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I have a m x k User-feature matrix (m >> k) obtained by factorizing an original User-websites matrix (m x n) that has #page views as entries. Additionally, there are users (say r) who have been labeled as being part of a particular group. I'm now looking to find a way to see who among the remaining (m-r) users is 'similar' to these pre-classified r users. This seems like a possible scenario for a one-class SVM, but I'd like to know if there are any other methods that I should consider.

On a related note, I'm not sure if there is a way I can fit a multivariate distribution to the pre-classified r users, and then for each of the (m-r) users, get a probability of being part of that distribution. One could then use some kind of a cutoff to decide the 'similar' users.

I'm using R for my analysis, so any pointers on specific packages to consider would be helpful as well.

Thanks in advance!

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This is called learning from positive and unlabeled data (PU learning for short). Positives in this case refer to the labeled users, everyone else being unlabeled.

I strongly advise against using one-class SVM for such problems as it is known to be suboptimal. The unlabeled data can provide valuable information regarding the structure of the positive class vis-a-vis the rest, which is ignored entirely by one-class SVM. An additional problem with one-class SVM in this setting is its sensitivity to false positives, which do exist in most practical applications.

I work on this problem myself. A series of techniques exist to tackle such issues, such as biased SVM, bagging SVM and (recently) RESVM. I suggest reading my paper for a simple approach (currently under review). In the paper you can also find references to the main existing approaches, so it's good to get started.

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