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 > > >
