Exploring an opinion network for taste prediction: An empirical study

Abstract

We develop a simple statistical method to find affinity relations in a large opinion network which is represented by a very sparse matrix. These relations allow us to predict missing matrix elements. We test our method on the Eachmovie data of thousands of movies and viewers. We found that significant prediction precision can be achieved and it is rather stable. There is an intrinsic limit to further improve the prediction precision by collecting more data, implying perfect prediction can never obtain via statistical means.

Bipartite network projection and personal recommendation

“…Hence we applied the coarse-graining method similar to what is used in Ref. [19]: A movie has been collected by a user iff the giving rating is at least 3. The original data contains 10 5 ratings, 85.25% of which are ≥ 3, thus the user-movie bipartite network after the coarse gaining contains 85250 edges.…”

“…Although the collaboration network is usually displayed by the onemode projection on actors (see later the definition), its fully representation is a bipartite network. The other one is named opinion network [18,19], where each node in the user-set is connected with its collected objects in the object-set. For example, listeners are connected with the music groups they collected from music-sharing library (e.g.…”

Negative ratings play a positive role in information filtering

“…For example, in Ref. [33], an object is considered to be collected by a user if and only if the given rating is at least 3. A similar coarse-graining method has been used in many other algorithms.…”

Information filtering via self-consistent refinement

“…For example, Amazon.com uses one's purchase record to recommend books [1], and AdaptiveInfo.com uses one's reading history to recommend news [2]. Motivated by the significance in economy and society, the design of an efficient recommendation algorithm becomes a joint focus from engineering science [3,4] to marketing practice [5,6], from mathematical analysis [7,8] to physics community [9,10,11,12,13,14,15,16].…”

“…Taking into account the different evaluation scales of different users [12,16], we subtract the corresponding user average from each evaluated entry in the matrix R and get a new matrix R ′ . The similarity between items α and β is given by:…”