Back

Recommender systems with social regularization

Hao MaDengyong ZhouChao LiuMichael R. LyuIrwin King

article2011WSDM1,715 citationsTest of Time Award

Proposes a matrix factorization framework that incorporates social network constraints and friend taste diversity as regularizers to improve recommendation accuracy over standard collaborative filtering.

Listen

Online recommender systems are essential tools for e-commerce, media, and digital platforms to filter information and personalize user experiences. However, traditional systems typically assume users act independently and ignore the social networks connecting them. While people routinely rely on friends for advice, existing algorithms struggle to incorporate social relationships effectively or confuse mutual social friendships with unilateral trust lists. As online social platforms expand rapidly, platforms face the challenge of accurately capturing social network signals without distorting user preferences.

The main objective of the article is to formulate and demonstrate a general matrix factorization framework that incorporates social network connections to improve rating prediction accuracy. It specifically evaluates how constraining user preference models with social relationships and taste-similarity metrics enhances recommendation performance across both friendship and trust networks.

The researchers developed two social regularization models: an average-based approach that pulls a user’s profile toward the weighted average of their friends' tastes, and an individual-based approach that enforces pairwise alignment between a user and each friend individually. To validate the models, the article performed extensive empirical evaluations on two large real-world datasets: Douban (comprising over 129,000 users, 58,000 items, 16.8 million ratings, and 1.69 million friendship links) and Epinions (comprising over 51,000 users, 83,000 items, 631,000 ratings, and 511,000 trust links). The evaluation compared the proposed methods against standard baseline models and state-of-the-art trust-aware algorithms using standard prediction error metrics across various data sparsity settings.

The findings show that incorporating social regularization significantly and consistently outperforms traditional matrix factorization and trust-aware models across all test configurations. The individual-based regularization model achieved the highest accuracy, outperforming the average-based model by preserving diverse tastes and capturing taste propagation across extended networks. Furthermore, weighting social ties with statistical similarity metrics (such as the Pearson Correlation Coefficient) proved critical; assigning uniform or random weights to connections degraded performance. The analysis also revealed that tuning the balance between social influence and individual ratings is vital, as over-relying or under-relying on social signals reduces recommendation quality.

These results demonstrate that platforms can achieve substantial gains in recommendation quality by treating social connections as soft constraints rather than strict filters. Differentiating between close-taste friends and divergent acquaintances mitigates noise and avoids inaccurate recommendations. Unlike older trust-specific methods, this framework provides a flexible architecture that generalizes effectively to mutual social graphs, unilateral trust networks, and potentially other contextual data such as user tags or demographic attributes.

Organizations operating recommendation platforms should consider incorporating individual-based social regularization while applying correlation-based similarity weighting to filter social noise. Future technical initiatives should focus on clustering users to identify domain-specific friend groups (such as consulting specific friends for movies versus books) and incorporating item-side features like tags to further refine accuracy.

The findings are supported by strong empirical evidence and low variance across large datasets. However, decision-makers should note that the evaluation relied on offline historical rating data, and performance in live environments will depend on the availability of active social connections and proper parameter tuning for network density.

MicrosoftThe Chinese University of Hong Kongclustering algorithmscorrelation coefficientdata sparsitysocial regularizationsocial recommender systemstrust-aware recommender systems
Ma et al (2011).pdf
  • Paper: Graph Neural Networks for Social Recommendation, Wenqi Fan et al. (2019). GraphRec modernizes social regularization concepts by utilizing graph neural networks and attention mechanisms to jointly model user-to-user social relations and user-item interactions.
  • Paper: Learning to Discover Social Circles in Ego Networks, Julian McAuley et al. (2012). This work advances the source's suggestion of handling diverse, domain-specific friend groups by automatically discovering fine-grained social circles in ego networks.
  • Paper: Graph Neural Networks in Recommender Systems: A Survey, Shiwen Wu et al. (2020). This comprehensive survey categorizes the evolution of network-based collaborative filtering from traditional social regularization into deep graph neural network architectures.
  • Paper: Neural Graph Collaborative Filtering, Xiang Wang et al. (2019). Neural Graph Collaborative Filtering extends network-regularized representation learning by explicitly propagating collaborative signals through multi-layer graph structures.
  • Paper: LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation, Xiangnan He et al. (2020). LightGCN refines graph-based collaborative filtering by stripping away non-linear neural complexities to focus purely on linear neighborhood propagation over relational graphs.
  • Paper: Self-supervised Graph Learning for Recommendation, Jiancan Wu et al. (2020). Self-Supervised Graph Learning enhances graph-based recommender architectures through contrastive learning, tackling network sparsity and noise issues that social regularization first sought to mitigate.
Cover for Recommender systems with social regularization

Abstract

Although Recommender Systems have been comprehensively analyzed in the past decade, the study of social-based recommender systems just started. In this paper, aiming at providing a general method for improving recommender systems by incorporating social network information, we propose a matrix factorization framework with social regularization. The contributions of this paper are four-fold: (1) We elaborate how social network information can benefit recommender systems; (2) We interpret the differences between social-based recommender systems and trust-aware recommender systems; (3) We coin the term Social Regularization to represent the social constraints on recommender systems, and we systematically illustrate how to design a matrix factorization objective function with social regularization; and (4) The proposed method is quite general, which can be easily extended to incorporate other contextual information, like social tags, etc. The empirical analysis on two large datasets demonstrates that our approaches outperform other state-of-the-art methods.

Topics

clustering algorithmscorrelation coefficientdata sparsitye-commercematrix factorizationspearson correlationpearson correlation coefficientsrecommendationrecommendation performanceregularization

Keywords

social regularizationsocial recommender systemstrust-aware recommender systemscollaborative filteringprobabilistic matrix factorizationuser-item rating matrixindividual-based regularizationlow-rank matrix factorizationsocial trust

Table of Contents

  • 1. INTRODUCTION
  • 2. RELATED WORK
  • 2.1 Traditional Recommender Systems
  • 2.2 Trust-aware Recommender Systems
  • 2.3 Social Recommender Systems
  • 3. PROBLEM DEFINITION
  • 4. LOW-RANK MATRIX FACTORIZATION
  • 5. SOCIAL REGULARIZATION
  • 5.1 Model 1: Average-based Regularization
  • 5.2 Model 2: Individual-based Regularization
  • 5.3 Similarity Function
  • 5.4 Extensions
  • 6. EXPERIMENTAL ANALYSIS
  • 6.1 Datasets
  • 6.2 Metrics
  • 6.3 Comparisons
  • 6.4 Impact of Parameters α and β
  • 6.5 Impact of Similarity Functions
  • 7. CONCLUSION AND FUTURE WORK
  • Acknowledgments
  • 8. REFERENCES

Knowls

  1. Knowl 1 — Individual-based Social Regularization Model (SR2)

    model/method

    The individual-based social regularization model (SR2) constrains each user's latent feature vector directly against the latent feature vector of each individual social friend or trusted user, weighted by their pairwise taste similarity. This prevents information loss from averaging and allows indirect propagation of tastes across connected paths in the social graph.

    Let R∈Rm×nR \in \mathbb{R}^{m \times n} be a rating matrix of mm users and nn items, with observed ratings indicated by Iij∈{0,1}I_{ij} \in \{0, 1\}. Let U∈Rl×mU \in \mathbb{R}^{l \times m} and V∈Rl×nV \in \mathbb{R}^{l \times n} be the low-rank user and item factor matrices of dimension ll, where Ui∈RlU_i \in \mathbb{R}^l denotes the preference vector of user uiu_i and Vj∈RlV_j \in \mathbb{R}^l denotes the factor vector of item vjv_j. Let F+(i)\mathcal{F}^+(i) denote the set of outlink friends/trusted users of user uiu_i, F−(i)\mathcal{F}^-(i) denote the set of inlink friends/trustors of user uiu_i, and Sim(i,f)∈[0,1]\text{Sim}(i, f) \in [0, 1] denote the similarity between uiu_i and ufu_f.

    The objective function to minimize is: min⁡U,VL2(R,U,V)=12∑i=1m∑j=1nIij(Rij−UiTVj)2+β2∑i=1m∑f∈F+(i)Sim(i,f)∥Ui−Uf∥F2+λ12∥U∥F2+λ22∥V∥F2\min_{U, V} L_2(R, U, V) = \frac{1}{2} \sum_{i=1}^m \sum_{j=1}^n I_{ij} (R_{ij} - U_i^T V_j)^2 + \frac{\beta}{2} \sum_{i=1}^m \sum_{f \in \mathcal{F}^+(i)} \text{Sim}(i, f) \|U_i - U_f\|_F^2 + \frac{\lambda_1}{2} \|U\|_F^2 + \frac{\lambda_2}{2} \|V\|_F^2 where β>0\beta > 0 is the social regularization weight, λ1,λ2>0\lambda_1, \lambda_2 > 0 are L2L_2 regularization parameters, and ∥⋅∥F\| \cdot \|_F denotes the Frobenius norm.

    A local minimum is computed via gradient descent on latent feature vectors UiU_i and VjV_j using the partial derivatives: ∂L2∂Ui=∑j=1nIij(UiTVj−Rij)Vj+λ1Ui+β∑f∈F+(i)Sim(i,f)(Ui−Uf)+β∑g∈F−(i)Sim(i,g)(Ui−Ug)\frac{\partial L_2}{\partial U_i} = \sum_{j=1}^n I_{ij} (U_i^T V_j - R_{ij}) V_j + \lambda_1 U_i + \beta \sum_{f \in \mathcal{F}^+(i)} \text{Sim}(i, f) (U_i - U_f) + \beta \sum_{g \in \mathcal{F}^-(i)} \text{Sim}(i, g) (U_i - U_g) ∂L2∂Vj=∑i=1mIij(UiTVj−Rij)Ui+λ2Vj\frac{\partial L_2}{\partial V_j} = \sum_{i=1}^m I_{ij} (U_i^T V_j - R_{ij}) U_i + \lambda_2 V_j

  2. Knowl 2 — Average-based Social Regularization Model (SR1)

    model/method

    The average-based social regularization model (SR1) regularizes each user's latent feature vector towards the similarity-weighted average latent feature vector of all of the user's outlink friends.

    Let R∈Rm×nR \in \mathbb{R}^{m \times n} be an observed rating matrix where Iij=1I_{ij} = 1 if user uiu_i rated item vjv_j and 00 otherwise. Let Ui∈RlU_i \in \mathbb{R}^l and Vj∈RlV_j \in \mathbb{R}^l denote the ll-dimensional latent feature vectors for user uiu_i and item vjv_j, respectively. Let F+(i)\mathcal{F}^+(i) denote the set of outlink friends of user uiu_i, F−(i)\mathcal{F}^-(i) denote the set of inlink friends of uiu_i, and Sim(i,f)∈[0,1]\text{Sim}(i, f) \in [0, 1] be the pairwise user similarity score.

    The objective function is formulated as: min⁡U,VL1(R,U,V)=12∑i=1m∑j=1nIij(Rij−UiTVj)2+α2∑i=1m∥Ui−∑f∈F+(i)Sim(i,f)Uf∑f∈F+(i)Sim(i,f)∥F2+λ12∥U∥F2+λ22∥V∥F2\min_{U, V} L_1(R, U, V) = \frac{1}{2} \sum_{i=1}^m \sum_{j=1}^n I_{ij} (R_{ij} - U_i^T V_j)^2 + \frac{\alpha}{2} \sum_{i=1}^m \left\| U_i - \frac{\sum_{f \in \mathcal{F}^+(i)} \text{Sim}(i, f) U_f}{\sum_{f \in \mathcal{F}^+(i)} \text{Sim}(i, f)} \right\|_F^2 + \frac{\lambda_1}{2} \|U\|_F^2 + \frac{\lambda_2}{2} \|V\|_F^2 where α>0\alpha > 0 governs the social regularization strength and λ1,λ2>0\lambda_1, \lambda_2 > 0 are regularizers preventing overfitting.

    The partial derivatives for gradient descent updates are: ∂L1∂Ui=∑j=1nIij(UiTVj−Rij)Vj+λ1Ui+α(Ui−∑f∈F+(i)Sim(i,f)Uf∑f∈F+(i)Sim(i,f))+α∑g∈F−(i)−Sim(i,g)(Ug−∑f∈F+(g)Sim(g,f)Uf∑f∈F+(g)Sim(g,f))∑f∈F+(g)Sim(g,f)\frac{\partial L_1}{\partial U_i} = \sum_{j=1}^n I_{ij} (U_i^T V_j - R_{ij}) V_j + \lambda_1 U_i + \alpha \left( U_i - \frac{\sum_{f \in \mathcal{F}^+(i)} \text{Sim}(i, f) U_f}{\sum_{f \in \mathcal{F}^+(i)} \text{Sim}(i, f)} \right) + \alpha \sum_{g \in \mathcal{F}^-(i)} \frac{-\text{Sim}(i, g) \left( U_g - \frac{\sum_{f \in \mathcal{F}^+(g)} \text{Sim}(g, f) U_f}{\sum_{f \in \mathcal{F}^+(g)} \text{Sim}(g, f)} \right)}{\sum_{f \in \mathcal{F}^+(g)} \text{Sim}(g, f)} ∂L1∂Vj=∑i=1mIij(UiTVj−Rij)Ui+λ2Vj\frac{\partial L_1}{\partial V_j} = \sum_{i=1}^m I_{ij} (U_i^T V_j - R_{ij}) U_i + \lambda_2 V_j

  3. Knowl 3 — User Similarity Metrics for Social Regularization

    definition

    Social regularization frameworks compute pairwise user similarity Sim(i,f)∈[0,1]\text{Sim}(i, f) \in [0, 1] over the set of items co-rated by user uiu_i and user ufu_f, denoted I(i)∩I(f)I(i) \cap I(f). Two primary formulations are used:

    1. Vector Space Similarity (VSS): SimVSS(i,f)=∑j∈I(i)∩I(f)Rij⋅Rfj∑j∈I(i)∩I(f)Rij2⋅∑j∈I(i)∩I(f)Rfj2\text{Sim}_{\text{VSS}}(i, f) = \frac{\sum_{j \in I(i) \cap I(f)} R_{ij} \cdot R_{fj}}{\sqrt{\sum_{j \in I(i) \cap I(f)} R_{ij}^2} \cdot \sqrt{\sum_{j \in I(i) \cap I(f)} R_{fj}^2}} where RijR_{ij} and RfjR_{fj} are the ratings given to item vjv_j by users uiu_i and ufu_f, respectively. SimVSS(i,f)\text{Sim}_{\text{VSS}}(i, f) naturally lies in [0,1][0, 1].

    2. Pearson Correlation Coefficient (PCC) with Linear Rescaling: To account for differences in user rating biases and scales, the Pearson Correlation Coefficient is computed: PCC(i,f)=∑j∈I(i)∩I(f)(Rij−Rˉi)(Rfj−Rˉf)∑j∈I(i)∩I(f)(Rij−Rˉi)2⋅∑j∈I(i)∩I(f)(Rfj−Rˉf)2\text{PCC}(i, f) = \frac{\sum_{j \in I(i) \cap I(f)} (R_{ij} - \bar{R}_i)(R_{fj} - \bar{R}_f)}{\sqrt{\sum_{j \in I(i) \cap I(f)} (R_{ij} - \bar{R}_i)^2} \cdot \sqrt{\sum_{j \in I(i) \cap I(f)} (R_{fj} - \bar{R}_f)^2}} where Rˉi\bar{R}_i and Rˉf\bar{R}_f are the average ratings of users uiu_i and ufu_f. Since PCC(i,f)∈[−1,1]\text{PCC}(i, f) \in [-1, 1], it is transformed into the range [0,1][0, 1] via the mapping: SimPCC(i,f)=PCC(i,f)+12\text{Sim}_{\text{PCC}}(i, f) = \frac{\text{PCC}(i, f) + 1}{2}

  4. Knowl 4 — Recommendation Performance of Social Regularization Models

    data/table

    The recommendation accuracy of the social regularization models (SR1 with VSS/PCC, SR2 with VSS/PCC) was evaluated against non-social baselines (UserMean, ItemMean, Non-negative Matrix Factorization [NMF], Probabilistic Matrix Factorization [PMF]) and a trust-aware model (RSTE). Evaluations were conducted with latent dimensionality l=10l=10, regularizers λ1=λ2=0.001\lambda_1 = \lambda_2 = 0.001, and social regularization parameters α=β=0.001\alpha = \beta = 0.001 on Douban (129,490 users, 58,541 movies, 16,830,839 ratings, 1,692,952 social edges) and α=β=0.01\alpha = \beta = 0.01 on Epinions (51,670 users, 83,509 items, 631,064 ratings, 511,799 trust edges).

    Dataset Training Metrics UserMean ItemMean NMF PMF RSTE SR1vss_{\text{vss}} SR1pcc_{\text{pcc}} SR2vss_{\text{vss}} SR2pcc_{\text{pcc}}
    Douban 80% MAE 0.6809 0.6288 0.5732 0.5693 0.5643 0.5579 0.5576 0.5548 0.5543
    RMSE 0.8480 0.7898 0.7225 0.7200 0.7144 0.7026 0.7022 0.6992 0.6988
    60% MAE 0.6823 0.6300 0.5768 0.5737 0.5698 0.5627 0.5623 0.5597 0.5593
    RMSE 0.8505 0.7926 0.7351 0.7290 0.7207 0.7081 0.7078 0.7046 0.7042
    40% MAE 0.6854 0.6317 0.5899 0.5868 0.5767 0.5706 0.5702 0.5690 0.5685
    RMSE 0.8567 0.7971 0.7482 0.7411 0.7295 0.7172 0.7169 0.7129 0.7125
    Epinions 90% MAE 0.9134 0.9768 0.8712 0.8651 0.8367 0.8290 0.8287 0.8258 0.8256
    RMSE 1.1688 1.2375 1.1621 1.1544 1.1094 1.0792 1.0790 1.0744 1.0739
    80% MAE 0.9285 0.9913 0.8951 0.8886 0.8537 0.8493 0.8491 0.8447 0.8443
    RMSE 1.1817 1.2584 1.1832 1.1760 1.1256 1.1016 1.1013 1.0958 1.0954

    SR2 consistently achieves lower MAE and RMSE than SR1 across all train/test splits on both datasets. Furthermore, similarity weighting using PCC slightly outperforms VSS in all configurations.

  5. Knowl 5 — Sensitivity of Recommendation Error to Social Regularization Hyperparameters

    empirical result

    The hyperparameters α\alpha (in SR1) and β\beta (in SR2) control the balance between fitting observed ratings and enforcing social regularization constraints. When varying β\beta across the range from 10−610^{-6} to 10010^0 on Douban (at 40%, 60%, and 80% training ratios) and Epinions (at 80% and 90% training ratios):

    1. As β\beta increases from very small values (10−610^{-6}), MAE and RMSE monotonically decrease as social constraints provide informative regularization.
    2. When β\beta surpasses a dataset-dependent threshold (yielding point), prediction errors begin to increase because excessive regularization causes the social graph topology to dominate the user-item rating signal.
    3. The optimal recommendation performance is achieved at β≈0.001\beta \approx 0.001 for Douban and β≈0.01\beta \approx 0.01 for Epinions. The impact of parameter α\alpha exhibits the same convex error curve.

  6. Knowl 6 — Effect of User Similarity Weighting versus Unweighted Social Relations

    data/table

    An ablation study evaluated the necessity of distinguishing friend tastes using similarity metrics in model SR2 (with latent factor dimension l=10l=10). Performance under PCC (extSR2pcc ext{SR2}_{\text{pcc}}) and VSS (extSR2vss ext{SR2}_{\text{vss}}) was compared to two unweighted/degraded variants: setting all friend similarities to 1 (Sim=1\text{Sim}=1) and assigning uniform random similarities drawn from [0,1][0, 1] (Sim=Ran\text{Sim}=\text{Ran}).

    Dataset Training Metrics SR2 (Sim=1) SR2 (Sim=Ran) SR2vss_{\text{vss}} SR2pcc_{\text{pcc}}
    Douban 80% MAE 0.5579 0.5592 0.5548 0.5543
    RMSE 0.7034 0.7047 0.6992 0.6988
    60% MAE 0.5631 0.5643 0.5597 0.5593
    RMSE 0.7083 0.7098 0.7046 0.7042
    40% MAE 0.5724 0.5737 0.5690 0.5685
    RMSE 0.7195 0.7209 0.7129 0.7125
    Epinions 90% MAE 0.8324 0.8345 0.8258 0.8256
    RMSE 1.0794 1.0809 1.0744 1.0739
    80% MAE 0.8511 0.8530 0.8447 0.8443
    RMSE 1.1002 1.1018 1.0958 1.0954

    Both Sim=1\text{Sim}=1 and Sim=Ran\text{Sim}=\text{Ran} yield higher MAE and RMSE than SR2vss\text{SR2}_{\text{vss}} and SR2pcc\text{SR2}_{\text{pcc}}, demonstrating that weighting social relations by rating-based similarity is essential to capture the taste diversity among a user's social connections.

  7. Knowl 7 — Distinction Between Social Friend Networks and Trust Networks in Recommendation

    definition

    Social recommendation and trust-aware recommendation differ in network properties and behavioral assumptions:

    1. Edge Reciprocity: Real-world social friend networks (e.g., Facebook, Douban) consist of bidirectional, cooperative relationships where outlinks equal inlinks (F+(i)=F−(i)\mathcal{F}^+(i) = \mathcal{F}^-(i)). Trust networks (e.g., Epinions) are unilateral/directed, where uiu_i trusting ufu_f does not imply ufu_f trusts uiu_i (F+(i)≠F−(i)\mathcal{F}^+(i) \neq \mathcal{F}^-(i)).
    2. Taste Homogeneity: Trust-aware systems assume that a user shares similar tastes with trusted users. Social recommender systems recognize that real-world friends often have diverse, dissimilar tastes, necessitating explicit similarity weighting rather than assuming uniform taste alignment.

  8. Knowl 8 — Limitations in Friend Selection and Item-Side Information Modeling

    limitation

    The social regularization framework has two primary limitations:

    1. Global Friend Inclusion: The models incorporate all social connections F+(i)\mathcal{F}^+(i) for each user. In real-world scenarios, users consult specific subsets of friends depending on domain expertise (e.g., asking movie enthusiast friends for movie suggestions), so non-selective inclusion of all friends can introduce noise.
    2. User-Centric Regularization: Regularization terms are applied exclusively to user latent vectors UU, while item latent vectors VV only receive standard Frobenius norm penalties. Auxiliary item relationships (e.g., item tags, categories, genres) are not regularized on the item side.

Coverage note — None was omitted; all key models (SR1, SR2), similarity functions, experimental comparisons, ablation studies, hyperparameter analyses, definitions, and limitations were extracted.

References

  1. 1.D. Agarwal and B.-C. Chen. flda: matrix factorization through latent dirichlet allocation. In Proc. of WSDM '10, pages 91–100, New York, New York, USA, 2010.
  2. 2.P. Bedi, H. Kaur, and S. Marwaha. Trust based recommender system for semantic web. In Proc. of IJCAI'07, pages 2677–2682, 2007.
  3. 3.R. Bell, Y. Koren, and C. Volinsky. Modeling relationships at multiple scales to improve accuracy of large recommender systems. In Proc. of KDD '07, pages 95–104, San Jose, California, USA, 2007.
  4. 4.J. S. Breese, D. Heckerman, and C. Kadie. Empirical analysis of predictive algorithms for collaborative filtering. In Proc. of UAI '98, 1998.
  5. 5.J. Canny. Collaborative filtering with privacy via factor analysis. In Proc. of SIGIR '02, pages 238–245, Tampere, Finland, 2002.
  6. 6.M. Deshpande and G. Karypis. Item-based top-n recommendation. ACM Transactions on Information Systems, 22(1):143–177, 2004.
  7. 7.I. Guy, N. Zwerdling, D. Carmel, I. Ronen, E. Uziel, S. Yogev, and S. Ofek-Koifman. Personalized recommendation of social software items based on social relations. In Proc. of RecSys '09, pages 53–60, New York, New York, USA, 2009.
  8. 8.T. Hofmann. Collaborative filtering via gaussian probabilistic latent semantic analysis. In Proc. of SIGIR '03, pages 259–266, Toronto, Canada, 2003.
  9. 9.T. Hofmann. Latent semantic models for collaborative filtering. ACM Transactions on Information Systems, 22(1):89–115, 2004.
  10. 10.Z. Huang, H. Chen, and D. Zeng. Applying associative retrieval techniques to alleviate the sparsity problem in collaborative filtering. ACM Trans. Inf. Syst., 22(1):116–142, 2004.
  11. 11.M. Jahrer, A. T¨oscher, and R. Legenstein. Combining predictions for accurate recommender systems. In Proc. of KDD '10, pages 693–702, Washington, DC, USA, 2010.
  12. 12.R. Jin, J. Y. Chai, and L. Si. An automatic weighting scheme for collaborative filtering. In Proc. of SIGIR '04, pages 337–344, Sheffield, United Kingdom, 2004.
  13. 13.A. Kohrs and B. Merialdo. Clustering for collaborative filtering applications. In Proceedings of CIMCA, 1999.
  14. 14.Y. Koren. Factorization meets the neighborhood: a multifaceted collaborative filtering model. In Proc. of KDD '08, pages 426–434, Las Vegas, Nevada, USA, 2008.
  15. 15.Y. Koren. Collaborative filtering with temporal dynamics. In Proc. of KDD '09, pages 447–456, Paris, France, 2009.
  16. 16.D. D. Lee and H. S. Seung. Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755):788–791, Oct. 1999.
  17. 17.G. Linden, B. Smith, and J. York. Amazon.com recommendations: Item-to-item collaborative filtering. IEEE Internet Computing, pages 76–80, Jan/Feb 2003.
  18. 18.F. Liu and H. J. Lee. Use of social network information to enhance collaborative filtering performance. Expert Syst. Appl., 37(7):4772–4778, 2010.
  19. 19.N. N. Liu and Q. Yang. Eigenrank: a ranking-oriented approach to collaborative filtering. In Proc. of SIGIR '08, pages 83–90, Singapore, Singapore, 2008.
  20. 20.Y. Lu, P. Tsaparas, A. Ntoulas, and L. Polanyi. Exploiting social context for review quality prediction. In Proc. of WWW '10, pages 691–700, Raleigh, North Carolina, USA, 2010.
  21. 21.H. Ma, I. King, and M. R. Lyu. Effective missing data prediction for collaborative filtering. In Proc. of SIGIR '07, pages 39–46, Amsterdam, The Netherlands, 2007.
  22. 22.H. Ma, I. King, and M. R. Lyu. Learning to recommend with social trust ensemble. In Proc. of SIGIR '09, pages 203–210, Boston, MA, USA, 2009.
  23. 23.H. Ma, H. Yang, M. R. Lyu, and I. King. SoRec: Social recommendation using probabilistic matrix factorization. In Proc. of CIKM '08, pages 931–940, Napa Valley, USA, 2008.
  24. 24.P. Massa and P. Avesani. Trust-aware collaborative filtering for recommender systems. In Proceedings of CoopIS/DOA/ODBASE, pages 492–508, 2004.
  25. 25.P. Massa and P. Avesani. Trust-aware recommender systems. In Proc. of RecSys '07, pages 17–24, Minneapolis, MN, USA, 2007.
  26. 26.Q. Mei, D. Cai, D. Zhang, and C. Zhai. Topic modeling with network regularization. In Proc. of WWW '08, pages 101–110, Beijing, China, 2008.
  27. 27.J. O’Donovan and B. Smyth. Trust in recommender systems. In Proc. of IUI '05, pages 167–174, San Diego, California, USA, 2005.
  28. 28.J. D. M. Rennie and N. Srebro. Fast maximum margin matrix factorization for collaborative prediction. In Proc. of ICML '05, 2005.
  29. 29.P. Resnick, N. Iacovou, M. Suchak, P. Bergstrom, and J. Riedl. Grouplens: An open architecture for collaborative filtering of netnews. In Proc. of CSCW '94, 1994.
  30. 30.R. Salakhutdinov and A. Mnih. Bayesian probabilistic matrix factorization using markov chain monte carlo. In Proc. of ICML '08, 2008.
  31. 31.R. Salakhutdinov and A. Mnih. Probabilistic matrix factorization. In Advances in Neural Information Processing Systems, volume 20, 2008.
  32. 32.B. Sarwar, G. Karypis, J. Konstan, and J. Reidl. Item-based collaborative filtering recommendation algorithms. In Proc. of WWW '01, pages 285–295, Hong Kong, Hong Kong, 2001.
  33. 33.L. Si and R. Jin. Flexible mixture model for collaborative filtering. In Proc. of ICML '03, 2003.
  34. 34.N. Srebro and T. Jaakkola. Weighted low-rank approximations. In Proc. of ICML '03, pages 720–727, 2003.
  35. 35.N. Srebro, J. D. M. Rennie, and T. Jaakkola. Maximum-margin matrix factorization. In NIPS, 2004.
  36. 36.J. Wang, A. P. de Vries, and M. J. T. Reinders. Unifying user-based and item-based collaborative filtering approaches by similarity fusion. In Proc. of SIGIR '06, pages 501–508, Seattle, Washington, USA, 2006.
  37. 37.X. Xin, I. King, H. Deng, and M. R. Lyu. A social recommendation framework based on multi-scale continuous conditional random fields. In Proc. of CIKM '09, pages 1247–1256, Hong Kong, China, 2009.
  38. 38.G.-R. Xue, C. Lin, Q. Yang, W. Xi, H.-J. Zeng, Y. Yu, and Z. Chen. Scalable collaborative filtering using cluster-based smoothing. In Proc. of SIGIR '05, pages 114–121, Salvador, Brazil, 2005.
  39. 39.K. Yu, S. Zhu, J. Lafferty, and Y. Gong. Fast nonparametric matrix factorization for large-scale collaborative filtering. In Proc. of SIGIR '09, pages 211–218, Boston, MA, USA, 2009.
  40. 40.Y. Zhang and J. Koren. Efficient bayesian hierarchical user modeling for recommendation system. In Proc. of SIGIR '07, pages 47–54, Amsterdam, The Netherlands, 2007.
  41. 41.S. Zhu, K. Yu, and Y. Gong. Stochastic relational models for large-scale dyadic data using mcmc. In Advances in Neural Information Processing Systems, volume 21, 2009.

Citation

MLA
Ma, H., et al. “Recommender Systems with Social Regularization”. Proceedings of the Fourth ACM International Conference on Web Search and Data Mining, 2011, pp. 287–96, https://doi.org/10.1145/1935826.1935877.
APA
Ma, H., Zhou, D., Liu, C., Lyu, M. R., & King, I. (2011). Recommender systems with social regularization. Proceedings of the Fourth ACM International Conference on Web Search and Data Mining, 287–296. https://doi.org/10.1145/1935826.1935877
Chicago
Ma, H., D. Zhou, C. Liu, M. R. Lyu, and I. King. 2011. “Recommender Systems with Social Regularization”. Proceedings of the Fourth ACM International Conference on Web Search and Data Mining, 287–96. https://doi.org/10.1145/1935826.1935877.
Harvard
Ma, H. et al. (2011) “Recommender systems with social regularization”, Proceedings of the fourth ACM international conference on Web search and data mining. ACM, pp. 287–296. Available at: https://doi.org/10.1145/1935826.1935877.
Vancouver
1. Ma H, Zhou D, Liu C, Lyu MR, King I (2011) Recommender systems with social regularization. In: Proceedings of the fourth ACM international conference on Web search and data mining. ACM, pp 287–296

BibTeX

@inproceedings{Ma_2011, series={WSDM′11}, title={Recommender systems with social regularization}, url={http://dx.doi.org/10.1145/1935826.1935877}, DOI={10.1145/1935826.1935877}, booktitle={Proceedings of the fourth ACM international conference on Web search and data mining}, publisher={ACM}, author={Ma, Hao and Zhou, Dengyong and Liu, Chao and Lyu, Michael R. and King, Irwin}, year={2011}, month=Feb, pages={287–296}, collection={WSDM′11} }
Metadata:Crossref

Access the Paper

This paper is available from its original source. Click below to access the PDF.

Open PDF