recommending people to follow using asymmetric...
TRANSCRIPT
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.
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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.
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number on the right side is the evaluation metric MAP.
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• 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.
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