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ICA

ICA

A model type for constructing a independent component analysis model, based on MultivariateStats.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

ICA = @load ICA pkg=MultivariateStats

Do model = ICA() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in ICA(outdim=...).

Independent component analysis is a computational technique for separating a multivariate signal into additive subcomponents, with the assumption that the subcomponents are non-Gaussian and independent from each other.

Training data

In MLJ or MLJBase, bind an instance model to data with

mach = machine(model, X)

Here:

  • X is any table of input features (eg, a DataFrame) whose columns are of scitype Continuous; check column scitypes with schema(X).

Train the machine using fit!(mach, rows=...).

Hyper-parameters

  • outdim::Int=0: The number of independent components to recover, set automatically if 0.
  • alg::Symbol=:fastica: The algorithm to use (only :fastica is supported at the moment).
  • fun::Symbol=:tanh: The approximate neg-entropy function, one of :tanh, :gaus.
  • do_whiten::Bool=true: Whether or not to perform pre-whitening.
  • maxiter::Int=100: The maximum number of iterations.
  • tol::Real=1e-6: The convergence tolerance for change in the unmixing matrix W.
  • mean::Union{Nothing, Real, Vector{Float64}}=nothing: mean to use, if nothing (default) centering is computed and applied, if zero, no centering; otherwise a vector of means can be passed.
  • winit::Union{Nothing,Matrix{<:Real}}=nothing: Initial guess for the unmixing matrix W: either an empty matrix (for random initialization of W), a matrix of size m × k (if do_whiten is true), or a matrix of size m × k. Here m is the number of components (columns) of the input.

Operations

  • transform(mach, Xnew): Return the component-separated version of input Xnew, which should have the same scitype as X above.

Fitted parameters

The fields of fitted_params(mach) are:

  • projection: The estimated component matrix.
  • mean: The estimated mean vector.

Report

The fields of report(mach) are:

  • indim: Dimension (number of columns) of the training data and new data to be transformed.
  • outdim: Dimension of transformed data.
  • mean: The mean of the untransformed training data, of length indim.

Examples

using MLJ

ICA = @load ICA pkg=MultivariateStats

times = range(0, 8, length=2000)

sine_wave = sin.(2*times)
square_wave = sign.(sin.(3*times))
sawtooth_wave = map(t -> mod(2t, 2) - 1, times)
signals = hcat(sine_wave, square_wave, sawtooth_wave)
noisy_signals = signals + 0.2*randn(size(signals))

mixing_matrix = [ 1 1 1; 0.5 2 1; 1.5 1 2]
X = MLJ.table(noisy_signals*mixing_matrix)

model = ICA(outdim = 3, tol=0.1)
mach = machine(model, X) |> fit!

X_unmixed = transform(mach, X)

using Plots

plot(X.x2)
plot(X.x2)
plot(X.x3)

plot(X_unmixed.x1)
plot(X_unmixed.x2)
plot(X_unmixed.x3)

See also PCA, KernelPCA, FactorAnalysis, PPCA