Re: Multidimensional matrix

[Alberto Frigerio]

OK, you are right, I explained the problem in a terrible way. Let's restart with "usual" matrices.

I have a matrix V (sive(V)=[d,t]) of positive elements and, using an iterative algorithm, I found its non negative matrix factorization, V = W*H, where size(W)= [d,r] and size(H)=[r,t]. What I want now to do is improving the same thing for a multidimensional matrix.

Hence, if size(V)=[d,t,s] I wanna find two matrices W and H such as V = W*H . My first idea was to consider V(:,:,1) , to find W1 and H1 such as V(:,:,1)=W1*H1 with my algorithm, and then to repeat it for V(:,:,2) , V(:,:,3) , etc . At the end I will consider W={W1,W2,W3, etc.} and H={H1,H2,H3, etc.} .
But in this way I will consider V(:,:,1) , V(:,:,2) ,... as completely indipendent matrices, but it is not true. What I would like to do is to find the matrices W and H using, at the same time, all the V(:,:,i)'s. I don't know if I'm talking about something possible or not, it is just an idea I had yesterday looking at my algorithm ...

Hope I explained the problem in a better way!!!!!

2009/11/5 David Grundberg <address@hidden>

I have absolutely no idea what you are trying to say. Your idea of "multiplication" is not something I recognize as multiplication.

Also, if you want to find W and H given V, it is misleading to say that you are "extending the usual matrix product".


Alberto Frigerio wrote:

OOPS I forgot one important information.

In my mind I would like to extend the usual matrix product using multidimensional matrix. Hence, given a (d,t,s) matrix ,V I want to find two matrices W (d,r,s1) and H (r,t,s2) so that V = W*H  (eventually s=s1=s2) .In my problem I have s=2, i.e. every element of the matrix V is a couple of elements.

I could obviously take the matrices V(:,:,1) , V(:,:,2) , etc, find the corrispective Wi and Hi and then create the matrices W and H by taking W(:,:,i)=Wi and H(:,:,i)=Hi. But it would mean to work in parallel, while I introduced the second parameter in s to have a better representation of V by W and H.

2009/11/5 Carlo de Falco <address@hidden <mailto:address@hidden>>

   On 5 Nov 2009, at 10:35, Alberto Frigerio wrote:


       Hi everyone, I've some questions about multidimensional matrix.

       *) It is possible to create (maybe using a list) a
       multidimensional matrix
       A, i.e. every element of A is not a number but a couple,
       triplet, etc. of
       numbers ?

   you could use a multi-index matrix

   A = rand (2,4,5);
   A (:,2,4)

   or a cell-array of matrices

   for ii=1:4
   for jj=1:5
   A{ii,jj} = rand(3,1);
   endfor
   endfor

   A {2,4}


       *) How can I multiply two multidimensional matrices ?


   in the second case you could use
   cellfun (@(x,y) (x'*y), A, A, 'UniformOutput', false)

       Thanks everybody,
        Alberto

   c.