I should have been made a different comment earlier. What you said was right in spirit, but off in the details. I complained about the details rather than pointing out the what was right.
If you have multiple characteristics of an object like a user, what you have is multiple matrices, not a tensor. In such a case, you can just adjoin the matrices column-wise and decompose to your heart's content. There is no need for tensor decompositions. So, Prasenjit, you were absolutely correct that you can decompose on multiple features at once. The only catch is that it is easier than you were suggesting. On Mon, Nov 23, 2009 at 12:52 AM, prasenjit mukherjee < [email protected]> wrote: > Agreed there isn't a unique definition of SVD for tensors, but there > have been attempts to extend matrix SVD to higher order > decompositions ( although not orthogonal but diagonal ) to achieve > multi-way clustering. Geometrical interpretations are still fairly > difficult to comprehend though. > > Found this article a bit relevant : > www.graphanalysis.org/SIAM-PP08/Dunlavy.pdf > > -Prasen > > On Mon, Nov 23, 2009 at 11:49 AM, Ted Dunning <[email protected]> > wrote: > > I don't think that there is a unique definition for singular value > > decompositions for either Clifford algebras or for tensors. > > > > You can define an analogous decomposition using LDA. > > > > On Sun, Nov 22, 2009 at 8:48 PM, prasenjit mukherjee < > > [email protected]> wrote: > > > >> Hi Jake, > >> Do you intend to contribute some of the Random Indexing code ? I > >> am working on a multi-way clustering problem and was thinking of using > >> tensor SVD to do that. In that context was wondering if anyone has > >> used Random Indexing to solve Higher Order SVD problem. I guess we > >> can extend the current 2d approach to higher dimensions while > >> generating the context vectors via iterating over the individual > >> contexts. > >> > >> My concern is that ( still working that out ) whether I am violating > >> any other constraints between the non-reducing dimensions. > >> > >> -Prasen > >> > >> On Sun, Nov 22, 2009 at 10:37 PM, Jake Mannix <[email protected]> > >> wrote: > >> > >> <snipped/> > >> > >> > The machinery to do the above in parallel on "ridiculously big" data > on > >> > Hadoop > >> > should be coming in soon with some of the stuff I'm working on > >> contributing > >> > to Mahout. > >> > > >> > -jake > >> > > >> > > > > > > > > -- > > Ted Dunning, CTO > > DeepDyve > > > -- Ted Dunning, CTO DeepDyve
