Neural Explainable Collective Non-negative Matrix Factorization for
Recommender Systems
Felipe Costa and Peter Dolog
Aalborg Uiversity, Selma Lagerløfs Vej 300, 9220, Aalborg, Denmark
Keywords:
Explainability, Recommender Systems, Matrix Factorization.
Abstract:
Explainable recommender systems aim to generate explanations for users according to their predicted scores,
the user’s history and their similarity to other users. Recently, researchers have proposed explainable recom-
mender models using topic models and sentiment analysis methods providing explanations based on user’s
reviews. However, such methods have neglected improvements in natural language processing, even if these
methods are known to improve user satisfaction. In this paper, we propose a neural explainable collective non-
negative matrix factorization (NECoNMF) to predict ratings based on users’ feedback, for example, ratings
and reviews. To do so, we use collective non-negative matrix factorization to predict user preferences accord-
ing to different features and a natural language model to explain the prediction. Empirical experiments were
conducted in two datasets, showing the model’s efficiency for predicting ratings and generating explanations.
The results present that NECoNMF improves the accuracy for explainable recommendations in comparison
with the state-of-art method in 18.3% for NDCG@5, 12.2% for HitRatio@5, 17.1% for NDCG@10, and
12.2% for HitRatio@10 in the Yelp dataset. A similar performance has been observed in the Amazon dataset
7.6% for NDCG@5, 1.3% for HitRatio@5, 7.9% for NDCG@10, and 3.9% for HitRatio@10.
1 INTRODUCTION
Recommender systems have become an important
method in online services, aiming to help users to fil-
ter items of their preferences, such as movies, places,
or products. The most well-known model to rec-
ommend top-N items is collaborative filtering (CF),
which recommend items according to the user’s simi-
larities with other users and/or items. However, tradi-
tionally CF methods focus on users, items, and their
interactions to recommend a sorted list of N items.
Among CF techniques, matrix factorization (MF)
has been widely applied in recommender systems be-
cause of its accuracy in providing personalized rec-
ommendation based on user-item interactions, for ex-
ample, overall ratings. However, users may have dif-
ferent preferences about specific features of the same
item as seen in Figure 1. Hence it is a challenge to
infer whether a user would prefer a specific feature
from an item based on overall rating. For example, in
the restaurant domain, one user may rate a restaurant
3-stars due to service, while another user may give the
same rating due to food. This example, shows the im-
portance to model different features when developing
a recommendation method, since those features may
help to explain why a CF model recommends a spe-
cific list of items to a user.
Food
Service
Location
Ambiance
Family
Friendly
Music
Recommendation
Figure 1: Example of Review-aware Recommendation.
Online services provide other explicit feedback
besides the overall ratings, such as item’s content
features, contextual information, sentiments, and re-
views. Items’ content features describe attributes of
an item, for example, which food is served in the
restaurant. Contextual information defines the situ-
ation experienced by a user, for example, if a user
has been in a restaurant for business or leisure. Sen-
timents describes the positive or negative experience
of a user regarding an item. Reviews are user’s per-
sonal assessment about an item, which may describe
items’ content features according to her/his prefer-
Costa, F. and Dolog, P.
Neural Explainable Collective Non-negative Matrix Factorization for Recommender Systems.
DOI: 10.5220/0006893700350045
In Proceedings of the 14th International Conference on Web Information Systems and Technologies (WEBIST 2018), pages 35-45
ISBN: 978-989-758-324-7
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
35

ences. Those explicit feedback have been applied sep-
arately as feature to predict user preferences, however
as aforementioned, a user may like or dislike an item’s
content feature in different contexts.
We propose to align those features using non-
negative collective matrix factorization model, called
NECoNMF. NECoNMF factorizes ratings, item’s
content features, contextual information, and senti-
ment in four non-negative low-rank matrices, repre-
sented in a common latent space. The hypothesis is
that jointly decomposition of different matrices into
the same factor space (for example, users’ prefer-
ences, items’ content features, contextual informa-
tion, and sentiment) improves the prediction of top-N
recommendation.
Moreover, the reviews represent an additional in-
formation for collaborative filtering. Recent research
has modeled reviews to generate explanations for rec-
ommender systems, which are known as explainable
recommendations. Explicit factor model (EFM) de-
veloped by (Zhang et al., 2014) extracts features and
user opinions by phrase-level sentiment analysis on
user generated reviews, and explain the recommenda-
tion based on the extracted information. TriRank pro-
posed by (He et al., 2015) uses a tripartite graph to en-
rich the user-item binary relation to a user-item-aspect
ternary relation. Both projects propose to extract as-
pects from reviews to generate explainable recom-
mendations, but they do not consider influence maxi-
mization in social relation as a source of explanation.
Recently, (Ren et al., 2017) propose the social col-
laborative viewpoint regression model (sCVR), which
detects viewpoints and uses social relations as a la-
tent variable model. sCVR is represented as a tuple of
concept-topic-sentiment from both user reviews and
trusted social relations.
The aforementioned techniques have shown im-
provements in explaining recommendations, however
they neglected how to present the textual explanations
while keeping their accuracy in top-N recommen-
dation. Recently, natural language processing tech-
niques have applied deep learning methods, such as
recurrent neural network (RNN), which has demon-
strated significant improvement in character-level lan-
guage generation, due to the ability to learn latent in-
formation. However, RNN does not capture depen-
dencies among characters, since it suffers from gradi-
ent vanishing problem (Bengio et al., 1994). To solve
this issue, long short-term memory (LSTM) have
been introduced by (Hochreiter and Schmidhuber,
1997; El Hihi and Bengio, 1995) revealing good re-
sults in generating text upon different datasets (Karpa-
thy et al., 2015) and machine translation (Sutskever
et al., 2014).
In this paper, we propose a neural explainable
collective non-negative matrix factorization based on
two steps: (1) prediction of user’s preferences by col-
lectively factorizing ratings, items’ content features,
contextual information and sentiments; and (2) gen-
erative text reviews given a vector of ratings, which
shows specific opinions about different items’ fea-
tures.
The experiments were performed using two real-
world datasets: Yelp and Amazon, where our method
outperforms the state-of-art in terms of Hit Ration and
NDCG.
This paper presents the following contributions:
• Neural Explainable Collective Non-negative Ma-
trix Factorization;
• Collective factorization of four matrices: ratings,
item’s content features, contextual information,
and sentiments;
• Text generation model using neural networks;
• Results according to empirical experiments in two
real-world datasets.
2 RELATED WORKS
Related work can be divided in two tasks: top-N rec-
ommendations and explainable recommendations.
Top-N Recommendations. The most well-known
methods are Popular Items (PopItem) (Cremonesi
et al., 2010) and PageRank (Haveliwala, 2002), since
they present reasonable results and simple implemen-
tation. Another widely applied method is matrix fac-
torization (MF), for example SVD (Koren et al., 2009)
and NMF (Lee and Seung, 2000). SVD was first ap-
plied on the Netflix dataset, presenting good results
in terms of prediction accuracy. Likewise, NMF has
received attention, due to its easy interpretability for
matrices decomposition.
Matrix factorization has been extended over the
years to improve its effectiveness, where collective
matrix factorization has shown good performance.
This technique was applied in multi-view clustering,
where it splits objects into clusters based on multiple
representations of the object, as shown by (Liu et al.,
2013; He et al., 2014). (Liu et al., 2013) proposed
MultiNMF, using a connection between NMF and
PLSA, and (He et al., 2014) proposed a co-regularized
NMF (CoNMF), where comment-based clustering is
formalized as a multi-view problem using pair-wise
and cluster-wise CoNMF.
Local collective embeddings (LCE) is a collective
matrix factorization method proposed by (Saveski and
WEBIST 2018 - 14th International Conference on Web Information Systems and Technologies
36

Mantrach, 2014), which exploits user-document and
document-terms matrices, identifying a common la-
tent space to both item features and rating matrix.
LCE has shown effectiveness in cold-start problem
for news recommendation, however, it has some lim-
itations. The method does not perform well in our
domain which covers online services as restaurants
and e-commerce, because it uses only two matrices
as input and multiplicative update rules as learning
model. An extension of LCE is proposed by (Costa
and Dolog, 2018), named CHNMF, where collective
factorization is applied in three different matrices us-
ing hybrid regularization term. In this paper, we ex-
tend the CHNMF approach decomposing a matrix as
a product of four matrices: ratings, item’s content fea-
tures, contextual information, and sentiments. Con-
tent features are data from each item’s metadata, rat-
ings represents user’s preferences, contextual infor-
mation is the situation where the user rates an item,
and sentiment is the positive (1) or negative (−1) pref-
erence given by a user to an item’s feature.
Explainable Recommendations. Explainable rec-
ommendation aims to improve transparency, effec-
tiveness, scrutability, and user trust (Zhang et al.,
2014). These criteria can be achieved by different
methods to explain the recommendation to a user,
such as graph or table, however for this project we se-
lected two baselines which uses textual information to
justify their predictions. (Zhang et al., 2014) proposes
the explicit factor model based on sentiment lexicon
construction and (He et al., 2015) proposed TriRank
algorithm to improve the ranking of items for review-
aware recommendation.
Our proposal differs from these models in two as-
pects: we collectively factorize ratings, item’s con-
tent features, contextual information, and sentiments;
and apply a character-level explanation model for rec-
ommendation using LSTM for text generation (Costa
et al., 2018).
3 PROBLEM FORMULATION
The research problem investigated in this paper is
defined as followed: Explain the recommended list
of items to each user based on ratings, item’s con-
tent features, contextual information, and sentiments
from user-item interactions. Modeling the rating data
X
u
from a set of users U to a set of items I under
X
a
types of content, X
c
types of context, and X
s
ex-
plicit sentiments as four two-dimensional matrices.
We can formally define them as: user-item matrix
X
u
= {x
u
∈ R
u×i
|1 ≤ x
u
≤ 5}; user-content feature
matrix X
a
= {x
a
∈ Z
u×a
|0 ≤ x
a
≤ 1}; user-context ma-
trix X
c
= {x
c
∈ Z
u×c
|0 ≤ x
c
≤ 1}; and user-sentiment
matrix X
s
= {x
s
∈ Z
u×s
||x
s
| = 1}. Where, u is the
number of users, i is the number of items, a is the
content size, c is the context, and s is the sentiment
regarding item features.
Factor models aim to decompose the original user-
item interaction matrix into two low-rank approxima-
tion matrices. Collective non-negative matrix factor-
ization is a generalization of the classic matrix fac-
torization, where the latent features are stored in four
low-rank matrices: ratings as W × H
u
; content fea-
tures as W × H
a
; context as W × H
c
; and sentiment as
W ×H
s
. Where, H
u
denotes a row vector representing
the latent features for user u. Similarly, H
a
represents
the content’s latent features a, H
c
represents the con-
text’s latent features c, and H
s
defines the sentiment’s
latent features. Finally, W represents the common la-
tent space.
The matrix factorization method does not provide
human-oriented explanations. To address this partic-
ular issue, our model is defined to target the problem
of generating natural language review-oriented expla-
nations.
We formulate the explanation for rating prediction
as: given input ratings vector r
ui
= (r
1
, . . . , r
|r
ui
|
) we
aim to generate item explanation e
i
= (w
1
, . . . , w
|t
i
|
)
by maximizing the conditional probability p(e|r).
Note, rating r
ui
is a vector of the user’s overall and
specific rating of different features from a target item
i. While the review t
i
is considered a sequence of
characters of variable length. For Yelp dataset, we
set |r| as 5, representing 5 different features: f ood,
service, ambiance, location, and f amily f riendly.
The model learns to compute the likelihood of gen-
erated reviews given a set of input ratings. This con-
ditional probability p(e|r) is represented in Equation
1.
p(e|r) =
|e|
∏
s=1
p(w
s
|w < s, r)
(1)
where w < s = (w
1
, . . . , w
t−1
)
4 METHODOLOGY
In this section, we describe NECoNMF for rating pre-
diction and natural language generation model.
4.1 Collective Matrix Factorization
We propose collective non-negative matrix factoriza-
tion applied to domains with specific available infor-
mation, such as, ratings, content features, context, and
Neural Explainable Collective Non-negative Matrix Factorization for Recommender Systems
37

sentiment. This information is decomposed into four
matrices in a common latent space, i.e., each user-
item can be related to item’s content features, contex-
tual situation, sentiment, and ratings.
X
u
X
a
X
s
X
c
[3, 4, food, 3, service, 2, ambiance, 3,
location, positive, weekend]
Explicit
Features
H
u
H
a
V H
s
H
c
Hidden
Features
r"
Predicted
rating
Figure 2: Collective Non-Negative Matrix Factorization.
Considering an online restaurant service as seen
in Figure 2, where a user may rate a specific restau-
rant (here defined as an item) according to different
criteria, such as, f ood, service, ambiance, and
location. Furthermore, the user may write a review
and give an overall rating about the item. Based on
this example, we may retrieve content-feature matrix
X
a
, user-item matrix X
u
, user-context matrix X
c
,
and user-sentiment matrix X
s
. If we factorize X
a
in
two low-dimensional matrices, we will observe the
content features is belonging to an item. Factorizing
X
u
leads to find the items according to the users’
preferences. While factorizing matrix X
c
allow us to
identify the hidden contextual factors related to the
item. Likewise, factorizing X
s
highlight the positive
and negative sentiments from a user given to an item’s
feature. If each matrix is factorized independently it
will represent a different latent space and there will
be no correlation between content feature, context,
sentiment, and rating matrix. The idea of collective
non-negative matrix factorization is that each entity:
users, items, content features, contexts, and sentiment
should be represented in a common latent space,
meaning that each item can be described by a set
of sentiments (for example, positive), and by a set
of explicit feedback (for example, ratings). The
proposal is to collectively factorize X
u
, X
a
, X
c
, and X
s
into a low-dimensional representation in a common
latent space. The formal definition, is given as the
following optimization problem:
min : f (W ) =
1
2
[αkX
u
−WH
u
k
2
2
+ βkX
a
−WH
a
k
2
2
+γkX
c
−WH
c
k
2
2
+ ωkX
s
−WH
s
k
2
2
+λ(kW k
2
+ kH
u
k
2
+ kH
a
k
2
+ kH
c
k
2
) + kH
s
k
2
)]
s.t.W ≥ 0, H
u
≥ 0, H
a
≥ 0, H
c
≥ 0, H
c
≥ 0,
(2)
where the first four terms correspond to the fac-
torization of the matrices X
u
, X
a
, X
c
, and X
s
. The ma-
trix W represents the common latent space, and H
u
,
H
a
, H
c
, and H
s
are matrices representing the hidden
factors for each item-user interaction feature. The
hyper-parameters are defined by α, β, γ, and ω to
control the importance of each factorization with val-
ues between 0 and 1. Setting the hyper-parameters
as 0.25 gives equal importance to the matrices de-
composition, while values of α, β, γ, and ω set as
> 0.25 (or < 0.25) give more importance to the fac-
torization of X
u
(or X
a
, or X
c
, or X
s
), respectively.
The Tikhonov regularization of W is controlled by the
hyper-parameter λ ≥ 0 to enforce the smoothness of
the solution and avoid overfitting.
4.1.1 Optimization
Alternating optimization is required in NECoNMF
to minimize the objective function, since perform-
ing collective factorization leads us to find a common
low-dimensional space that is optimal for the linear
approximation of the user and item data points. As-
sume the data from user and item has a common dis-
tribution where it can exploit a better low-dimensional
space, i.e., two data points, u
i
and v
j
, are close to each
other in the low-dimensional space, if they are geo-
metrically close in the distribution. This assumption
is known as the manifold assumption and is applied
in algorithms for dimensionality reduction and semi-
supervised learning (Saveski and Mantrach, 2014).
We model the local geometric structure through a
nearest neighbour graph on a scatter of data points as
seen in (Saveski and Mantrach, 2014). Considering a
nearest neighbour graph, we represent each data point
as node n. Then, we find the k nearest neighbours for
each node, and we connect these nodes in the graph.
The edges may have: (1) binary representation, where
1 defines one of the nearest neighbours and otherwise
0; (2) or weights representation, for example, pearson
correlation. The result of this process is an adjacency
matrix A, which may be used to find the local close-
ness of two data points u
i
and v
j
.
Based on this assumption, we assume the collec-
tive factorization reduces the data point u
i
from a ma-
trix X, into a common latent space W as w
i
. Then,
applying Euclidean distance kw
i
− w
j
k
2
, we can cal-
culate the distance between two low-dimensional data
WEBIST 2018 - 14th International Conference on Web Information Systems and Technologies
38

points and map them into the matrix A. We repeat the
process until the stationary point or the established
number of maximum iterations, as follows:
M =
1
2
n
∑
i, j=1
kw
i
− w
j
k
2
A
i j
=
n
∑
i=1
(w
T
i
− w
i
)D
ii
−
n
∑
i, j=1
(w
T
i
− w
i
)D
ii
= Tr(W
T
DW ) − Tr(W
T
AW ) = Tr(W
T
LW ),
(3)
where Tr(•) is the trace function, and D is the di-
agonal matrix whose entries are row sums of A (or
column, as A is symmetric). To enforce the non-
negative constraints, we need to define the Laplacian
matrix as D
i
i =
∑
i
A
i
j; L = D − A.
We can re-write the optimization problem of func-
tion f (W ) as:
min : f (W ) =
1
2
[αkX
u
−WH
u
k
2
2
+ βkX
a
−WH
a
k
2
2
+γkX
c
−WH
c
k
2
2
+ ωkX
s
−WH
s
k
2
2
+ϕTr(W
T
LW )
+λ(kW k
2
+ kH
u
k
2
+ kH
a
k
2
+ kH
c
k
2
+ kH
s
k
2
)]
s.t.W ≥ 0, H
u
≥ 0, H
a
≥ 0, H
c
≥ 0, H
s
≥ 0
(4)
where ϕ is a hyper-parameter controlling the ob-
jective function, and the hyper-parameters α, β, γ, ω,
and λ have the same semantics as in Equation 2.
4.2 Multiplicative Update Rule
Multiplicative update rule (MUR) is applied in the
model as regularization term of W . MUR updates the
scores in each iteration to reach the stationary point,
where we fix the value of W while minimizing f (W )
over H
u
, H
a
, H
c
, and H
s
. We formalize the partial
derivative function in Equation 5 before calculating
the update rules.
∇ f (W ) = αW H
u
H
T
u
− αY
u
H
T
u
+ βW H
a
H
T
C
− βY
a
H
T
a
+γW H
c
H
T
c
− γY
c
H
T
c
+ ωW H
s
H
T
s
− ωY
s
H
T
s
+ λI
k
(5)
where k is the number of factors and I
k
is the iden-
tity matrix with k × k dimensions.
The update rules are formalized as in Equation
6, after calculating the derivatives of f (W ), f (H
u
),
f (H
a
), f (H
c
), and f (H
s
) from Equation 5.
W =
[αY
u
H
T
u
+ βY
a
H
T
a
+ γY
c
H
T
c
+ ωY
s
H
T
s
]
[αH
U
H
T
U
+ βH
a
H
T
a
+ γH
c
H
T
c
+ ωH
s
H
T
s
+ λI
k
]
(6)
where
•
•
corresponds to left division.
The results of each iteration give us the solution
for pair-wise division, where the objective function
and the delta decrease on each iteration of the above
update rule, guaranteeing the convergence into a sta-
tionary point. Note, we map any negative values from
W matrix to zero, becoming non-negative after each
update.
4.3 Barzilai-Borwein
The Brasilai-Borwein regularization term is used to
optimize the hidden factor matrices H
u
, H
a
, H
c
, and
H
s
. We represent the hidden factor matrices as H
for the input matrices X
u
, X
a
, X
c
, and X
s
, since they
present equal problem as shown in Equation 7:
min
W ≥0
: f (H) =
1
2
kX −W Hk
2
F
(7)
We map all the negative values into zero through
P(•) for any α > 0, as we defined for W in the previ-
ous section. Equation 8 formally describes the state-
ment as:
kP[H − α∇ f (H)]− Hk
F
= 0.
(8)
Applying ε
H
in Equation 8 lead us to the following
regularization term kP[H − α∇ f (H)] − Hk
F
≤ ε
H
,
where ε
H
= max(10
−3
, ε)kP[H − α∇ f (H)] − Hk
F
.
We decrease the stopping tolerance by ε = 0.1ε
H
, if
the Borzilai-Borwein algorithm defined in (Costa and
Dolog, 2018) solves Equation 7 without any itera-
tions.
The gradient ∇ f (W ) of f (H) is Lipschitz term
with constant L = kW
T
W k
2
. L is not expensive to ob-
tain, since Equation 4 defines W
T
W with dimensions
k × k and k  min{m, n}. For a given H
0
≥ 0:
L (H
0
) = {H| f (H) ≤ f (H
0
), H ≥ 0}.
(9)
Following the definition of Equation 9 we have the
stationary point of the Barzilai-Borwein method.
4.4 Top-N Recommendation Process
Factorizing the input matrices return the trained ma-
trices W , H
u
, H
a
, H
c
, and H
s
allows us to use the
hidden factor elements for prediction. Given the new
items’ vector v
i
, we can predict the most preferable
items according to the user’s interest v
u
. To solve
this issue we project the items vector v
i
to the com-
mon latent space by solving the overdetermined sys-
tem v
i
= wH
u
using the least squares method. The
vector w, captures the factors, in the common latent
space, that explain the preferable items v
i
. Then, by
using the low-dimensional vector w we infer the miss-
ing part of the query: v
u
← wH
t
where H
t
is the con-
catenation of content feature, context, and sentiment
Neural Explainable Collective Non-negative Matrix Factorization for Recommender Systems
39

matrices H
t
= H
a
||H
c
||H
s
. Each element of v
u
repre-
sents a score of how likely the user will like a new
item. Then, given these scores, we may sort the list of
items.
Moreover, given the sorted list of items and their
rating scores, we explain the predicted ratings using
the natural language generation model. The expla-
nation model uses the ratings as attention model to
generate personalized sentences according to user’s
writing style. The training model identifies positive
and negative sentences according to the user’s previ-
ous reviews.
4.5 Natural Language Explanation
The natural language generation model is divided in
(1) four sub-models: context encoder, LSTM net-
work, attention layer, and generator model; and (2)
two input sources: review text and concatenated char-
acter embeddings of user, item, and rating vector, as
presented in Figure 3. First, users and items em-
beddings are learned from doc2vec model (Le and
Mikolov, 2014), where characters of reviews are con-
verted to one-hot vectors, corresponding to the input
time-steps of LSTM network. Second, the embed-
dings are concatenated with the outputs of LSTM,
which are inputs for the following attention layer. Fi-
nally, the generator model produce sentences using
outputs from the attention layer.
r"
doc2vec
LSTM
g
[3,4]
r
[3,4]
e
[3,4]
a
[3,4]
t
[3,4]
<EOF>
[3,4]
Attention
Generator Explanation
<STR>
[3,4]
g
[3,4]
r
[3,4]
e
[3,4]
a
[3,4]
t
[3,4]
LSTM LSTM LSTM LSTM LSTM
Figure 3: Natural Language Explainability model.
Context Encoder. It aims to encode the input char-
acter into one-hot encoding, then concatenate the rat-
ings given by a user according to different item’s con-
tent features. This data will later become the input
for our LSTM network as seen in Fig. 3. To do so,
we created a dictionary for the characters in the cor-
pus to define their positions. The dictionary is used to
encode the characters during the training step and to
decode during the generating step. One-hot encoding
vector is generated for each character in the reviews
based on its position in the dictionary. Furthermore,
the vector is concatenated with a set of ratings varying
from 0 to 1, as shown in Equation 10.
X
0
t
= [onehot(x
char
);x
aux
]
(10)
LSTM Network. LSTM is an extended version
of recurrent neural network (RNN), where neurons
transmit information among other neurons and layers
simultaneously, as presented in Figure 3. Therefore,
LSTM is built upon a sequential connection of forget,
input and output gates. The forget gate aims to de-
cide which old information should be forgotten; the
input gate updates the current cell state; and the out-
put gate selects the information to go to the next layer
and cell. First, the LSTM network receives the input
data x
t
at time t and the cell state C
t−1
from previous
time step t − 1. Second, the input data feed the for-
get gate, where it chooses which information will be
discarded. In Equation 11, f
t
defines the forget gate
in time t, where W
f
and b
f
refers to the weight ma-
trix and bias, respectively. The third step is to define
which information should be stored in cell state by
the input gate i
t
. During the fourth step, the cell cre-
ates a candidate state C
0
t
by a tanh layer. We update
the current state C
t
according to the candidate state,
the previous cell state, the forget gate, and the input
gate. During the final step, the data goes to the output
gate, where it uses sigmoid function layer to define
the output and multiply the tanh with the current cell
state C
t
to return the next character with the highest
probability.
f
t
= σ([x
t
,C
t−1
] W
f
+ b
f
)
i
t
= σ([x
t
,C
t−1
] W
i
+ b
i
)
C
0
t
= tanh([x
t
,C
t−1
] W
c
+ b
c
)
C
t
= f
t
C
t−1
+ i
t
C
0
t
o
t
= σ([x
t
,C
t−1
] W
o
+ b
o
)
h
t
= o
t
 tanh(C
t
)
(11)
Attention Layer. The attention layer adaptively
learns soft alignments h
t
between character depen-
dencies c
t
and attention inputs. Equation 12 formally
describes the character dependencies using attention
layer h
attention
t
as explained by (Dong et al., 2017).
c
t
=
attention
∑
i
exp(tanh(W
s
 [h
t
, attention
i
]))
∑
exp(tanh(W
s
 [h
t
, attention
i
]))
attention
i
h
attention
t
= tanh(W
1
 c
t
+W
2
 h
t
)
(12)
Generator Model. The generator model is built on
character-level. To do so, we have to maximize a non-
linear softmax function to compute the conditional
WEBIST 2018 - 14th International Conference on Web Information Systems and Technologies
40

probability p among the characters, as presented in
Equation 13. The text generation task concatenates
an initial prime text as the start symbol in each gener-
ated review-based explanation according to different
item’s content features. Finally, the network feeds the
softmax layer with its output data, as shown in Equa-
tion 13.
p = softmax(H
attention
t
W + b), char = argmax p
(13)
where H
attention
t
is the output of a LSTM cell, W
and b are the weight and bias of the softmax layer,
respectively.
This procedure produces a character char recur-
sively for each time step, until it finds the pre-defined
end symbol.
5 EXPERIMENTS
In this section, we describe our experiment setup. We
start by detailing the datasets, the evaluation metrics
and the baselines.
5.1 Datasets
We use two datasets to conduct our experiments: Yelp
and Amazon.
The original Yelp dataset was published in April
2013 and has been used by the recommender systems
community, due to the user reviews. The dataset has
45,981 users, 11,537 items, and 22,907 reviews, how-
ever it is sparse, since 49% of the users have only one
review, making it difficult to evaluate in top-N recom-
mendation. We filtered the users with more than 10
reviews as (Zhang et al., 2014; He et al., 2015). The
Amazon dataset contains more than 800k users, 80k
items and 11.3M reviews, however it is more sparse
than Yelp, making us adopt the same strategy as ap-
plied in the previous dataset. Table 1 summarizes the
dataset information.
Table 1: Dataset Summarization.
Yelp Amazon
#users 3,835 2,933
#items 4,043 14,370
#reviews 114,316 55,677
#density 0.74% 0.13%
The experiments were performed in a Unix server
with the following settings: 32GB of RAM and 8 core
CPU Intel Xeon with 2.80GHz. The parameters for
collective matrix factorization were set as: learning
rate = 0.001; k = 45; iterations = 50 (to ensure the
convergence point); and λ = 0.5. The LSTM net-
work has two hidden layers with 1024 LSTM cells per
layer, where the input data was split in 100 batches
with size equal to 128 and each batch has a sequence
length equal to 280. For this experiment, we ap-
plied cross-validation to avoid overfitting, where each
dataset were divided into 5 − f olds.
5.2 Evaluation Metrics
The output of the algorithms is a ranked list of items
considering the user’s feedback. For this list, the
effectiveness of the top-N recommendation is mea-
sured according to information retrieval ranking met-
rics: NDCG and Hit Ratio (HR). We apply NDCG to
measure the ranking quality as defined by Equation
14, where the metric gives higher score to the items at
the top rank, and lower scores to the items at the low
rank.
NDCG@N = Z
N
N
∑
i=1
2
r
i
− 1
log
2
(i + 1)
(14)
where Z
N
normalizes the values, which guaran-
tees the perfect ranking has a value of 1; and r
i
is
the graded relevance of item at position i. We define
r
i
= 1 if the item is in the test dataset, and otherwise
0.
Hit Ratio has been commonly applied in top-
N evaluation for recommender systems to asses the
ranked list with the ground-truth test dataset (GT). A
hit is denoted when an item from the test dataset ap-
pears in the recommended list. We calculate it as:
Hit@N =
Numbero f Hits@N
|GT |
(15)
The number of listed item in the trained dataset is
defined by N. Therefore, we set N = 5 and N = 10,
due to large values of N would result in extra work for
the user to filter among a long list of relevant items.
High values of NDCG or HR indicate better perfor-
mance.
5.3 Comparison Baselines
We list the related works in Section 2, where we high-
lighted the techniques based on their recommendation
tasks: top-N and explainable recommendations. In
this section we describe four baselines, where two are
popular techniques for top-N recommendations and
the two other are recent techniques applying review-
based explanations.
Neural Explainable Collective Non-negative Matrix Factorization for Recommender Systems
41

Table 2: NDCG and Hit Ratio results for NECoNMF and compared methods at rank 5 and 10.
Dataset Yelp Amazon
Metric NDCG@5 HIT@5 NDCG@10 HIT@10 NDCG@5 HIT@5 NDCG@10 HIT@10
Top-N Algorithms
ItemPop 0.0110 0.0136 0.0185 0.0306 0.0077 0.0082 0.0136 0.0238
PageRank 0.0235 0.0278 0.0313 0.0452 0.0978 0.1070 0.1029 0.1200
Explainable Recommendation
TriRank 0.0258 0.0313 0.0353 0.0527 0.1033 0.1127 0.1086 0.1266
EFM 0.2840 0.0448 0.2955 0.0678 0.3615 0.1284 0.3670 0.1429
NECoNMF 0.3366 0.0503 0.3461 0.0763 0.3892 0.1301 0.3962 0.1486
Top-N Recommendation
• ItemPop. The method ranks items by their popu-
larity given by the number of ratings. It usually
presents good performance, because users tend to
consume popular items.
• PageRank. Personalized Pagerank is a widely
used method for top-N recommendation. We ap-
plied the configuration proposed by (He et al.,
2015), considering the user-item graph and the
damping parameter is respectively optimized to
0.9 and 0.3 for Yelp and Amazon datasets.
Explainable Recommendation
• EFM. The model applies a phrase-level sentiment
analysis of user reviews for personalized recom-
mendation. It extracts explicit product features
and user opinions from reviews, then incorporates
user-feature and item-feature relations as well as
user-item ratings into a hybrid matrix factoriza-
tion framework. The method has k as hyper-
parameter to define the number of most cared
features, which we define k = 45 as reported in
(Zhang et al., 2014) to have the best performance
in the Yelp dataset.
• TriRank. The model ranks the vertices of user—
item—aspect tripartite graph by regularizing the
smoothness and fitting constraints. TriRank is
used for review-aware recommendation, where
the ranking constraints directly model the col-
laborative and aspect filtering. The authors de-
scribe in (He et al., 2015) an experiment regard-
ing the parameters used by TriRank algorithm,
where setting item − aspect, user − aspect, and
aspect − query as 0 results in poor performance.
For the experiments in this paper we use the de-
fault settings α = 9, β = 6, and γ = 1.
6 RESULTS AND DISCUSSIONS
In this section we present the results regarding the rat-
ing prediction for top-N recommendation, and discuss
the explanations for rating prediction.
6.1 Overall Performance
This section describes the overall performance of
NECoNMF regarding the rating prediction for top-N
recommendation in comparison with other methods.
Analyzing the NDCG@5 score of NECoNMF in
comparison with ItemPop in Table 2 we observe an
improvement of 30× for the Yelp dataset and 50×
for the Amazon dataset, while HIT@5 is 4× better
for the Yelp dataset and 16× for the Amazon dataset.
ItemPop has shown the poorest overall performance
because it does not apply personalization during its
prediction task.
On the other hand, personalized PageRank had a
good performance due to apply the user’s historical
information to predict the user’s preferences. De-
spite the good performance, PageRank does not use
latent information to infer the recommendation, for
example item’s content features, context, sentiment,
and ratings, what may explain the lower performance
when compared to NECoNMF. Comparing the re-
sults for the Yelp dataset the accuracy of NECoNMF
compared to PageRank was improved in 14.4× for
NDCG@5 and 2× for HIT@5. Applying the recom-
mendation model for the Amazon dataset leads us to
a similar result where NECoNMF performs better in
3.9× for NDCG@5 and 21% for HIT@5.
TriRank performed poorer in comparison to
NECoNMF, because it applies tripartite graph ap-
proach to predict users’ preferences making it unable
to identify hidden features. During the experiments
for the Yelp dataset the accuracy was improved in
13× for NDCG@5 and 60% for HIT@5. Likewise,
for the Amazon dataset we observed an improvement
of 3.7× for NDCG@5 and 15.4× for HIT@5. Ob-
serving Hit Ratio scores in Table 2 we noticed PageR-
WEBIST 2018 - 14th International Conference on Web Information Systems and Technologies
42

Table 3: Example explanations produced by NECoNMF on the Yelp dataset.
User Item Rating Generated Explanation
A X 1 i was disappointed . it was too small and noisy . food was good , but i just can’t come back with my family .
A Y 3 this was a nice restaurant . i liked the service and the location . i’m not sure i’d recommend the food there.
B X 5 i loved this restaurant . i could not leave it. i loved the service and the food . i will be back again next weekend .
5 10 15 20 25 30 35 40 45 50
N
0
0.1
0.2
0.3
0.4
0.5
NDCG@N
ItemPop
PageRank
TriRank
EFM
ECoNMF
5 10 15 20 25 30 35 40 45 50
N
0
0.05
0.1
0.15
0.2
0.25
0.3
Hit@N
ItemPop
PageRank
TriRank
EFM
ECoNMF
Figure 4: Empirical evaluation on Yelp dataset for N from
5 to 50.
ank and TriRank have close scores, however TriRank
performed better because it applies tripartite graph
user–item–aspect, allowing TriRank to incorporate
one more feature during the recommendation process.
Comparing NECoNMF and EFM, we ob-
serve a close performance between them, however
NECoNMF presented an improvement for top-N rec-
ommendation. Considering the results in Table 2
we observe an improvement of 18.3% in NDCG@5,
12.2% in HIT@5, 17.1% in NDCG@10, and 12.2%
in HIT@10 for the Yelp dataset. Similar improve-
ment was observed in the Amazon dataset, 7.6% in
NDCG@5, 1.3% in HIT@5, 7.9% in NDCG@10,
and 3.9% in HIT@10. NECoNMF factorizes item’s
content features and contextual information as addi-
tional features allowing a better user modeling in the
vectorial space and improving the personalized rec-
ommendation task. On the other hand, EFM mod-
els the user’s behaviour based only on ratings and as-
pects. Those features play an important role in achiev-
ing better NDCG score, hence it defines users’ in-
terests in specifics scenarios, for example, brunch in
a restaurant on a Sunday. Furthermore, EFM fac-
torizes its input matrices into four different latent
spaces, while NECoNMF collectively factorizes into
one common latent space among the matrices. There-
fore, jointly factorizing the matrices may identify hid-
den latent features not selected by EFM model during
the recommendation process.
Moreover, the models presented better perfor-
mance for top@10 than top@5 recommendation, due
5 10 15 20 25 30 35 40 45 50
N
0
0.1
0.2
0.3
0.4
0.5
NDCG@N
ItemPop
PageRank
TriRank
EFM
ECoNMF
5 10 15 20 25 30 35 40 45 50
N
0
0.05
0.1
0.15
0.2
0.25
0.3
Hit@N
ItemPop
PageRank
TriRank
EFM
ECoNMF
Figure 5: Empirical evaluation on Amazon dataset for N
from 5 to 50.
to the error is minimized when the system has a
higher number of items. Analyzing Figures 4 and 5
we observe NECoNMF presents higher accuracy per-
formance for top-N recommendation when N varies
from 5 to 50.
6.2 Explainability
NECoNMF presents the ability to provide explainable
recommendation, however explainability for recom-
mendation is not easy to evaluate. We apply the evalu-
ation method described by (Zhang et al., 2014), where
they assess the quality of explanations throughout ex-
amples generated by the explainable model.
Table 3 shows three explanations outcomes
according to different predicted user’s ratings.
NECoNMF presents an explanation according to
user’s writing style for each tuple user-item-rating,
where the dark grey represents negative sentiment,
and the light grey describes positive sentiment regard-
ing different item’s features. Furthermore, the mid-
grey scale represents the contextual feature such as
family, location and weekend. Note, the generated
explanation is presented in a personalized item’s re-
view style, because reviews have a high influence in
user’s decision. Comparing to (Zhang et al., 2014) ex-
planations, we observe a better readability in Table 3
when using review-based explanation, due to natural
language text generation.
Neural Explainable Collective Non-negative Matrix Factorization for Recommender Systems
43

7 CONCLUSIONS
We proposed a neural explainable collective non-
negative matrix factorization (NECoNMF) for recom-
mender systems combining ratings, content features,
sentiment, and contextual information in a common
latent space. Furthermore, we introduced a neural ex-
plainable model to interpret the predicted top-N rec-
ommendation. Finally, we presented the results re-
garding the experiments in two datasets, where we ob-
served that NECoNMF outperforms the state-of-the-
art methods.
The top-N recommendation task was addressed
using four different matrices as input for collective
non-negative matrix factorization. The combination
of content features, contexts, ratings, and sentiment
play an important role in explaining the recommended
list of items to a user.
The explainable model proved to be effective for
the review-oriented explanation task. The generated
explanations may help users during their decision
regarding specific item’s features, as users tend to
trust in the review-based explanation. Moreover, the
character-level text generation has the benefit of gen-
erating readable personalized text.
We would like to improve the readability pre-
sented by the explainable model and further extend
the project into a general explainable recommender
system, which is able to explain any recommendation
method. Furthermore, investigate technical improve-
ments related to the cold-start problem.
ACKNOWLEDGEMENTS
The authors wish to acknowledge the financial sup-
port and the fellow scholarship given to this re-
search from the Conselho Nacional de Desenvolvi-
mento Cient
´
ıfico e Tecnol
´
ogico - CNPq (grant#
206065/2014-0)
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