ICA_BlindSourceSeparation

demo()

Plots the whitened data in the foetal_ecg database.

estimate_cumulants(X::AbstractMatrix)

Returns cumulant matrix.

Estimation of cumulant matrices

gradient(Y, psiY)

Compute the gradient of the contrast function with respect to the input signals.

Arguments

• Y::AbstractMatrix{<:Real}: an N×T matrix where each row is a signal component over T samples.
• psiY::AbstractMatrix{<:Real}: the elementwise derivative of the contrast function, same size as Y.

Returns

• An N×N matrix representing the relative gradient

JADE Algorithm for ICA source separation

ica_picard(dataset::sensorData, m::Int, maxiter::Int, tol::Real, lambda_min::Real, ls_tries::Int; verbose::Bool=false)

Perform Independent Component Analysis (ICA) using the Picard algorithm with limited-memory BFGS optimization.

Arguments

• dataset::sensorData
• m::Int: Size of L-BFGS's memory. Typical values are in the range 3-15
• maxiter::Int: Maximal number of iterations
• tol::real: tolerance for the stopping criterion. Iterations stop when the norm of the projected gradient gets smaller than tol.
• lambda_min::Real: Minimum eigenvalue for regularizing the Hessian approximation.
• ls_tries::Int: Number of tries allowed for the backtracking line-search. When that number is exceeded, the direction is thrown away and the gradient is used instead.
• verbose::Bool=false: If true, prints the informations about the algorithm.

Returns

• sensorData: A new sensorData object containing the unmixed data.

ica_shibbs(dataset::sensorData, m::Integer, maxSteps::Integer)

Outer loop of the shibbs algorithm. Whitens data and loops untile diagonalization result is within threshold. Returns the dataset combined with transformation matrix as well as the transformation Matrix

joint_diagonalize(CM_in::AbstractMatrix, thresh::Real, max_iters::Integer)

Returns diagonalization matrix and rotation size

l_bfgs_direction(G, h, s_list, y_list, r_list)

Compute a search direction using the limited-memory BFGS (L-BFGS) algorithm.

Arguments

• `G::AbstractMatrix{<:Real}: the current gradient.
• h::AbstractMatrix{<:Real}: a diagonal approximation to the Hessian.
• s_list::Vector{AbstractMatrix{<:Real}}: list of previous update vectors.
• y_list::Vector{AbstractMatrix{<:Real}}: list of previous gradient differences.
• r_list::Vector{Float64}: list of scalars for each pair (s, y).

Returns

• the descent direction computed using the L-BFGS two-loop recursion.

function line_search(Y, direction, signs, current_loss; ls_tries)

Perform a backtracking line search using a matrix exponential update.

Arguments

• Y::AbstractMatrix{<:Real}: current signal matrix (N×T).
• direction::AbstractMatrix{<:Real}: descent direction matrix of the same size as Y.
• signs::AbstractVector{<:Real}: sign weights for the loss, same size as Y.
• current_loss::Real: current loss value, or Inf to force recomputation.
• ls_tries::Integer (keyword): maximum number of backtracking steps.

Returns

• A tuple (converged, Y_new, new_loss, alpha) where
• converged::Bool indicates whether a successful step was found,
• Y_new::AbstractMatrix{<:Real} is the updated signal matrix (or original if no step succeeded),
• new_loss::Real is the loss at Y_new,
• alpha::Real is the final step size.

loss(Y, signs)

Compute the total loss for a set of signals.

Arguments

• Y::AbstractMatrix{<:Real}: matrix of shape N×T, where each row is a signal component over T samples.
• signs::AbstractMatrix{<:Real}: matrix of the same shape as Y, containing signs or weights for each signal value.

Returns

• A scalar representing the average contrast-based loss across all components and time steps.

plot_matrix(dataset::sensorData)

Plots each column of the dataset against the timestamp vector

proj_hessian_approx(Y, psidY_mean, G)

Compute an approximation of the projected Hessian matrix.

Arguments

• Y::AbstractMatrix{<:Real}: an N×T matrix of current signal components.
• psidY_mean::AbstractVector{<:Real}: a length-N vector containing the average of the second derivative (or negative squared derivative) of the contrast function for each component.
• G::AbstractMatrix{<:Real}: the gradient matrix of size N×N.

Returns

• An N×N symmetric matrix approximating the projected Hessian.

read_dataset(filename::String) -> sensorData

Reads a file containing numbers separated by spaces or tabs. Number of columns is detected by analyzing the first valid line. Returns an instance of sensorData.

regularize_hessian(h, lambda_min)

Clip the diagonal values of the Hessian approximation from below, ensuring all values are at least lambda_min.

Arguments

• h::AbstractMatrix{<:Real}: a diagonal matrix, where diagonal elements approximate eigenvalues.
• lambda_min::Real: minimum allowed eigenvalue

Returns

• A matrix of the same size as h, with all values less than lambda_min replaced by lambda_min

score(Y::AbstractArray{<:Real})

Apply the hyperbolic tangent elementwise to each entry of Y.

Arguments

• Y::AbstractArray{<:Real}: input array (vector, matrix, or higher‑dimensional array) of real numbers.

Returns

• an array with the same shape as Y, where each element is tanh(y).

score_der(psiY::AbstractMatrix{<:Real})

Computes the average derivative of the hyperbolic tangent nonlinearity for each row of psiY.

Arguments

• psiY::AbstractMatrix{<:Real}: input array of size N×T, where each row is a signal component over T observations.

Returns

• a vebtor in which each entry represents the average derivative of the tanh nonlinearity, evaluated at each value in the corresponding row of psiY.

solve_hessian(G, h)

Compute the product of the inverse Hessian approximation with the gradient.

Arguments

• G::AbstractMatrix{<:Real}: the gradient matrix.
• h::AbstractMatrix{<:Real}: diagonal approximation of the Hessian.

Returns

• A matrix of same size as G, where each element is G[i,j] / h[i,j].

sort_by_energy(B::AbstractMatrix)

Sort rows of B to put most energetic sources first Returns sorted matrix

whiten_dataset(X::sensorData, m::Int64) -> sensorData, W::Matrix{Float64}, iW::Matrix{Float64}

Applies PCA whitening to TxN data matrix to decorrelate m sources T: number of samples n: number of sensors m: number of sources Returns the whitened dataset (Txm data matrix), whitening matrix W (mxn), pseudo-inverse whitening matrix iW (nxm)

whiten_dataset(X::sensorData)

Applies PCA whitening to TxN data matrix T: number of samples N: number of sensors Returns the whitened dataset.