I'm doing some collaborative filtering using this approach. I'm trying to compare the consequent user and item matrices to see where there may be users with preferences that aren't being met by the available items.
In my case, despite the fact that the users and item matrices are specified in the same 'n-dimensional latent space' the variance of the users across each dimension is much larger than that of the items. In my case, I have approximately 100 times more users than items (and think that this might have something to do with it).
Could anyone provide insight on:
- If a user has only rated one item with the maximum possible rating, should their latent space vector not be close to that show?
- Does it make sense that the user space has a much larger variance i.e. is much 'bigger' than the item space (in the same dimensions) when the preferences should correspond to the items and hence the item locations in that space might 'bound' the preference space.
Any information is much appreciated.