How to get my desired dimension using pca in MATLAB?

My matrix is of dimension 101x64. After applying PCA the matrix got reduced to 64x64. I want my reduced matrix to be of form 1xN. How can i do this?

[nathan welch]

I don't think Principle Component Analysis (PCA) can reduce your matrix to a row vector.

If you're using it in a similar manner to Singular Value Decomposition (SVD) and factorizing your rectangular matrix into the form:

Then the information you problem want is the scalar data from the diagonal matrix

If you can get hold of this then you can extract the diagonal elements using: s = diag(Sigma)'

This should then give you a 1x64 set of values.

Answer 1

[Aditya]

Hi Sunil,

To reduce your matrix to a form of (1 \times N) using PCA, you'll need to perform a few steps. Typically, PCA reduces the dimensionality by projecting the data onto a smaller number of principal components. Here's a general approach to achieve a (1 \times N) matrix:

% Assume X is your original 101x64 data matrix
X = rand(101, 64); % Example data

% Center the data
X_centered = X - mean(X);

% Compute the covariance matrix
covMatrix = cov(X_centered);

% Perform eigen decomposition
[eigenVectors, eigenValues] = eig(covMatrix);

% Sort eigenvectors by eigenvalues in descending order
[~, sortedIndices] = sort(diag(eigenValues), 'descend');
eigenVectors = eigenVectors(:, sortedIndices);

% Project the data onto the principal components
% Here, we project onto all 64 components (can be reduced as needed)
projectedData = X_centered * eigenVectors;

% Flatten the projected data to form a 1xN vector
% Here, N is 64*64 = 4096 for full projection
flattenedData = reshape(projectedData', 1, []);

% If you want fewer components, adjust the number of columns in eigenVectors
% For example, to keep only the first 10 components:
numComponents = 10;
projectedDataReduced = X_centered * eigenVectors(:, 1:numComponents);
flattenedDataReduced = reshape(projectedDataReduced', 1, []);