I am having trouble understanding the interpretation of a sparse matrix: I am studying Non Negative Matrix Factorization, and I noticed that, even without specifying any constraint, I often obtain sparse matrix. Is it linked to uncorrelated or correlated data? Why does it happen and what is the possible interpretation?
I thought it has something to do with "learning by parts", so that every vector can represent a particular feature of the data(for example, in images picturing faces every vector could represent a part of the face), but I am not totally sure.
Moreover,is there any additional advantage of having a sparse matrix as a solution, besides the computational one?
Thanks in advance for any help,
Valentina
EDIT1 The matrix to be factorized (X) has a client for every row and the variables (columns) are the number of a certain kind of products purchased by each client, one column for product. I ran a simple code using R (if you need it I can paste it, but I do not know if I can here), giving only the X in input, and I noticed that the results are sparse. I was wondering if there is a reason (maybe correlated data?) which may lead to this results.
PS I posted this same question on Stack Overflow, but a user suggested to post it here.