Natalia, It sounds like you are starting from the assumption that ratings are being done.
This can happen, but in production recommendation settings, ratings is typically a very low value input because the meaning of a rating is very complex and because so few users actually do ratings unless forced into unnatural acts. Instead, you typically wind up using other kinds of actions. If you do use ratings, it is often better to ignore the value of the rating and use the mere fact of the rating. It is also common to assume that all users *could* have interacted with any item even if they didn't. This assumption is suspect, but it is better than assuming that lack of interaction really means lack of opportunity. Adjusting your assumptions to fit these leads, I think, to the approach used by Mahout. On Thu, Dec 11, 2014 at 2:51 AM, Gruszowska Natalia < natalia.gruszow...@grupaonet.pl> wrote: > Mario, > I think in terms of correctness. In similarities like Euclidean, Pearson > correlation or Cosine Similarity better results are if we consider only > common users (users who rated both compared items). This assumption let to > find similar item for those which are unpopular, otherwise we recommend > only very popular items. For my data it is unacceptable. > > "But if you take, for example, the cosine similarity, you shouldn't throw > away the data." - you should, it result in dimension reduction and it is > good. Everything is still in the same space but for each pair the space is > reduced. > > My question is why someone who wrote this code ignored this so important > assumption? It was by accident or due to some important reasons like > effectiveness or computational complexity? > > > Natalia > > > -----Original Message----- > From: mario.al...@gmail.com [mailto:mario.al...@gmail.com] > Sent: Wednesday, December 10, 2014 7:05 PM > To: user@mahout.apache.org > Subject: Re: Collaborative filtering item-based in mahout - without > isolating users > > Hi Natalia > > Regarding example 1, if you think in terms of likelihood that the two > products have been bought together because they are similar (opposed to by > chance), the similarity is undefined. As everyone buys 12, of course the > person who bought 11 bough also 12, right? > > This if you compute the similarity through a co-occurence matrix (and > loglikelihood ratio) > > But you say "In the theory, similarity between two items should be > calculated only for users who ranked both items". > > I guess you mean: "Users [1,2,4] don't know about item 11, therefore they > do not collaborate in building the similarity between the two items. User > [3], on the contrary, does, and gives the same rating to the two products, > therefore the similarity is 1". > > But if you take, for example, the cosine similarity, you shouldn't throw > away the data. Here, you build a space with four dimensions -the ratings of > four users. You can't say product 11 is on another space when it relates > with user 1,2,4 because hasn't been rated by those users. They all are > there. They are dimensions, like in physics. Therefore you must use this > information too. Items are in the user-space... all. > > Even intuitively, items 11 and 12 are not similar at all -one has been > bought by every customer, the other by just one customer. How could you > tell the next customer who buys 12 (everyone does...) that she would really > like 11...? > > Mario > > > On Wed, Dec 10, 2014 at 4:40 PM, Gruszowska Natalia < > natalia.gruszow...@grupaonet.pl> wrote: > > > Hi All, > > > > In mahout there is implemented method for item based Collaborative > > filtering called itemsimilarity, which returns the "similarity" > > between each two items. > > In the theory, similarity between two items should be calculated only > > for users who ranked both items. During testing I realized that in > > mahout it works different. > > Below two examples. > > > > Example 1. items are 11-12 > > In below example the similarity between item 11 and 12 should be equal > > 1, but mahout output is 0.36. It looks like mahout treats null as 0. > > Similarity between items: > > 101 102 0.36602540378443865 > > > > Matrix with preferences: > > 11 12 > > 1 1 > > 2 1 > > 3 1 1 > > 4 1 > > > > Example 2. items are 101-103. > > Similarity between items 101 and 102 should be calculated using only > > ranks for users 4 and 5, and the same for items 101 and 103 (that > > should be based on theory). Here (101,103) is more similar than > > (101,102), and it shouldn't be. > > Similarity between items: > > 101 102 0.2612038749637414 > > 101 103 0.4340578302732228 > > 102 103 0.2600070276638468 > > > > Matrix with preferences: > > 101 102 103 > > 1 1 0.1 > > 2 1 0.1 > > 3 1 0.1 > > 4 1 1 0.1 > > 5 1 1 0.1 > > 6 1 0.1 > > 7 1 0.1 > > 8 1 0.1 > > 9 1 0.1 > > 10 1 0.1 > > > > > > Both examples were run without any additional parameters. > > Is this problem solved somewhere, somehow? Any ideas? Why null is > > treated as 0? > > Source: http://files.grouplens.org/papers/www10_sarwar.pdf > > > > > > > > Kind regards, > > Natalia Gruszowska > > > > > > >
