Truncated SVD returns unexpected 1*1 result

Hi,

I am currently prefoming SVD on six channels varying in time of the same type of biometric data. The recorded channels are similar as therefore they feature high correlation.

I want to take these six channels and reduce them to a single channel using SVD, I take my data, rescale it and then preform the svd, so far so good. Where I run into problems is the reconstruction. If I want the orignal data X = U*S*V '.Instead I am trying to preform a truncation by only taking the first PC as this accounts for over 95% of the information anyways.

Instead of PC1 returning a vector (1 channel * given number of samples) I am returned a single value (1*1). I am assuming I have a matrix the wrong way around but I can't see how I am getting this result (Though I know that I am the likely problem). I will attach some open source data too.

data = rescale(data(1:6,:),0,1); % Rescale the data for reobustness between patients
[U,S,V] = svd(data(:,:),'econ'); % Preform SVD
PC1 = V(:,1)'*data(1,:)';        % Atempt to eqivilent single channel  

I also know I can compute something similar with the code below, but I would just really like to know where I am going wrong now!

[coeff,score,latent] = pca(data');
new_matrix_for_classification = score(:,1);

Thank you,

Christopher

Answer 1

[Matt J]

Well, you're multiplying a row vector by a column vector, so a scalar is the only result that is possible.

Shouldn't a 1-component reconstruction be,

PC1=data*V(:,1);

[Christopher McCausland]

Hi Matt,

Thank you for the reply! Being totally honest I have gotten myself very confused. My input is a 6*10000, which is six channels and 10000 individual samples. I was expecting an output of 1*10000 which would essentially comprise of a combinded output channel due to SVD truncation of the same duration. I tired something similar to your soloution earlier but it gives a 1*6 output. SVD truncation information is a bit ropey to say the least, and this is my first time working with the method so I am a bit confused!

Christopher

[Matt J]

The samples are supposed to be in the rows, not the column of your data matrix.

[Christopher McCausland]

Hi Matt,

Thanks for getting back to me and for your help! I appreciate this is probably very obvious to you but I really don't get the process. Starting from the beginning with your comments gives me:

data = rescale(data(1:6,:),0,1); % Rescale the data for robustness between patients 
data = data(:,:)'; % Change samples into rows
[U,S,V] = svd(data(:,:)','econ'); % Preform SVD
PC1=data*V(:,1); 

Currently PC1 will throw an error as the matrix sizes are not compatible for multiplication. I have tried to move around the order of the data and V array and transpose them too but am still left with a 1*6 output rather than the 1*100000 (one channel * total signal duration) that I was expecting.

As I haven't used SVD before, it's been quite a furstrating process!

Thank you,

Christopher

[Matt J]

I have tried to move around the order of the data and V array and transpose them too but am still left with a 1*6 output

If you did, you should have gotten a 10000x1 output, as below.

data=rand(1e4,6);
[U,S,V] = svd(data,'econ'); % Preform SVD
PC1=data*V(:,1); 

whos PC1

  Name          Size            Bytes  Class     Attributes

  PC1       10000x1             80000  double              

[Christopher McCausland]

Hi Matt,

Thank you so much! I had forgotten to remove the additional transpose in my third line. So I was transposing the data back to its orignal orientation. This is now working as I would expect, thank you!!

One additional thing that cropped up is a large negitive DC offset was added to the waveform, I can remove this with DSP techniques (which is what I am much more comfortable with), however I was wondering if you had any idea for what would cause such a shift post svd processing? (Probably) more out of intrest than usefulness.

Thank you again for all your help!

Christopher