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(step1-13 in Alg. 4) in the continu-ous case. For advogato data set, we directly report the results on all the six snapshots (i.e., advogato-1, . . . , advogato-6). For PGP, we use its subsets to study the scalability. The result is shown in Fig. 6, which is consistent with the complex-ity analysis in Section 4.3. As we can see from the figure, MATRI scales linearly wrt to both n and |K|, indicating that it is suitable for large-scale applications. The scalability result for the binary case is similar, and we omit the figures for brevity.
- (b) (c) (d)
Fig. 3. Scalability of the proposed MATRI for continuous case. MATRI scales linearly wrt the data size (n and |K|). (a) Wall-clock time vs. n on advogato. (b) Wall-clock time vs. |K| on advogato. (c) Wall-clock time vs. n on PGP. (d) Wall-clock time vs. |K| on PGP.
Fig. 4. Comparisons of alternative solutions of MATRI. Compared to MATRI-AA, MATRI-SS and MATRI-AS are more than 10x faster while preserving more than 90% accuracy on both data sets. (a) advogato data set. (b) PGP data set.
(C) Comparisons of the Alternatives of MATRI. As men-tioned before, the stochastic gradient descent method (SGD) could also be used for the continuous trust inference prob-lem in computing propagation vector and solving Eq. (5). We now experimentally evaluate the efficiency of all the four alternatives of MATRI. We use MATRI-AA to denote the original MATRI, MATRI-SA to denote the case when we use SGD in the propagation step, MATRI-AS.
VI RELATED WORK
In this section, we briefly review related work, includ-ing trust propagation models, multi-aspect trust inference models, etc.
Trust Propagation Models. To date, a large body of trust inference models are based on trust propagation where trust is propagated along connected users in the trust net-work, i.e., the web of locally-generated trust ratings. Based on the interpretation of trust propagation, we further cate-gorize these models into two classes: path interpretation and component interpretation.The proposed MATRI integrates the trust propagation with two other important properties, i.e., the multi-aspect of trust and trust bias. In addition, our multi-aspect model offers a natural way to speed up on-line query response; as well as to mitigate the sparsity or coverage problem in trust inference where some trustor and trustee might not be connected with each other – both are known limitations with the current trust propagation models .
Multi-Aspect Trust Inference Models. Social scientists have explored the multi-aspect property of trust for several years . In computer science, there also exist a few trust inference models that explicitly explores the trust propagation.
Trust Bias in Trust Inference. In sociology, it was dis-covered a long time ago that trust bias is an integral part in the final trust decision . Nonetheless, this important aspect has been largely ignored in most of the existing trust inference models. One exception is from Nguyen et al. , which learns the importance of several trust bias related features derived from a social trust framework. Recently, Mishra et al.  propose an iterative algorithm to compute trust bias. Different from these existing works, our focus is to incorporate various types of trust bias as specified factors/aspects to increase the accuracy of trust inference.
In this paper, we have proposed a trust inference model, as well as a family of algorithms to apply the model to both continuous and binary inference scenarios. The basic idea of the proposed MATRI is to leverage the multi-aspect property of trust by characterizing several aspects/factors for each trustor and trustee based on the existing trust relationships. In addition, MATRI incorporates the trust propagation and trust bias; and further learns their rela-tive weights. By integrating all these important properties, our experimental evaluations on real benchmark data sets show that MATRI leads to significant improvement over several benchmark approaches in prediction accuracy, for both quantifying numerical trustworthiness scores and pre-dicting binary trust/distrust signs. The proposed MATRI is also nimble – it is up to 7 orders of magnitude faster than the existing trust propagation methods in the on-line query response, and in the meanwhile it enjoys the linear scalabil-ity for the pre-computational stage in both time and space. Future work includes investigating the capability of MATRI to address the trust dynamics.
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