Inverse ICA for denoising

nbagg · July 16, 2022, 9:23pm

Hi there,

I am trying to use ICA to denoise an EEG signal. I am currently using the MultivariateStats.jl to perform the ICA:

W = fit(ICA, data, num_elec)

This returns the mixing matrix as an ICA model. I want the inverse of this matrix. However, W is an ICA model and not a matrix so I get an error when I try to do:

inverse_W = inv(W)

I get this error:
MethodError: no method matching inv(::ICA{Float64})

How can I get the inverse of this matrix or apply the inverse of the ICA?

Thank you!

baggepinnen · July 17, 2022, 7:56am

Hello and welcome to the community!

Inside the ICA model struct, there’s a field called W

github.com

JuliaStats/MultivariateStats.jl/blob/master/src/ica.jl#L10


      
          # Independent Component Analysis
          
          
"""
          This type contains ICA model parameters: mean and component matrix ``W``.
          
          
**Note:** Each column of the component matrix ``W`` corresponds to an independent component.
          """
          struct ICA{T<:Real} <: LinearDimensionalityReduction
              mean::Vector{T}   # mean vector, of length m (or empty to indicate zero mean)
              W::Matrix{T}      # component coefficient matrix, of size (m, k)
          end
          function show(io::IO, M::ICA)
              indim, outdim = size(M)
              print("ICA(indim=$indim, outdim=$outdim)")
          end
          
          
"""
              size(M::ICA)
          
          
Returns a tuple with the input dimension, *i.e* the number of observed mixtures, and

So you could get the matrix by calling

model = fit(ICA, data, num_elec)
inverse_W = inv(model.W)

Note that you an only invert this matrix if it’s square, so you must opt to calculate as many components as there are features in the data.

nbagg · July 19, 2022, 1:47pm

This is exactly what I was looking for, thank you!