Heat Conduction Process on Community Networks as a Recommendation Model

Using heat conduction mechanism on a social network we develop a systematic method to predict missing values as recommendations. This method can treat very large matrices that are typical of internet communities. In particular, with an innovative, exact formulation that accommodates arbitrary boundary condition, our method is easy to use in real applications. The performance is assessed by comparing with traditional recommendation methods using real data.

Figure 1

Comparison between the exact solution (bold line) Eqs. (9, 10) and our approximation. For both cases we plot the “hottest” nodes. For better visualization we shifted the profiles such that the first nodes coincide in the graph. We observe a good agreement between the exact solution and the approximation for $M=10$ in our artificial network.

Figure 2

Prediction performance on the movielens database. The heat conduction model outperforms the mean predictor and the Pearson correlation based method as well. $\xi$ denotes the fraction of possible votes in the matrix. The vertical line, corresponding approximately to the giant cluster formation threshold in the movie—movie network, has vote density $\xi \approx 2N^{-1/2}{M}^{-1/6}$ [17], where $N$ is the number of users, $M$ is the number of movies.