Heat Conduction Process on Community Networks as a Recommendation Model

TL;DR

The paper addresses recommendation in large online communities by treating missing values through heat conduction on social networks. It develops an exact Green’s-function formulation for individualized boundary conditions and evaluates it against traditional methods on real data.

• Problem

  Large internet communities generate more information than individuals can process, creating a need for recommendation methods that predict what users may select from prior choices.

• Method

  The model uses heat conduction on a network, assigning source and sink temperatures and solving the discrete Laplace problem for remaining nodes under individualized boundary conditions.

• Results

  The approximation agrees well with the exact solution at about M = 10 on an artificial network, while the heat conduction model outperforms mean and Pearson-correlation predictors on MovieLens.

• Takeaways & Limitations

  A Green’s function computed once can be reused for different boundary conditions, making the method more computationally convenient for recommendation settings.

• Takeaways & Limitations

  Directly solving the boundary-value problem requires a huge matrix solve for each individual, which is prohibitively expensive in communities with millions of members.