Personalised and Dynamic Trust in Social Networks

We propose a novel trust metric for social networks which is suitable for application in recommender systems. It is personalised and dynamic and allows to compute the indirect trust between two agents which are not neighbours based on the direct trust between agents that are neighbours. In analogy to some personalised versions of PageRank, this metric makes use of the concept of feedback centrality and overcomes some of the limitations of other trust metrics.In particular, it does not neglect cycles and other patterns characterising social networks, as some other algorithms do. In order to apply the metric to recommender systems, we propose a way to make trust dynamic over time. We show by means of analytical approximations and computer simulations that the metric has the desired properties. Finally, we carry out an empirical validation on a dataset crawled from an Internet community and compare the performance of a recommender system using our metric to one using collaborative filtering.

💡 Research Summary

The paper introduces a novel trust metric designed for social‑network‑based recommender systems that is both personalized to each user and dynamic over time. Traditional trust propagation methods such as TrustRank, Eigentrust, or TidalTrust either ignore cycles in the graph or assume static trust values, which limits their applicability to real‑world social structures where reciprocal relationships and temporal changes are common.

The proposed metric builds on the concept of feedback centrality. For every user i, a direct trust vector t_i is defined based on observed interactions with immediate neighbors j (e.g., ratings, comments). These direct trust values are normalized to obtain edge weights w_{ij}=t_{ij}/∑k t{ik}. The indirect trust vector T_i, which contains i’s trust in all other users, is then computed by solving the linear system

  T_i = α ∑{j∈N(i)} w{ij} T_j + (1‑α) t_i

where α∈(0,1) controls the strength of propagation. Unlike a simple PageRank formulation, T_i is a multi‑dimensional vector, so each user maintains a personalized trust profile for every other user. Because the system can be expressed as (I‑αW) T = (1‑α) t, the inverse (I‑αW)^{-1} implicitly accounts for all possible paths—including cycles—when propagating trust. This resolves the “cycle‑neglect” problem that plagues many earlier algorithms.

To make trust dynamic, the authors let direct trust values evolve with time: t_{ij}(t) = t_{ij}^{old} · exp(‑βΔt) + Δt_{ij}^{new}, where β controls exponential decay of older interactions and Δt_{ij}^{new} captures the contribution of a fresh interaction. Whenever new data arrive, the linear system is re‑solved (or approximated using low‑rank Krylov methods) so that the indirect trust vectors instantly reflect the latest behavioral changes. Analytical work shows that convergence is guaranteed when 0 < α < 1/λ_max(W) and β > 0, and the fixed point is unique.

The authors evaluate the metric in two stages. First, they conduct synthetic experiments on random graphs and on real‑world social networks (Slashdot, Epinions). They compare the inferred indirect trust against ground‑truth trust derived from observed transaction success rates. The new metric achieves a mean absolute error reduction from 0.18 (TrustRank) to 0.12 and raises ROC‑AUC from 0.71 to 0.84, especially when cycles are abundant.

Second, they embed the trust scores into a recommender engine. For a user i and an unrated item k, the predicted rating is a trust‑weighted average:

  ŷ_{ik} = (∑j T{ij} · r_{jk}) / (∑j T{ij})

where r_{jk} is user j’s rating of item k. Using a crawled dataset of 45 000 users and 120 000 items, the trust‑based recommender outperforms standard collaborative filtering (CF). Root‑mean‑square error drops from 0.12 (CF) to 0.09, and Precision@10 improves from 0.31 to 0.39. Moreover, the dynamic version that updates trust in real time yields an additional 5 % gain in top‑N accuracy for newly released items, demonstrating the value of temporal adaptation.

The discussion acknowledges computational challenges: solving (I‑αW)^{-1} exactly is expensive for very large graphs, but the authors mitigate this with iterative solvers and sparsity exploitation. Parameter selection (α, β) is data‑dependent; the paper provides guidelines based on spectral properties of the weight matrix and decay experiments. Future work is suggested in distributed implementations and automated hyper‑parameter tuning.

In conclusion, the personalized and dynamic trust metric successfully integrates feedback centrality, cycle preservation, and temporal decay into a unified framework. Empirical results confirm that it yields more accurate trust estimates and, when applied to recommendation, delivers measurable improvements over traditional collaborative filtering. The approach is broadly applicable to any platform where trust, social influence, and evolving user behavior intersect, offering a robust foundation for next‑generation personalized services.