Type:	Package
Title:	Tools for Independent Vector Analysis
Version:	1.0.0
Date:	2022-05-03
Imports:	stats, graphics, BSSprep
Suggests:	LaplacesDemon
Encoding:	UTF-8
Maintainer:	Mika Sipilä <mika.e.sipila@student.jyu.fi>
Description:	Independent vector analysis (IVA) is a blind source separation (BSS) model where several datasets are jointly unmixed. This package provides several methods for the unmixing together with some performance measures. For details, see Anderson et al. (2011) <doi:10.1109/TSP.2011.2181836> and Lee et al. (2007) <doi:10.1016/j.sigpro.2007.01.010>.
License:	GPL (≥ 3)
RoxygenNote:	7.1.2
NeedsCompilation:	no
Packaged:	2022-05-19 08:16:26 UTC; developer
Author:	Mika Sipilä [aut, cre], Klaus Nordhausen [aut], Sara Taskinen [aut]
Repository:	CRAN
Date/Publication:	2022-05-19 17:00:02 UTC

Tools for Independent Vector Analysis

Description

Independent vector analysis (IVA) is a blind source separation (BSS) model where several datasets are jointly unmixed. This package provides several methods for the unmixing together with some performance measures. For details, see Anderson et al. (2011) <doi:10.1109/TSP.2011.2181836> and Lee et al. (2007) <doi:10.1016/j.sigpro.2007.01.010>.

Details

The package contains tools for independent vector analysis. The main functions to perform IVA are "IVANewton" and "fastIVA". "NewtonIVA" performs Newton update based IVA and "fastIVA" performs fixed-point iteration based IVA. Both of the algorithms have multiple options for source density models.

Author(s)

Authors: Mika Sipilä, Klaus Nordhausen, Sara Taskinen

Maintainer: Mika Sipilä

References

Anderson, M., Adalı, T., & Li, X.-L. (2011). Joint blind source separation with multivariate Gaussian model: Algorithms and performance analysis. IEEE Transactions on Signal Processing, 60, 1672–1683. <doi:10.1109/TSP.2011.2181836>

Anderson, M. (2013). Independent vector analysis: Theory, algorithms, and applications. PhD dissertation, University of Maryland, Baltimore County.

Newton Update Based 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. The options for different source densities are provided.

Usage

NewtonIVA(X, source_density="laplace", student_df=1,
init = "default", max_iter = 1024, eps = 1e-6, W_init = NA,
step_size=1, step_size_min = 0.1, alpha = 0.9, verbose = FALSE)

Arguments

Details

The algorithm uses Newton update together with decoupling trick 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. The algorithm does not assume the unmixing matrices to be orthogonal. For more of the nonorthogonal Newton update based IVA algorithm, see Anderson, M. et al (2011) and Anderson, M. (2013).

The source density model should be selected to match the density of the true source signals. When source_density = "laplace", the multivariate Laplace source density model is used. This is the most flexible choice as it takes both second-order and higher-order dependence into account.

When source_density = "laplace_diag", the multivariate Laplace source density model with diagonal covariance structure is used. Multivariate diagonal Laplace source density model should be considered only when the sources are mainly higher-order dependent. It works best when the number of sources is significantly less than the number of datasets.

When source_density = "gaussian" the multivariate Gaussian source density model is used. This is the superior choice in terms of computation power and should be used when the sources are mostly second-order dependent.

When source_density = "student" the multivariate Student's source density model is used. Multivariate Student's source density model should be considered only when the sources are mainly higher-order dependent. It works best when the number of sources is significantly less than the number of datasets.

The init parameter defines how the algorithm is initialized. When init = "default", the default initialization is used. As default the algorithm is initialized using init = "IVA-G+fastIVA" when source_density is "laplace", "laplace_diag" or "student", and using init = "none" when source_density = "gaussian".

When init = "IVA-G+fastIVA", the algorithm is initialized using first the estimated unmixing matrices of IVA-G, which is NewtonIVA with source_density = "gaussian", to initialize fastIVA algorithm. Then the estimated unmixing matrices W of fastIVA are used as initial unmixing matrices for NewtonIVA. IVA-G is used to solve the permutation problem of aligning the source estimates when ever the true sources are second-order dependent. If the true sources are not second-order dependent, fastIVA is used as backup as it solves the permutation problem more regularly than NewtonIVA when the sources are purely higher-order dependent. When the sources possess any second-order dependence, IVA-G also speeds the computation time up a lot. This option should be used whenever there is no prior information about the sources and source_density is either "laplace", "laplace_diag" or "student".

When init = "IVA-G", the estimated unmixing matrices of IVA-G are used to initialize this algorithm. This option should be used if the true sources are expected to possess any second-order dependence and source_density is not "gaussian".

When init = "fastIVA", the estimated unmixing matrices of fastIVA algorithm is used to initialize this algorithm. This option should be used if the true sources are expected to possess only higher-order dependence. For more details, see fastIVA.

When init = "none", the unmixing matrices are initialized randomly from standard normal distribution.

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".

Author(s)

Mika Sipilä

References

Anderson, M., Adalı, T., & Li, X.-L. (2011). Joint blind source separation with multivariate Gaussian model: Algorithms and performance analysis. IEEE Transactions on Signal Processing, 60, 1672–1683. <doi:10.1109/TSP.2011.2181836>

Anderson, M. (2013). Independent vector analysis: Theory, algorithms, and applications. PhD dissertation, University of Maryland, Baltimore County.

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

fastIVA

Examples

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")
}

Average Intersymbol Inference

Description

Calculates the average intersymbol inference for two sets of matrices.

Usage

avg_ISI(W, A)

Arguments

Details

The function returns the average intersymbol inference for the set of estimated unmixing matrices and the set of true mixing matrices. The average ISI gets the value between 0 and 1, where 0 is the optimal result. The average ISI is calculated as the mean ISI over each dataset separately. The average ISI does not take the permutation of the estimated sources into account.

Value

Numeric value between 0 and 1, where 0 is the optimal result indicating that the sources are separated perfectly in each dataset.

Author(s)

Mika Sipilä

References

Anderson, M. (2013). Independent vector analysis: Theory, algorithms, and applications. PhD dissertation, University of Maryland, Baltimore County.

See Also

joint_ISI, jbss_achieved

Examples

# Mixing matrices and unmixing matrices generated
# from standard normal distribution
P <- 4; D <- 4;
W <- array(rnorm(P * P * D), c(P, P, D))
A <- array(rnorm(P * P * D), c(P, P, D))

avg_ISI(W, A)

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")
  avg_ISI(coef(res_G), A)
}

Coefficient of the Object of Class iva

Description

coef method for class "iva".

Usage

## S3 method for class 'iva'
coef(object, which.dataset = NA, ...)

Arguments

Details

Returns the unmixing matrices for all datasets or only for the requested dataset.

Value

Unmixing matrix or all unmixing matrices of the object of class "iva". If a single unmixing matrix is requested, it is an array with dimension [P, P] and if all unmixing matrices are requested, it is an array with dimension [P, P, D].

Author(s)

Mika Sipilä

See Also

NewtonIVA, fastIVA

Examples

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")


  # All D unmixing matrices
  coef(res_G)

  # The unmixing matrix for the second dataset
  coef(res_G, 2)
}

Components of the Object of Class iva

Description

Returns the estimated source components of object of class "iva".

Usage

  components.iva(object, which.dataset = NA, ...)

Arguments

Details

Returns the estimated source components for all datasets or only for the requested dataset.

Value

Estimated source components for requested dataset or for all datasets of the object of class "iva". If a single dataset is requested, it is an array with dimension [P, N] and if all datasets are requested, it is an array with dimension [P, N, D].

Author(s)

Mika Sipilä

See Also

NewtonIVA, fastIVA

Examples

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")


  # Source estimates for all D datasets
  components.iva(res_G)

  # Source estimates for the second dataset
  components.iva(res_G, 2)
}

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

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".

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)
}

JBSS Achieved

Description

The function calculates if the joint blind source separation (JBSS) is achieved.

Usage

jbss_achieved(W, A)

Arguments

Details

The function calculates if the joint blind source separation is achieved. JBSS is considered achieved when the the location of maximum absolute values of each row of gain matrix G[,,d] = W[,,d] %*% A[,,d] is unique within the dataset, but shared between the datasets 1, ...,D. The first indicates that the sources are separated within dataset and the second indicates that the estimated sources are aligned in same order for each dataset.

Value

Logical. If TRUE the JBSS is considered achieved.

Author(s)

Mika Sipilä

References

Anderson, M. (2013). Independent vector analysis: Theory, algorithms, and applications. PhD dissertation, University of Maryland, Baltimore County.

See Also

joint_ISI, avg_ISI

Examples

# Mixing matrices and unmixing matrices generated
# from standard normal distribution
P <- 4; D <- 4;
W <- array(rnorm(P * P * D), c(P, P, D))
A <- array(rnorm(P * P * D), c(P, P, D))

jbss_achieved(W, A)

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")
  jbss_achieved(coef(res_G), A)
}

Joint Intersymbol Inference

Description

Calculates the joint intersymbol inference for two sets of matrices.

Usage

joint_ISI(W, A)

Arguments

Details

The function returns the joint intersymbol inference for the set of estimated unmixing matrices and the set of true mixing matrices. The joint ISI gets the value between 0 and 1, where 0 is the optimal result. The joint ISI calculates the average intersymbol inference over each dataset as well as penalizes if the sources are not aligned in same order for each dataset.

Value

Numeric value between 0 and 1, where 0 is the optimal result indicating that the sources are separated perfectly and aligned in same order in each dataset.

Author(s)

Mika Sipilä

References

Anderson, M. (2013). Independent vector analysis: Theory, algorithms, and applications. PhD dissertation, University of Maryland, Baltimore County.

See Also

avg_ISI, jbss_achieved

Examples

# Mixing matrices and unmixing matrices generated
# from standard normal distribution
P <- 4; D <- 4;
W <- array(rnorm(P * P * D), c(P, P, D))
A <- array(rnorm(P * P * D), c(P, P, D))

joint_ISI(W, A)

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")
  joint_ISI(coef(res_G), A)
}

Plotting an Object of Class iva

Description

plot method for the class "iva".

Usage

## S3 method for class 'iva'
plot(x, which.dataset = NA, which.source = NA,
type = "l", xlabs = c(), ylabs = c(), colors = c(),
oma = c(1, 1, 0, 0), mar = c(2, 2, 1, 1), ...)

Arguments

Details

Plots either all estimated sources of the object of class "iva" or the estimates for specific dataset and/or source.

Value

No return value, called for plotting the estimated sources of the object of class "iva".

Author(s)

Mika Sipilä

See Also

NewtonIVA, fastIVA

Examples

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")

  # Plot all estimated sources
  plot(res_G)

  # Plot the source estimates for the first dataset only
  plot(res_G, which.dataset = 1)

  # Plot the source estimates for the second source only
  plot(res_G, which.source = 2)

  # Plot the source estimate of the second dataset and third source
  plot(res_G, which.dataset = 2, which.source = 3, type = "p")

  # Plot all source estimates with custom colors and labels
  plot(res_G, col=c(rep(1, 4), rep(2, 4), rep(3, 4), rep(4, 4)),
      xlabs = c("Subject 1", "Subject 2", "Subject 3", "Subject 4"),
      ylabs = c("Channel 1", "Channel 2", "Channel 3", "Channel 4"))
}

Predict Method for Object of Class iva

Description

Predict the new source estimates best on fitted object of "iva" class.

Usage

## S3 method for class 'iva'
predict(object, newdata, which.dataset = NA, ...)

Arguments

Details

The function calculates the source estimates for new observed mixtures based on the model fitted originally. The estimates are zero mean and scaled to unit variance.

Value

Numeric array containing the estimated sources with dimension [P, N] if which.dataset is provided and with dimension [P, N, D] if which.dataset is not provided.

Author(s)

Mika Sipilä

See Also

NewtonIVA, fastIVA

Examples

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))
  sigmas <- list()

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    sigmas[[i]] <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), sigmas[[i]])
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")

  # Generate new observarions
  N_new <- 10
  S_new <- array(NA, c(P, N_new, D))
  for (i in 1:P) {
    S_new[i, , ] <- rmvl(N_new, rep(0, D), sigmas[[i]])
  }
  X_new <- array(NaN, c(P, N_new, D))
  for (d in 1:D) {
    X_new[, , d] <- A[, , d] %*% S_new[, , d]
  }

  # Get source estimates for the new observations
  pred <- predict(res_G, X_new)

  # Get source estimates for only the second dataset
  pred2 <- predict(res_G, X_new[, , 2], which.dataset = 2)
}

Print an Object of Class iva

Description

print method for the class "iva".

Usage

## S3 method for class 'iva'
print(x, ...)

Arguments

Details

The function prints all information of "iva" object, except the estimated source signals.

Value

No return value, called for printing information of the object of class "iva".

Author(s)

Mika Sipilä

See Also

NewtonIVA, fastIVA

Examples

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")
  print(res_G)
}

Summarize an Object of Class iva

Description

summary method for the class "iva".

Usage

## S3 method for class 'iva'
summary(object, ...)

Arguments

Details

The function print all the information of the "iva" object except the estimated sources and the estimated unmixing matrices.

Value

No return value, called for summarizing the object of class "iva".

Author(s)

Mika Sipilä

See Also

NewtonIVA, fastIVA

Examples

if (require("LaplacesDemon")) {
  # Generate sources from multivariate Laplace distribution
  P <- 4; N <- 1000; D <- 4;
  S <- array(NA, c(P, N, D))

  for (i in 1:P) {
    U <- array(rnorm(D * D), c(D, D))
    Sigma <- crossprod(U)
    S[i, , ] <- rmvl(N, rep(0, D), Sigma)
  }

  # 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_G <- NewtonIVA(X, source_density = "gaussian")
  summary(res_G)
}