# Aspect-Aware Latent Factor Model:
Rating Prediction with Ratings and Reviews

Zhiyong Cheng  National University of Singapore<EMAIL_ADDRESS>,
Ying Ding  Vipshop Inc., USA<EMAIL_ADDRESS>,  Lei Zhu  Shandong
Normal University, China<EMAIL_ADDRESS>and  Mohan Kankanhalli  National
University of Singapore<EMAIL_ADDRESS>
(2018)

###### Abstract.

Although latent factor models (e.g., matrix factorization) achieve good
accuracy in rating prediction, they suffer from several problems including
cold-start, non-transparency, and suboptimal recommendation for local users or
items. In this paper, we employ textual review information with ratings to
tackle these limitations. Firstly, we apply a proposed aspect-aware topic
model (ATM) on the review text to model user preferences and item features
from different _aspects_ , and estimate the _aspect importance_ of a user
towards an item. The aspect importance is then integrated into a novel aspect-
aware latent factor model (ALFM), which learns user’s and item’s latent
factors based on ratings. In particular, ALFM introduces a weighted matrix to
associate those latent factors with the same set of aspects discovered by ATM,
such that the latent factors could be used to estimate aspect ratings.
Finally, the overall rating is computed via a linear combination of the aspect
ratings, which are weighted by the corresponding aspect importance. To this
end, our model could alleviate the data sparsity problem and gain good
interpretability for recommendation. Besides, an aspect rating is weighted by
an aspect importance, which is dependent on the targeted user’s preferences
and targeted item’s features. Therefore, it is expected that the proposed
method can model a user’s preferences on an item more accurately for each
user-item pair locally. Comprehensive experimental studies have been conducted
on 19 datasets from Amazon and Yelp 2017 Challenge dataset. Results show that
our method achieves significant improvement compared with strong baseline
methods, especially for users with only few ratings. Moreover, our model could
interpret the recommendation results in depth.

Aspect-aware, Matrix Factorization, Recommendation, Review-aware, Topic Model

††copyright: rightsretained††journalyear: 2018††copyright:
iw3c2w3††conference: The 2018 Web Conference; April 23–27, 2018; Lyon,
France††booktitle: WWW 2018: The 2018 Web Conference, April 23–27, 2018, Lyon,
France††doi: 10.1145/3178876.3186145††isbn: 978-1-4503-5639-8/18/04††ccs:
Information systems Social recommendation††ccs: Information systems
Personalization††ccs: Information systems Recommender systems††ccs:
Information systems Collaborative filtering††ccs: Computing methodologies
Topic modeling††ccs: Computing methodologies Factor analysis

##  1\. Introduction

When making comments on an item (e.g., _product_ , _movie_ , and _restaurant_)
in the online review/business websites, such as Yelp and Amazon, reviewers
also provide an overall rating, which indicates their overall preference or
satisfaction towards the corresponding items. Hence, predicting users’ overall
ratings to unrated items or _personalized rating prediction_ is an important
research problem in recommender systems. Latent factor models (e.g., matrix
factorization (Koren et al., 2009; Zhang et al., 2016a; Cheng et al., 2017b))
are the most widely used and successful techniques for rating prediction, as
demonstrated by the Netflix Prize contest (Bell and Koren, 2007). These
methods characterize user’s interests and item’s features using _latent
factors_ inferred from rating patterns in user-item rating records. As a
typical collaborative filtering technique, the performance of MF suffers when
the ratings of items or users are insufficient ( also known as the cold-start
problem) (He et al., 2015). Besides, a rating only indicates the overall
satisfaction of a user towards an item, it cannot explain the underlying
rationale. For example, a user could give a restaurant a high rating because
of its delicious food or due to its nice ambience. Most existing MF models
cannot provide such fine-grained analysis. Therefore, relying solely on
ratings makes these methods hard to explicitly and accurately model users’
preferences (Wang et al., 2018; He et al., 2015; Ling et al., 2014; McAuley
and Leskovec, 2013; Wu and Ester, 2015).

Moreover, MF cannot achieve optimal rating prediction locally for each user-
item pair, because it learns the latent factors of users ($\bm{p_{u}}$) and
items ($\bm{q_{i}}$) via a global optimization strategy (Christakopoulou and
Karypis, 2016). In other words, $\bm{p_{u}}$ and $\bm{q_{i}}$ are optimized to
achieve a global optimization over all the user-item ratings in the training
dataset.111In the paper, unless otherwise specified, notations in bold style
denote matrices or vectors, and the ones in normal style denote scalars. As a
result, the performance could be severely compromised locally for individual
users or items. MF predicts an unknown rating by the dot product of the
targeted user $u$’s and item $i$’s latent factors (e.g.,
$\bm{p_{u}}^{T}\bm{q_{i}}$). The overall rating of a user towards an item
($\hat{r}_{u,i}$) is decided by the importance/contribution of all factors.
Take the $k$-th factor as an example, its contribution is $p_{u,k}*q_{i,k}$.
For accurate prediction, it is important to accurately capture the importance
of each latent factor for a user towards an item. It is well-known that
different users may care about different _aspects_ of an item. For example, in
the domain of restaurants, some users care more about the taste of _food_
while others pay more attention to the _ambience_. Even for the same aspect,
the preference of users could be different from each other. For example, in
the _food_ aspect, some users like _Chinese cuisines_ while some others favor
_Italian cuisines_. Similarly, the characteristics of items on an aspect could
also be different from each other. Thus, it is possible that “a user $u$
prefers item $i$ but dislikes item $j$ on a specific aspect”, while “another
user $u^{\prime}$ favors item $j$ more than item $i$ on this aspect”.
Therefore, in MF, the importance of a latent factor for users towards an item
should be treated differently. At first glance, MF achieves the goal as the
influence of a factor (e.g., $k$-th factor) is dependent on both $p_{u,k}$ and
$q_{i,k}$ (i.e., $p_{u,k}*q_{i,k}$). However, it is suboptimal to model the
importance of a factor by a fixed value of an item or a user. In fact, MF
treats each factor of an item with the same importance to all users (i.e.,
$q_{i,k}$); and similarly, each factor of a user is equally important to all
items (i.e., $p_{u,k}$) in rating prediction. Take the previous example, “ _a
user $u$ prefers item $i$ but dislikes item $j$ on an aspect_”, i.e., a factor
(e..g, $k$) in MF), which means $p_{u,k}*q_{i,k}$ should be larger than
$p_{u,k}*q_{j,k}$ (i.e., $p_{u,k}*q_{i,k}>p_{u,k}*q_{j,k}$). On the other
hand, “ _user $u^{\prime}$ favors item $j$ more than item $i$ on this
aspect_”, thus $p_{u^{\prime},k}*q_{j,k}$ should be larger than
$p_{u^{\prime},k}*q_{i,k}$ (i.e.,
$p_{u^{\prime},k}*q_{i,k}<p_{u^{\prime},k}*q_{j,k}$). Because the values of
$p_{u,k}$ and $p_{u^{\prime},k}$ are kept the same when predicting ratings, it
is impossible for MF to satisfy the local requirements
$p_{u,k}*q_{i,k}>p_{u,k}*q_{j,k}$ and
$p_{u^{\prime},k}*q_{i,k}<p_{u^{\prime},k}*q_{j,k}$ simultaneously for these
user-item pairs. A straightforward solution is to assign different weights
(e.g., $w_{u,i,k}$) to different user-item pairs (e.g., $p_{u,k}*q_{i,k}$).
However, how to compute a proper weight for each user-item pair is
challenging.

A large amount of research effort has been devoted to deal with these
weaknesses of MF methods. For example, various types of side information have
been incorporated into MF to alleviate the cold-start problem, such as tags
(Shi et al., 2013; Zhang et al., 2014), social relations (Ma et al., 2011;
Wang et al., 2017), reviews (Ling et al., 2014; McAuley and Leskovec, 2013;
Zhang and Wang, 2016), and visual features (He and McAuley, 2016). Among them,
the accompanied review of a rating contains important complementary
information. It not only encodes the information of user preferences and item
features but also explains the underlying reasons for the rating. Therefore,
in recent years, many models have been developed to exploit reviews with
ratings to tackle the cold-start problem and also enhance the explainability
of MF, such as HFT (McAuley and Leskovec, 2013), CTR (Wang and Blei, 2011),
RMR (Ling et al., 2014), and RBLT (Tan et al., 2016). However, a limitation of
these models is that they all assume an _one-to-one correspondence
relationship_ between latent topics (learned from reviews) and latent factors
(learned from ratings), which not only limits their flexibility on modeling
reviews and ratings but also may not be optimal. In addition, they cannot deal
with the suboptimal recommendation for local users or items in MF. In fact,
very few studies in literature have considered this problem.

In this paper, we focus on the problem of _personalized rating prediction_ and
attempt to tackle the above limitations together by utilizing reviews with
ratings. Specifically, an _A_ spect-aware _T_ opic _M_ odel (ATM) is proposed
to extract _latent topics_ from reviews, which are used to model users’
preferences and items’ features in different _aspects_. In particular, each
_aspect_ of users/items is represented as a probability distribution of latent
topics. Based on the results, the relative importance of an aspect (i.e.,
_aspect importance_) for a user towards an item can be computed. Subsequently,
the aspect importance is integrated into a developed _A_ spect-aware _L_ atent
_F_ actor _M_ odel (ALFM) to estimate _aspect ratings_. In particular, a
weight matrix is introduced in ALFM to associate the latent factors to the
same set of aspects discovered by ATM. In this way, our model avoids referring
to external sentiment analysis tools for aspect rating prediction as in (Zhang
et al., 2015; Diao et al., 2014). The overall rating is obtained by a linear
combination of the _aspect ratings_ , which are weighted by the importance of
corresponding aspects (i.e., _aspect importance_). Note that the latent topics
and latent factors in our model are not linked directly; instead, they are
correlated via the _aspects_ indirectly. Therefore, the number of latent
topics and latent factors could be different and separately optimized to model
reviews and ratings respectively, which is fundamentally different from the
_one-to-one_ mapping in previous models (McAuley and Leskovec, 2013; Wang and
Blei, 2011; Ling et al., 2014; Tan et al., 2016; Bao et al., 2014; Zhang and
Wang, 2016). Besides, our model could learn an aspect importance for each
user-item pair, namely, assigning a different weight to each
$p_{u,k}*q_{i,k}$, and thus could alleviate the suboptimal local
recommendation problem and achieve better performance.

A set of experimental studies has been conducted on 19 real-world datasets
from Yelp and Amazon to validate the effectiveness of our proposed model.
Experimental results show that our model significantly outperforms the state-
of-the-art methods which also use both reviews and ratings for rating
prediction. Besides, our model also obtains better results for users with few
ratings, demonstrating the advantages of our model on alleviating the cold-
start problem. Furthermore, we illustrate the interpretability of our model on
recommendation results with examples. In summary, the main contributions of
this work include:

  * •

We propose a novel aspect-aware latent factor model, which could effectively
combine reviews and ratings for rating prediction. Particularly, our model
relaxes the constraint of one-to-one mappings between the latent topics and
latent factors in previous models and thus could achieve better performance.

  * •

Our model could automatically extract explainable aspects, and learn the
aspect importance/weights for different user-item pairs. By associating latent
factors with aspects, the aspect weights are integrated with latent factors
for rating prediction. Thus, the proposed model could alleviate the suboptimal
problem of MF for individual user-item pairs.

  * •

We conduct comprehensive experimental studies to evaluate the effectiveness of
our model. Results show that our model is significantly better than previous
approaches on tasks of rating prediction, recommendation for sparse data, and
recommendation interpretability.

##  2\. Related Work

A comprehensive review on the recommender system is beyond the scope of this
work. We mainly discuss the works which utilize both reviews and ratings for
rating prediction. Some works assume that the review is available when
predicting the rating score, such as SUIT (Li et al., 2014), LARAM (Wang et
al., 2011), and recent DeepCoNN (Zheng et al., 2017). However, in real world
recommendation settings, the task should be predicting ratings for the
uncommented and unrated items. Therefore, the review is unavailable when
predicting ratings. We broadly classify the approaches for the targeted task
in three categories: (1) sentiment-based, (2) topic-based, and (3) deep
learning-based. Our approach falls into the second category.

Sentiment-based. These works analyze user’s sentiments on items in reviews to
boost the rating prediction performance, such as (Pappas and Popescu-Belis,
2013; Pero and Horváth, 2013; Diao et al., 2014; Zhang et al., 2015). For
example, (Pappas and Popescu-Belis, 2013) estimated a sentiment score for each
review to build a user-item sentiment matrix, then a traditional collaborative
filtering method was applied. Zhang et al. (Zhang et al., 2015) analyzed the
sentiment polarities of reviews and then jointly factorize the user–item
rating matrix. These methods rely on the performance of external NLP tools for
sentiment analysis and thus are not self-contained.

Topic-based. These approaches extract latent topics or aspects from reviews.
An early work (Ganu et al., 2009) in this direction relied on domain knowledge
to manually label reviews into different aspects, which requires expensive
domain knowledge and high labor cost. Later on, most works attempt to extract
latent topics or aspects from reviews automatically (McAuley and Leskovec,
2013; Bao et al., 2014; Diao et al., 2014; He et al., 2015; Ling et al., 2014;
McAuley and Leskovec, 2013; Wu and Ester, 2015; Zhang and Wang, 2016; Tan et
al., 2016). A general approach of these methods is to extract latent topics
from reviews using topic models (Wang and Blei, 2011; McAuley and Leskovec,
2013; Ling et al., 2014; Zhang and Wang, 2016; Tan et al., 2016) or non-
negative MF (Bao et al., 2014; Qiu et al., 2016) and learn latent factors from
ratings using MF methods. HFT (McAuley and Leskovec, 2013) and TopicMF (Bao et
al., 2014) link the latent topics and latent factors by using a defined
transform function. ITLFM (Zhang and Wang, 2016) and RBLT (Tan et al., 2016)
assume that the latent topics and latent factors are in the same space, and
linearly combine them to form the latent representations for users and items
to model the ratings in MF. CTR (Wang and Blei, 2011) assumes that the latent
factors of items depend on the latent topic distributions of their text, and
adds a latent variable to offset the topic distributions of items when
modeling the ratings. RMR (Ling et al., 2014) also learns item’s features
using topic models on reviews, while it models ratings using a mixture of
Gaussian rather than MF methods. Diao et al. (Diao et al., 2014) propose an
integrated graphical model called JMARS to jointly model aspects, ratings and
sentiments for movie rating prediction. Those models all assume an one-to-one
mapping between the learned latent topics from reviews and latent factors from
ratings. Although we adopt the same strategy to extract latent topics and
learn latent factors, our model does not have the constraint of one-to-one
mapping. Besides, Zhang et al. (Zhang et al., 2015) extracted aspects by
decomposing the user–item rating matrix into item–aspect and user–aspect
matrices. He et al. (He et al., 2015) extracted latent topics from reviews by
modeling the user-item-aspect relation with a tripartite graph.

Deep learning-based. Recently, there has been a trend of applying deep
learning techniques in recommendation (He et al., 2017; Covington et al.,
2016). For example, He et al. generalized matrix factorization and
factorization machines to neural collaborative filtering and achieved
promising performance (He et al., 2017; He and Chua, 2017). Textual reviews
have also been used in deep learning models for recommendation (Zhang et al.,
2016b; Zheng et al., 2017; Catherine and Cohen, 2017; Zhang et al., 2017). The
most related works in this direction are DeepCoNN (Zheng et al., 2017) and
TransNet (Catherine and Cohen, 2017), which apply deep techniques to reviews
for rating prediction. In DeepCoNN, reviews are first processed by two CNNs to
learn user’s and item’s representations, which are then concatenated and
passed into a regression layer for rating prediction. A limitation of DeepCoNN
is that it uses reviews in the testing phase. (Catherine and Cohen, 2017)
shows that the performance of DeepCoNN decreases greatly when reviews are
unavailable in the testing phase. To deal with the problem, TransNet
(Catherine and Cohen, 2017) extends DeepCoNN by introducing an additional
layer to simulate the review corresponding to the target user-item pair. The
generated review is then used for rating prediction.

Table 1. Notations and their definitions Notation | Definition
---|---
$\mathcal{D}$ | corpus with reviews and ratings
$d_{u,i}$ |  review document of user $u$ to item $i$
$s$ |  a sentence in a review $d_{u,i}$
$\mathcal{U}$, $\mathcal{I}$, $\mathcal{A}$ | user set, item set, and aspect set, respectively
$M,N,A$ | number of users, items, and aspects, respectively
$N_{w,s}$ |  number of words in a sentence $s$
$K$ | number of latent topics in ATM
$y$ | an indicator variable in ATM
$a_{s}$ |  assigned aspect $a$ to sentence $s$
$\pi_{u}$ |  the parameter of Bernoulli distribution $P(y=0)$
$\eta$ |  Beta priors ($\eta=\\{\eta_{0},\eta_{1}\\}$)
$\bm{\alpha_{u}},\bm{\alpha_{i}}$ | Dirichlet priors for aspect-topic distributions
$\bm{\gamma_{u}},\bm{\gamma_{i}}$ | Dirichlet priors for aspect distributions
$\bm{\beta_{w}}$ | Dirichlet priors for topic-word distributions
$\bm{\theta_{u,a}}$ |  user’s aspect-topic distribution: denoting user’s preference on $a$
$\bm{\psi_{i,a}}$ |  item’s aspect-topic distribution: denoting item’s features on $a$
$\bm{\lambda_{u}},\bm{\lambda_{v}}$ | aspect distributions of user and item, respectively
$\bm{\phi_{w}}$ | topic-text word distribution
$f$ | number of latent factors in ALFM
$\mu_{\cdot}$ | regularization coefficients
$b_{\cdot}$ |  bias terms, e.g., $b_{u},b_{i},b_{0}$
$w_{a}$ |  weight vector for aspect $a$
$p_{u}$, $q_{i}$ |  latent factors of user $u$ and item $i$, respectively
$r_{u,i}$ |  rating of user $u$ to item $i$
$r_{u,i,a}$ |  aspect rating of user $u$ towards item $i$ on aspect $a$
$\rho_{u,i,a}$ |  aspect importance of $a$ for $u$ with respect to $i$
$s_{u,i,a}$ |  the degree of item $i$’s attributes matching user $u$’s preference
|  on aspect $a$
|

##  3\. Proposed Model

###  3.1. Problem Setting

Let $\mathcal{D}$ be a collection of reviews of item set $\mathcal{I}$ from a
specific category (e.g., restaurant) written by a set of users $\mathcal{U}$,
and each review comes with an overall rating $r_{u,i}$ to indicate the overall
satisfaction of user $u$ to item $i$. The primary goal is to predict the
unknown ratings of items that the users have not reviewed yet. A review
$d_{u,i}$ is a piece of text which describes opinions of user $u$ on different
aspects $a\in\mathcal{A}$ towards item $i$, such as _food_ for _restaurants_.
In this paper, we only consider the case that all the items are from the same
category, i.e., they share the same set of aspects $\mathcal{A}$. Aspects that
users care for items are latent and learned from reviews by our proposed topic
model, in which each aspect is represented as a distribution of the same set
(e.g., $K$) of latent topics. Table 1 lists the key notations. Before
introducing our method, we would like to first clarify the concepts of
_aspects_ , _latent topics_ , and _latent factors_.

  * •

Aspect \- it is a high-level semantic concept, which represents the attribute
of items that users commented on in reviews, such as _“food”_ for _restaurant_
and _“battery”_ for _mobile phones_.

  * •

Latent topic & latent factor \- in our context, both concepts represent a more
fine-grained concept than _“aspect”_. A latent topic or factor can be regarded
as a _sub-aspect_ of an item. For instance, for the “food” aspect, a related
latent topic could be “ _breakfast_ ” or “ _Italian cuisine_ ”. We adopt the
terminology of _latent topic_ in topic models and _latent factor_ in matrix
factorization. Accordingly, “latent topics” are discovered by topic model on
reviews, and “latent factors” are learned by matrix factorization on ratings.

###  3.2. Aspect-aware Latent Factor Model

Based on the observations that (1) different users may care for different
aspects of an item and (2) users’ preferences may differ from each other for
the same aspect, we claim that the overall satisfaction of a user $u$ towards
an item $i$ (i.e., the overall rating $r_{u,i}$) depends on $u$’s satisfaction
on each aspect $a$ of $i$ (i.e., _aspect rating_ $r_{u,i,a}$) and the
importance of each aspect (of $i$) to $u$ (i.e., _aspect importance_
$\rho_{u,i,a}$). Based on the assumptions, the overall rating $r_{u,i}$ can be
predicted as:

(1)
$\vspace{-2pt}\hat{r}_{u,i}=\sum_{a\in\mathcal{A}}\overbrace{\rho_{u,i,a}}^{\mbox{\scriptsize\begin{tabular}[]{@{}c@{}}aspect
importance\end{tabular}}}\underbrace{r_{u,i,a}}_{\mbox{\scriptsize\begin{tabular}[]{@{}c@{}}aspect
rating\end{tabular}}}\vspace{-2pt}$

####  3.2.1. Aspect rating estimation.

Aspect rating (i.e., $r_{u,i,a}$) reflects the satisfaction of a user $u$
towards an item $i$ on the aspect $a$. To receive a high aspect rating
$r_{u,i,a}$, an item should at least possess the characteristics/attributes in
which the user is interested in this aspect. Moreover, the item should satisfy
user’s expectations on these attributes in this aspect. In other words, the
item’s attributes on this aspect should be of high quality such that the user
likes it. Take the “food” aspect as an example, for a user who likes Chinese
cuisines, to receive a high rating on the _“food”_ aspect from the user, a
restaurant should provide Chinese dishes and the dishes should suit the user’s
taste. Based on user’s text reviews, we can learn users’ preferences and
items’ characteristics on each aspect and measure _how the attributes of an
item $i$ on aspect “$a$” suit a user $u$’s requirements on this aspect_,
denoted by $s_{u,i,a}$. We compute $s_{u,i,a}$ based on results of the
proposed Aspect-aware Topic Model (ATM) (described in Sect. 3.3), in which
user’s preferences and item’s characteristics on each aspect are modeled as
multinomial distributions of latent topics, denoted by $\bm{\theta_{u,a}}$ and
$\bm{\psi_{i,a}}$, respectively. $s_{u,i,a}\in[0,1]$ is then computed as :

(2)
$\vspace{-2pt}s_{u,i,a}=1-JSD(\bm{\theta_{u,a}},\bm{\psi_{i,a}})\vspace{-1pt}$

where $JSD(\bm{\theta_{u,a}},\bm{\psi_{i,a}})$ denotes the Jensen–Shannon
divergence (Endres and Schindelin, 2003) between $\bm{\theta_{u,a}}$ and
$\bm{\psi_{i,a}}$. Notice that a large value of $s_{u,i,a}$ does not mean a
high rating $r_{u,i,a}$ \- an item providing all the features that a user $u$
requires does not mean that it satisfies $u$’s expectations, since the
provided ones could be of low quality. For instance, a restaurant provides all
the Chinese dishes the user $u$ likes (i.e., high score $s_{u,i,a}$), but
these dishes taste bad from $u$’s opinion (i.e., low rating $r_{u,i,a}$).
Therefore, we can expect that for this restaurant: users discuss its Chinese
dishes in reviews with negative opinions and thus give low ratings. Instead of
analyzing the review sentiments for aspect rating estimation by using external
NLP tools (such as (Zhang et al., 2015)), we refer to the matrix factorization
(MF) (Koren et al., 2009) technique.

MF maps users and items into a latent factor space and represents users’
preferences and items’ features by $f$-dim latent factor vectors (i.e.,
$\bm{p_{u}}\in\mathbb{R}^{f\times 1}$ and $\bm{q_{i}}\in\mathbb{R}^{f\times
1}$). The dot product of the user’s and item’s vectors
($\bm{p_{u}}^{T}\bm{q_{i}}$) characterizes the user’s overall interests on the
item’s characteristics, and is thus used to predict the rating $r_{u,i}$. To
extend MF for aspect rating prediction, we introduce a binary matrix
$\bm{W}\in\mathbb{R}^{f\times A}$ to associate the latent factors to different
aspects, where $A$ is the number of aspects considered. We call this model
aspect-aware latent factor model (ALFM), in which the weight vector
$\bm{w_{a}}$ in the $a$-th column of $\bm{W}$ indicates which factors are
related to the aspect $a$. Thus, $\bm{p_{u,a}}=\bm{w_{a}}\odot\bm{p_{u}}$
denotes user’s interests in the aspect $a$, where $\odot$ represents element-
wise product between vectors. Therefore, $(\bm{p_{u,a}})^{T}(\bm{q_{i,a}})$
represents the aspect rating of user $u$ to item $i$ on aspect $a$. Finally,
we integrate the matching results of aspects (i.e., $s_{u,i,a}$) into ALFM to
estimate the aspect ratings:

(3)
$\small\vspace{-2pt}r_{u,i,a}=s_{u,i,a}\cdot(\bm{w_{a}}\odot\bm{p_{u}})^{T}(\bm{w_{a}}\odot\bm{q_{i}})\vspace{-1pt}$

As a high aspect rating $r_{u,i,a}$ requires large values of both $s_{u,i,a}$
and $(\bm{w_{a}}\odot\bm{p_{u}})^{T}(\bm{w_{a}}\odot\bm{q_{i}})$, it is
expected that the results learned from reviews could guide the learning of
latent factors.

####  3.2.2. Aspect importance estimation.

We rely on user reviews to estimate $\rho_{u,i,a}$, as users often discuss
their interest topics of aspects in reviews, such as different _cuisines_ in
the _food_ aspect. In general, the more a user comments on an aspect in
reviews, the more important this aspect is (to this user). Thus, we estimate
the importance of an aspect according to the possibility of a user writing
review comments on this aspect. When writing a review, some users tend to
write comments from the aspects according to their own preferences, while
others like commenting on the most notable features of the targeted item.
Based on this consideration, we introduce (1) $\pi_{u}$ to denote the
probability of user $u$ commenting an item based on his own preference and (2)
$\lambda_{u,a}$ ($\sum_{a\in\mathcal{A}}\lambda_{u,a}=1$) to denote the
probability of user $u$ commenting on the aspect $a$ based on his own
preference. Accordingly, $(1-\pi_{u})$ denotes the probability of the user
commenting from the item $i$’s characteristics
($\sum_{a\in\mathcal{A}}\lambda_{i,a}=1$), and $\lambda_{i,a}$ is the
probability of user $u$ commenting item $i$ from the item’s characteristics on
the aspect $a$. Thus, the probability of a user $u$ commenting an item $i$ on
an aspect $a$ (i.e., $\rho_{u,i,a}$) is:

(4)
$\small\vspace{-2pt}\rho_{u,i,a}=\pi_{u}\lambda_{u,a}+(1-\pi_{u})\lambda_{i,a}\vspace{-1pt}$

$\lambda_{u,a}$, $\lambda_{i,a}$, and $\pi_{u}$ are estimated by ATM, which
simulates the process of a user writing a review, as detailed in the next
subsection.

###  3.3. Aspect-aware Topic Model

Given a corpus $\mathcal{D}$, which contains reviews of users towards items
$\\{d_{u,i}|d_{u,i}\in\mathcal{D},u\in\mathcal{U},i\in\mathcal{I}\\}$, we
assume that a set of latent topics (i.e., $K$ topics) covers all the topics
that users discuss in the reviews. $\bm{\lambda_{u}}$ is a probability
distribution of aspects in user $u$’s preferences, in which each value
$\lambda_{u,a}$ denotes the relative importance of an aspect $a$ to the user
$u$. Similarly, $\bm{\lambda_{i}}$ is the probability distribution of aspects
in item $i$’s characteristics, in which each value $\lambda_{i,a}$ denotes the
importance of an aspect $a$ to the item $i$. As the $K$ latent topics cover
all the topics discussed in reviews, an aspect will only relate to some of the
latent topics closely. For example, topic “ _breakfast_ ” is closely related
to aspect “food”, while it is not related to aspects like “ _service_ ” or “
_price_ ”. The relation between aspects and topics is also represented by a
probabilistic distribution, i.e., $\bm{\theta_{u,a}}$ for users and
$\bm{\psi_{i,a}}$ for items. More detailedly, the interests of a user $u$ in a
specific aspect $a$ is represented by $\bm{\theta_{u,a}}$, which is a
multinomial distribution of the latent topics; the characteristics of an item
$i$ in a specific aspect $a$ is represented by $\bm{\psi_{i,a}}$, which is
also a multinomial distribution of the same set of latent topics.
$\bm{\theta_{u,a}}$ is determined based on all the reviews
$\\{d_{u,i}|i\in\mathcal{I}\\}$ of user $u$ writing for items.
$\bm{\psi_{i,a}}$ is learned from all the reviews
$\\{d_{u,i}|u\in\mathcal{U}\\}$ of $i$ written by users. A latent topic is a
multinomial distribution of text words in reviews. Based on these assumptions,
we propose an aspect-aware topic model ATM to estimate the parameters
$\\{\bm{\lambda_{i}}$, $\bm{\lambda_{i}}$, $\bm{\theta_{u,a}}$,
$\bm{\psi_{i,a}}$, $\pi_{u}\\}$ by simulating the generation of the corpus
$\mathcal{D}$.

Figure 1. The graphical representation of the ATM model.

The graphical representation of ATM is shown in Fig. 1. In the figure, the
shaded circles indicate observed variables, while the unshaded ones represent
the latent variables. ATM mimics the processing of writing a review sentence
by sentence. A sentence usually discusses the same topic $z$, which could be
from user’s preferences or from item’s characteristics. To decide the topic
$z_{s}$ for a sentence $s$, our model introduces an indicator variable
$y\in\\{0,1\\}$ based on a Bernoulli distribution, which is parameterized by
$\pi_{u}$. Specifically, when $y=0$, the sentence is generated from user’s
preference; otherwise, it is generated according to item $i$’s
characteristics. $\pi_{u}$ is user-dependent, indicating the tendency to
comment from $u$’s personal preferences or from the item $i$’s characteristics
is determined by $u$’s personality. The generation process of ATM is shown in
Algorithm 1. Let $a_{s}$ denote the aspect assigned to a sentence $s$. If
$y=0$, $a_{s}$ is drawn from $\lambda_{u}$ and $z_{s}$ is then generated from
$u$’s preferences on aspect $a_{s}$: $\bm{\theta_{u,a_{s}}}$; otherwise, if
$y=1$, $a_{s}$ is drawn from $\lambda_{i}$ and $z_{s}$ is then generated from
$i$’s characteristics on aspect $a_{s}$: $\bm{\psi_{i,a_{s}}}$. Then all the
words $w$ in sentence $s$ is generated from $z_{s}$ according to the word
distribution: $\bm{\phi_{z_{s},w}}$.

1for  _each topic $k=1,...,K$ _ do

2 Draw $\bm{\phi_{k,w}}\sim Dir(\cdot|\bm{\beta_{w}})$;

3

4for  _each user $u\in\mathcal{U}$_ do

5 Draw $\bm{\lambda_{u}}\sim Dir(\cdot|\bm{\gamma_{u}})$;

6

7for  _each item $i\in\mathcal{I}$_ do

8 Draw $\bm{\lambda_{i}}\sim Dir(\cdot|\bm{\gamma_{i}})$;

9

10for  _each user $u\in\mathcal{U}$, each aspect $a\in\mathcal{A}$_ do

11 Draw $\bm{\theta_{u,a}}\sim Dir(\cdot|\bm{\alpha_{u}})$;

12

13for  _each item $i\in\mathcal{I}$, each aspect $a\in\mathcal{A}$_ do

14 Draw $\bm{\psi_{i,a}}\sim Dir(\cdot|\bm{\alpha_{i}})$;

15

16for  _each review $d_{u,i},u\in\mathcal{U},i\in\mathcal{I}$ _ do

17 for  _each sentence $s\in d_{u,i}$ _ do

18 Draw $y\sim Bernoulli(\cdot|\pi_{u})$;

19 if  _$y_{s}==0$_ then

20 Draw $a_{s}\sim Multi(\bm{\lambda_{u}})$ and then draw $z_{s}\sim
Multi(\bm{\theta_{u,a_{s}}})$ ;

21 if  _$y_{s}==1$_ then

22 Draw $a_{s}\sim Multi(\bm{\lambda_{i}})$ and then draw $z_{s}\sim
Multi(\bm{\psi_{i,a_{s}}})$;

23

24 for  _each word $w\in s$ _ do

25 Draw $w\sim Multi(\phi_{z_{s},w})$

26

27

Algorithm 1 Generation Process of ATM

In ATM, $\bm{\alpha_{u}}$, $\bm{\alpha_{i}}$, $\bm{\gamma_{u}}$,
$\bm{\gamma_{i}}$, $\bm{\beta}$, and $\eta$ are pre-defined hyper-parameters
and set to be symmetric for simplicity. Parameters need to be estimated
including $\bm{\lambda_{i}}$, $\bm{\lambda_{i}}$, $\bm{\theta_{u,a}}$,
$\bm{\psi_{i,a}}$, and $\pi_{u}$. Different approximate inference methods have
been developed for parameter estimation in topic models, such as variation
inference (Blei et al., 2003) and collapsed Gibbs sampling (Griffiths and
Steyvers, 2004). We apply collapsed Gibbs sampling to infer the parameters,
since it has been successfully applied in many large scale applications of
topic models (Cheng and Shen, 2016; Cheng et al., 2017a). Due to the space
limitation, we omit the detailed inference steps in this paper.

###  3.4. Model Inference

With the results of ATM, $\rho_{u,i,a}$ and $s_{u,i,a}$ can be computed using
Eq. 4 and 2, respectively. With the consideration of bias terms (i.e.,
$b_{u},b_{i},b_{0}$) in ALFM, the overall rating can be estimated as222In our
experiments, we tried to normalize $\rho_{u,i,a}$ or $\rho_{u,i,a}\cdot
s_{u,i,a}$ in Eq. 5, but no improvement has been observed.,

(5) $\hat{r}_{u,i}=\sum_{a\in\mathcal{A}}(\rho_{u,i,a}\cdot
s_{u,i,a}\cdot(\bm{w_{a}}\odot\bm{p_{u}})^{T}(\bm{w_{a}}\odot\bm{q_{i}}))+b_{u}+b_{i}+b_{0}$

where $b_{0}$ is the average rating, $b_{u}$ and $b_{i}$ are user and item
biases, respectively. The estimation of parameters is to minimize the rating
prediction error in the training dataset. The optimization objective function
is

(6)
$\begin{split}\vspace{-2pt}\underset{p*,q*}{\text{min}}\frac{1}{2}\sum_{u,i}(r_{u,i}&-\hat{r}_{u,i})^{2}+\frac{\mu_{u}}{2}||\bm{p_{u}}||_{2}^{2}+\frac{\mu_{i}}{2}||\bm{q_{i}}||_{2}^{2}\\\
&+\mu_{w}\sum_{a}||\bm{w_{a}}||_{1}+\frac{\mu_{b}}{2}(||b_{u}||_{2}^{2}+||b_{i}||_{2}^{2});\vspace{-2pt}\end{split}$

where $||\cdot||_{2}$ denotes the $\ell_{2}$ norm for preventing model
overfitting, and $||\cdot||_{1}$ denotes the $\ell_{1}$ norm.
$\mu_{u},\mu_{i},\mu_{w}$, and $\mu_{b}$ are regularization parameters, which
are tunable hyper-parameters. In practice, we relax the binary requirement of
$\bm{w_{a}}$ by using $\ell_{l}$ norm. It is well known that $\ell_{l}$
regularization yields sparse solution of the weights (Mairal et al., 2010).
The $\ell_{2}$ regularization of $\bm{p_{u}}$ and $\bm{q_{i}}$ prevents them
to have arbitrarily large values, which would lead to arbitrarily small values
of $\bm{w_{a}}$.

Optimization. We use the stochastic gradient descent (SGD) algorithm to learn
the parameters by optimizing the objective function in Eq. 6. In each step of
SGD, the localized optimization is performed on a rating $r_{u,i}$. Let $L$
denote the loss, and the gradients of parameters are given as follows:

$\displaystyle\small\vspace{-2pt}\frac{\partial L}{\partial p_{u}}$
$\displaystyle=\sum_{i=1}^{N}(\sum_{a}\rho_{u,i,a}s_{u,i,a}w_{a}^{2})(\hat{r}_{u,i}-r_{u,i})q_{i}+\mu_{u}p_{u}$
$\displaystyle\frac{\partial L}{\partial q_{i}}$
$\displaystyle=\sum_{u=1}^{M}(\sum_{a}\rho_{u,i,a}s_{u,i,a}w_{a}^{2})(\hat{r}_{u,i}-r_{u,i})p_{u}+\mu_{i}q_{i}$
$\displaystyle\frac{\partial L}{\partial w_{a}}$
$\displaystyle=\sum_{u=1}^{M}\sum_{i=1}^{N}\rho_{u,i,a}s_{u,i,a}(\hat{r}_{u,i}-r_{u,i})p_{u}q_{i}w_{a}+\frac{\mu_{w}w_{a}}{\sqrt{(w_{a}^{2}+\epsilon)}}\vspace{-2pt}$

Here, we omit the gradients of $b_{u}$ and $b_{i}$, as they are the same as in
the standard biased MF (Koren et al., 2009). $M$ and $N$ are the total number
of users and items in the dataset. Notice that in the deriving of the gradient
for $w_{a}$, we use $\sqrt{w_{a}^{2}+\epsilon}$ in place of $||w_{a}||_{1}$,
because $\ell_{1}$ norm is not differentiable at 0. $\epsilon$ can be regarded
as a “smoothing parameter” and is set to $10^{-6}$ in our implementation.

##  4\. Experimental Study

To validate the assumptions when designing the model and evaluate our proposed
model, we conducted comprehensive experimental studies to answer the following
questions:

  * •

RQ1: How do the important parameters (e.g., the number of latent topics and
latent factors) affect the performance of our model? More importantly, is the
setting $f=K$ optimal, which is a default assumption for many previous models?
(Sect. 4.3)

  * •

RQ2: Can our ALFM model outperform the state-of-the-art recommendation
methods, which consider both ratings and reviews, on rating prediction? (Sect.
4.4)

  * •

RQ3: Compared to other methods which also use textual reviews and ratings, how
does our ALFM model perform on the cold-start setting when users have only few
ratings? (Sect. 4.5)

  * •

RQ4: Can our model explicitly interpret the reasons for a high or low rating?
(Sect. 4.6)

Table 2. Statistics of the evaluation datasets Datasets | #users | #items | #ratings | Sparsity
---|---|---|---|---
Instant Video | 4,902 | 1,683 | 36,486 | 0.9956
Automotive | 2,788 | 1,835 | 20,218 | 0.9960
Baby | 17,177 | 7,047 | 158,311 | 0.9987
Beauty | 19,766 | 12,100 | 196,325 | 0.9992
Cell Phones | 24,650 | 10,420 | 189,255 | 0.9993
Clothing | 34,447 | 23,026 | 277,324 | 0.9997
Digital Music | 5,426 | 3,568 | 64,475 | 0.9967
Grocery | 13,979 | 8,711 | 149,434 | 0.9988
Health | 34,850 | 18,533 | 342,262 | 0.9995
Home & Kitchen | 58,901 | 28,231 | 544,239 | 0.9997
Musical Instruments | 1,397 | 900 | 10,216 | 0.9919
Office Products | 4,798 | 2,419 | 52,673 | 0.9955
Patio | 1,672 | 962 | 13,077 | 0.9919
Pet Supplies | 18,070 | 8,508 | 155,692 | 0.9990
Sports & Outdoors | 31,176 | 18,355 | 293,306 | 0.9995
Tools & Home | 15,438 | 10,214 | 133,414 | 0.9992
Toys & Games | 17,692 | 11,924 | 166,180 | 0.9992
Video Games | 22,348 | 10,672 | 228,164 | 0.9990
Yelp 2017 | 169,257 | 63,300 | 1,659,678 | 0.9998

###  4.1. Dataset Description

We conducted experiments on two publicly accessible datasets that provide user
review and rating information. The first dataset is Amazon Product Review
dataset collected by (McAuley and Leskovec,
2013)333http://jmcauley.ucsd.edu/data/amazon/, which contains product reviews
and metadata from Amazon. This dataset has been widely used for rating
prediction with reviews and ratings in previous studies (McAuley and Leskovec,
2013; Ling et al., 2014; Tan et al., 2016; Catherine and Cohen, 2017). The
dataset is organized into 24 product categories. In this paper, we used 18
categories (See Table 2) and focus on the 5-core version, with at least 5
reviews for each user or item. The other dataset is from Yelp Dataset
Challenge 2017444http://www.yelp.com/dataset_challenge/, which includes
reviews of local business in 12 metropolitan areas across 4 countries. For the
Yelp 2017 dataset, we also processed it to keep users and items with at least
5 reviews. From each review in these datasets, we extract the corresponding
“userID”, “itemID”, a rating score (from 1 to 5 rating stars), and a textual
review for experiments. Notice that for all the datasets, we checked and
removed the duplicates, and then filtered again to keep them as 5-core.
Besides, we removed the infrequent terms in the reviews for each
dataset.555The thresholds of infrequent terms varied across different
datasets. For example, for the “Yelp 2017” dataset, which is relatively large,
a term that appears less than 10 times in reviews is defined as an infrequent
term; and the thresholds are smaller for relatively small datasets (e.g., the
threshold is 5 for the “Music Instruments” dataset).) Some statistics of the
datasets are shown in Table 2.

###  4.2. Experimental Settings

For each dataset, we randomly split it into training, validation, and testing
set with ratio 80:10:10 for each user as in (McAuley and Leskovec, 2013; Ling
et al., 2014; Catherine and Cohen, 2017). Because we take the 5-core dataset
where each user has at least 5 interactions, we have at least 3 interactions
per user for training, and at least 1 interaction per user for validation and
testing. Note that we only used the review information in the training set,
because the reviews in the validation or testing set are unavailable during
the prediction process in real scenarios. The number of aspect is set to 5 in
experiments.666We tuned the number of aspects from 1 to 8 for all the
datasets, and found that the performance does not change much unless setting
the aspect number to 1 or 2.

Baselines: We compare the proposed ALFM model with the following baselines. It
is worth noting that these methods are tuned on the validation dataset to
obtain their optimal hyper-parameter settings for fair comparisons.

  * •

BMF (Koren et al., 2009). It is a standard MF method with the consideration of
bias terms (i.e., user biases and item biases). This method only leverages
ratings when modeling users’ and items’ latent factors. It is typically a
strong baseline model in collaborative filtering (Koren et al., 2009; Ling et
al., 2014).

  * •

HFT (McAuley and Leskovec, 2013). It models ratings with MF and review text
with latent topic model (e.g., LDA (Blei et al., 2003)). We use it as a
representative of the methods which use an exponential transformation function
to link the latent topics with latent factors, such as TopicMF (Bao et al.,
2014). The topic distribution can be modeled on either users or items. We use
the topic distribution based on items, since it achieves better results. Note
that in experiments, we add bias terms into HFT, which can achieve better
performance.

  * •

CTR (Wang and Blei, 2011). This method also utilizes both review and rating
information. It uses a topic model to learn the topic distribution of items,
which is then used as the latent factors of items in MF with an addition of a
latent variable.

  * •

RMR (Ling et al., 2014). This method also uses both ratings and reviews.
Different from HFT and CTR, which use MF to model rating, it uses a mixture of
Gaussian to model the ratings.

  * •

RBLT (Tan et al., 2016). This method is the most recent method, which also
uses MF to model ratings and LDA to model review texts. Instead of using an
exponential transformation function to link the latent topics and latent
factors (as in HFT (McAuley and Leskovec, 2013)), this method linearly
combines the latent factors and latent topics to represent users and items,
with the assumption that the dimensions of topics and latent factors are equal
and in the same latent space. The same strategy is also adopted by ITLFM
(Zhang and Wang, 2016). Here, we use RBLT as a representative method for this
strategy.

  * •

TransNet (Catherine and Cohen, 2017). This method adopts neural network
frameworks for rating prediction. In this model, the reviews of users and
items are used as input to learn the latent representations of users and
items. More descriptions about this method could be found in Section 2. We
used the codes published by the authors in our experiments and tuned the
parameters as described in (Catherine and Cohen, 2017).

The standard root-mean-square error (RMSE) is adopted in evaluation. A smaller
RMSE value indicates better performance.

Table 3. Comparisons of adopted methods in terms of RMSE with $f=K=5$.

Datasets |  BMF |  HFT |  CTR |  RMR |  RBLT |  TransNet |  ALFM | Improvement(%)
---|---|---|---|---|---|---|---|---
(a) |  (b) |  (c) |  (d) |  (e) |  (f) |  (g) |  g vs. a |  g vs. b |  g vs. c |  g vs. d |  g vs. e |  g vs. f
Instant Video |  1.162 |  0.999 |  1.014 |  1.039 |  0.978 |  0.996 |  0.967 |  16.79 |  3.19 |  4.63* |  6.94* |  1.12** |  2.88
Automotive |  1.032 |  0.968 |  1.016 |  0.997 |  0.924 |  0.918 |  0.885 |  14.26* |  8.58** |  12.86* |  11.19* |  4.24** |  3.56*
Baby |  1.359 |  1.112 |  1.144 |  1.178 |  1.122 |  1.110 |  1.076 |  20.83** |  3.24 |  5.98* |  8.66** |  4.11 |  3.05*
Beauty |  1.342 |  1.132 |  1.171 |  1.190 |  1.117 |  1.123 |  1.082 |  19.39** |  4.47 |  7.65** |  9.12** |  3.18** |  3.65**
Phones |  1.432 |  1.216 |  1.271 |  1.289 |  1.220 |  1.207 |  1.167 |  18.47** |  3.98* |  8.18* |  9.4** |  4.33 |  3.27**
Clothing |  1.073 |  1.103 |  1.142 |  1.145 |  1.073 |  1.064 |  1.032 |  3.8** |  6.47** |  9.65 |  9.9** |  3.86** |  2.96*
Digital Music |  1.093 |  0.918 |  0.921 |  0.960 |  0.918 |  1.061 |  0.920 |  15.82 |  -0.15 |  0.13* |  4.49** |  -0.15** |  4.13**
Grocery |  1.192 |  1.016 |  1.045 |  1.061 |  1.012 |  1.022 |  0.982 |  17.66** |  3.36** |  6.07 |  7.46** |  3.01** |  3.94*
Health |  1.263 |  1.073 |  1.105 |  1.135 |  1.070 |  1.114 |  1.042 |  17.48* |  2.83 |  5.65* |  8.20 |  2.56** |  6.46**
Home & Kitchen |  1.297 |  1.083 |  1.123 |  1.149 |  1.086 |  1.123 |  1.049 |  19.16** |  3.15** |  6.62 |  8.7** |  3.41** |  6.61**
Musical Instruments |  1.004 |  0.972 |  0.979 |  0.983 |  0.946 |  0.901 |  0.893 |  11.08 |  8.17** |  8.83** |  9.2** |  5.61 |  0.95
Office Products |  1.025 |  0.879 |  0.898 |  0.934 |  0.872 |  0.898 |  0.848 |  17.29** |  3.55** |  5.61* |  9.26** |  2.77** |  5.67**
Patio |  1.180 |  1.041 |  1.062 |  1.077 |  1.032 |  1.046 |  1.001 |  15.19** |  3.84* |  5.7* |  7.07* |  2.96 |  4.33**
Pet Supplies |  1.367 |  1.137 |  1.177 |  1.200 |  1.139 |  1.149 |  1.099 |  19.64** |  3.41* |  6.67* |  8.41 |  3.54** |  4.38**
Sports & Outdoors |  1.130 |  0.970 |  0.998 |  1.019 |  0.964 |  0.990 |  0.933 |  17.42** |  3.8* |  6.47 |  8.4* |  3.2** |  5.77**
Tools & Home |  1.168 |  1.013 |  1.047 |  1.090 |  1.011 |  1.041 |  0.974 |  16.63** |  3.90 |  6.98 |  10.68** |  3.7** |  6.51**
Toys & Games |  1.072 |  0.926 |  0.948 |  0.974 |  0.923 |  0.951 |  0.902 |  15.81** |  2.59* |  4.82** |  7.39** |  2.3** |  5.11*
Video Games |  1.321 |  1.096 |  1.115 |  1.150 |  1.094 |  1.123 |  1.070 |  19.02* |  2.43 |  4.03** |  6.97* |  2.24** |  4.77*
Yelp 2017 |  1.415 |  1.174 |  1.233 |  1.266 |  1.202 |  1.190 |  1.155 |  18.35* |  1.60** |  6.33** |  8.74* |  3.88** |  2.92*
Average |  1.207 |  1.044 |  1.074 |  1.097 |  1.037 |  1.049 |  1.004 |  14.56** |  2.84* |  7.16** |  8.31* |  3.37** |  4.26**

  * •

The improvements with * are significant with $p-value<0.05$, and the
improvements with ** are significant with $p-value<0.01$ with a two-tailed
paired t-test.

Figure 2. Effects of factors and topics in our model.

(a) Clothing (b) Yelp 2017

Figure 3. Effects of #factors v.s. #topics.

###  4.3. Effect of Important Parameters (RQ1)

In this subsection, we analyze the influence of _the number of latent factors_
and _the number of latent topics_ on the final performance of ALFM. As we
know, in MF, more latent factors will lead to better performance unless
overfitting occurs (He et al., 2016; Koren et al., 2009); while the optimal
number of latent topics in topic models (e.g., LDA) is dependent on the
datasets (Blei, 2012; Arun et al., 2010). Accordingly, the optimal number of
latent topics in topic model and the optimal number of latent factors in MF
should be tuned separately. However, in the previous latent factor models
(e.g., HFT, TopicMF (Bao et al., 2014), RMR, CTR, and RBLT), the number of
factors (i.e., #factors) and the number of topics (i.e., #topics) are assumed
to be the same, and thus cannot be optimized separately. Since our model does
not have such constraint, we studied the effects of #factors and #topics
individually. Fig. 2 show the performance variations with the change of
#factors and #topics by setting the other one to 5. We only visualize the
performance variations of three datasets, due to the space limitation and the
similar performance variation behaviors of other datasets. From the figure, we
can see that with the increase of #factors, RMSE consistently decreases
although the degree of decline is small. Notice that in our model, the rating
prediction still relies on MF technique (Eq. 5). Therefore, the increase of
#factors could lead to better representation capability and thus more accurate
prediction. In contrast, the optimal number of latent topics is different from
dataset to dataset.

To better visualize the impact of #factors and #topics, we also present 3D
figures by varying the number of factors and topics in $\\{5,10,15,20,25\\}$,
as shown in Fig. 3. In this figure, we use the performance of three datasets
as illustration. From the figure, we can see that the optimal numbers of
topics and latent factors are varied across different datasets. In general,
more latent factors usually lead to better performance, while the optimal
number of latent topics is dependent on the reviews of different datasets.
This also reveals that setting #factors and #topics to be the same may not be
optimal.

###  4.4. Model Comparison (RQ2)

We show the performance comparisons of our ALFM with all the baseline methods
in Table 3, where the best prediction result on each dataset is in bold. For
fair comparison, we set the number of latent factors ($f$) and the number of
latent topics ($K$) to be the same as $f=K=5$. Notice that our model could
obtain better performance when setting $f$ and $K$ differently. Still, ALFM
achieves the best results on 18 out of the 19 datasets. Compared with BMF,
which only uses ratings, we achieve much better prediction performance (16.49%
relative improvement on average). More importantly, our model outperforms CTR
and RMR with large margins - 6.28% and 8.18% relative improvements on average,
respectively. Compared to the recently proposed RBLT and TransNet, ALFM can
still achieve 3.37% and 4.26% relative improvement on average respectively
with significance testing. It is worth mentioning that HFT achieves better
performance than RMR and comparable performance with recent RBLT, because we
added bias terms to the original HFT in (McAuley and Leskovec, 2013). TransNet
applies neural networks, which has exhibited strong capabilities on
representation learning, in reviews to learn users’ preferences and items’
characteristics for rating prediction. However, it may suffer from (1) noisy
information in reviews, which would deteriorate the performance; and (2)
errors introduced when generating fake reviews for rating prediction, which
will also cause bias in the final performance. Compared to those baselines,
the advantage of ALFM is that it models users’ preferences on different
aspects; and more importantly, it captures a user’s specific attention on each
aspect of a targeted item. The substantial improvement of ALFM over those
baselines demonstrates the benefits of modeling users’ specific preferences on
each aspect of different items.

(a) Clothing

(b) Yelp 2017

(c) All Datasets

Figure 4. Gain in RMSE for user with limited training data on two individual
datasets and overall 19 datasets.

###  4.5. Cold-Start Setting (RQ3)

As shown in Table 2, the datasets are usually very sparse in practical
systems. It is inherently difficult to provide satisfactory recommendation
based on limited ratings. In the matrix factorization model, given a few
ratings, the penalty function tends to push $q_{u}$ and $p_{i}$ towards zero.
As a result, such users and items are modeled only with the bias terms (Ling
et al., 2014). Therefore, matrix factorization easily suffers from the cold-
start problem. By integrating reviews in users’ and items’ latent factor
learning, our model could alleviate the problem of cold-start to a great
extent, since reviews contain rich information about user preferences and item
features.

To demonstrate the capability of our model in dealing with users with very
limited ratings, we randomly split the datasets into training, validation, and
testing sets in ratio 80:10:10 based on the number of ratings in each set. In
this setting, it is not guaranteed that a user has at least 3 ratings in the
training set. It is possible that a user has no rating in the training set.
For the users without any ratings in the training set, we also removed them in
the testing set. Then we evaluate the performance of users who have the number
of ratings from 1 to 10 in the training set. In Fig. 4, we show the Gain in
RMSE ($y$-axis) grouped by the number of ratings ($x$-axis) of users in the
training set. The value of Gain in RMSE is equal to the average RMSE of
baselines _minus_ that of our model (e.g., “BMF-TALFM”). A positive value
indicates that our model achieves better prediction. As we can see, our ALFM
model substantially improves the prediction accuracy compared with the BMF
model. More importantly, our model also outperforms all the other baselines
which also utilize reviews. This demonstrates that our model is more effective
in exploiting reviews and ratings, because it learns user’s preferences and
item’s features in different aspects and is capable of estimating the aspect
weights based on the targeted user’s preferences and targeted item’s features.

Table 4. Top ten words of each aspect for a user (index 1511) from _Clothing_. Each column is corresponding to an aspect attached with an “interpretation” label. Value | Comfort | Accessories | Shoes | Clothing
---|---|---|---|---
price | size | ring | socks | shirt
color | fit | pretty | foot | back
quality | wear | dress | boots | bra
worth | comfortable | time | comfort | top
cute | bra | beautiful | sandals | feel
comfortable | small | gift | walk | soft
fits | color | earrings | toe | black
ring | fits | compliments | pairs | jeans
dress | perfect | chain | hold | pants
shirt | material | jewelry | strap | tight
material | long | shoes | pockets | material
Table 5. Interpretation for why the “user 1511” rated “item 1” and “item 2” with 5 and 2, respectively, from _Clothing_. Aspects | Value | Comfort | Accessories | Shoes | Clothing
---|---|---|---|---|---
Importance (1) | 0.621 | 0.042 | 0.241 | 0.001 | 0.095
Matching (1) | 0.982 | 0.596 | 0.660 | 0.759 | 0.638
Polarity (1) | + | - | + | - | +
Importance (2) | 0.621 | 0.042 | 0.241 | 0.001 | 0.094
Matching (2) | 0.920 | 0.303 | 0.362 | 1.000 | 0.638
Polarity (2) | - | - | - | - | +

###  4.6. Interpretability (RQ4)

In our ALFM model, a user’s preference on an item is decomposed into user’s
preference on different aspects and the importance of those aspects. An aspect
is represented as a distribution of latent topics discovered based on reviews.
A user’s attitude/sentiment on an aspect of the targeted item is decided by
the latent factors (learned from ratings) associating with the aspect. Based
on the topic distribution of an aspect ($\bm{\theta_{u,a_{s}}}$) and the word
distribution of topics ($\bm{\phi_{w}}$), we can semantically represent an
aspect by the top words in this aspect. Specifically, the probability of a
word $w$ in an aspect $a_{s}$ of a user $u$ can be computed as
$\sum_{k=1}^{K}\theta_{u,a_{s},k}\phi_{k,w}$. The top 10 aspect words (#aspect
$=5$) of “user 1511” from _Clothing_ dataset discovered by our model are shown
in Table 4. Notice that in order to obtain a better visualization of each
aspect, we removed the “background” words that belong to more than 3 aspects.
As shown in Table 4, the five aspects can be semantically interpreted to
“value”777“Value” means value for money, “comfort”, “accessories”, “shoes”,
and “clothing”. Next, we illustrate the interpretability of our ALFM model on
high or low ratings by examples from the same dataset. Table 5 shows the
aspect importance (i.e., $\rho_{u,i,a}$ in Eq. 4) of the “user 1511” , the
aspect matching scores (i.e., $s_{u,i,a}$ in Eq. 2) as well as sentiment
polarity (obtained by Eq. 5) on the five aspects with respect to “item 1” and
“item 2” in _Clothing_ dataset. From the results, we can see that “user 1511”
pays more attention to “Value” and “Accessories” aspects. On the “Value”
aspect, both “item 1” and “item 2” highly match her preference, however, she
has a positive sentiment on “item 1” while a negative sentiment on “item
2”.888As a reminder, the aspect matching is based on the reviews. It is
possible that both item 1 and item 2 contains comments on aspect “value”.
However, “item 1” has a high value while “item 2” has a low value. For the
“Accessories” aspect, “item 1” has a higher matching score than “item 2”; and
more importantly, the sentiment is positive on “item 1” while negative on
“item 2”. As a result, “user 1511” rated “item 1” with 5 while rated “item 2”
with 2. From the examples, we can see that our model could provide
explanations for the recommendations in depth with _aspect semantics_ ,
_aspect matching score_ , as well as _aspect ratings_ (which shows sentiment
polarity).

##  5\. Conclusions

In this paper, we proposed an aspect-aware latent factor model for rating
prediction by effectively combining reviews and ratings. Our model correlates
the latent topics learned from review text and the latent factors learned from
ratings based on the same set of aspects, which are discovered from textual
reviews. Accordingly, our model does not have the constraint of one-to-one
mapping between latent factors and latent topics as previous models (e.g.,
HFT, RMR, RBLT, etc.), and thus could achieve better user preference and item
feature modeling. Besides, our model is able to estimate aspect ratings and
assign weights to different aspects. The aspect weight is dependent on each
user-item pair, since it is estimated based on user’s personal preferences on
the corresponding aspect towards an item. Experimental results on 19 real-
world datasets show that our model greatly improves the rating prediction
accuracy compared to the state-of-the-art methods, especially for users who
have few ratings. With the extracted aspects from textual reviews, estimated
aspect weights, and aspect ratings, our model could provide interpretation for
recommendation results in great detail.

###### Acknowledgements.

This research is supported by the National Research Foundation, Prime
Minister’s Office, Singapore under its International Research Centre in
Singapore Funding Initiative. The authors would like to thank Rose Catherine
Kanjirathinkal (from CMU)’s great help on fine-tuning the results of TransNet
on all datasets.

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