Getting the SVD But Setting a Threshold to Improve Computation

Hi,

I am currently trying to take the svd(X), where X is a 400,000 x 75 matrix. Of course this leads to memory error.

My question is that is it possible to do an estimate of [u,s,v] such as in this case:

"...there are cases where e.g. A is a full rank square matrix, hence it has no zero singular values, however a threshold is chosen and all terms in the sum A=∑ri=1σiuivTi corresponding to singular values less than this threshold are discarded. In that way, A is approximated by a simpler matrix à , whose behavior is, for practical purposes, essentially the same as that of the original matrix."

Can I get à in this situation for myself using MATLAB commands? If so, how can I do this.

[Image Analyst]

Do you need to use all that data? I'd bet you'd get the same answer if you used just a small subset of that.

[Walter Roberson]

Is the formula A = ∑r(i) = 1 *σ(i) * u(i) * v * T(i)

The spacing is not completely clear. Also the reason for multiplying by 1 is not clear.

Answer 1

[Matt J]

You could use the pca command if you have the appropriate Toolbox, however, your out-of-memory problems should be addressable using svd()'s economy mode, e.g.,

      >> A=rand(4e5,75);
      >> [U,S,V]=svd(A,0);
      >> whos U S V
        Name           Size                Bytes  Class     Attributes

        S             75x75                45000  double              
        U         400000x75            240000000  double              
        V             75x75                45000  double