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Knowledge-Based Systems 128 (2017) 71–77

Contents lists available at ScienceDirect

Knowle dge-Base d Systems

journal homepage: www.elsevier.com/locate/knosys

Improving performance of tensor-based context-aware recommenders

using Bias Tensor Factorization with context feature auto-encoding

Wenmin Wu

, Jianli Zhao

a , ∗

, Chunsheng Zhang

, Fang Meng

, Zeli Zhang

, Yang Zhang

Qiuxia Sun

School of Information Science & Engineering, Shandong University of Science and Technology, Qingdao, China

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China

a r t i c l e i n f o

Article history:

Received 16 November 2016

Revised 15 April 2017

Accepted 24 April 2017

Available online 26 April 2017

Keywords:

Context-aware recommendation

Tensor factorization

Regression tree

Context features selection

a b s t r a c t

In this paper, we focus on the problem of context-aware recommendation using tensor factorization. Tra-

ditional tensor-based models in context-aware recommendation scenario only consider user-item-context

interactions. In this paper, we argue that rating can’t be totally explained by the interactions and the rat-

ing also inﬂuenced by the combined impact of overall mean, user bias, item bias and context bias. Based

on this hypothesis, we propose a novel context-aware recommendation model named Bias Tensor Fac-

torization, which take all this factors into account. Additionally, traditional context-aware recommenders

with tensor factorization still have three main drawbacks: (1) the model complexity of those models

increase exponentially with the number of context features, (2) those models can only handle context

features with categorical values and (3) the models fail to select effective features from available con-

text features. To address those problems, we propose a context features auto-encoding algorithm based

on regression tree which can both handle numerical features and select effective features. Then we inte-

grate this algorithm with Bias Tensor Factorization. Experiments on a real world contextual dataset and

Movielens show that our proposed algorithms outperform the state-of-art context-aware recommenda-

tion algorithms, namely tensor factorization and factorization machine.

This is an open access article under the CC BY-NC-ND license.

( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

1. Introduction

Recommender Systems (RSs) [1,2] are information ﬁltering tools

to help users overcome the information overload problem and

are more and more popular in different application areas [28,29] .

The core of RSs is recommendation algorithm. Traditional rec-

ommendation algorithms like user-based collaborative ﬁltering

[3,4,5] , item-based collaborative ﬁltering [6] and matrix factoriza-

tion [7] mostly rely on the information of user, item and the in-

teractions (e.g. rate, purchase, etc.) between them. In the real rec-

ommender system, there is plenty of information about the situa-

tion of the interaction happens, e.g. the time, the location, or the

mood of the user. Such additional information are called context

and have been proven to be important to inferring the users’ pref-

erences. Recommenders which take this information into account

are called context-aware recommendation algorithms.

∗

Corresponding author:.

E-mail addresses: wuwenmin1991@gmail.com (W. Wu), jlzhao@sdust.edu.cn (J.

Zhao).

Tensor factorizations [8,9,10,11,23] are one of the most success-

ful approaches to context-aware recommendations. But, traditional

context-aware recommenders based on tensor factorization have

three main drawbacks: (1) these models use user-item-context in-

teractions to explain the whole rating. We argue that besides the

interactions the rating can be affected by some biases, e.g. some

users in general give higher rating to movies, for instance, they are

optimistic people. (2) These models fail to select effective features

from available context features which will make them not applica-

ble to real recommender systems since there are tens of contextual

features in real data. (3) These models only work for context fea-

tures with categorical features.

In this work, the main objective is to make tensor-based rec-

ommenders applicable to real world recommender systems as well

as improve their performance. To do this, we propose a Bias Ten-

sor Factorization model and a Context Features Auto-encoding Al-

gorithm. The contribution of our paper is summarized as follows:

• We propose a Bias Tensor Factorization model which takes the

inﬂuences of user bias, item bias, context bias and the overall

mean into account.

http://dx.doi.org/10.1016/j.knosys.2017.04.011

( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

72 W. Wu et al. / Knowledge-Based Systems 128 (2017) 71–77

• We propose a context feature auto-encoding algorithm based

on regression tree, which can both handle the continuous con-

text features and control the dimension of encoded context fea-

tures by only selecting the useful context features.

• We integrate context feature auto-encoding algorithm with Bias

Tensor Factorization and conduct several experiments to show

that our proposed models outperform the state-of-art context

modeling algorithms namely classical tensor factorization and

factorization machine. To the best of our knowledge, this paper

is the ﬁrst to integrate tree-based feature selection algorithm

with tensor-based recommenders.

2. Related work

Context-aware Recommendation has drawn much research at-

tentions in recent years. This is probably because the context in-

formation is much easier to get today and the success stories of

some contextual applications (e.g. Frappe

)

Adomavicius and Tuzhilin give a thorough review of approaches

to contextual recommendations and categorize context-aware rec-

ommendation methods into three types [16] : contextual pre-

ﬁltering, contextual post-ﬁltering and contextual modeling . In contex-

tual pre-ﬁltering and post-ﬁltering, a context-unaware recommen-

dation algorithm is applied and the data is either preprocessed

based on the given context or the results are post-processed ac-

cording to the context [17] . Examples for pre-processing are di-

mension reduction [18] and item splitting [19] . The main advan-

tage of pre-processing and post-processing is we can use tra-

ditional context-unaware recommendation algorithms. However,

both of them suffer from the lack of effective context generalized

methods.

The models proposed in this paper belong to the contextual

modeling . Several contextual modeling methods have been pro-

posed so far. Oku introduced a Context-aware Support Vector

Machine which considers support vectors in a multidimensional

space and ﬁnd the separating hyperplane [20] . Koren proposed a

temporal matrix factorization model called timeSVD ++ and show

its effectiveness in the Netﬂix Prize. Alexandros proposed a ten-

sor factorization model for Context-aware Collaborative Filtering

[21] which is a basis of this paper. Rendle introduced a factoriza-

tion model namely factorization machine which is a panacea of

regression problem. Barmpoutis proposed a new tensor structure

that grasps both user and image relations for image tag recom-

mendation problem [24] . Shan proposed a fully coupled interac-

tions tensor factorization model based on Tucker decomposition to

model three pairwise interactions between the user, publisher, and

advertiser for CTR estimation problem in Real Time Bidding (RTB)

[25] . In [26] , Panagiotis combined the clustering of tags with the

application of High Order Singular Value Decomposition on ten-

sors which pre-grouping neighboring tags and produces represen-

tative tag centroid which are inserted into the tensor to alleviate

the data sparsity problem in Social Tagging System. Kim proposed

the 4-way Tensor, a parallel tensor factorization algorithm, to ac-

celerate the tensor factorization of large datasets to support eﬃ-

cient context-aware recommendations [27] .

However, none of those works address the context features se-

lection problem. To address this problem, we utilize regression tree

for context features selecting after got inspiration from the work of

Facebook [22] .

3. Tensor-based recommenders

In this section, we will ﬁrstly introduce classical tensor factor-

ization with CP model [11] which is a basis of our contributions

http://baltrunas.info/research-menu/frappe .

Fig. 1. Illustration of tensor factorization with CP model.

followed by the main contributions of this paper: (1) our pro-

posed Bias Tensor Factorization model ; (2) a novel context features

auto-encoding algorithm based on regression tree; and (3) an inte-

grated model of Bias Tensor Factorization and context features auto-

encoding.

3.1. Classical tensor factorization

The classical tensor factorization assumes that the rating ten-

sor R ∈ R

M×N×K

from M users to N items under K types of context

can be factorized into a product of three low rank matrices U

M × D

N × D

and C

K × D

as shown in Fig. 1 . Then user m ’s rating to item

i under context k can be predicted as following:

mik



d=1

(1)

3.2. Bias Tensor Factorization

3.2.1. Model

Bias Tensor Factorization which takes the overall mean, user

bias, item bias, context bias into account which can be represented

by the following equation.

mik

= μ + b

+ b



d=1

(2)

In this model, we explain the rating with 5 components: (1) the

overall mean denoted by μ; (2) the rating bias of user m denoted

by b

; (3) the score bias when users rating item i denoted by b

;

(4) the score bias when users rating under context k denoted by

; and (5) the interaction of user, item and context which is the

whole component in classical tensor factorization model.

3.2.2. Training

The parameters in Bias Tensor Factorization can be learned by

minimizing the following equation:

min

b∗,U∗,V ∗,C∗



(

u,i,k

)

∈ Y



mik

−

mik







+  V

+  C

+ b



(3)

Note that, we add the Frobenius norms of the model param-

eters to avoid overﬁtting and the model complexity can be con-

trolled by λ.

We use stochastic gradient descent [12] to minimize the objec-

tive function Eq. (3) , the loss function for each observed rating r

mik

in R can be deﬁned as below:

L =



mik

−

mik



(

 U

+  V

+  C



+ b



(4)

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