Question

I have trained a SVD model to recommend items based on userId. However, is there any way to recommend items based on items list instead of userId?

For example, given a list of items, [1,2,3,4,5], SVD model finds the most similar items [9,10]. My solution is to find the similar items for each item from input [9,10], and get the common items as the output.

That is,

• the items which are similar to item 1 are [9,10,12] and
• the items which are similar to item 2 are [9,10,13].

So that the common items are [9,10], but I don’t know whether there is a better way to do it.

Answer 1

Not very clear about what you described. I guess you mean you want item-based recommendations, like what Amazon is doing? .

The similarity between two
items can be determined in various ways, but a common method is to
use the cosine measure we described earlier, in which
each vector corresponds to an item rather than a
customer, and the vector’s M dimensions correspond
to customers who have purchased that item.

This algorithm needs intensive off-line processing to prepare nearest items. Once they are done, a response to similar-item-query is very fast.

edit

Once you know the top k similar items for each item, you have a score for each item pair, that is how similar two items are, or score(i,j)

Given a list of items: [1,2,3]

First you find top k items for each item in the list. You also have a score for each of them. Suppose k=3:

`[100,44,99]` are the top 3 items that are similar to item 1. 
score(1, 100) = 0.84, score(1, 44) = 0.4, score(1, 99) = 0.33
score(2, 44 ) = 0.3,  score(2, 33) = 0.2, score(2, 70) = 0.15
score(3, 99)  = 0.4,  score(3, 44) = 0.15, score(3, 70) = 0.01

Then you aggregate score for all items present in score([1-3],__), that is:

score(100) = 0.84
score(44) = 0.4 + 0.3 + 0.13 = 0.83
score(99) = 0.33 + 0.2 = 0.53
score(33) = 0.2
score(70) = 0.15+0.01=0.16

After sorting, you know top to bottom items should be:

100-> 0.84
44 -> 0.83
99 -> 0.53
33 -> 0.2
70 -> 0.16

Of course, in the final list of recommendation item, you might want to remove anything that is already in the given list (items user already has).

Notice that in the above example, though item 44 presents in 3 rows, all their similarity scores are low. We still choose item 100 as the best match. The intuition is that we accumulate the similarity contribution and compare their aggregated contributions.