Efficient Algorithm for finding closest match in a graph -

Efficient Algorithm for finding closest match in a graph -

edit: include concrete explanation of problem (as correctly deduced billiska): "set set of users. set b set of products. each user rates 1 or more products. rating 1 10. want deduce each user, other user has similar taste him."

"the other half choosing how want rank similarity of a-elements." - part of problem. sense users have rated across products have closed affinity, @ same time want avoid user1 , user2 many mediocre matches beingness matched ahead of user1 , user3 have few matches (perhaps need non-linear score).

disclaimer: have never used graph database.

i 2 sets of info , b. has relationship 0 many bs. each relationship has fixed value.

e.g.

a1--5-->b10

a1--1-->b1000

so initial thought "yay, thats graph, time larn graph databases!" before carried away.... reason doing can reply question....

for each find set of similar based on weights, want take in consideration

the difference in weights (assuming 1 10) 10 , 10 scored higher 10 , 1; have issue how handle is no pairing (or - not sure) the number of vertices (ignoring weights) 2 sets have in common. intention rank 2 lots of vertices same bs higher 2 have single matching vertices.

what best approach doing this?

(supplementary - realise may count sec question): how approach alter if set of in millions , b in 100 thousands , needed real-time answers?

not finish answer. don't understand technique either. know it's relevant.

if view info matrix. e.g. have rows correspond set a, have columns correspond set b, , entries weight. it's matrix missing values.

one technique used in recommender system (under category of collaborative filtering) low-rank approximation.

it's based on assumption said user-product rating matrix have low-rank. in rough sense, said matrix have low-rank if rows of many users expressed linear combination of other users' row.

i hope give start farther reading.

yes, see in low-rank approximation wiki page technique can used guess missing entries (the missing rating). know it's different problem, related.

algorithm graph-databases