As long as the 100 vectors fit in memory, it shouldn't be too bad. I think the commonly used algorithm to find the first singular vectors is Lanczos iteration, where the key operation is multiplying the 100 vectors by the large matrix. I don't know if there's an existing library for this though...
I've used this, it works pretty quickly and produces exact results, unlike a gradient descent approach. Unfortunately, assuming I did everything correctly, it doesn't ignore the zeros in the data. I think this because after centering the data (subtracting the mean and dividing by the standard deviation for each row in the matrix), it just doesn't finish. I must have left it running for two days before I gave up on it. My assumption is that it was trying to approximate all the zeros which, due to centering, now were seen as the average rating for that user. I'm sure you could modify it to ignore those values, though.
edit: Please note that I could be way off in that my interpretation of the program not finishing. If someone knows I'm wrong, please tell me.
Maybe you encountered some numerical instability in SVDLIBC, but I would guess that there probably was a bug in the parameters you passed to SVDLIBC. Might want to try it again with a smaller matrix and compare it against MATLAB or something to flush out any bugs.
Comments
As long as the 100 vectors fit in memory, it shouldn't be too bad. I think the commonly used algorithm to find the first singular vectors is Lanczos iteration, where the key operation is multiplying the 100 vectors by the large matrix. I don't know if there's an existing library for this though...
There is indeed, http://tedlab.mit.edu/~dr/svdlibc/ this is a sparse svd solver using the Lanczos approach.
I've used this, it works pretty quickly and produces exact results, unlike a gradient descent approach. Unfortunately, assuming I did everything correctly, it doesn't ignore the zeros in the data. I think this because after centering the data (subtracting the mean and dividing by the standard deviation for each row in the matrix), it just doesn't finish. I must have left it running for two days before I gave up on it. My assumption is that it was trying to approximate all the zeros which, due to centering, now were seen as the average rating for that user. I'm sure you could modify it to ignore those values, though.
edit: Please note that I could be way off in that my interpretation of the program not finishing. If someone knows I'm wrong, please tell me.
Maybe you encountered some numerical instability in SVDLIBC, but I would guess that there probably was a bug in the parameters you passed to SVDLIBC. Might want to try it again with a smaller matrix and compare it against MATLAB or something to flush out any bugs.