PCA 3d Matrix

Hello,

I'm trying to use the pca function from matlab to generate loads that I can use to forecast a 3d surface. Having said that, all the examples that I could find only talk about a 2d matrix (row representing the difference values that the column variables assume) Does somebody has an good approach to deal with 3d data ? matrix(x,y,z) instead of a matrix(x,y) ? One way that I thought was to "unwrap" my data, so I transform all the row collumn combinations in different variables (so a matrix 3d 2x2 matrix become a 1d with 4 variables (A,C - A,D - B,C - B,D ) But I don't know if that is the correct approach

Any help will be more than welcomed :)

Cheers,

Answer 1

[Aditya]

Hi Antonio,

When dealing with 3D data in MATLAB and you want to apply PCA, you'll need to reshape your data into a 2D matrix because PCA operates on 2D matrices. The idea is to treat each 3D data point as a single observation with multiple features. Here are the steps to achieve this:

% Example 3D data
data = rand(10, 10, 5); % 10x10 grid with 5 layers

% Reshape the 3D matrix into a 2D matrix
% Each row is a flattened version of the 3D grid
[nx, ny, nz] = size(data);
data2D = reshape(data, nx * ny, nz);

% Apply PCA
[coeff, score, latent] = pca(data2D);

% coeff contains the principal component coefficients
% score contains the representation of data in the new PCA space
% latent contains the variance explained by each principal component

% Example: Reconstruct the first principal component back to 3D
pc1 = reshape(score(:, 1), nx, ny);

% Visualize the first principal component as a 2D surface
figure;
surf(pc1);
title('First Principal Component');
xlabel('X');
ylabel('Y');
zlabel('PC1 Intensity');