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Most literature focus on either explicit rating data or implicit (like/unknown) data. Are there any good publications to handle like/dislike/unknown data? That is, in the data matrix there are three values, and I'd like to recommend from unknown entries.

And are there any good open source implementations on this?

Thanks.

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This is very similar to the netflix problem, most matrix factorization methods can be adapted so that the error function is only evaluated at known points. For instance, you can take the gradient descent approach to SVD (minimizing the frobenius norm) but only evaluate the error and calculate the gradient at known points. I believe you can easily find code for this.

Another option would be exploiting the binary nature of your matrix and adapting binary matrix factorization tools in order to enforce binary factors (if you require them). I'm sure you can adapt one of the methods described here to work with unknown data using a similar trick as the one above.

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