On 9/2/10 7:41 PM, Jeff Eastman wrote:
Hopefully answering my own question here but ending up with another.
The svd matrix I'd built from the eigenvectors is the wrong shape as I
built it. Taking Jake's "column space" literally and building a matrix
where each of the columns is one of the eigenvectors does give a
matrix of the correct shape. The math works with DenseMatrix,
producing a new data matrix which is 15x7; a significant
dimensionality reduction from 15x39.
In this example, with 15 samples having 39 terms and 7 eigenvectors:
A = [15x39]
P = [39x7]
A P = [15x7]
<snip>
Representing the eigen decomposition math in the above notation, A P is
the projection of the data set onto the eigenvector basis:
If:
A = original data matrix
P = eigenvector column matrix
D = eigenvalue diagonal matrix
Then:
A P = P D => A = P D P'
Since we have A and P is already calculated by DistributedLanczosSolver
it is easy to compute A P and we don't need the eigenvalues at all. This
is good because the DLS does not output them. Is this why it doesn't bother?
