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A matrix factorization technique with trust propagation for recommendation in social networks

Mohsen JamaliMartin Ester

article2010RecSys1,726 citations

Proposes SocialMF, a matrix factorization framework that incorporates trust propagation into user latent feature learning to significantly improve rating prediction accuracy for cold start users in social networks.

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Online platforms increasingly rely on recommender systems to guide users through massive catalogs of products, media, and services. While traditional collaborative filtering relies primarily on past user ratings, it struggles severely with cold start users who have rated few or no items. Although modern platforms can leverage social networks to infer preferences, previous model-based techniques failed to capture trust propagation—the indirect social influence that travels across multi-step connections in a network. Addressing this limitation is critical for improving personalization and user engagement across modern social platforms.

The article develops and evaluates SocialMF, a model-based recommendation framework that incorporates social trust propagation directly into a matrix factorization approach. The primary objective is to demonstrate that aligning a user's latent preference profile with those of their direct and indirect social connections significantly improves recommendation accuracy, particularly for users with sparse rating histories.

To evaluate this approach, the authors conducted five-fold cross-validation experiments comparing SocialMF against standard collaborative filtering, baseline matrix factorization, and the existing state-of-the-art social model (STE). The evaluation utilized two real-world datasets: the public Epinions platform (comprising 71,000 users and 575,000 ratings across general consumer categories) and a newly crawled, large-scale Flixster dataset (covering 1 million users and 8.2 million movie ratings collected between November 2005 and November 2009).

The findings confirm that modeling trust propagation provides substantial performance and efficiency gains. First, SocialMF consistently outperformed all baseline methods, reducing overall recommendation error by roughly 5% to 6% compared to STE and achieving more than double the improvement that STE provided over baseline factorization. Second, the accuracy gains were most pronounced for cold start users, reducing prediction errors by 11.5% on Epinions and 8.5% on Flixster compared to STE. Third, SocialMF proved drastically faster in training and execution; on the massive Flixster dataset, total model training completed in 5.5 hours compared to 9 days for STE—an acceleration factor of approximately 40 times due to lower gradient computational complexity.

These results demonstrate that trust propagation is a vital mechanism for commercial recommender systems. By enabling the system to infer meaningful preferences for users with zero or few ratings based solely on their social ties, organizations can mitigate the cold start problem and boost early user retention. Furthermore, the massive reduction in computational overhead lowers cloud and infrastructure costs while making frequent model retraining practical for large-scale enterprise deployments.

Organizations operating social-enabled platforms should consider integrating trust propagation architectures like SocialMF into their recommendation pipelines, especially where cold start drop-off is high. However, decision-makers should note key limitations: the model currently does not address cold start items (new products with no ratings), cannot natively account for negative social ties (distrust), and requires manual tuning of the social influence weighting parameter. Further development should focus on automated parameter tuning, incorporating item-side cold start handling, and extending the framework to support signed networks before broad deployment.

Simon Fraser Universitycold start problemscollaborative filteringcross validationmatrix factorizationtrust propagationSocialMF
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Abstract

Recommender systems are becoming tools of choice to select the online information relevant to a given user. Collaborative filtering is the most popular approach to building recommender systems and has been successfully employed in many applications. With the advent of online social networks, the social network based approach to recommendation has emerged. This approach assumes a social network among users and makes recommendations for a user based on the ratings of the users that have direct or indirect social relations with the given user. As one of their major benefits, social network based approaches have been shown to reduce the problems with cold start users. In this paper, we explore a model-based approach for recommendation in social networks, employing matrix factorization techniques. Advancing previous work, we incorporate the mechanism of trust propagation into the model. Trust propagation has been shown to be a crucial phenomenon in the social sciences, in social network analysis and in trust-based recommendation. We have conducted experiments on two real life data sets, the public domain Epinions.com dataset and a much larger dataset that we have recently crawled from Flixster.com. Our experiments demonstrate that modeling trust propagation leads to a substantial increase in recommendation accuracy, in particular for cold start users.

Topics

cold start problemscollaborative filteringcross validationmatrix factorizationspersonalizationsrecommendationrecommendation accuracysocial influenceuser ratingvalidation

Keywords

matrix factorizationtrust propagationSocialMFtrust-based recommendationsocial rating networkcollaborative filteringuser-item rating matrixcold start users

Table of Contents

  • 1. INTRODUCTION
  • 2. PROBLEM DEFINITION AND PRELIMINARIES
  • 3. RELATED WORK
  • 4. THE SOCIALMF MODEL
  • 4.1 Desirable properties of the proposed model
  • 4.2 Complexity analysis of parameter learning
  • 5. DATASETS
  • 5.1 Flixster dataset
  • 5.2 Epinions dataset
  • 6. EXPERIMENTS
  • 6.1 Experimental Setup
  • 6.2 Experimental Results
  • 6.3 Impact of λ T on the results
  • 6.4 Performance on cold start users
  • 6.5 Analysis of learning runtime
  • 7. CONCLUSIONS AND FUTURE WORK
  • 8. REFERENCES

Knowls

  1. Knowl 1 — SocialMF Probabilistic Formulation for Recommendation with Trust Propagation

    model/method

    SocialMF is a probabilistic matrix factorization framework that incorporates trust propagation into user latent feature learning. Given a set of NN users U={u1,…,uN}\mathcal{U} = \{u_1, \dots, u_N\} and MM items I={i1,…,iM}\mathcal{I} = \{i_1, \dots, i_M\}, the observed ratings are denoted by an N×MN \times M rating matrix R=[Ru,i]R = [R_{u,i}], where ratings are normalized to the interval [0,1][0, 1]. Social trust relationships are given by an N×NN \times N matrix T=[Tu,v]T = [T_{u,v}], where Tu,v∈[0,1]T_{u,v} \in [0, 1] represents the direct trust user uu has in user vv, row-normalized such that ∑v∈NuTu,v=1\sum_{v \in \mathcal{N}_u} T_{u,v} = 1 for the set of direct trust neighbors Nu\mathcal{N}_u of user uu.

    The model factorizes the user-item interaction using KK-dimensional latent user vectors Uu∈RKU_u \in \mathbb{R}^K (columns of U∈RK×NU \in \mathbb{R}^{K \times N}) and latent item vectors Vi∈RKV_i \in \mathbb{R}^K (columns of V∈RK×MV \in \mathbb{R}^{K \times M}).

    The conditional probability of the observed ratings is defined as: p(R∣U,V,σR2)=∏u=1N∏i=1M[N(Ru,i∣g(UuTVi),σR2)]Iu,iRp(R \mid U, V, \sigma_R^2) = \prod_{u=1}^N \prod_{i=1}^M \left[ \mathcal{N}\left(R_{u,i} \mid g(U_u^T V_i), \sigma_R^2\right) \right]^{I^R_{u,i}} where N(x∣μ,σ2)\mathcal{N}(x \mid \mu, \sigma^2) is the Gaussian distribution, Iu,iRI^R_{u,i} is an indicator function equal to 11 if user uu rated item ii and 00 otherwise, and g(x)=11+e−xg(x) = \frac{1}{1 + e^{-x}} is the logistic sigmoid function mapping predictions to [0,1][0, 1].

    To model trust propagation and social influence, the latent feature vector UuU_u of user uu is conditioned on the weighted average of the feature vectors of uu's direct neighbors U^u=∑v∈NuTu,vUv\widehat{U}_u = \sum_{v \in \mathcal{N}_u} T_{u,v} U_v, combined with a zero-mean Gaussian prior: p(U∣T,σU2,σT2)∝∏u=1NN(Uu∣0,σU2I)×∏u=1NN(Uu∣∑v∈NuTu,vUv,σT2I)p(U \mid T, \sigma_U^2, \sigma_T^2) \propto \prod_{u=1}^N \mathcal{N}\left(U_u \mid 0, \sigma_U^2 I\right) \times \prod_{u=1}^N \mathcal{N}\left(U_u \mid \sum_{v \in \mathcal{N}_u} T_{u,v} U_v, \sigma_T^2 I\right) where II is the K×KK \times K identity matrix.

    The item latent feature matrix VV follows a zero-mean Gaussian prior: p(V∣σV2)=∏i=1MN(Vi∣0,σV2I)p(V \mid \sigma_V^2) = \prod_{i=1}^M \mathcal{N}\left(V_i \mid 0, \sigma_V^2 I\right)

    Because the direct neighbors' latent vectors are in turn conditioned on their own direct neighbors' latent vectors, trust propagates recursively through indirect social connections in the network.

  2. Knowl 2 — SocialMF Optimization Objective Function

    equation

    Under the SocialMF probabilistic model, maximizing the log-posterior probability ln⁡p(U,V∣R,T,σR2,σT2,σU2,σV2)\ln p(U, V \mid R, T, \sigma_R^2, \sigma_T^2, \sigma_U^2, \sigma_V^2) with fixed noise and prior variances is equivalent to minimizing the regularized sum-of-squared-errors loss function L(R,T,U,V)\mathcal{L}(R, T, U, V):

    L(R,T,U,V)=12∑u=1N∑i=1MIu,iR(Ru,i−g(UuTVi))2+λU2∑u=1NUuTUu+λV2∑i=1MViTVi+λT2∑u=1N(Uu−∑v∈NuTu,vUv)T(Uu−∑v∈NuTu,vUv)\mathcal{L}(R, T, U, V) = \frac{1}{2} \sum_{u=1}^N \sum_{i=1}^M I^R_{u,i} \left(R_{u,i} - g(U_u^T V_i)\right)^2 + \frac{\lambda_U}{2} \sum_{u=1}^N U_u^T U_u + \frac{\lambda_V}{2} \sum_{i=1}^M V_i^T V_i + \frac{\lambda_T}{2} \sum_{u=1}^N \left( U_u - \sum_{v \in \mathcal{N}_u} T_{u,v} U_v \right)^T \left( U_u - \sum_{v \in \mathcal{N}_u} T_{u,v} U_v \right)

    where:

    • NN is the number of users and MM is the number of items.
    • Uu∈RKU_u \in \mathbb{R}^K and Vi∈RKV_i \in \mathbb{R}^K are KK-dimensional latent feature vectors for user uu and item ii, respectively.
    • Ru,i∈[0,1]R_{u,i} \in [0, 1] is the normalized observed rating of user uu on item ii.
    • Iu,iR∈{0,1}I^R_{u,i} \in \{0, 1\} is an indicator variable denoting whether user uu has rated item ii.
    • g(x)=11+e−xg(x) = \frac{1}{1 + e^{-x}} is the logistic sigmoid function.
    • Nu\mathcal{N}_u is the set of direct social trust neighbors of user uu.
    • Tu,v∈[0,1]T_{u,v} \in [0, 1] is the row-normalized trust weight user uu assigns to neighbor vv, satisfying ∑v∈NuTu,v=1\sum_{v \in \mathcal{N}_u} T_{u,v} = 1.
    • λU=σR2/σU2\lambda_U = \sigma_R^2 / \sigma_U^2, λV=σR2/σV2\lambda_V = \sigma_R^2 / \sigma_V^2, and λT=σR2/σT2\lambda_T = \sigma_R^2 / \sigma_T^2 are regularizers corresponding to the user prior, item prior, and social trust network constraint, respectively (with λU=λV\lambda_U = \lambda_V in practice).

  3. Knowl 3 — Gradient Descent Optimization for SocialMF

    algorithm

    To minimize the SocialMF objective function L(R,T,U,V)\mathcal{L}(R, T, U, V), gradient descent updates the latent feature matrices U∈RK×NU \in \mathbb{R}^{K \times N} and V∈RK×MV \in \mathbb{R}^{K \times M}. The partial derivatives with respect to user latent vector UuU_u and item latent vector ViV_i are:

    ∂L∂Uu=∑i=1MIu,iRVig′(UuTVi)(g(UuTVi)−Ru,i)+λUUu+λT(Uu−∑v∈NuTu,vUv)−λT∑{v∣u∈Nv}Tv,u(Uv−∑w∈NvTv,wUw)\frac{\partial \mathcal{L}}{\partial U_u} = \sum_{i=1}^M I^R_{u,i} V_i g'(U_u^T V_i) \left(g(U_u^T V_i) - R_{u,i}\right) + \lambda_U U_u + \lambda_T \left( U_u - \sum_{v \in \mathcal{N}_u} T_{u,v} U_v \right) - \lambda_T \sum_{\{v \mid u \in \mathcal{N}_v\}} T_{v,u} \left( U_v - \sum_{w \in \mathcal{N}_v} T_{v,w} Uw \right)

    ∂L∂Vi=∑u=1NIu,iRUug′(UuTVi)(g(UuTVi)−Ru,i)+λVVi\frac{\partial \mathcal{L}}{\partial V_i} = \sum_{u=1}^N I^R_{u,i} U_u g'(U_u^T V_i) \left(g(U_u^T V_i) - R_{u,i}\right) + \lambda_V V_i

    where g′(x)=e−x(1+e−x)2g'(x) = \frac{e^{-x}}{(1 + e^{-x})^2} is the derivative of the logistic function g(x)g(x), and {v∣u∈Nv}\{v \mid u \in \mathcal{N}_v\} denotes the set of users who directly place trust in user uu.

    Input: Rating matrix RR, row-normalized trust matrix TT, latent dimension KK, learning rate γ\gamma, regularization parameters λU,λV,λT\lambda_U, \lambda_V, \lambda_T, maximum iterations MaxIterMaxIter
    Output: User latent matrix U∈RK×NU \in \mathbb{R}^{K \times N}, Item latent matrix V∈RK×MV \in \mathbb{R}^{K \times M}
    Initialize UU and VV with random zero-mean Gaussian noise
    for iter=1iter = 1 to MaxIterMaxIter do
        for each user u∈Uu \in \mathcal{U} do
            Compute ∇UuL=∑i=1MIu,iRVig′(UuTVi)(g(UuTVi)−Ru,i)+λUUu+λT(Uu−∑v∈NuTu,vUv)−λT∑{v∣u∈Nv}Tv,u(Uv−∑w∈NvTv,wUw)\nabla_{U_u} \mathcal{L} = \sum_{i=1}^M I^R_{u,i} V_i g'(U_u^T V_i)(g(U_u^T V_i) - R_{u,i}) + \lambda_U U_u + \lambda_T (U_u - \sum_{v \in \mathcal{N}_u} T_{u,v} U_v) - \lambda_T \sum_{\{v \mid u \in \mathcal{N}_v\}} T_{v,u} (U_v - \sum_{w \in \mathcal{N}_v} T_{v,w} U_w)
        end for
        for each item i∈Ii \in \mathcal{I} do
            Compute ∇ViL=∑u=1NIu,iRUug′(UuTVi)(g(UuTVi)−Ru,i)+λVVi\nabla_{V_i} \mathcal{L} = \sum_{u=1}^N I^R_{u,i} U_u g'(U_u^T V_i)(g(U_u^T V_i) - R_{u,i}) + \lambda_V V_i
        end for
        for each user u∈Uu \in \mathcal{U} do
            Uu←Uu−γ∇UuLU_u \leftarrow U_u - \gamma \nabla_{U_u} \mathcal{L}
        end for
        for each item i∈Ii \in \mathcal{I} do
            Vi←Vi−γ∇ViLV_i \leftarrow V_i - \gamma \nabla_{V_i} \mathcal{L}
        end for
        if converged then
            break
        end if
    end for
    return U,VU, V

  4. Knowl 4 — Computational Complexity and Inference Efficiency of SocialMF

    theoretical result

    Let NN denote the total number of users, KK the latent feature dimensionality, rˉ\bar{r} the average number of ratings per user, and tˉ\bar{t} the average number of direct trust neighbors per user.

    1. Objective Function Evaluation Complexity: Evaluating the SocialMF loss L\mathcal{L} requires O(NrˉK+NtˉK)\mathcal{O}(N \bar{r} K + N \bar{t} K) operations. Because rating and trust matrices in social rating networks are sparse, rˉ\bar{r} and tˉ\bar{t} are small constants relative to NN, making objective evaluation strictly linear in the number of users NN.
    2. Gradient Computation Complexity: Computing analytical gradients ∂L∂Uu\frac{\partial \mathcal{L}}{\partial U_u} and ∂L∂Vi\frac{\partial \mathcal{L}}{\partial V_i} across all users and items has time complexity O(NrˉK+Ntˉ2K)\mathcal{O}(N \bar{r} K + N \bar{t}^2 K), which is linear in NN. In comparison, the Social Trust Ensemble (STE) model incurs a gradient complexity of O(Nrˉtˉ2K)\mathcal{O}(N \bar{r} \bar{t}^2 K). Therefore, SocialMF is theoretically faster than STE per gradient iteration by a factor of: rˉtˉ2rˉ+tˉ2\frac{\bar{r} \bar{t}^2}{\bar{r} + \bar{t}^2}
    3. Prediction / Inference Complexity: In SocialMF, the predicted rating for user uu on item ii is computed directly as R^u,i=g(UuTVi)\widehat{R}_{u,i} = g(U_u^T V_i) in O(K)\mathcal{O}(K) time. STE requires taking an average of estimated ratings across all direct neighbors via g(αUuTVi+(1−α)∑v∈NuTu,vUvTVi)g\left(\alpha U_u^T V_i + (1 - \alpha)\sum_{v \in \mathcal{N}_u} T_{u,v} U_v^T V_i\right), requiring O(∣Nu∣K)\mathcal{O}(|\mathcal{N}_u| K) time per prediction.

  5. Knowl 5 — Flixster and Epinions Social Rating Network Datasets

    data/table

    The empirical evaluation was conducted on two real-world datasets: the public Epinions dataset and a dataset crawled from Flixster.com (spanning November 2005 to November 2009). In Flixster, social connections are undirected friendship relations, whereas Epinions features directed trust relations. To prevent bias from promotional Facebook/Myspace app ratings, ratings for the top 50 initial default movies on Flixster were removed, and non-numerical ratings ("Want To See", "Not Interested") were excluded, leaving ratings in [0.5,5.0][0.5, 5.0] with step 0.5. Epinions contains items across multiple product categories (e.g., cameras, DVD players, software), while Flixster items are exclusively movies.

    Statistics Flixster Epinions
    Users 1,000,000 71,000
    Social Relations 26,700,000 508,000
    Ratings 8,200,000 575,000
    Items 49,000 104,000
    Users with Rating 150,000 47,000
    Users with Friend 980,000 60,000

    In Flixster, active users who rated at least one movie have an average of 55 ratings. Furthermore, 850,000 users in Flixster participate exclusively in the social network with zero ratings, emphasizing the need for models that propagate latent representations across trust paths.

  6. Knowl 6 — Overall Rating Prediction Performance Across Latent Dimensions

    empirical result

    SocialMF was evaluated against User-Based Collaborative Filtering (CF), Baseline Probabilistic Matrix Factorization (BaseMF), and Social Trust Ensemble (STE, with α=0.4\alpha = 0.4) using 5-fold cross-validation (80% training, 20% test). Regularization parameters were set to λU=λV=0.1\lambda_U = \lambda_V = 0.1, with λT=5\lambda_T = 5 for Epinions and λT=1\lambda_T = 1 for Flixster.

    Epinions Flixster
    Method K=5K=5 K=10K=10 K=5K=5 K=10K=10
    CF 1.180 1.180 0.911 0.911
    BaseMF 1.175 1.195 0.878 0.863
    STE 1.145 1.150 0.864 0.852
    SocialMF 1.075 1.085 0.821 0.815

    SocialMF achieves the lowest Root Mean Squared Error (RMSE) across both datasets:

    • On Epinions, SocialMF reduces RMSE by 6.2% (K=5K=5) and 5.7% (K=10K=10) relative to STE. The error reduction of SocialMF over STE is more than twice the gain of STE over BaseMF (2.5%).
    • On Flixster, SocialMF improves RMSE over STE by 5.0% (K=5K=5), which is more than three times the gain of STE over BaseMF (1.5%).
    • Increasing KK from 5 to 10 improves prediction on Flixster due to dataset size and density, but leads to slight overfitting and higher RMSE on the smaller Epinions dataset.

  7. Knowl 7 — Recommendation Accuracy on Cold Start Users

    empirical result

    Cold start users are defined as users who have expressed fewer than 5 ratings. In both the Epinions and Flixster datasets, cold start users constitute more than 50% of all users with ratings. SocialMF leverages social trust propagation to constrain the latent representations of cold start users toward the representations of their direct neighbors ∑v∈NuTu,vUv\sum_{v \in \mathcal{N}_u} T_{u,v} U_v, enabling effective feature learning despite rating sparsity.

    The table below reports the Root Mean Squared Error (RMSE) on cold start users for latent dimensionality K=5K = 5:

    Method Epinions Flixster
    CF 1.361 1.228
    BaseMF 1.352 1.213
    STE 1.295 1.152
    SocialMF 1.159 1.057

    SocialMF outperforms all baseline models on cold start users:

    • On Epinions, SocialMF achieves an RMSE of 1.159, representing an 11.5% reduction in error over STE (1.295) and a 14.3% reduction over BaseMF (1.352).
    • On Flixster, SocialMF achieves an RMSE of 1.057, representing an 8.5% reduction in error over STE (1.152) and a 12.9% reduction over BaseMF (1.213).
    • The relative performance gain of SocialMF over STE on cold start users (11.5% on Epinions, 8.5% on Flixster) is substantially higher than the gain on the entire user population (6.2% on Epinions, 5.0% on Flixster), confirming the effectiveness of trust propagation under extreme rating sparsity.

  8. Knowl 8 — Impact of the Social Regularization Parameter $\lambda_T$ on Prediction Error

    empirical result

    The regularization hyperparameter λT=σR2/σT2\lambda_T = \sigma_R^2 / \sigma_T^2 governs the trade-off between fitting observed ratings and aligning user feature vectors with the average of their direct social neighbors in SocialMF.

    • As λT→0\lambda_T \to 0, social network influence vanishes, causing the model to revert to standard matrix factorization (BaseMF).
    • For very large λT\lambda_T, the objective function becomes dominated by neighbor proximity, sacrificing rating reconstruction accuracy.

    Evaluating λT∈[0.1,20]\lambda_T \in [0.1, 20] under 5-fold cross-validation shows distinct optimal settings per dataset:

    • Epinions: RMSE decreases steadily from ≈1.175\approx 1.175 at λT=0.1\lambda_T = 0.1 to a minimum of 1.0751.075 at λT=5\lambda_T = 5, and then rises sharply to over 1.251.25 for λT≥10\lambda_T \ge 10.
    • Flixster: RMSE achieves its global minimum of 0.8210.821 at λT=1\lambda_T = 1, and then increases monotonically as λT\lambda_T increases from 11 to 2020 (reaching ≈0.88\approx 0.88 at λT=20\lambda_T = 20).

  9. Knowl 9 — Training Runtime and Convergence Comparison Between SocialMF and STE

    empirical result

    The actual training runtimes of SocialMF and the Social Trust Ensemble (STE) model were measured on a machine with an Intel Core2 Duo 2.16 GHz processor, 2 GB RAM, and Windows XP.

    Single Iteration Time Total Training Time
    Model Epinions Flixster Epinions Flixster
    SocialMF 2.8 sec 29 sec 40 min 5.5 hr
    STE 37 sec 27 min 5 hr 9 days

    Key empirical findings:

    • On Epinions, SocialMF requires 2.8 seconds per gradient descent iteration compared to 37 seconds for STE (a 13.2-fold speedup per iteration), reaching convergence in ≈700\approx 700 iterations (40 minutes total) versus ≈550\approx 550 iterations (5 hours total) for STE (a 7.5-fold total speedup).
    • On Flixster, which is substantially denser and larger, SocialMF takes 29 seconds per iteration versus 27 minutes for STE (a 55.8-fold speedup per iteration), requiring 5.5 hours for full convergence versus 9 days for STE (a 39.3-fold total speedup).

  10. Knowl 10 — Limitations of the SocialMF Framework

    limitation

    The SocialMF recommendation model has four principal limitations:

    1. Positive Trust Assumption: SocialMF only supports non-negative trust relations (Tu,v≥0T_{u,v} \ge 0) and cannot handle negative trust (distrust) links present in certain social networks.
    2. Cold Start Items: While SocialMF handles cold start users via social network propagation, it lacks a mechanism to infer latent feature vectors for newly introduced items with no observed ratings.
    3. Manual Regularization Tuning: The social influence weight λT\lambda_T must be tuned manually across discrete candidate ranges rather than being determined automatically during training.
    4. Unrated User Evaluation Constraint: Although SocialMF learns latent feature representations for users with zero ratings through their connected neighbors, offline evaluation depends on withholding observed ratings, precluding empirical verification of recommendation quality for entirely rating-free users.

Coverage note — None was omitted; all key contributions including the SocialMF model, objective function, optimization algorithm, complexity analysis, dataset statistics, empirical evaluations, and limitations are fully covered.

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Citation

MLA
Jamali, M., and M. Ester. “A Matrix Factorization Technique with Trust Propagation for Recommendation in Social Networks”. Proceedings of the Fourth ACM Conference on Recommender Systems, 2010, pp. 135–42, https://doi.org/10.1145/1864708.1864736.
APA
Jamali, M., & Ester, M. (2010). A matrix factorization technique with trust propagation for recommendation in social networks. Proceedings of the Fourth ACM Conference on Recommender Systems, 135–142. https://doi.org/10.1145/1864708.1864736
Chicago
Jamali, M., and M. Ester. 2010. “A Matrix Factorization Technique with Trust Propagation for Recommendation in Social Networks”. Proceedings of the Fourth ACM Conference on Recommender Systems, 135–42. https://doi.org/10.1145/1864708.1864736.
Harvard
Jamali, M. and Ester, M. (2010) “A matrix factorization technique with trust propagation for recommendation in social networks”, Proceedings of the fourth ACM conference on Recommender systems. ACM, pp. 135–142. Available at: https://doi.org/10.1145/1864708.1864736.
Vancouver
1. Jamali M, Ester M (2010) A matrix factorization technique with trust propagation for recommendation in social networks. In: Proceedings of the fourth ACM conference on Recommender systems. ACM, pp 135–142

BibTeX

@inproceedings{Jamali_2010, series={RecSys ’10}, title={A matrix factorization technique with trust propagation for recommendation in social networks}, url={http://dx.doi.org/10.1145/1864708.1864736}, DOI={10.1145/1864708.1864736}, booktitle={Proceedings of the fourth ACM conference on Recommender systems}, publisher={ACM}, author={Jamali, Mohsen and Ester, Martin}, year={2010}, month=Sept, pages={135–142}, collection={RecSys ’10} }
Metadata:Crossref

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