Tianle Ma1, Yujiu Yang1, Liangwei Wang2 and Bo Yuan1

Recommending People to Follow Using Asymmetric Factor Models with Social Graphs

Introduction

Related Work

Asymmetric Factor Models for People Recommendation

Experiment and Results

Conclusion and Future Work

Introduction

Related Work

Asymmetric Factor Models for People Recommendation

Experiment and Results

Conclusion and Future Work

With huge amount of data generated on social media

sites every moment, online social networking services

have become tremendously popular these days.

For example, there are more than 200 million

registered users in Tencent-Weibo (similar to Twitter

in China), generating 40 million messages each day.

One one hand, this large scale benefits

social media users with extremely rich

content;

One the other hand, it can flood users

with huge volumes of information and

hence puts them at the risk of

information overload.

To cope with the issue of information overload, it is

important to develop effective social recommender

systems (SRSs) to present the most attractive and

relevant contents to users.

Social recommender systems aim at alleviate

information overload by presenting the most attractive

and relevant contents to users, often using

personalization techniques adopted for the specific

users.

In addition to recommending content to consume, new

types of recommendations emerge within social media,

such as recommending people and communities to

connect with, to follow, or to join.

In this paper, we focus on the topic of recommending

people to follow within social media sites which has

not been studied thoroughly.

Traditional recommendation techniques often rely on

the user-item rating matrix, which explicitly

represents users’ preference among items. One of the

challenges of recommending people to follow within

social media sites lies in the lack of the user-item

rating matrix.

In this paper, we compared several approaches to

recommend items, which can be persons,

organizations, or groups, for users to follow. We found

that by incorporating social graph information into

asymmetric factor models (AFMs), the

recommendation accuracy can be significantly

improved.

Sequential patterns, clickthrough rates (CTR) bias,

temporal dynamics, etc. were also taken into

consideration which further boosted the

recommendation accuracy.

Introduction

Related Work

Asymmetric Factor Models for People Recommendation

Experiment and Results

Conclusion and Future Work

The motivation of recommender systems is to

automatically suggest items to each user that s/he may

find appealing.

Existing recommender systems generally follow three

strategies: collaborative filtering, content-based

recommendation, and hybrid approaches. See [3] for

an overview.

As one of the most successful approaches, collaborative

filtering (CF) uses the known preferences of a group of

users to make recommendation or prediction of the

unknown preferences for other users, often based on the

mining of the user-item rating matrix [5-8].

In general, there are three main categories of CF techniques:

memory-based, model-based and hybrid CF algorithms.

You may found a brief summary of these approaches in our

paper.

The memory-based CF explores the user-item rating matrix

and makes recommendation based on the ratings of a set of

users whose rating profiles are most similar with each other.

While these approaches are easy to implement, they cannot

address cold start problem well.

On the other hand, model-based approaches learn and only

store a set of parameters of the model, thus can better

address data sparsity, scalability, and other issues.

However, there is a trade-off between recommendation

accuracy and scalability.

Recently, the memory-based approaches [17,18] have been

proposed for recommendation in social rating networks.

These methods typically explore the social network and

find a neighborhood of users trusted (directly and indirectly)

by a user and perform the recommendation by aggregating

their ratings.

Model-based approaches [19-21] have also been applied to

social rating networks by exploiting matrix factorization

techniques to learn latent features for users and items

from the observed ratings and have produced competitive

performance.

However, due to the sensitive nature of social data, there

are very few public social rating network datasets. Most of

the related research studies discussed above are based on

the Epinions dataset [18-21] or dataset crawled from

Flixster.com.

In this paper, we focused on people recommendation

prediction task. We investigated Task 1 in KDD Cup 2012,

which is a prediction task that involves predicting whether

or not a user will follow an item that has been

recommended to the user in Tencent-Weibo, one of the

most popular social media sites in China similar to Twitter.

Tencent provided the largest dataset ever published for

competition which contains social network information.

By adopting the more general concept of utility instead of

ratings and some other modifications, we successfully

apply the popular matrix factorization techniques to People

Recommendation.

To address cold start issue, which is serious in People

Recommendation, we apply the asymmetrical factor

models incorporating social graphs which greatly improves

the recommendation prediction accuracy.

Factors such as sequential patterns, clickthrough rate bias,

and temporal aspects are also taken into consideration to

further improve the performance.

Introduction

Related Work

Asymmetric Factor Models for People Recommendation

Experiment and Results

Conclusion and Future Work

Let U = {𝑢1, 𝑢2, ⋯ , 𝑢𝑛} 𝑎𝑛𝑑 I = {𝑖1, 𝑖2, ⋯ , 𝑖𝑚} be users set

and items set, respectively. In people recommendation, items can

be persons, organizations, or groups, just as users.

Let 𝒓𝒖𝒊 be a utility function [3] that measures the usefulness of item 𝒊 to

user 𝒖 𝒓: 𝑼 × 𝑰 → 𝑹,

where 𝑅 is a totally ordered set (e.g., non-negative integers or real

numbers within a certain range). Ratings in traditional recommendation

tasks can be viewed as specific utilities.

For each user , we want to choose such an item that maximizes the user’s

utility:

𝒊 ∈ argmax𝑰𝒓𝒖𝒊 , 𝒖 ∈ 𝑼

Practically, we may rank the utilities of items to a specific user and

recommend the top-k items with the highest utilities to the user.

The problem is how to measure the utilities? This is central in

designing recommender systems.

Algorithms Select Item 𝒊 with Item Features 𝒒𝒊 (keywords, content categories, …)

User 𝒖

with user features

𝒑𝒖 (the higher, the better)

(𝒖, 𝒊): utility 𝒓𝒖𝒊

(demographics,

social graph,

follow history, … )

Which items should we select? Those with the highest utilities

Those with the highest probability for

accepance

In latent factor models, 𝒑𝒖 and 𝒒𝒊 are latent factor vectors

Feature-based (Content-based) Approach

--User features to predict response

• User features: age, gender, geo-location, …

• Item features: category, keywords, topics, …

• Linear regression, SVM, mixture models, …

--Bottleneck: Needed Predictive Features

• Cannot distinguish between users and items having the same feature vectors

Collaborative Filtering (CF)

--Make recommendation based on past user-item interaction

• User-user, item-item, matrix factorization

• Good performance for users and items with enough data

--Considering Temporal Dynamics

--Incorporating Social Graphs

Collaborative Filtering

Neighborhood Models (Content-

based)

Item-based

User-based

Latent Factor Models (Model-

based)

SVD, AFM and other variants

PCA, LDA, …

We mainly adopt latent factor models, such as SVD, AFM, which

has proved to be most effective in recommendation prediction.

Given a user u, an item i,

𝑟𝑢𝑖 𝑡 ----the utility of user u for item i at time t

𝑟 𝑢𝑖 𝑡 ----estimate of 𝑟𝑢𝑖 𝑡

Model each user or item as a vector of factors (learned from data).

K≪ min (𝑀,𝑁)

M=number of users

N=number of items

𝑟𝑢𝑖 = 𝑝𝑢𝑘 ∙ 𝑞𝑖𝑘 =𝑞𝑖𝑇 ∙ 𝑝𝑢 ⇔ 𝑅 = 𝑃 ∙ 𝑄

item feature vector user feature factor

𝑀 ×𝑁 𝑀 × 𝐾 𝐾 × 𝑁

SVD: Factoring matrices into a series of linear approximations that

expose the underlying structure of the matrix.

A B C

Simha 4 4 5

Ateeq 4 5 5

Smith 3 3 2

Greg 4 5 4

Mcq 4 4 4

Ramin

3 5 4

Xiao 4 4 3

Wu 2 4 4

Riz 5 5 5

Predicted Score = User Baseline Rating * Movie Average Score

4.34 -0.18 -0.90

4.69 -0.38 -0.15

2.66 0.80 0.40

4.36 0.15 0.47

4.00 0.35 -0.29

4.05 -0.67 0.68

3.66 0.89 0.33

3.39 -1.29 0.14

5.00 0.44 -0.36

0.91 1.07 1.00

0.82 -0.20 -0.53

-0.21 0.76 -0.62 = *

In the plain SVD model, a user is represented by the

feature vector 𝑝𝑢. The AFM model represents a user by the

items he has accepted or followed. Thus, no explicit user feature is

stored as parameter. In other words, the AFM model parameterizes

only item features. Also called “virtual user feature”

𝑝𝑢 = 𝑁(𝑢)−12 𝑞𝑗𝑗∈𝑁(𝑢)

𝑞𝑗 are item-dependent features. One can show that the special

normalization 𝑁(𝑢) −1

2 of the item feature sum is necessary, when

assuming normal-distributed feature values.

𝑁(𝑢) → all items that user 𝒖 has followed or accepted

Integration of new data and new users without retraining the

whole model.

The prediction time is constant (like SVD), because one can

store the precalculated virtual user features after training,

𝑟𝑢𝑖 = 𝑞𝑖𝑇 ∙ ( 𝑁(𝑢) −

1

2 𝑞𝑗𝑗∈𝑁(𝑢) )

Training time is similar to SVD, because the AFM is trained with

stochastic gradient descent and a batch update on the virtual

features 𝑞𝑗.

𝑁(𝑢) → all items that user 𝒖 has followed or accepted

In People Recommendation, items can be persons, organizations,

or group. just as users. both the users’ follow history and social

graph can be incorporated into AFM.

𝑟𝑢𝑖 = 𝑞𝑖𝑇 ∙ ( 𝑁(𝑢) −

1

2 𝑞𝑗𝑗∈𝑁(𝑢) )

𝑁(𝑢) contains two parts: one is from user 𝒖′ follow history, and

the other is from user 𝒖′ social graph. Here we incorporate social

graphs into our AFM.

Actually, users’ follow history has relationships with social graphs

which may be derived from users’ follow history. However, there

is a difference: social graphs only contains all the items each user

has followed; while users’ follow history contains both users’

acceptance and rejection for items recommended the users.

𝑁(𝑢) → all items that user 𝒖 has followed or accepted

Temporal Dynamics in People Recommendation: A user may

be more likely accept an item when he is in a good mood. How

to capture this dynamics?

We divide a week into 168 time bins with an hour a bin. We

adopt latent factor model to capture interactions between users

and time bins.

𝑟𝑢𝑖(𝑡𝑢𝑖) = 𝑞𝑡𝑇(𝑡𝑢𝑖) ∙ 𝑝𝑢𝑡(𝑡𝑢𝑖)

Here 𝑝𝑢𝑡(𝑡𝑢𝑖) and 𝑞𝑡(𝑡𝑢𝑖) represent user 𝑢 ′ latent feature

vector and time bin’s latent feature vector, respectively. We use

their inner product to model the interaction and capture

temporal dynamics of users’ behaviors.

Users 𝒃𝒖. Also, the popularity of items could be different, so item bias 𝒃𝒊 is

also added.

Users of different age or gender may have different appetite

and thus have different CTR.

To capture CTR bias, first we divide all the users into groups

based on their age and gender, and calculate the items’ CTR of

these groups 𝑐𝑢𝑖. Then we model CTR bias as follows:

𝑟𝑢𝑖 = 𝛼𝑢 ∙ 𝑐𝑢𝑖 Here 𝛼𝑢 is the coefficient which should be learned in the

training process.

Besides CTR bias, we may need to add user bias, 𝒃𝒖 since each

user has his own appetite. Also, the popularity of items could

be different, so item bias 𝒃𝒊 is also added.

𝑟𝑢𝑖 = 𝑏𝑢 + 𝑏𝑖 + 𝛼𝑢 ∙ 𝑐𝑢𝑖

user bias item bias CTR bias

Here we may use these global bias as baseline predictor for the

utility 𝑟𝑢𝑖.

As mentioned before, 𝑟 𝑢𝑖(t) is estimate of 𝑟𝑢𝑖(𝑡), the utility

of user u for item i at time t. The measurement of 𝑟𝑢𝑖(𝑡) is

central in designing recommendation algorithms.

𝑟 𝑢𝑖 𝑡 = 𝑏𝑢 + 𝑏𝑖 + 𝛼𝑢 ∙ 𝑐𝑢𝑖 + 𝑞𝑡𝑇(𝑡) ∙ 𝑝𝑢𝑡(𝑡)

+𝑞𝑖𝑇 ∙ ( 𝑁(𝑢) −

1

2 𝑞𝑗𝑗∈𝑁(𝑢) )

Our combination model includes the global bias (user bias,

item bias, CTR bias), the temporal dynamics, and the AFM

term.

Data inputs:

• Recommendation log used for training

• Social graphs used in AFM

• User profile information for CTR bias

𝑟 𝑢𝑖 𝑡 = 𝑏𝑢 + 𝑏𝑖 + 𝛼𝑢 ∙ 𝑐𝑢𝑖 + 𝑞𝑡𝑇(𝑡) ∙ 𝑝𝑢𝑡(𝑡)

+𝑞𝑖𝑇 ∙ ( 𝑁(𝑢) −

1

2 𝑞𝑗𝑗∈𝑁(𝑢) )

All the parameters 𝑏𝑢, 𝑏𝑖, 𝛼𝑢, 𝑞𝑖, 𝑝𝑢𝑡(𝑡), 𝑞𝑡(𝑡) should be

learned through training.

From the recommendation log, we get utilities 𝒓𝒖𝒊 which can

be treated as ratings in traditional recommender systems. And

we minimize the RMSE(Root Mean Square Error) and use

SGD(Stochastic Gradient Descent) to learn all the parameters.

In recommendation log, if a user 𝒖 accept an item 𝒊, we let the

utility 𝒓𝒖𝒊=1. Otherwise the utility 𝒓𝒖𝒊 < 𝟏. Simply, we can

treat all the rejection records as 𝒓𝒖𝒊=0. In this paper, we

explore sequence patterns to get more reasonable utilities , as

explained in Section 4.1.

))((

)()ˆ(min

22

),( )(

222222

utuitt

Kiu uNj

juuiiuiui

ptq

qbbqrr

end

end

)λb(eδbb ),λb(eδbb

)λpq(eδpp

)λqp(eδqq

r̂re ,pqbbr̂

:instanceeach for

δtiteration

δδδ , : stepiteration

:iterationeach for

)()ˆ(min

uuituuiuitii

uiuituu

iuuitii

uiuiuiu

T

iuiui

112

t21

),(

22222

,, ***

Kiu

uiuiuiuibqp

bbpqrr

In recommendation log, users’ negative feedbacks(rejection of

recommended items) are much more than positive feedbacks.

So the training set is seriously unbalanced. It is ineffective and

costly for us to train our model on the whole recommendation

log.

Meanwhile, a negative result itself is not a strong indication

that a user did not want to accept the recommendation and had

no interest in the item at all. Instead, chances are that the user

may follow the item the next time when the item is

recommended to him/her.

As a result, the original training dataset was re-sampled before

training our asymmetric factor models. All records with

positive results were retained while the negative cases were

randomly down sampled to be roughly the same size as the

positive cases.

The reason why we don’t directly use RMSE to evaluate our

models is that our problem is one-class classification problem

without explicit ratings and the utility defined in our model is

derived.

Suppose there are m items in an ordered list recommended to

one user, who may click one or more or none of them to follow,

then, by adapting the definition of average precision in IR, the

average precision at n for this user is

ap@n = Σ k=1,...,n P(k) / (number of items clicked in m items)

As for the statistical validation, we use MAP (Mean average

precision) to evaluate our models instead of RMSE which has

a strong correlation with MAP in our problem.

The average precision for N users at position n is the average

of the average precision of each user, i.e.,

AP@n = Σ i=1,...,N ap@ni / N

which is exactly the evaluation metric used in KDD Cup 2012,

track 1.

http://www.kddcup2012.org/c/kddcup2012/track1/details/Evaluation

For example, if among the 5 items recommended to the user,

the user clicked #1, #3, #4, then ap@3 = (1/1 + 2/3)/3 ≈

0.56; If among the 4 items recommended to the user, the user

clicked #1, #2, #4, then ap@3 = (1/1 + 2/2)/3 ≈ 0.67.

Introduction

Related Work

Asymmetric Factor Models for People Recommendation

Experiment and Results

Conclusion and Future Work

The task 1 of KDD Cup 2012 is a recommendation prediction

task that involves predicting whether or not a user will follow

an item recommended to the user. Tencent provided the largest

dataset ever published for competition, including

recommendation log, social graphs, user profile information,

etc.

The recommendation log consists of two parts: the training

dataset (rec_log_train.txt) contains about one month’s

recommendation log records and users’ follow history; the test

dataset (rec_log_test.txt) contains only recommendation history

without users’ follow history. We need to predict whether or

not a user will follow the recommended items in the test

dataset.

The datasets contain more than 2,320,895 users!

The recommendation log contains 108,120,214 records!

Social graph contains 50,655,143 following relations.

Cold Start Problem : More than half of the users in the test

dataset (rec_log_test.txt) don’t appear in the training

dataset(rec_log_train.txt). As a result, the exploit of social

graph is crucial.

Firstly, we introduce three baseline algorithms used for

comparsion with our AFM models: Common-Follow

Algorithm, Common-Retweet Algorithm, and Hot-Degree

Algorithm.

Common-Follow Algorithm is based on the intuition that a user

will follow an item if his/her friends also follow it. Actually,

many social network sites such as Facebook use similar

methods to recommend people to connect with. In our work,

when an item was recommended to a user, we calculated the

percentage of his/her followees who also followed the same

item. For example, if the percentage of user 𝑢′ followees who

followed item 𝑖 is 𝑝, the utility of 𝑖 to 𝑢 was defined as

𝑟𝑢𝑖 = 𝑙𝑜𝑔2(𝑝 + 1) .

Common-Retweet algorithm is similar to Common-Follow

Algorithm. There difference is that we calculate the percentage

of retweet times of item 𝑖 from the followees of user 𝑢. For

example, if the percentage of retweet times of the item 𝑖 from

the followees of user 𝑢 is 𝑝, the utility of 𝑖 to 𝑢 was defined as

𝑟𝑢𝑖 = 𝑙𝑜𝑔2(𝑝 + 1).

Hot-Degree Algorithm does not take personalization into

consideration. We calculated the click rates of each item from

the recommendation log, and then recommended the hottest

items with highest acceptance rates to the user.

i

T

uui qpr ˆBasic SVD: 0.31

utui

T

t

uNj

j

T

iuiui ptqquNqbbr )()(ˆ

)(

2

1

uiu

uNj

j

T

iuiui cquNqbbr

)(

2

1

)(ˆ

uiuutui

T

t

uNj

j

T

iuiui cptqquNqbbr

)()(ˆ

)(

2

1

0.37076

)(

2

1

)(ˆ

uNj

j

T

iuiui quNqbbr

0.37028

0.37132

0.37009

This part is exactly the same as described in Section 3. The

number on the right side is the evaluation metric MAP.

)(

2

1

)()(ˆ

uNj

j

T

iuiut

T

ituiuuiui quNqtpqcbbr

))((

)()ˆ(min

22

),( )(

222222

utuitt

Kiu uNj

juuiiuiui

ptq

qbbqrr

)(

2

1

)()( )( ˆ

uNj

juu

T

i

T

iuiui yuNtpptqqbr

• Baseline predictors + Time affects +AFM term

Unified SVD model: Stable

part

Temporal part

Combination model:

Optimization function:

Table 1. Results of Different Recommendation Algorithms

Algorithms Public Leaderboard

Private Leaderboard

Common-Follow 0.23611 0.23541

Common-Retweet 0.22182 0.21882

Hot-Degree 0.33383 0.32831

Basic SVD 0.30548 0.28697

SVD + CTR bias 0.31446 0.29664

AFM with social graphs(AFMS) 0.36983 0.36016

AFMS + sequential patterns 0.37009 0.36035

AFMS + sequential patterns + Temporal Dynamics

0.37028 0.36055

AFMS + sequential patterns + CTR bias

0.37076 0.36093

AFMS + sequential patterns + Temporal Dynamics + CTR bias

0.37132 0.36143

In table 1, the public leaderboard and private leaderboard are

just two consecutive parts of the test datasets in KDD Cup

2012. As the two leaderboards have a temporal order, we can

see that the results were always better for public leaderboard

than private leaderboard since it is temporally more close to the

training dataset.

The evaluation metric in both leaderboards is MAP as

described before, the higher, the better.

The AFM with social graphs significantly improved the results.

The adoption of sequential patterns, temporal dynamics, and

CTR bias also contributed to the improvement of the results.

Here we empirically validate the effectiveness of our methods

Introduction

Related Work

Asymmetric Factor Models for People Recommendation

Experiment and Results

Conclusion and Future Work

One of the major differences between traditional recommender

systems and social recommender systems is that there are no

explicit ratings in social networks. To cope with this issue, we used

the utility of an item to a user instead of ratings and developed

several latent factor models to calculate the utilities.

Social graph information has proved to be useful in improving

recommendation accuracy. In this paper, we proposed to

incorporate social graph information into asymmetrical factor

models for People Recommendation.

To empirically validate the effectiveness of the proposed models,

we have done experiments on the datasets of KDD Cup 2012

which is a people recommendation prediction task.

Experimental results show that AFM with social graph information

can significantly improve the recommendation accuracy, compared

to a number of standard recommendation algorithms. In the

meantime, additional factors were also taken into consideration,

such as sequential patterns, CTR bias, and temporal dynamics,

which further boosted the predication accuracy.

Future work: In this paper, the model was optimized in terms of

RMSE. However, the evaluation metric in Task 1 of KDD Cup 2012

is MAP. Although RMSE and MAP are highly positively correlated,

we can try to adapt our model to optimize MAP directly in the

future. Also, we can build a directed weighted social graph that can

be used to build a more elaborated model.

1. Niu, Y., Wang, Y., Sun, G., Yue, A., Dalessandro, B., Perlich, C., Hamner, B.: The Tencent Dataset and KDD-Cup’12. In KDD-Cup Workshop, (2012) 2. Jannach, D., Zanker, M., Felfernig, A., Friedrich, G.: Recommender Systems: An Introduction. Cambridge University Press (2010) 3. Adomavicius, G., Tuzhilin, A.: Toward the Next Generation of Recommender Systems: A Survey of the State-of-the-art and Possible Extensions. Knowledge and Data Engineering, IEEE Transactions on 17 (6), 734-749 (2005) 4. Yang, X., Steck, H., Guo, Y., Liu, Y.: On Top-k Recommendation using Social Networks. In: Proceedings of 6th ACM Conference on Recommender Systems. ACM, Dublin, Ireland (2012) 5. Paterek, A.: Improving Regularized Singular Value Decomposition for Collaborative Filtering. In: Proceedings of KDD Cup and Workshop 2007, pp. 5-8. ACM, San Jose, California (2007)

6. Keshavan, R.H., Montanari, A., Oh, S.: Matrix Completion From Noisy Entries. The Journal of Machine Learning Research 11, 2057-2078 (2010) 7. Pan, R., Zhou, Y., Cao, B., Liu, N.N., Lukose, R., Scholz, M., Yang, Q.: One-class Collaborative Filtering. In: Proceedings of the 8th IEEE International Conference on Data Mining, pp. 502-511. IEEE, Pisa, Italy (2008) 8. Srebro, N., Jaakkola, T.: Weighted Low-rank Approximations. In: Proceedings of the 20th International Conference on Machine Learning, pp. 720-727. AAAI Press, Washington, DC, USA (2003) 9. Jahrer, M., Töscher, A., Legenstein, R.: Combining Predictions for Accurate Recommender Systems. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 693-702. ACM, Washington, DC, USA (2010) 10. Su, X., Khoshgoftaar, T.M.: A Survey of Collaborative Filtering Techniques. Advances in Artificial Intelligence 2009, (2009)

11. Goldberg, D., Nichols, D., Oki, B.M., Terry, D.: Using Collaborative Filtering to Weave an Information Tapestry. Commun Acm 35 (12), 61-70 (1992) 12. Melville, P., Mooney, R.J., Nagarajan, R.: Content-boosted Collaborative Filtering for Improved Recommendations. In: Proceedings of the 18th National Conference on Artificial Intelligence and 14th Conference on Innovative Application of Artificial Intelligence, pp. 187-192. AAAI Press; MIT Press; Edmonton, Alberta, Canada (2002) 13. Koren, Y.: Collaborative Filtering with Temporal Dynamics. Commun Acm 53 (4), 89-97 (2010) 14. Koren, Y.: Factorization Meets the Neighborhood: a Multifaceted Collaborative Filtering Model. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 426-434. ACM, Las Vegas, Nevada, USA (2008)

15. Koren, Y., Bell, R., Volinsky, C.: Matrix Factorization Techniques for Recommender Systems. IEEE Computer 42 (8), 30-37 (2009) 16. Singla, P., Richardson, M.: Yes, There is a Correlation: - From Social Networks to Personal Behavior on the Web. In: Proceedings of the 17th International Conference on World Wide Web, pp. 655-664. ACM, Beijing, China (2008) 17. Massa, P., Avesani, P.: Trust-aware Recommender Systems. In: Proceedings of the 2007 ACM conference on Recommender systems, pp. 17-24. ACM, Minneapolis, MN, USA (2007) 18. Jamali, M., Ester, M.: TrustWalker: A Random Walk Model for Combining Trust-based and Item-based Recommendation. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 397-406. ACM, Paris, France (2009)

19. Ma, H., King, I., Lyu, M.R.: Learning to Recommend with Social Trust Ensemble. In: Proceedings of the 32nd Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 203-210. ACM, Boston, MA, USA (2009) 20. Jamali, M., Ester, M.: A Matrix Factorization Technique with Trust Propagation for Recommendation in Social Networks. In: Proceedings of the 2010 ACM Conference on Recommender Systems, pp. 135-142. ACM, Barcelona, Spain (2010) 21. Ma, H., Yang, H., Lyu, M.R., King, I.: Sorec: Social Recommendation Using Probabilistic Matrix Factorization. In: Proceedings of the 17th ACM Conference on Information and Knowledge Management, pp. 931-940. ACM, Napa Valley, California, USA (2008) 22. Golbeck, J.A.: Computing and Applying Trust in Web-based Social Networks. University of Maryland at College Park College Park, MD, USA (2005)

23. Jamali, M., Ester, M.: Using a Trust Network to Improve Top-N Recommendation. In: Proceedings of the 2009 ACM Conference on Recommender Systems, pp. 181-188. ACM, New York, NY, USA (2009) 24. Koren, Y.: Factor in the Neighbors: Scalable and Accurate Collaborative Filtering. ACM Transactions on Knowledge Discovery from Data 4 (1), 1-24 (2010)