also

NewtonIVA

Examples

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 2; N <- 1000; D <- 5;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    S[i, , ] <- rmvl(N, rep(0, D), diag(D))
  }

  # Generate mixing matrices from standard normal distribution
  A <- array(rnorm(P * P * D), c(P, P, D))

  # Generate mixtures
  X <- array(NaN, c(P, N, D))
  for (d in 1:D) {
    X[, , d] <- A[, , d] %*% S[, , d]
  }

  # Estimate sources and unmixing matrices
  res <- fastIVA(X)
}