Discussion Paper No. 115
Customer Review Analysis
Using Word Embedding
Model Considering Text Topics

Mirai Igarashi, P. K. Kannan
and Nobuhiko TeruiJune, 2020

 Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku

Sendai 980-8576, JAPANCustomer Review Analysis Using Word Embedding
Model Considering Text Topics
Mirai Igarashi ∗P. K. Kannan †Nobuhiko Terui ‡May 2020

Abstract
Customers often give feedback on their evaluations and experiences with the products
and service in the form of customer reviews, and developing the technology of customer
review analysis plays an important role in the modern marketing research. Existingstudies on marketing have used topic models to capture the review generating behaviors, but this approach ignores the word ordering, that is, it assumes a bag-of-words,
and thus cannot adequately consider the context of text even with topic models. In
this study, we propose a model combining supervised topic model and word embedding model for estimating the relationship between the product attributes mentioned
in the customer review and their satisfactions while capturing the context of review
text customers generate. In the empirical analysis, we apply the proposed model toa real customer review data on mascara-related products on a cosmetics e-commerce
site, and the results show that our model captures some interpretable topics related tomascara products and estimates their eﬀects on satisfaction scores, for example, the“eyelash” topic mentioned in the review tends to result in high levels of satisfaction,
while the “brush” topic is associated with low levels of satisfaction.
Keywords: Customer review analysis, Word embedding, Skip-gram model, Topic
model, Supervised learning∗

Mirai Igarashi is Doctoral Student, Graduate School of Economics and Management, Tohoku University,
27-1, Kawauchi Aoba-ku, Sendai, 980-8576, Japan (E-mail: mirai.igarashi.s7@dc.tohoku.ac.jp). Igarashi
acknowledges a grant by JSPS KAKENHI 18J20698.
†
P. K. Kannan is Professor, Robert H. Smith School of Business, University of Maryland (E-mail: pkkannan@rhsmith.umd.edu)‡
Nobuhiko Terui is Professor, Graduate School of Economics and Management, Tohoku University (Email: terui@tohoku.ac.jp). Terui acknowledges a grant by JSPS KAKENHI (A) 17H01001.

1

Introduction

With the development of e-commerce sites, it has become commonplace that consumers
purchase products online and give feedback on their evaluations and experiences with the
products in the form of customer reviews. Companies utilize this wealth of information tounderstand consumer preference structures and make use of it in a variety of marketing
activities, such as product development, market analysis, and advertising strategy planning.
Therefore, developing the technology of customer review analysis plays a vital role in themodern marketing research.
In the literature, modeling the consumer behavior of creating customer reviews has beenstudied by many researchers to reveal the preference structure behind them. Many of them
adopt the topic model, or latent Dirichlet allocation (LDA, Blei et al., 2003), to model thereview generating behavior (e.g., Tirunillai and Tellis, 2014). In such studies, it is assumed
that when consumers write reviews, they have certain topics, or product attributes, in mind
and generate text by selecting words from own vocabulary to describe their evaluations andexperiences with respect to these attributes.
From the perspective of text modeling, however, LDA has a major problem of ignoring
the important information of context because it applies bag-of-words—meaning that word
ordering does not matter. The LDA takes into account whether words of interest (e.g., aproduct name and its evaluation such like good and bad) co-occurs in the same textual unit
(e.g., a review), but it cannot understand the semantic relationships between the words. For
example, if a review describes the good points of one product attribute and the bad pointsof another attribute, LDA regards that the good attribute co-occurs with some words used
to describe the bad attribute.
On the other hand, word embedding model, or the word2vec (Mikolov et al., 2013), isa machine learning method that has a great success in the ﬁeld of text modeling. The
word2vec deﬁnes the probability of word generation given the surrounding words (i.e., theskip-gram model) while it projects words into a feature space. Therefore, the word2vec
1

can understand the word context in terms of considering the words in the window because
the word2vec regards that words related to a product attribute co-occur only with theirsurrounding words which can be considered to qualify the words, not with words related
to another attribute which are at a distance in the same document. This approach can beapplied in a variety of domains from sentiment classiﬁcation (Zhang et al., 2015) to item
recommendations (Caselles-Dupré et al., 2018).
However, because we aims to understand preference structures behind review generating
behavior, there are not many advantages of using word2vec as it is. The feature vectorsof words resulting from embedding learning are usually very high dimensional, and it is
impossible to interpret each dimension, as in factor analysis or principal component analysis.
Therefore, even if word2vec is applied to customer review analysis, we may not know what
consumers express about which attributes in their reviews.
In this study, we propose a model for review generating behaviors based on word2vec and
LDA by leaning vectors with respect to not only words but also topics projected into thesame feature space. The purpose of this study is to clarify the eﬀects of product attributes
mentioned in customer reviews on the customers’ satisfactions while considering the contexts
by combining the word embedding model and topic model.
In the following sections, ﬁrst we discuss related works in the relevant body of literature.
Next, we describe the model structure that combines word and topic embedding systems
and regression model. In the empirical study, we apply the proposed model to a real dataset
on e-commerce sites about cosmetics. Finally, we provide concluding remarks and directions
for future research.

2

Literature Review

In the literature, researchers proposed some approaches using interviews and questionnaires
to clarify the consumer preference structure (Fischer et al., 1999; Hoeﬄer, 2003). However,2because these approaches are costly to implement and the obtained data is limited, it was
required to use new data sources, such as information on the internet (Netzer et al., 2008).
As alternatives to the approaches using interviews and questionnaires, the use of customer
reviews has been proposed. Decker and Trusov (2010) estimated the impact of productattributes that were positively or negatively mentioned in the customer reviews on customer
satisfactions using a latent class Poisson regression. Archak et al. (2011) proposed a demand
estimation model that captures the eﬀects of product attributes on sales considering theheterogeneity of each word that qualiﬁes the attributes. Companies and marketers can use
the relationship between product attributes and customer satisfactions or sales for a variety
of marketing activities, such as to analyze the market structure (Lee and Bradlow, 2011;
Moon and Kamakura, 2017) and to improve the product search algorithm (Ghose et al.,2012).
In these studies, they extract the product attributes mentioned in the customer reviews,
and then propose models to captures their relationships with objective variables such as
review ratings and sales. In other words, the product attributes are regarded as just observed
variables. In contrast, some studies simultaneously model the generation of customer reviews
and the formation of customer satisfaction, and they often apply topic models, in which the
product attributes are treated as the latent variables (e.g., Qi et al., 2016; Puranam et al.,2017; Bi et al., 2019). Topic modeling approach assumes that consumers have topics (productattributes) in their mind and their evaluations and experiences about the topics are embodied
in the text and ratings of customer reviews.
However, since topic model or LDA regards the observed text information as the sets ofwords ignoring their order, i.e., bag-of-words, the main disadvantage of this approach is thatit cannot consider the context of text (Berger et al., 2020). For example, if there are twosentences, “I prefer the macbook instead of the surface” and “I prefer the surface insteadof the macbook,” the LDA model considers them to be the same data, even though thesereviews state completely conﬂicting preferences. This characteristics can be a more serious

3

drawback in the customer review analysis.
In the marketing literature, some studies tackle to relax the bag-of-words assumption,for example, Büschken and Allenby (2016) propose the extended LDA model that assign
topics not to words independently but to sentences taking into account the within-sentence
dependencies. Liu and Toubia (2018) also extend the LDA model by considering hierarchically the contexts of related documents (e.g., search queries and results), and hence their
proposed model assigns topics which are related to topics in the correspondence documents
rather than independently assignment.
On the other hand, this study focuses on the skip-gram model using word embedding representation (Mikolov et al., 2013) to relax the bag-of-words assumption for the more appropriate text modeling. For the generating probability of a certain word, the skip-gram considers
the conditional probability given the surrounding words of the focal word. For example, if
considering a problem of predicting appropriate word in a sentence, “I ... a student.” (“...”is a masked word), the skip-gram deﬁnes the conditional probability, p(... | I, a, student).
Therefore, it is expected that p(am | I, a, student) is larger than p(are | I, a, student) if theskip-gram learns good embedding representations. While Büschken and Allenby (2016)’s
model takes a sentence as a unit to assign the same topic to the words in the sentence, theskip-gram takes a moving window as a unit to assign topics considering the co-occurrence
relationships of the words in the window.
Moreover, we focus on the word embedding approach which the word2vec (Mikolov et al.,2013), on which the proposed model is based, takes with the skip-gram model. Word embedding approach assumes an embedding vector in feature space for each word, and it canrepresent more ﬂexibly the semantically meanings of words compared to other naive vector
representation such as one-hot vector. The formulation of the skip-gram using word embedding approach is known as word2vec, and as described above,word2vec also considers the→conditional probability of the focal word given the surrounding word. Let −w i be the word i’sembedding representation, word2vec deﬁnes the conditional probability as the inner product4−→  exp(−
−
→
→
→
→
→
of the word vectors, p(−
wi | −w j ) = exp(−w
w
i w j )/
i w v ). In recent years, withv
the development of deep learning and related technologies, there are a number of research
aimed at acquiring embedding representations of not only words but also documents (Le and
Mikolov, 2014) and products (Barkan and Koenigstein, 2016).
However, it is diﬃcult to apply the word2vec approach to customer review analysis as itis because we cannot interpret each dimension of word embedding vector and linguisticallyunderstand the relationships among words. While word2vec approach may be eﬀective in
predicting text, it does not help us to understand the eﬀects of the product attributes
mentioned in customer reviews on the customers’ satisfactions, which is the purpose ofthis study. In this study, we propose a model combining word2vec with supervised topic
model by assuming embedding vectors for words and topics in the same feature space. Sincewords which have similar vector representations to the topic vector can be regarded to be
representative of that topic, we can interpret the extracted topics. Therefore, we achieve
the same objectives as the LDA model, obtaining summaries of the documents in the topic
dimensions, while relaxing the bag-of-words assumption.
The combination of the topic model and word2vec itself has been proposed in Moody(2016)’s LDA2vec, however, this study extends his model from the following two perspectives.
First perspective is that the proposed model combines with the supervised topic modelfor explaining the eﬀects of product attributes on the customer satisfactions, rather thanunsupervised learning such as LDA. We can extract topics or product attributes in thereviews considering not only the text structure but also the relationships between the topics
and the customer satisfaction through the supervised learning process. Second perspectiveis that we assume explicitly the topic assignment into the words as the augmented variable,
which is more oriented to the formulation of the original LDA model. As explained in thenext section, we apply diﬀerent estimation procedure—the stochastic optimization and theBayesian estimation— for estimation the embedding vectors and the regression parameters,
respectively, to reduce the computational cost, and this data augmentation simpliﬁes the5derivation of the conditional distributions and allows for the separation of the estimation
methods.

3

Model

In this section, we describe the formulation of the proposed model in the order of the wordembedding part and then the regression model part for the preference measurement. First, we
take two embedding vectors, word vector and topic vector, with a ﬁxed embedding dimension,−→→
M , and let −w i = {wi1 , . . . , wiM } and t k = {tk1 , . . . , tkM } be these vectors, respectively,
where wim , tkm ∈ R ∀i, k, m. Words and topics are projected into the same feature space. In
addition, it is assumed that a topic is assigned to the word i according to the topic proportion
vector speciﬁc to the document to which the word i belongs, zi ∼ Categorical(θdi ), wherezi represents the topic assignment for word i and θdi is the topic proportion vector of the
document to which the word i belongs.
The proposed model represents the context of the word i using a context vector represented by the sum of the word vector and the topic vector corresponding the topic assignment−→→→
to the word i,−ci = −
w i + t k , if zi = k. For example, the context of the word “small” ina sentence “The body of this mobile battery is small and convenient to carry out.” is expressed in a positive sense with the linguistic meaning of small if it is in a document withrespect to the topic of the mobile battery. In contrast, if the word “small” had been used
in a sentence about a mobile display, its contextual meaning would have a negative sense,
at least in modern times. The approach of constructing a context vector by the sum of theword vector and the topic vector has also been used in Moody (2016)’s LDA2vec. His model
constructs a document vector by the inner product of the topic proportion and the topic
vectors, and formulates the context vector as the sum of the word vector and the document
vector. In contrast, this study is more oriented to the formulation of the LDA model in thatthe context is directly formulated as the sum of the word meanings and its topic by assuming

6

the latent variables of topic assignment.
The proposed model considers its surrounding words to deﬁne the probability of generating the focal word. We deﬁne Si as a multiset that contains the surrounding words of theword i in the dataset. Let IP = {(i, j) | j ∈ Si } and IN = {(i, j) | j ∈/ Si } be the positive
and negative multisets, respectively, and ID = IP ∪ IN be the multiset of total vocabulary.
Then, we deﬁne G = {gij | (i, j) ∈ IG }, where gij is a random variable whose value is taken
to be 1 if (i, j) ∈ IP or −1 if (i, j) ∈ IN . In the proposed model, this random variable indicating whether the word i and the word j are in the same window is assumed to follow thebinomial logit model, which the probability of the variable is deﬁned as the standard sigmoid(or logistic) function of the inner product of the context vector and the surrounding word
−
→
−
→
→
→
→
vector, p(gij | −w i, −
w j , { t k }, zi ) = σ(gij · −c
i w j ), where σ(x) = 1/1 + exp(−x). Because→
the dependent variable of the logit model (−c i ) is also latent variable, this formulation can→→be seen as the factor model by regarding −c i as factor scores of the word i and −w j as factor→
loadings of the word j. However, this factor model has a constraint that factor score −c i can−→→→be decomposed into the word vector and the corresponding topic vector, −ci=−
w i + t k.
Therefore, the likelihood of the word embedding part is provided as follows:


V
V


−
→
→
−
→
→
p(G, {−
w i }, { t k }, Z | θ) =σ(gij · −cp(zi | θdi )i w j) ,(1)

j=1,i=ji=1

where V is the number of total vocabulary in the corpus. In the proposed model, theembedding vectors are trained to maximize the probability of the inner product of the context
vector and the surrounding word vector, so that word vectors which their correspondingwords often belong to the same window in a dataset will have similar values. Therefore,
we can obtain vector representations taking into account the co-occurrence of words withinwindow, that is, the context, while LDA uniformly considers the co-occurrence of words ina document.
However, the computation cost of the likelihood (1) is very high because the number of7total vocabulary is usually over thousands and the total cost of the likelihood is its square.
In this study, according to the approach proposed by Mikolov et al. (2013), we also apply
negative sampling technique to approximate the likelihood (1) with the following computable
formulation:⎧−→→p(G, {−
w i }, { t k }, Z | θ) ≈

V ⎨

i=1

⎩

p(zi | θdi )



−
→
→
σ(−
c
i w j) ×

N


−
→
→
σ(−−
c
i w n)n∼Pn (w)

j∈Si

⎫
⎬
⎭

,

(2)

where Pn (w) is the noise distribution as a free parameter, and we choose the unigram distribution raised to the 3/4 rd power according to the Mikolov et al. (2013)’s suggestion. The
number of negative samples, N , is suggested to be 5 − 20 for a small dataset and 2 − 5 for alarge dataset. In machine learning research, since they use a huge dataset containing millions
and sometimes billions words for training, our dataset is small in comparison to them andwe determine 15 words for the number of negative samples.
Next, we construct the prediction model for the customer review ratings using the ordered
probit model, which is the similar formulation to Büschken and Allenby (2016). Recallingthat the topic assignments is assumed to follow the categorical distribution of the topic
proportion, zi ∼ Categorical(θdi ), the topic proportion θd represents the summary of the
product attributes mentioned in the review d in the dimensions of topics and works as
dependent variables for explaining the customer satisfaction in the proposed model. Let yd
be the satisfaction score of the review d, which follows the ordered probit model:

yd = ryd∗ =if τr−1 ≤ yd∗ < τrKβk θdk + d ,

d ∼ N (0, 1),

(3)

k=1

where the thresholds {τr } work for realizing discrete satisfaction scores (yd ) through thelatent continuous variable (yd∗ ), and the both sides of thresholds, τ0 and τR , are set to−∞ and ∞, respectively. Since the proposed model contains no intercept term and the ﬁxed

8

variance parameter in the regression, the model can be identiﬁed for all remaining thresholds
parameters.
Therefore, the likelihood of the regression part for the customer satisfaction is provided
as follows:p(Y, β, τ | θ) =Dp(yd | yd∗ , τ )p(yd∗ | θd , β)× p(β),(4)d=1

where p(β) is the prior distribution for the regression coeﬃcients and the deﬁnition is explained in the appendix. Under the assumption of the conditional independence of likelihood(1) and (4) when the topic distributions are given, the full joint likelihood of the proposedmodel is obtained by the product of equations (1) and (4) multiplied by the prior density forthe topic distribution, which is assumed to be the Dirichlet prior p(θd | θ0 ) ∼ Dirichlet(θ0 )in this study.
In estimation procedure of the proposed model, we take a hybrid approach combining theMarkov Chain Monte Carlo (MCMC) sampling method and the gradient-based stochastic
optimization using Adam (Kingma and Ba, 2015). The proposed estimation procedure produces point estimates for two embedding vectors through the stochastic optimization, andthen apply the Metropolis-Hastings sampling for the topic distributions and the Gibbs sampling for the remaining parameters given the embedding vector estimates every for updating
via the optimization. The estimation procedure and the settings of analysis in the empirical
study are explained in more detail in the appendix.

4

Empirical Results

4.1

Data

In the empirical study, we use product reviews on the website www.sephora.com which is an
e-commerce site primarily dedicated to cosmetics, and they were collected by the authors in

9

January 2020. This dataset consists of 8,551 customer reviews on 52 mascara products of 25
brands generated from January 1, 2019 to December 31, 2019. Prior to data analysis, thereviews were preprocessed including the removal of symbols, substituting with lower-caseletters, and the removal of reviews consisting of less than 10 words. As a result, the numberof words used in the ﬁnal dataset is 376,033, and the number of unique words is 7,853. The
number of words in the review is from 10 words to 287 words, and the histogram distribution
is right-skewed. The average of the number of words in the review is 44.0 words per review,the median is 37 words, and the standard deviation is 29.5.
The review includes not only the text but also the satisfaction (rating) scores for the
products observed on a ﬁve-point scale. The frequency of the rating scores is 917, 736, 1,009,
1,751, and 4,143 in the order of 1 to 5. This positively skewed (J-shaped) characteristics iswell-known in many previous studies (e.g., Xiao et al., 2016).

4.2

Results

First, we determine the number of topics by comparing models with varying numbers throughmodel selection using the criterion, where in this study, we use the log marginal density(LMD) calculated by the method of Newton and Raftery (1994). Table 1 reports the LMDs
for the rating scores in the range of the number of topics from 5 to 10, and the model with10 topics is the largest. In the following analysis, we use the proposed model with 10 topics.
Next, we interpret each dimension of the topics by interpreting the coherency of word
meanings from the words associated with the topic. In the proposed model, since we estimate the embedding vectors of words and topics in the same feature space, we can consider
the word whose word vector is the closest to the topic vector as the most related word tothat topic. Table 2 displays the top 20 words corresponding to the closest word vectors toeach topic vector. The words for each topic provide some coherent descriptions of the mascara products, for example, topic 1 is a description of ﬂaking such that discusses how hard
the mascara is to peel oﬀ, as evidenced by the use of words such as “ﬂakes,” “hour,” and10

“smudges.” Topic 3 talks about contents of the mascaras because it consists of “volume,”“length(en),” and “color.” Additionally, topic 9 describes the attribute of brush (such as“brush” and “bristle”). Figure 1 shows the proportion of topics for which the topic distributions (θ) is aggregated for all the customer reviews. These topics 1, 3, and 9 are mentioned
in many reviews. Topic 2, 7, and 10 seem to be less discussed in the reviews but they area collection of words associated with reviews written by the consumers who received thecomplimentary samples. These three topics are closely related each other in the point of thesemantically meaning, but they are extracted as separate topics.
Finally, we discuss the estimation results of regression coeﬃcients and thresholds, andTable 3 provides the posterior mean estimates and the 95% highest posterior density (HPD).
The threshold parameters (τr ) indicate that an approximate 0.50 increase in the latentcontinuous rating is associated with a one-point increase in the observed discrete rating.
For example, if the proportion that a review mentions about the topic “Eyelash” increase by
one unit, the expected change in the latent rating is 0.538, translating to an almost one-point
increase in customer satisfaction.
Table 3 also provides some interesting ﬁndings related to the regression coeﬃcients. The
coeﬃcients of topics 3 and 5 for the satisfaction score are positively estimated with significance, and this ﬁndings indicates that satisﬁed customers are more likely to talk about“contents” and “eyelash” topics. In contrast, the coeﬃcients of topics 1 and 9 are negatively
estimated, which show that customers tend to be dissatisﬁed with the product attributes of“ﬂaking” and “brush”. Another topics 2, 7, and 10, which concern the critique of the use of
product by those who have been oﬀered free samples, are related to a little negative scoreor have no signiﬁcant relationship. In addition, topic 6, which may appear in the reviewsby the customers who have tried and bought the trial products such as smaller sizes, isnegatively estimated. This topic can be considered to be in similar situation to the complimentary topics in terms of the reviews by ﬁrst-time buyer, except that they do not allow to
oﬀer the free samples. Thus, the proposed model can estimate the impact of not only the11Table 1: Model comparison using log marginal density
Number of topics
5
Log marginal density -1492.66

6-1303.82

7-1383.23

8-1316.52

9-2226.84

10-1259.65

0.15

Proportion

0.10

0.05

0.00
1

2

3

4

5

6

7

8

9

10

Topic

Figure 1: The proportion of topic distribution

product attributes, such as eyelash and brush, but also the situation in purchasing, such ascomplimentary and trying, on the customer satisfaction.

5

Conclusion

We introduced a model for capturing review generating behaviors based on word embedding
approach and topic modeling by leaning feature vectors with respect to not only words but
also topics or product attributes projected into the same feature space. The proposed modelallows us to consider the order of words in the text and understand the context, which
the traditional topic modeling approach for the customer review analysis do not take into
account. To estimate the eﬀect of the product attributes mentioned in the review text on
customer satisfaction, we connect the proportion of the extracted topics in the review with

12

Table 2: Top 20 words in the proposed model
Topic 1
“Flaking”
eyes
oﬀ
under
raccoon
water
day
ﬂakes
eye
hours
hour
face
smudgesskinmorning
throughout
ﬂakingmakeupburneyelids
rubbing
Topic 6
“Trying”
reviewssize
try
sephorawas
thisboughtsamplepatbuybuying
mini
box
but
the
mascara
write
trial
play
beautyTopic 2“Complimentary”
complimentaryencourage
review
inﬂuenster
purposes
testing
receivedfreehonestopinions
voxboxproduct
item
iliabeauty
opinioncomplementary
inﬂuenstervoxbox
sampling
promotional
test
Topic 7“Complimentary”
recivedjuscomplimentary
purposesmonsieurbigmascara
testing
review
purposecomplimentry
complementary
received
inﬂuenster
honestsampling
product
freevoxboxcourtesy
fromexchange

Topic 3Topic 4
“Contents” “Eyebrows”
volumeweeks
andresults
gives
serum
does
using
lengtheyebrows
clump
see
doesn
noticedgreat
diﬀerencebuildablemonthsmascara
grown
not
brows
adds
grow
color
now
the
growthseparates
saw
lengthensweeklengthening
month
but
lash
lashesbeenbuildsconsistent
Topic 8Topic 9“Too faced”“Brush”
better
brush
sex
the
than
wand
mascarasbristlestried
comb
drugstoregetcameratube
cheaper
itself
faced
big
ysl
formuladior
applicatorbeneﬁt
gets
years
apply
jacobsclumpy
best
hard
nars
and
ever
tip
lancome
too
holy
mess
tarte
dries

13

Topic 5“Eyelash”
eyelasheslashes
look
makes
long
straight
short
them
naturally
curled
thin
and
fake
longerasian
curl
blonde
are
have
false
Topic 10
“Complimentary”
complimentary
inﬂuenster
voxboxfree
receivedfromtesting
test
sent
purposesreview
gift
recieved
product
complementaryaccessholidayvoxbox
reviewingvox
via

Table 3: The estimated coeﬃcients of the topic regression (bold numbers indicate the signiﬁcance of the posterior mean from the 95% HPD test)
PosteriorMean
τ1− 1.408
τ2−1.025
τ3−0.628τ4−0.074β1 (Flaking)−0.331β2 (Complimentary)
0.005
β3 (Contents)
0.331
β4 (Eyebrows)−0.018β5 (Eyelash)
0.538
β6 (Trying)−0.453β7 (Complimentary)−0.064β8 (Too faced)
0.119
β9 (Brush)−0.947β10 (Complimentary) −0.204
Parameter

95% HPDInterval[-1.446, -1.373][-1.041, -1.007][-0.647, -0.606][-0.081, -0.066][-0.458, -0.198][-0.160, 0.178][0.209, 0.450][-0.150, 0.117][0.397, 0.674][-0.585, -0.304][-0.233, 0.120][-0.029, 0.272][-1.070, -0.817][-0.369, -0.046]

the satisfaction rating score as the ordered probit regression. In the empirical study, weapply the proposed model for the e-commerce review dataset on the mascara products, andﬁnd some interpretable topics, such as “eyelash” and “brush”, and estimate the their eﬀects
on satisfaction scores.
However, additional research is needed in the three aspects: First aspect is developing as
marketing model through a consideration word sentiments and product brands. Referring to
the existing literature, it is important for estimation of their impact on customer satisfaction
to consider what emotions are used in conjunction with the product attributes and how muchthe unique inﬂuence of the product brand is, which are not taken into account in this study.
Second aspect is validation of the advantages by taking a word embedding approach throughmodel comparison. This study has only proposed a model for customer review analysis using
word embedding and has not yet conducted comparison analysis to show an advantage overother existing models. Third aspect is the expansion of the empirical analysis to generalize
the ﬁndings. In order to generalize the results such as those found in this empirical study,14

it is necessary to analyze multiple product categories, in addition to the mascara category
data conducted in this study.

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Appendix
A

Estimation Procedure

In this appendix, we describe the details of estimating procedure for the proposed model. In
this study, we apply a hybrid approach combining the gradient-based stochastic optimizationand Markov Chain Monte Carlo (MCMC) sampling method. First, we describe the algorithmof the optimization for embedding vector parameters, which is known as Adam (Kingma andBa, 2015). The objective loss function to minimize is deﬁned as the negative mean of log
likelihood:L(φ) = −

⎧
⎨

1
−
→
→
log σ −ci wj +
V i=1 ⎩j∈S
V

i

N

−
→
→
log σ −−ci wn

n∼Pn (w)

⎫
⎬
⎭

,

(A.1)

(s)

where φ represents the set of parameters for embedding vectors. Let fh = ∂L(φ(s) )/∂φh be
the gradient of the loss function with respect to h-th parameter at s-th iteration, and wedeﬁne two momentum terms as
(s)

(s−1)

(s)

mh = γ 1 × mh(0)

+ (1 − γ1 ) × fh , mh = 0

2
(s)
(s−1)
(s)
(0)
vh = γ 2 × vh
+ (1 − γ2 ) × fh
, vh = 0

(A.2)
(A.3)

(s)

m̂h =

(s)

mh
1 − γ1s

(A.4)

(s)
v̂h =

vh
,
1 − γ2s

(A.5)

(s)

where γ1 and γ2 are coeﬃcients used for computing running averages of the gradient and its
square, and they are set to be 0.9 and 0.999, respectively, in this empirical study. Finally,17

we update the focal parameter value using the following update rule,
(s+1)

φh

(s)

= φh − 

η
(s)

(s)

× m̂h ,

(A.6)

v̂h + where η is a learning rate parameter and set to be 0.001, and  is a small value added to thedenominator to improve numerical stability and set to be 10−8 . Updating the embedding
vectors via Adam optimization, we obtain their point estimates for each iteration. Next,
given these embedding vector estimates, we conduct the MCMC sampling for the remaining
parameters.
The conditional probability density and the sampling equations for the remaining parameters, the topic assignment zi = k, the latent continuous rating yd∗ , regression coeﬃcients β,
and the thresholds τr , are given as:

−
→
→
→
−
→
w i }, { t k }, θdi ) ∝ θdi ×σ −c
p(zi = k | {−i wj ×yd∗ | yd , θd , β, τ ∼ N

 K



N


→
−
→ 
σ −−
c
i wn

(A.7)

n∼Pn (w)j∈Siβk θdk , 1 , truncated to (τr−1 , τr ] if yd = r
k=1

β | Y ∗ , θ ∼ N (μβ , Σβ ) ,

 D
Σβ =

−1
θd θd + b−1
0 ·I

d=1

τr | Y, Y ∗ , τq ∼ U [τ−∗ , τ+∗ ],

(A.8)

 D
,

μβ = Σβyd∗ θd(A.9)

d=1

r = 1, . . . , R − 1, q = r

τ−∗ = max(max{yd∗ ; yd = r}, τr−1 ),τ+∗ = min(min{yd∗ ; yd = r + 1}, τr ),(A.10)

where b0 is a hyper parameter of the precision for the coeﬃcients and set to be 0.01. Then,we employ the independence chain Metropolis-Hastings algorithm to estimate the topic distribution because the joint conditional density of θd is given by the product of the truncatednormal density for yd∗ , the multinomial density of the topic assignments, and the Dirichlet
density for the prior distribution, which the constant term of this posterior density is unknown. In the procedure of the sampling, we generate the candidate θdcand from the proposal

18

density which is the Dirichlet distribution of the posterior density of the latent Dirichlet
allocation model, Dirichlet(Nd· + θ0 ), where Nd· is a vector of the number of words to which
each topic is assigned, and θ0 is a hyper parameter of the Dirichlet prior distribution andset to be 0.8. As a result of this generation for the candidate, all elements in the Metropolis
acceptance ratio α cancel out, except for the likelihood component of the regression model.
Therefore, the Metropolis ratio is given by the ratio of the truncated normal distribution,α=p(yd∗ | yd , θdcand , β, τ ).
p(yd∗ | yd , θd , β, τ )(A.11)In the empirical study, we repeat the above updating process and the MCMC process
10,000 times, and then we use the 5,000 samples excluding the burn-in samples to calculate
the posterior means and the intervals of the highest posterior density.

19