Suitability of RcppML:nmf for binary sparse matrix

[ashwini-kr-sharma]

Hi Zachary, thanks for this super useful package.

I was hoping to get your advice on whether your tool is suitable to use with binary sparse matrix (with 0's and 1's only). Technically, this is a non-negative matrix so the functions from the package work fine, but I was wondering if this is recommended?

There seems to be a package in CRAN specifically for binary matrix - https://cran.r-project.org/web/packages/nmfbin/index.html but is quite slow for large matrix.

[zdebruine]

Thanks for raising this idea. Yes, you can currently use a binary sparse matrix if it is stored as a dgCMatrix. Unfortunately, the way dgCMatrix is implemented is not very efficient, as you will need to store not only the indices that are present but also an associated value of 1 (in double type...).

Yes, NMF with an NNLS objective will fit to a binary matrix very well. Obviously, the model will not be binary, as that would not accurately reconstruct the data. It is possible that an algorithm may exist where the loss itself would be computed based on some logistic transform of the model reconstruction, but I am afraid these types of algorithms will never have as good of convergence guarantees as that of pure NNLS-based NMF.

I had thought about introducing specializations for binary matrices, but other than memory utilization there would be negligible performance benefits to doing so. If so, I would likely prefer ngCMatrix. PRs welcome!

I notice that nmfbin prefers nndsvd as a default initialization. I do not recommend that as it is itself a local minima and often precludes convergence towards better local minima during model fitting.

[ashwini-kr-sharma]

Thanks Zachary for the detailed respose. Really appreciate it !