PCA Sound Compression using Matlab - matlab

Question

I'm trying to build a sound compressor using PCA (Principal Component Analysis).
The input sound is always a mono-channel one, so the resulting matrix is a column matrix called sampledData in the code.
Compressing the sound requires the matrix to be transformed in a 2D one. So, one would need to group the samples the following way :
Here the grouping size is 3 with a sound composed of 7 samples
[sample1 sample2 sample3
sample4 sample5 sample6
sample7 0 0 ]
What does it change to have low grouping size (= number of columns wanted for the matrix) e.g. 10 or a high one e.g. 100 or more?
[sampledData, sampleRate] = audioread("soundFile.wav");
data = sampledData;
groupingSize = 10; %Number of columns wanted from the data
%Make data size a multiple of groupingSize and fill with 0
data(end + 1:groupingSize*ceil(numel(data)/groupingSize))=0;
%Make data a matrix of x rows and groupingSize columns
data = transpose(reshape(data,groupingSize,[]));
Here is the remaining code I'm using for the sound compression. Unfortunately I have an error when percentagePC is less than 100, saying that the number of columns of the compressed matrix need to have the same number of columns as the number of rows of the inverse of eigenVec.
To illustrate, I use groupingSize = 100 which gives me a compressed matrix of 100 columns and eigenVec is a matrix of 100 row and 100 columns. If I set percentagePC = 90 I then get a compressed matrix of 90 columns (I keep 90% of the data that is most useful), so to be able to multiply both matrixes I theoretically need to reduce the size of the eigenVec matrix by 10 columns. Is this correct reasoning according to PCA?
percentagePC = 90; %Percentage of principal component to keep
[rows, cols] = size(data);
%get eigenvalues and eigenvector by centering data matrix and getting its covariance
dataCR =(data-ones(size(data,1),1)*mean(data))./(ones(size(data,1),1)*std(data,1));
dataCov = cov(dataCR);
[eigenVec, eigenVal] = eig(dataCov);
%Sort eigenvectors (desc)
[~, index] = sort(diag(eigenVal), 'descend');
eigenVec = eigenVec(:, index);
%principal components calculation
P = zeros(rows,cols);
for i = 1:cols
P(:,i) = dataCR * eigenVec(:,i);
end
%Number of principal components wanted according to percentagePC
iterations = ceil((groupingSize*percentagePC)/100);
compressed = zeros(rows,iterations);
for i = 1: iterations
compressed (:,i) = P(:,i);
end
%Fuse principal components between each other to get final compressed signal
final_compressed = zeros(rows*iterations,1);
z=1;
z = 1;
for i = 1:iterations:rows*iterations
for j = 1:iterations
final_compressed(i+j-1,1) = P(z,j);
end
z = z + 1;
end
% Decompression of compressed signal
decompressed = compressed * (eigenVec^(-1)); % /!\ ERROR IS HERE /!\
[rowsD,colsD] = size(decompressed);
final_decompressed = zeros(rowsD*colsD,1);
z = 1;
for i = 1:colsD:rowsD*colsD
for j = 1:colsD
final_decompressed(i+j-1,1) = decompressed(z,j);
end
z = z + 1;
end
filenameC = fullfile('compress.wav');
filenameD = fullfile('decompress.wav');
audiowrite(filenameC, final_compressed/max(abs(final_compressed)), round(sampleRate/(groupingSize/iterations)));
audiowrite(filenameD, decompressed, sampleRate);