How to find the independent subspace components from independent components in Matlab?

Hi,

I am trying to find the independent subspace components for an image. Could anyone please tell me how to get independent subspace components (ISA components) from independent components (ICA components)? How can the inverse ISA be done to get the image?

Regards, Manu

Answer 1

[Hari]

Hi Curious Thinker,

I understand that you want to extract independent subspace components (ISA) from independent component analysis (ICA) components of an image and then perform an inverse operation to reconstruct the image.

I assume you have already computed the ICA components.

In order to find the independent subspace components and perform the inverse operation, you can follow the below steps:

Compute ICA Components:

First, ensure you have the ICA components of your image. You can use the “fastica” function to achieve this.

[icaComponents, ~, ~] = fastica(imageData);

Group ICA Components:

Group the ICA components into subspaces. This can be done by clustering or manually defining groups based on your understanding of the data.

% Example: Group first two components together
subspace1 = icaComponents(1:2, :);

Compute ISA Components:

For each subspace, compute the ISA components by projecting the ICA components onto the subspace.

isaComponents = subspace1 * subspace1';

Inverse ISA Transformation:

To reconstruct the image, perform an inverse transformation using the ISA components and the mixing matrix.

reconstructedImage = isaComponents * mixingMatrix';

Example Reconstruction:

Display the reconstructed image to verify the inverse transformation.

imshow(uint8(reconstructedImage));

Refer to the documentation of “fastica” function to know more about its usage:

• https://www.mathworks.com/matlabcentral/fileexchange/104820-fastaci-toolbox

Hope this helps!