信任驱动的社会化协同过滤推荐
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"这篇PDF文件是关于2017年发表在《IEEE Transactions on Pattern Analysis and Machine Intelligence》期刊上的一篇文章，题目为“基于信任的社会协同过滤”。文章探讨了如何利用用户之间的社会信任关系来改进协同过滤推荐系统的性能，特别针对数据稀疏和新用户冷启动问题提供解决方案。"
在当前的数字化时代，推荐系统已经成为个性化信息和服务提供的重要工具。它们的目标是准确且主动地向用户推荐可能感兴趣的内容或服务。协同过滤是最常用的一种推荐算法，其原理是通过分析用户的历史行为模式来预测他们可能的兴趣。然而，协同过滤面临两大挑战：一是数据稀疏性，即许多用户只对少数项目有评价，导致预测准确性降低；二是新用户冷启动问题，即新用户没有足够的历史记录供系统分析。
为了解决这些问题，文章提出了一种新颖的方法——TrustMF（基于信任的矩阵分解），它结合了用户给出的稀疏评分数据和这些用户之间的稀疏社会信任网络。这种方法是一种模型驱动的策略，它扩展了传统的协同过滤框架，引入了社会网络中的信任关系作为补充信息。信任在社会环境中起着关键作用，因为它可以揭示用户之间的互动模式，即使在缺乏直接评分的情况下，也能帮助理解用户喜好。
TrustMF方法首先通过矩阵分解技术将用户-项目评分矩阵分解为用户和项目的潜在特征表示，然后结合用户的社会信任关系矩阵，通过信任传播来调整用户特征向量。这种调整有助于减少因数据稀疏性导致的不确定性，同时利用社会信任信息来更好地预测未评分项的用户偏好。
在实验部分，作者对比了TrustMF与其他协同过滤方法，包括基于邻域的协同过滤和基于矩阵分解的协同过滤。结果显示，TrustMF在处理数据稀疏性和新用户冷启动问题时表现出了显著的优越性，提高了推荐的准确性和覆盖率。
这篇文章为推荐系统的研究提供了新的视角，展示了社会信任如何增强协同过滤的性能。通过整合社会网络中的信任信息，推荐系统能够更精确地理解用户的行为和偏好，从而提高推荐的质量和用户体验。这对于社交媒体、电子商务和在线服务等领域具有重要的实践意义。
0162-8828 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPAMI.2016.2605085, IEEE
Transactions on Pattern Analysis and Machine Intelligence
3
matrix to construct novel fusing models and to predict the
genuine interest of users in a more reasonably way.
Previously, we have published a conference paper to
briefly present and preliminarily validate the aforemen-
tioned idea [37], which will be extensively extended in this
work by supplementing new models, algorithms, theoretical
analysis as well as sufficient experimental results. The rest
of the paper is organized as follows. In Section 2 we propose
a novel matrix factorization based social CF method named
TrustMF. In Section 3, we discuss the rationale of TrustMF
from a probabilistic view and then contribute a more general
framework, named TrustPMF, to predict a user’s preferences
more effectively by fitting rating data and trust data in an
approximate, rather than deterministic, way. In Section 4,
we validate the performance of TrustMF and TrustPMF by
comparing them with several representative methods on
four large real-world datasets.
2 THE TRUSTMF MODEL
2.1 Factorization of Rating Matrix
Suppose we have a recommender system which involves m
users and n items. Let R = [R
ij
]
m×n
denote the observed
user-item rating matrix, where each known element R
ij
denotes the observed rating of item j given by user i, which
is normally an integer from 1 to R
max
(e.g., 1 to 5), and
each unknown element indicates the user has not rated the
item yet. By mapping users and items to a low-dimensional
feature (factor) space in which each factor can be deemed as
any aspect, topic, or other implicit feature relevant to items
or users’ interests [17], each user or item can be represented
by a low-dimensional vector. Let d-dimensional vectors U
i
and V
j
be the user-specific latent feature vector of user i
and item-specific latent feature vector of item j, respectively.
Then we have user feature matrix U ∈ R
d×m
and item
feature matrix V ∈ R
d×n
.
By employing low-rank approximation over the ob-
served rating matrix, we can recover unknown ratings by
U
T
V . Formally, the feature matrices U and V can be learned
by minimizing a loss function as follows:
L =
X
(i,j)∈Ω
(U
T
i
V
j
− R
ij
)
2
+ λ(kUk
2
F
+ kV k
2
F
)
where Ω = {(i, j) : R
ij
6= 0} denotes the locations of ob-
served ratings in rating matrix, k · k
F
denotes the Frobenius
norm, and parameter λ controls the model complexity to
avoid over-fitting.
To further avoid over-fitting when learning parame-
ters, a so-called weighted-λ-regularization was introduced
to above model [41]. It increases the penalization to the
feature vectors of users or items involving more ratings.
Correspondingly, the new objective is obtained as follows:
L =
X
(i,j)∈Ω
(U
T
i
V
j
−R
ij
)
2
+λ(
X
i
n
u
i
kU
i
k
2
F
+
X
j
n
v
j
kV
j
k
2
F
)
where n
u
i
and n
v
j
denote the numbers of ratings given by
user i and given to item j, respectively.
2.2 Factorization of Trust Network
Suppose we have a trust network N with m nodes, where
nodes represent users and arcs represent directional trust re-
lationships among users. The adjacent matrix T = [T
ik
]
m×m
can be used to describe the structure of N, in which T
ik
is normally a real number within the interval [0, 1], repre-
senting the extent user i trusts k (e.g.,“1” indicates user i
extremely trusts k ). Since i trusts k does not always means
that k trusts i in the same way, T may not be symmetric.
Due to the asymmetric property of trust, in this work
we map each user i as two distinct d-dimensional latent
feature vectors, depicted by truster-specific feature vector
B
i
and trustee-specific feature vector W
i
, respectively. B
i
and W
i
characterize the behaviors of “to trust others” and
“to be trusted by others” of user i, respectively. Given
such vectors, one can model trust value T
ik
as the inner
product of B
i
and W
k
. It is important to notice that, this
way of modeling trust relations is totally distinct from
existing methods, which explicitly explores the real-world
implications of feature vectors. We will see later this new
way of modeling trust values not only characterizes the
directional property of trust in a more accurate way, but also
gives a better interpretation of how the mutual trust among
users are generated and how they affect a user’s respective
opinions.
Provided we have only trust data, the feature matrices
B ∈ R
d×m
and W ∈ R
d×m
can be learned by minimizing
the objective function:
L =
X
(i,k)∈Ψ
(B
T
i
W
k
− T
ik
)
2
+ λ(kBk
2
F
+ kWk
2
F
)
where Ψ = {(i, k) : T
ik
6= 0} denotes the locations of
observed trust relations in the trust matrix.
2.3 TrustMF Model
We have performed matrix factorization just based on either
rating data or trust data. In this section, we will present our
matrix factorization model to fuse both.
2.3.1 Truster Model
As mentioned before, users of social networking such as
Epinions are able to browse and generate opinions (ratings
or reviews) on items they are interested in and then build
their respective trust nets based on such opinions. Through
tangled trust ties, the opinions of an individual will be
affected by others and vice versa. Here we first propose a
truster model to characterize the first aspect, or how others
will affect a specific user’s opinions.
Note that the m users getting involved in rating matrix R
and trust matrix T are the same. Therefore, one can associate
R and T into a single matrix factorization process by sharing
a common user-specific latent feature space. Fig.2(a) shows
the proposed truster model that is capable of characterizing
how a user i’s opinions in terms of ratings are affected by
other users he/she trusts by means of B
T
i
V
j
.
In this model, we choose the truster-specific feature
matrix B as the latent space commonly shared by R and
T , meaning the user feature matrix U is approximated by
truster feature matrix B. Here each vector B
i
simultane-
ously characterizes two aspects: how a user i trusts (or
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