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 >
