# Mixed Information Flow for Cross-domain Sequential Recommendations

Muyang Ma  Shandong UniversityJinanChina<EMAIL_ADDRESS>,  Pengjie Ren
Shandong UniversityJinanChina<EMAIL_ADDRESS>,  Zhumin Chen  Shandong
UniversityJinanChina<EMAIL_ADDRESS>,  Zhaochun Ren  Shandong
UniversityQingdaoChina<EMAIL_ADDRESS>,  Lifan Zhao  Shandong
UniversityQingdaoChina<EMAIL_ADDRESS>,  Jun Ma  Shandong
UniversityJinanChina<EMAIL_ADDRESS>and  Maarten de Rijke
0000-0002-1086-0202 University of Amsterdam and Ahold DelhaizeAmsterdam and
ZaandamThe Netherlands<EMAIL_ADDRESS>
(2020)

###### Abstract.

Cross-domain sequential recommendation is the task of predict the next item
that the user is most likely to interact with based on past sequential
behavior from multiple domains. One of the key challenges in cross-domain
sequential recommendation is to grasp and transfer the flow of information
from multiple domains so as to promote recommendations in all domains.
Previous studies have investigated the flow of _behavioral_ information by
exploring the connection between items from different domains. The flow of
knowledge (i.e., the connection between knowledge from different domains) has
so far been neglected. In this paper, we propose a mixed information flow
network for cross-domain sequential recommendation to consider both the flow
of behavioral information and the flow of knowledge by incorporating a
behavior transfer unit and a knowledge transfer unit. The proposed mixed
information flow network is able to decide when cross-domain information
should be used and, if so, which cross-domain information should be used to
enrich the sequence representation according to users’ current preferences.
Extensive experiments conducted on four e-commerce datasets demonstrate that
mixed information flow network is able to further improve recommendation
performance in different domains by modeling mixed information flow.

Cross-domain recommendation, Sequential recommendation, Knowledge base, Graph
transfer

Pengjie Ren and Zhumin Chen are the corresponding authors.

††copyright: acmcopyright††journalyear: 2020††doi:
xx.xxxx/xxxxxxx.xxxxxxx††price: 15.00††isbn: 978-1-4503-9999-9/18/06††journal:
TKDD††ccs: Information systems Recommender systems

##  1\. Introduction

Sequential recommendation (SR) aims to predict the next item that the user is
most likely to interact with based on her/his past sequential behavior (e.g.,
clicks on items) (Quadrana et al., 2017). Recently, cross-domain sequential
recommendation (CDSR) has emerged as a way to promote recommendation
performance by leveraging and combining information from different domains (Ma
et al., 2019a). Users usually have related preferences in different domains,
such as finding a movie with a certain style or looking for a book written by
a well-known author, as illustrated in Figure 1. One of the key challenges in
CDSR is to capture and transfer useful information about related preferences
across different domains.

Figure 1. Illustration of a connection between a user’s behavioral information
across domains via a knowledge graph. Lines in different colors represent
different connections.

Zhuang et al. (2018) and Ma et al. (2019a) have shown that behavioral
information across domains is helpful for improving recommendation
performance. However, behavioral information by itself can only support the
use of cross-domain connections in a limited manner. Behavioral information
may be insufficient for a model to capture fine-grained connections between
item attributes or features. For example, as illustrated in Figure 1, assume
there is a user who has read Harry Potter (the book) and watched Captain
America (the movie). If there is no external knowledge to indicate that both
items belong to the category of “fantasy,” it is difficult for the model to
capture this connection based solely on the user’s behavior from both domains.
We hypothesize that enabling a flow of knowledge across different domains is
able to alleviate this issue. As a result, for a user who has read the book
The Great Gatsby, we then can recommend her/him a movie having the same name
or movies featuring the same category of “tragic love,” such as Atonement,
Waterloo Bridge, and so on, when she/he logs on to the movie recommendation
system.

There is a growing body of work aimed at improving recommendation performance
by using knowledge (Ren et al., 2020b; Lin et al., 2019). Of particular
relevance to us is work that has proposed to incorporate knowledge and combine
it with behavioral information for sequential recommendation (SR) (see, e.g.,
Huang et al., 2018; Wu et al., 2019; Huang et al., 2019). However, this work
targets a single domain recommendation scenario. The situation is dramatically
different in cross-domain scenarios where it is necessary to distinguish
information from different domains and effectively link them. We need to
select behavioral and knowledge related to users’ current preference, and
determine when and what to use in order to learn a better sequence
representation.

To address the issue of using behavioral information and knowledge across
domains, we propose a mixed information flow network (MIFN) to consider mixed
information flow across domains, i.e., the flow of behavioral information as
well as the flow of knowledge. The former is based on user’s behavior, which
captures the temporal connection between the items they have interacted with,
while the latter takes cross-domain knowledge as a bridge to connect different
domains to obtain better cross-domain sequence representations. First, we
employ a behavior transfer unit (BTU) to grasp useful information from the
flow of behavioral information, which can extract information related to the
user’s preference and then transfer it to another domain at the level of user
behavior level. Then, we propose a knowledge transfer unit (KTU) that is
guided by the user’s preference to model the connection between items from
different domains; we introduce a cross-domain graph convolutional mechanism
to distinguish items in the knowledge graph (KG) and grasp useful information
for fusion at the knowledge level. Finally, we generate recommendations based
on the fusion of the two types of information. During learning, mixed
information flow network (MIFN) is jointly trained on multiple domains in an
end-to-end back-propagation training paradigm. Experiments on the Amazon
datasets show that MIFN outperforms state-of-the-art methods in terms of MRR
and Recall.

To sum up, the contributions of this work are as follows:

  * •

We propose a mixed information flow framework, MIFN, for CDSR, which consists
of a behavior transfer unit and a knowledge transfer unit to simultaneously
model the flow of behavioral information and of knowledge across domains.

  * •

We devise a cross-domain graph convolutional mechanism to disseminate item
information in the KG, which leads to the better up-to-date item
representation.

  * •

We conduct experiments to demonstrate that MIFN is able to improve
recommendation performance in different domains by modeling mixed information
flow.

##  2\. Related work

In this section, we briefly introduce related work from the following
categories:  (1) sequential recommendation,  (2) cross-domain recommendation,
and  (3) knowledge-aware recommendation.

###  2.1. Sequential recommendations

Early work on recommender systems typically use collaborative filtering (CF)
to generate recommendations (Hu et al., 2018a) according to users’ preferences
reflected in similar items such as K-Nearest neighbors (KNN) or matrix
factorization (MF) algorithms. Such methods do not consider sequential
aspects. More recently, however, SR and next-basket recommendation have
witnessed rapid developments.

Before the widespread application of deep learning, Markov chainss (Zimdars et
al., 2001; Rendle et al., 2010; Chen et al., 2012; He and McAuley, 2016) and
Markov decision processs (Shani et al., 2005; Wu et al., 2013) have been used
to predict users’ next action given information about their past behavior
(Wang et al., 2015; Yap et al., 2012). All these methods take into account the
sequential characteristics. However, there are considerable challenges with
the size of the state when considering the entire sequence (Quadrana et al.,
2018).

RNN have been introduced to SR to handle variable-length sequential data.
Hidasi et al. (2016a) are the first to leverage recurrent neural networks for
SR. They utilize session-parallel mini-batch training and employ ranking-based
loss functions to train the model. Then, Tan et al. (2016) propose two
techniques to improve the performance, i.e., data augmentation and a method to
account for shifts in the input data distribution. Li et al. (2017)
incorporate an attention mechanism into the encoder to capture the users’ main
preference in the current sequence. Ren et al. (2019) point out the repeat
consumption in SR, where the same item is re-consumed repeatedly over time.
Quadrana et al. (2017) propose a hierarchical RNN model that can relay and
evolve latent hidden states of the RNNs across user sequences. Donkers et al.
(2017) explicitly model user information in a gated architecture with extra
input layers for gated recurrent unit (GRU). Memory enhanced RNN has been well
studied for SR recently. Chen et al. (2018) introduce a memory mechanism to SR
and design a memory-augmented neural network integrated with the insights of
CF. Wang et al. (2019c) propose two parallel memory modules: one to model a
user’s own information in the current sequence and the other to exploit
collaborative information in neighborhood sequences. Wu et al. (2019) argue
that prior work on conventional sequential methods neglects complex
transitions between items. They model the sequence as graph-structured data
and then represent it as the composition of global preference and the current
preference of that sequence using an attention network. Zhang et al. (2019)
propose a feature-level deeper self-attention network to capture transition
patterns between features of items by integrating various heterogeneous
features. Sun et al. (2019) argue that previous work often assumes a rigidly
ordered sequence, which is not always practical. They employ deep
bidirectional self-attention to model a user’s behavioral sequences.

In addition to sequential information, auxiliary information is also vital for
SR. Hidasi et al. (2016b) investigate how to add item property information
such as text and images to an RNNs framework and introduce a number of
parallel RNN (p-RNN) architectures. Liu et al. (2016) incorporate contextual
information into SR and propose a context-aware RNN model to capture external
situations and lengths of time intervals. Bogina and Kuflik (2017) explore a
user’s dwell time based on an existing RNN-based framework by boosting items
above a predefined dwell time threshold. Ma et al. (2018a) propose a cross-
attention memory network for multi-modal tweets via both textual and visual
information. Li et al. (2019) study how to enlist the semantic signals covered
by user reviews for the task of CF. They propose a neural review-driven model
by considering users’ intrinsic preference and sequential patterns. To
investigate the influence of temporal sentiments on user preference, Zheng et
al. (2020) propose to generate preferences by guiding user behavior through
sequential sentiments. They design a dual-channel fusion mechanism to match
and guide sequential user behavior, and to assist in preference generation.
Ren et al. (2020a) model the effect of context information on SR and train the
model in an adversarial manner by proposing multiple context-specific
discriminators to evaluate the generated sub-sequence from the perspectives of
different contexts.

Although these studies have made great progress, none of them has considered
how to combine knowledge information under cross-domain situations.

###  2.2. Cross-domain recommendations

Cross-domain recommendation has emerged as a potential solution to the cold-
start and data-sparse problem (Berkovsky et al., 2008; Pan et al., 2010) in
RS. It aims to mitigate the lack of data by exploiting user preference and
item attributes in domains distinct but related to the target domain
(Fernández-Tobías et al., 2019).

Traditional methods for cross-domain recommendation can be grouped into two
main categories (Fernández-Tobías et al., 2012). One category of methods
aggregates information across different domains. According to different
aggregating strategies, such methods can be further divided into three groups
(Fernández-Tobías et al., 2019). The first group is merging user preference
(e.g., ratings, transaction behavior, and browsing logs) from different
domains to obtain better a preference representation so as to improve the
recommendation performance in the target domain. The merge operation is
performed by merging a multi-domain rating matrix (Berkovsky et al., 2007;
Sahebi and Brusilovsky, 2013), leveraging users’ social influence (Abel et
al., 2013; Fernández-Tobías et al., 2013), linking users’ preference by a
multi-domain graph (Cremonesi et al., 2011; Tiroshi et al., 2013) or user
behavioral information features (Loni et al., 2014; Ma et al., 2018b). The
second group is mediating user modeling data in the source domain to explore
the connection between users or items so as to make recommendations in the
target domain especially for cold start users. For example, Tiroshi and Kuflik
(2012) and Shapira et al. (2013) propose to find similar neighbors and
transfer user-user similarity to the target domain. The third group is
combining single-domain recommendations (e.g., rating matrices, probability
distributions), in which recommendations are generated independently for each
domain and later aggregated for the final recommendation. In contrast to the
second group, this type of aggregation strategy aims to model the weights
assigned to recommendations coming from different domains. For example, Givon
and Lavrenko (2009) focus on book recommendations accomplished by a CF method
and model-based recommendations, relying on the similarity of a book and the
user’s model, as well as the book content and tags. And the final
recommendations are combined in a weighted manner. The other category of
cross-domain recommendation aims to transfer information from the source
domain to the target domain by means of shared latent features or rating
patterns. Hu et al. (2013) propose tensor-based factorization to share latent
features between different domains by using the same parameters in both
factorization models. Li et al. (2009) propose a code-book-transfer by co-
clustering the source domain rating matrix and exploit it in the target domain
to transfer rating patterns across different domains. Similarly, Mirbakhsh and
Ling (2015) focus on extending clustering-based MF in a single domain into
multiple domains through overlapping users.

In order to model more complex connections across different domains, a variety
of deep learning methods have been proposed for cross-domain recommendation.
Elkahky et al. (2015) propose a multi-view deep learning recommendation system
by using rich auxiliary features to represent users from different domains.
Then, Lian et al. (2017) propose a multi-view neural framework of a dual
network for user and item, each network models CF information (user and item
embeddings) and content information (user preference for item features), which
ties CF and content-based filtering together. Hu et al. (2018b) propose a
model using a cross-stitch network (Misra et al., 2016) to learn complex user
behavioral information based on neural CF (He et al., 2017). Wang et al.
(2017) propose to combine user behavioral information in information domains
and user-user connection in social domains to do recommendation. Wang et al.
(2019a) embed item-level information and cluster-level correlative information
from different domains into a unified framework. Gao et al. (2019) transfer
item embeddings across domains without sharing user-relevant data. Li and
Tuzhilin (2019) develop a latent orthogonal mapping method to extract user
preference over multiple domains while preserving connection between users
across different latent spaces based on the mechanism of dual learning.
Krishnan et al. (2020) propose to guide neural CF with domain-invariant
components shared across the dense and sparse domains, improving user and item
representations learned in the sparse domains. They leverage contextual
invariances across domains to develop these shared modules. Zhao et al. (2020)
propose to model user preference transfer at the aspect-level derived from
reviews, which does not require overlapping users or items in all domains. Bi
et al. (2020) utilize cross-domain mechanism to promote recommendations for
cold start users in insurance domain. They design a meta-path based method
over complex insurance products to learn better item representations and learn
the mapping function between domains through the overlapping users. Despite
the fact that the listed methods above have been proven to be effective, they
cannot be directly applied to SRs.

Recently, cross-domain recommendation has been introduced to SRs as well.
Zhuang et al. (2018) propose a novelty seeking model based on sequences in
multi-domains to model an individual’s propensity by transferring novelty
seeking traits learned from a source domain for improving the accuracy of
recommendations in the target domain. Ma et al. (2019a) study CDSR in a
shared-account scenario. They propose a novel gating mechanism to extract and
share user-specific information between domains.

Although some studies have begun to explore CDSR, they only focus on user
behavioral information to conduct information transfer, and neglect to explore
extra knowledge to promote sequence representation across domains.

###  2.3. Knowledge-aware recommendations

Considerable efforts have been made to utilize side-information, especially
knowledge graphs, to enhance the performance of recommendations. Zhao et al.
(2016) propose a graph-based method to iteratively update user and item
distributions in a heterogeneous user-item graph and incorporate them as
features into the MF for item recommendations. Zhang et al. (2016) combine CF
with structural knowledge, textual knowledge and visual knowledge in a unified
framework. Ai et al. (2018) apply TransE on the graph including users, items
and their connections, which casts the recommendation task as a plausibility
prediction task. As graph convolutional networks have been shown to be
effective on many tasks (Kipf and Welling, 2017), there have been a number of
publications that propose variants of GCNs for recommendation by considering
different types of information. Wang et al. (2018) simulate users’
hierarchical preferences over knowledge entities by extending users’ potential
preferences along links in a KG. Wang et al. (2019d) consider the connections
among items based on higher-order entity features in KGs. Wang et al. (2019b)
explicitly model the high-order connections in KGs by employing an attention
mechanism to discriminate the importance of the neighbors. Ma et al. (2019b)
propose a joint framework to integrate the induction of explainable rules from
KGs with the construction of a rule-guided recommendation model. Xian et al.
(2019) perform explicit reasoning with knowledge so that the recommendations
are supported by an interpretable inference procedure via a policy-guided
reinforcement learning approach.

Not surprisingly, KGs has also been considered in SRs. Huang et al. (2018) are
the first to integrate KGs into SR; they utilize RNNs to capture user
sequential preference and knowledge memory networks to capture attribute-level
user preference. Song et al. (2019) model users’ social influence with a
graph-attention neural network, which dynamically infers the influencers based
on the users’ current preference. Huang et al. (2019) introduce a taxonomy-
aware memory-based multi-hop reasoning architecture by incorporating taxonomy
data as structural knowledge to enhance the reasoning capacity.

However, no previous work has considered KGs for SR in a cross-domain
scenario, which brings new challenges, e.g., how to find useful and accurate
cross-domain knowledge to improve information transfer across domains to
promote the performance in both domains.

##  3\. Method

In this section, we first give a formulation of the CDSR task. Then, we give
an overview of our model MIFN. Finally, we describe each component of MIFN in
detail. Table 1 summarizes the main symbols and notation used in this paper.

Table 1. Summary of main symbols and notation used in the paper. $\mathbbm{A}$ |  Item set for domain $A$.
---|---
$\mathbbm{B}$ |  Item set for domain $B$.
$n$ |  The number of item set for domain $A$, i.e., $n=|\mathbbm{A}|$.
$m$ |  The number of item set for domain $B$, i.e., $m=|\mathbbm{B}|$.
$A_{i}$ |  The interacted item at time step $i$ from domain $A$.
$B_{j}$ |  The interacted item at time step $j$ from domain $B$.
$S$ |  Hybrid interaction sequence, i.e., $S=[A_{1}$, $B_{1}$, $B_{2}$, …, $A_{i}$, …, $B_{j}$, $\ldots]$.
$\mathbb{S}$ |  Set of all hybrid interaction sequences in the training set.
$S_{A}$ |  A sub-sequence of $S$ which only contains items from domain $A$.
$S_{B}$ |  A sub-sequence of $S$ which only contains items from domain $B$.
$e_{A_{k}}\in E_{A}$ |  $e_{A_{k}}$ represents any entity in the KG from domain $A$; $E_{A}$ is the set of all entities from domain $A$.
$e_{B_{k}}\in E_{B}$ |  $e_{B_{k}}$ represents any entity in the KG from domain $B$; $E_{B}$ is the set of all entities from domain $B$.
$e_{k}\in E$ |  $e_{k}$ represents any entity in the KG; $E$ is the set of all entities; note that $E=E_{A}\cup E_{B}$.
$R$ |  Relation set in the KG.
$h_{A_{i}}\in H_{A}$ |  $h_{A_{i}}$ represents the item representation of item $A_{i}$; $H_{A}$ is the set of all item representations for $S_{A}$.
$h_{B_{j}}\in H_{B}$ |  $h_{B_{j}}$ represents the item representation of item $B_{j}$; $H_{B}$ is the set of all item representations for $S_{B}$.
$h_{(A\rightarrow B)_{i}}$ |  Transferred behavioral information flow from domain $A$ to domain $B$ at time step $i$.
$N_{i}(k)$ |  Neighbor entity set of entity $e_{k}$ from the same domain as $e_{k}$.
$N_{c}(k)$ |  Neighbor entity set of entity $e_{k}$ from the complementary domain.

###  3.1. Task formulation

CDSR aims to predict the next item the user is mostly likely to interact with
in multiple domains simultaneously, by mining users’ previous sequential
behavior over a period of time. In this work, we take two domains (i.e.,
domain $A$ and $B$) as an example, e.g., watching movies, reading books. Let
$\mathbbm{A}=\\{A_{1}$, $A_{2}$, $A_{3}$, …, $A_{n}\\}$ denote the item set
for domain $A$, which consist of $n$ unique items. Similarly, let
$\mathbbm{B}=\\{B_{1}$, $B_{2}$, $B_{3}$, …, $B_{m}\\}$ denote the item set
for domain $B$, which consist of $m$ unique items. A hybrid interaction
sequence from the two domains $A$ and $B$ has the form $S=[A_{1}$, $B_{1}$,
$B_{2}$, …, $A_{i}$, …, $B_{j}$, $\ldots]$, where $A_{i}\in\mathbbm{A}$
$(1\leq i\leq n)$ and $B_{j}\in\mathbbm{B}$ $(1\leq j\leq m)$ are the indices
of consumed items in domain $A$ and $B$, respectively.

We also associate each $S$ with a knowledge graph (KG), which is defined over
an entity set $E$ and a relation set $R$, containing a set of KG triples. A
triple $\langle e_{1},r,e_{2}\rangle$ represents a relation $r$ $\in$ $R$
between two entities $e_{1}$ and $e_{2}$ from $E$. In the cross-domain
scenario, entities in the KG come from different domains, hence we represent
them as $E_{A}$ and $E_{B}$. For example, the triple $\langle
e_{A_{1}},Is\\_the\\_same\\_category,e_{B_{3}}\rangle$ means that entity
$e_{A_{1}}$ from domain $A$ has the same category as entity $e_{B_{3}}$ from
domain $B$. Since we aim to link recommended items to KG entities, an item set
can be considered as a subset of KG entity set, i.e., $\mathbbm{A}\subseteq
E_{A}$ and $\mathbbm{B}\subseteq E_{B}$. When extracting KG information for
each sequence $S$, we also refer to the “items” in $S$ as “item entities”. We
will explain the details of the KG construction method in Section 3.2.

Based on these preliminaries, we are ready to define the CDSR task. Formally,
given $S$ and $\langle E,R\rangle$, we formulate CDSR as a task of evaluating
the recommendation probabilities for all candidates in both domains
respectively, as shown in Eq. 1:

(1) $\begin{split}P(A_{i+1}|S,\langle E,R\rangle)&\sim f_{A}(S,\langle
E,R\rangle)\\\ P(B_{j+1}|S,\langle E,R\rangle)&\sim f_{B}(S,\langle
E,R\rangle),\\\ \end{split}$

where $P(A_{i+1}|S,\langle E,R\rangle)$ denotes the probability of
recommending the next item $A_{i+1}$ in domain $A$ given the hybrid
interaction sequence $S$ and KG $\langle E,R\rangle$. $f_{A}(S,\langle
E,R\rangle)$ is the model or function used to estimate $P(A_{i+1}|S,\langle
E,R\rangle)$. Similar definitions apply to $P(B_{j+1}|S,\langle E,R\rangle)$
and $f_{B}(S,\langle E,R\rangle)$.

###  3.2. Knowledge graph construction

In this work, we extract data (entities and relations) from the Amazon product
collection111https://jmcauley.ucsd.edu/data/amazon as the complete KG, which
is collected from massive user logs. Besides, we also crawl some relations
between the entities from Wikipedia.222https://en.wikipedia.org/ The entities
include “movies,” “books,” “kitchenware,” and “food,” each of which
corresponds to one domain. The relations include “Also_buy,” “Also_view,”
“Buy_together,” “Buy_after_viewing,” “Adapted_from,” and
“Is_the_same_category.” For example, $\langle$steak (the food), Buy_together,
saucepan (the kitchenware)$\rangle$ means that the user also buys the saucepan
while buying the steak. However, the complete KG contains a large number of
related entities, and complicated relations among these entities, which will
raise memory and computational efficiency issues. Therefore, we propose to
extract a KG from the complete KG for each hybrid interaction sequence $S$. We
require that, given any pair of items from both domains respectively, we can
find at least one path in the KG that connects them.

Algorithm 1 KG construction algorithm for each hybrid interaction sequence.

0: Hybrid interaction sequence, $S$;Complete KG triples, $\langle
E,R,E\rangle$;Maximum hop count, $H$;Number of entities in the KG, $N$;

0: Multiple relational adjacency matrix, $A$;

1: Divide the hybrid interaction sequence $S$ into $S_{A}$ and $S_{B}$;

2: set $\vartheta^{0}_{1}$ = $S_{A}$, $\vartheta^{0}_{2}$ = $S_{B}$,
$\mathit{connected}=\mathit{false}$;

3: for $k\in range(H)$ do

4: Extract related triples $\vartheta^{k}_{1}=\\{(h,r,t)|(h,r,t)\in\langle
E,R,E\rangle$ and $h\in\vartheta^{k-1}_{1}\\}$;

5: Extract related triples $\vartheta^{k}_{2}=\\{(h,r,t)|(h,r,t)\in\langle
E,R,E\rangle$ and $h\in\vartheta^{k-1}_{2}\\}$;

6: $\mathit{connected}$ = Is_Connect($\vartheta^{k}_{1}$, $\vartheta^{k}_{2}$)

7: if $\mathit{connected}=\mathit{true}$ or $k$=$H$-1 then

8: $\theta$ = Select_triples($\vartheta^{k}_{1}$, $\vartheta^{k}_{2}$,
$S_{A}$, $S_{B}$);

9: $A$ = Construct_Adjacency_matrix($\theta$);

10: break;

11: end if

12: end for

13: return adjacency matrix $A$;

The KG construction algorithm is shown in Algorithm 1. $H$ represents the
maximum hop count and $N$ represents the number of entities in the final KG.
We extract all triples that are related to items involved in the hybrid
interaction sequence $S$ within $H$ hops. We stop extracting more hops if it
meets the requirement that there is a path for any given pair of items from
both domains. Finally, we construct the relational adjacency matrix for the
extracted KG.

Specifically, for the input $S$, we first divide it into two sub-sequences
$S_{A}$ and $S_{B}$ according to the domain to which the items belongs (see
line 1). We initialize $\vartheta^{0}_{1}$ or $\vartheta^{0}_{2}$ with the
item entities (see line 2). At each hop, we extract all triples connected to
the entities in the current KG (i.e., $\vartheta^{k}_{1}$ and
$\vartheta^{k}_{2}$), where $\vartheta^{k}_{1}=\\{(h,r,t)|(h,r,t)\in\langle
E,R,E\rangle$ and $h\in\vartheta^{k-1}_{1}\\}$, and
$\vartheta^{k}_{2}=\\{(h,r,t)|(h,r,t)\in\langle E,R,E\rangle$ and
$h\in\vartheta^{k-1}_{2}\\}$, $k$ = 1, 2, …, $H$, where $\vartheta^{0}_{1}$ =
$S_{A}$ and $\vartheta^{0}_{2}$ = $S_{B}$ (see line 4 to line 5). If there is
a path for any given pair of items from both domains (e.g, $A_{3}\rightarrow
e_{8}\rightarrow e_{26}\rightarrow e_{9}\rightarrow B_{6}$) or the hop reaches
the maximum hop $H$, we stop extracting other triples from the complete KG and
construct the relational adjacency matrix (see line 6 to line 12). Otherwise,
we continue to extract other related triples. When constructing the adjacency
matrix, we limit the number of entities in the KG to $N$. Therefore, we need
to select some triples if the number of entities in all related triples is
larger than $N$ (see line 8). To do so, we first gather all the entities that
connect a pair of item entities from two domains, e.g., $e_{8},e_{26},e_{9}$
in the path $A_{3}\rightarrow e_{8}\rightarrow e_{26}\rightarrow
e_{9}\rightarrow B_{6}$. Then, we select the entities according to their
smallest distance w.r.t. any item from the two domains until the number of all
entities meets $N$. After that, we construct the relational adjacency matrix
$A$ based on the selected triples (see line 10).

###  3.3. MIFN

In the following subsections, we will demonstrate the details of MIFN.
Generally, MIFN models $P(A_{i+1}|S,\langle E,R\rangle)$ and
$P(B_{j+1}|S,\langle E,R\rangle)$ (see Eq. 1) by taking two recommendation
modes into consideration, as shown as in Eq. 2:

(2) $\begin{split}P&(A_{i+1}|S,\langle E,R\rangle)=\\\ &P(M\\_S_{A}|S,\langle
E,R\rangle)P(A_{i+1}|M\\_S_{A},S,\langle E,R\rangle)+P(M\\_G_{A}|S,\langle
E,R\rangle)P(A_{i+1}|M\\_G_{A},S,\langle E,R\rangle)\\\ P&(B_{j+1}|S,\langle
E,R\rangle)=\\\ &P(M\\_S_{B}|S,\langle
E,R\rangle)P(B_{j+1}|M\\_S_{B},S,\langle E,R\rangle)+P(M\\_G_{B}|S,\langle
E,R\rangle)P(B_{j+1}|M\\_G_{B},S,\langle E,R\rangle).\\\ \end{split}$

Here, $M\\_S$ and $M\\_G$ denote sequence mode and graph mode, which make
recommendations at the user behavior level and the knowledge level,
respectively. $P(M\\_S_{A}|S,\langle E,R\rangle)$ and $P(M\\_G_{A}|S,\langle
E,R\rangle)$ represent the probabilities under the sequence mode and the graph
mode in domain $A$, respectively, $P(A_{i+1}|M\\_S_{A},S,\langle E,R\rangle)$
and $P(A_{i+1}|M\\_G_{A},S,\langle E,R\rangle)$ refer to the probabilities of
recommending the next item $A_{i+1}$ under the sequence mode and graph mode
given a hybrid interaction sequence $S$ and the KG triples $\langle
E,R\rangle$. The same definitions apply to domain $B$.

Figure 2. An overview of MIFN. Section 3.3 contains a walkthrough of the
model.

As shown in the left side of Figure 2, MIFN consists of four main components:
a sequence encoder, a behavior transfer unit (BTU), a knowledge transfer unit
(KTU), and a mixed recommendation decoder. The sequence encoder encodes the
interacted item sequence into a sequence of item representations. The BTU
takes the representations from the source domain as input, extracts behavioral
information flow, and transfers it to the target domain. The KTU aims to grasp
useful knowledge from the KG and propagates it to both domains. The mixed
recommendation decoder contains two decoders w.r.t. graph mode and sequence
mode, respectively. The graph recommendation decoder evaluates the probability
for all candidate items from the KG, corresponding to Eq. LABEL:g_rec. The
sequence recommendation decoder evaluates the probability of clicking items,
corresponding to Eq. LABEL:s_rec.

###  3.4. Sequence encoder

As with existing studies (Hidasi et al., 2016a, b), we use an RNN to encode
the sub-sequences $S_{A}$ and $S_{B}$. Here, we employ a GRU as the recurrent
unit. The initial state of the GRUs is set to zero vectors, i.e., $h_{0}=0$.
After that, we can obtain $H_{A}=\\{h_{A_{1}}$, $h_{A_{2}}$, …, $h_{A_{i}}$,
…, $h_{A_{n}}\\}$ for domain $A$, and
$H_{B}=\\{h_{B_{1}},h_{B_{2}},\ldots,h_{B_{j}},\ldots,h_{B_{m}}\\}$ for domain
$B$. Each $h_{A_{i}}$ or $h_{B_{j}}$ is the item representation of an item
$A_{i}$ in sequence $S_{A}$ or $B_{j}$ in $S_{B}$.

###  3.5. Behavior transfer unit

The outputs $H_{A}$ and $H_{B}$ from the sequence encoder are representations
of user behavior in single domains. It has been shown that there is connection
between $H_{A}$ and $H_{B}$ (Ma et al., 2019a). For example, a user who has
read the Harry Potter book (e.g., “Harry Potter and the Philosopher’s Stone”
or “Harry Potter and the Chamber of Secrets” and so on) has also watched the
“Pirates of the Caribbean” movie within the same time period. Based on
behavioral information from both domains, it is easier for the model to infer
that the user might like some magic and fantastic movies and books.

To achieve this, we employ the BTU to model the flow of behavioral information
from domain $A$ to domain $B$, i.e., $h_{A_{i}\rightarrow B}$, as follows:

(3) $\begin{split}f_{A_{i}}&{}=\sigma(W_{f_{A}}\cdot h_{A_{i}}+W_{f_{B}}\cdot
h_{B_{j}}+W_{f}\cdot h_{A_{i-1}\rightarrow B}+b_{f})\\\
\widehat{h_{A_{i}}}&{}=\tanh({W_{h}\cdot h_{A_{i}}+U_{h}\cdot
h_{A_{i-1}\rightarrow B}+b_{h}})\\\ h_{A_{i}\rightarrow
B}&{}=f_{A_{i}}\odot\widehat{h_{A_{i}}}+(1-f_{A_{i}})\odot
h_{A_{i-1}\rightarrow B},\end{split}$

where $h_{A_{i}}$ and $h_{B_{j}}$ are the representations of domain $A$ and
$B$ at timestamp $i$ and $j$, respectively. $f_{A_{i}}$ measures the degree of
connection between these two representations $h_{A_{i}}$ and $h_{B_{j}}$ from
both domains, which employs the gate mechanism to control how much information
is to be transferred from domain $A$ to domain $B$. $\widehat{h_{A_{i}}}$ is
the updated representation of the current input. $W_{A}$ and $W_{B}$ are the
parameters, $b_{f}$ is the bias term, $\odot$ indicates element-wise
multiplication. $h_{A_{i}\rightarrow B}$ can be seen as a combination of
$\widehat{h_{A_{i}}}$ and $h_{A_{i-1}\rightarrow B}$ balanced by $f_{A_{i}}$.
Note that the BTU can be applied bidirectionally from “domain $A$ to domain
$B$” and “domain $B$ to domain $A$”. Here, we take the “domain $A$ to domain
$B$” direction and achieve recommendations in domain $B$ as an example.

$h_{A_{i}\rightarrow B}$ is the information extracted from domain $A$, which
is ready to be transferred to domain $B$. Since it still belongs to domain
$A$, we employ an RNN structure to transfer it to domain $B$ as follows:

(4) $\begin{split}&h_{(A\rightarrow B)_{i}}=GRU(h_{(A\rightarrow
B)_{i-1}},h_{A_{i}\rightarrow B}).\\\ \end{split}$

After that, we can obtain the transferred behavioral representation
$h_{(A\rightarrow B)_{i}}$ in domain $B$ at time step $i$.

###  3.6. Knowledge transfer unit

The BTU only models the flow of behavioral information. We hypothesize that
this may be not enough for the model to be able to encode the connection
between items from the two domains in some cases. For example, if there is no
knowledge indicating that both “Pirates of the Caribbean” and “Harry Potter”
belong to fantasy, it is difficult for the model to capture the connection
between them solely based on behavioral information. To better transfer the
information of items from both domains, we propose the KTU, as shown in the
right side of the Figure 2.

For each hybrid interaction sequence $S$, we get the item representations
$\\{h_{A_{1}}$, $h_{A_{2}}$, …, $h_{A_{i}},\ldots\\}$ from the sequence
encoder (Section 3.4) and the transferred behavioral representations
$\\{h_{(A\rightarrow B)_{1}}$, $h_{(A\rightarrow
B)_{2}},\ldots,h_{(A\rightarrow B)_{i}},\ldots\\}$ from the BTU (Section 3.5).
We use the item representation of the last time step to denote the sequence
representation $h_{A}$ and the transferred behavioral representation
$h_{(A\rightarrow B)}$. We also obtain the relational adjacency matrix $A$ of
the KG, which consists of $N$ entities and the corresponding relations (§3.2).
Here, we represent these $N$ entities as $E$, the corresponding relations are
represented as $R$.

We initialize all entities in the KG and we can get the initialized entity
representations $h_{E^{0}}$. That is, for each entity $e_{k}\in E$, the
initialized entity representation is $h_{e_{k}^{0}}\in h_{E^{0}}$. Then we
learn a transferred entity representation $h_{e_{k}^{T}}\in h_{E^{T}}$ for
each entity $e_{k}$ by leveraging the relations in the KG, as shown in Eq. 5:

(5) $\begin{split}r&=\sigma(W_{r}\cdot
h_{e_{k}^{0}}+U_{r}\cdot\widetilde{h_{e^{L}_{k}}}+b_{r})\\\
f&=\sigma(W_{f}\cdot
h_{e_{k}^{0}}+U_{f}\cdot\widetilde{h_{e^{L}_{k}}}+V_{f}\cdot h_{A}+b_{f})\\\
\widehat{h_{e_{k}}}&=\tanh(W_{h}\cdot\widetilde{h_{e^{L}_{k}}}+U_{h}\odot(r\odot
h_{e_{k}^{0}}))\\\ h_{e_{k}^{T}}&=(1-f)\odot
h_{e_{k}^{0}}+f\odot\widehat{h_{e_{k}}}.\\\ \end{split}$

The explanations for the main parts of Eq. 5 are as follows:

  1. (i)

Gated functions. $r$ and $f$ are the update gate function and the forget gate
function, which aim to regulate how much of the update information should be
propagated. $W_{r}$, $U_{r}$, $W_{f}$, $U_{f}$ and $V_{f}$ are the parameters;
$b_{r}$ and $b_{f}$ are the bias term.

  2. (ii)

Candidate knowledge transfer representation. $\widehat{h_{e_{k}}}$ is the
candidate knowledge transfer representation, which is calculated based on the
cross-domain disseminated entity representation $\widetilde{h_{e^{L}_{k}}}$ at
the $L$-th hop layer (we will explain this later in Eq. 6) and the updated
entity representation $r\odot h_{e_{k}^{0}}$. $W_{h}$ and $U_{h}$ are the
parameters, $\odot$ indicates element-wise multiplication.

  3. (iii)

Transferred entity representation. The transferred entity representation
$h_{e_{k}^{T}}$ is a combination of the initialized entity representation
$h_{e_{k}^{0}}$ and the candidate knowledge transfer representation
$\widehat{h_{e_{k}}}$ balanced by the forget gate $f$, where the information
among entities has been disseminated through $L$ hop layers.

Graph convolutional techniques are commonly used to disseminate information
among entities based on their relations (Kipf and Welling, 2017; Wang et al.,
2019d; Wang et al., 2018). However, in the cross-domain scenario that we
consider, the information disseminated by entities from different domains is
different. Hence, we propose a cross-domain graph convolutional mechanism that
can distinguish entities from different domains and adopt different modeling
methods to disseminate their information so as to get better entity
representation. In this manner, the information in the KG is disseminated
between both domains, which can be considered as a flow of knowledge in the
hybrid interaction sequence. Suppose the information can be disseminated
within $L$ hop layers. At the $l$-th hop layer ($0\leq l\leq L$), the
information of each entity and its cross-domain neighbor entities via various
relations will be disseminated to the next hop layer $l+1$ and is used to
update the entity representation. The process of cross-domain information
dissemination is defined in Eq. 6:

(6)
$\begin{split}\mbox{}\widetilde{h_{e^{l+1}_{k}}}=\sigma\left[f_{0}(\widetilde{h_{e^{l}_{k}}})+\frac{1}{|N_{i}(k)|}\sum_{r\in
R}\sum_{p\in
N_{i}(k)}f_{i}(\alpha_{p}\cdot\widetilde{h_{e^{l}_{p}}})+\frac{1}{|N_{c}(k)|}\sum_{r\in
R}\sum_{q\in
N_{c}(k)}f_{c}(\beta_{q}\cdot\widetilde{h_{e^{l}_{q}}}+c_{q}\cdot\widetilde{h_{e^{l}_{q}}})\right],\mbox{}\end{split}$

where $e_{k}$ is any entity in the entity set $E$; $N_{i}(k)$ is the neighbor
entity set of entity $e_{k}$ from the same domain as $e_{k}$; $N_{c}(k)$ is
the neighbor entity set of entity $e_{k}$ from the complementary domain.
$f_{0}$, $f_{i}$ and $f_{c}$ represent the transformation functions for
initialization, in-domain and cross-domain respectively; $\alpha_{p}$ is the
in-domain attention weight calculated between each entity $e_{p}\in N_{i}(k)$
and the sequence representation $h_{A}$; $\beta_{q}$ is the cross-domain
attention weight calculated between each entity $e_{q}\in N_{c}(k)$ and the
transferred behavioral representation $h_{(A\rightarrow B)}$; $c_{q}$ shows
the sum of similarities between entity $e_{q}$ and each entity $e_{p}\in
N_{i}(k)$, which is defined as: $c_{q}=\sum_{p\in N_{i}(k)}e_{p}\cdot e_{q}$;
$\widetilde{h_{e^{l}_{k}}}$ denotes the cross-domain disseminated
representation of entity $e_{k}$ at the $l$-th hop layer, which aggregates the
information from itself and cross-domain neighbor entities as the new
representation for the next hop layer. At the first hop layer, the cross-
domain disseminated representation is assigned by the gated entity
representation, i.e., $\widetilde{h_{e^{0}_{k}}}=h_{e_{A_{k}}}$ if the entity
$e_{k}$ is from domain $A$, otherwise
$\widetilde{h_{e^{0}_{k}}}=h_{e_{B_{k}}}$:

(7) $\begin{split}c&=\sigma\left(W_{c}\cdot concat[h_{A},h_{(A\rightarrow
B)},h_{E_{0}}]+b_{c}\right)\\\ h_{e_{A_{k}}}&=c\odot\left(\alpha_{A_{k}}\cdot
h_{e_{A_{k}}^{0}}\right)\\\ h_{e_{B_{k}}}&=(1-c)\odot\left(\beta_{B_{k}}\cdot
h_{e_{B_{k}}^{0}}\right),\\\ \end{split}$

where $W_{c}$ is the parameter; $b_{c}$ is the bias term; $h_{e_{A_{k}}}$ is
the gated entity representation of entity $e_{A_{k}}\in E_{A}$,
$h_{e_{B_{k}}}$ is the gated representation of entity $e_{B_{k}}\in E_{B}$.
$c$ is a cross-domain information gate to handle the situation where the
proportion of entities from different domains in the KG is different (e.g.,
when there are 1000 entities from domain $A$, but only 10 entities from domain
$B$). So we define the gated entity representations $h_{e_{A_{k}}}$ for domain
$A$ and $h_{e_{B_{k}}}$ for domain $B$ based on their initial entity
representations respectively, which aims to balance information from both
domains. $\alpha_{A_{k}}$ is the attention weight of $e_{A_{k}}$ for sequence
representation $h_{A}$; $\beta_{B_{k}}$ is the attention weight of $e_{B_{k}}$
for the transferred behavioral representation $h_{(A\rightarrow B)}$. These
attention weights act as an information controller to identify entities of
different importance in the KG, the definitions of which are shown in Eq. 8:

(8)
$\begin{split}s_{A_{k}}&=\mathbf{v_{1}}^{\mathsf{T}}\tanh{\left(W_{A_{1}}\cdot
h_{A}+W_{A_{2}}\cdot h_{e_{A_{k}}^{0}}\right)}\\\
\alpha_{A_{k}}&=\frac{\exp{(s_{A_{k}})}}{\sum_{i}\exp{(s_{A_{i}}})}\\\
s_{B_{k}}&=\mathbf{v_{2}}^{\mathsf{T}}\tanh{\left(W_{B_{1}}\cdot
h_{(A\rightarrow B)}+W_{B_{2}}\cdot h_{e_{B_{k}}^{0}}\right)}\\\
\beta_{B_{k}}&=\frac{\exp{(s_{B_{k}})}}{\sum_{j}\exp{(s_{B_{j}}})},\\\
\end{split}$

where $h_{e_{A_{k}}^{0}}$ and $h_{e_{B_{k}}^{0}}$ are the initialized entity
representations of entity $e_{A_{k}}$ and $e_{B_{k}}$ respectively. $h_{A}$ is
the sequence representation and $h_{(A\rightarrow B)}$ is the transferred
behavioral representation as mention above. $\mathbf{v_{1}}$,
$\mathbf{v_{2}}$, $W_{A_{1}}$, $W_{A_{2}}$, $W_{B_{1}}$ and $W_{B_{2}}$ are
learnable parameters.

###  3.7. Mode switch

Recall that $P(M\\_S_{B}|S,\langle E,R\rangle)$ and $P(M\\_G_{B}|S,\langle
E,R\rangle)$ are the probabilities of conducting recommendations under
sequence mode and graph mode, respectively. We model the mode switch as a
binary classifier. Specifically, we first combine the sequence representation
$h_{B}$, the transferred behavioral representation $h_{(A\rightarrow B)}$ and
the sum of all transferred entity representation $\sum_{k}(h_{e_{k}^{T}})$
(where $h_{e_{k}^{T}}\in h_{E^{T}}$). Then, we employ a softmax regression to
transform the total representation into the mode probability distributions, as
follows:

(9) $\begin{split}P(M\\_G_{B}|S,\langle E,R\rangle),P(M\\_S_{B}|S,\langle
E,R\rangle)=\text{softmax}\left(W_{m}\cdot concat\left[h_{B},h_{(A\rightarrow
B)},\sum_{k}(h_{e_{k}^{T}})\right]+b_{m}\right),\end{split}$

where $W_{m}$ is the weight matrix and $b_{m}$ is the bias term.

###  3.8. Graph recommendation decoder

The graph recommendation decoder evaluates the probabilities of recommending
items involved in the KG. Here we directly use the representations of entities
to learn the attention weights and take these weights as the final predicted
recommendation probability. The recommendation probability for each item
$B_{j+1}\in E_{B}$ is computed as follows:

(10) $\begin{split}&P(B_{j+1}|M\\_G_{B},S,\langle
E,R\rangle)=\begin{cases}0&\text{if }{B_{j+1}\notin\mathbbm{B}}\\\
\frac{\exp(h_{e_{B_{j+1}}^{T}})}{\sum_{k}^{m}\exp(h_{e_{k}^{T}})}&\text{if
}{B_{j+1}\in\mathbbm{B}},\end{cases}\end{split}$

where $h_{e_{B_{j+1}}^{T}}$ is the transferred entity representation of
$e_{B_{j+1}}$ (corresponding to $h_{e_{k}^{T}}$ in Eq. 5 when $e_{k}$ is an
item entity from domain $B$). $m$ is the number of the item set $\mathbbm{B}$.
Note that $e_{B_{j+1}}\in E_{B}$ is an item entity corresponding to item
$B_{j+1}\in\mathbbm{B}$. The recommendation probabilities are set to zero for
those items that do not exist in $\mathbbm{B}$.

###  3.9. Sequence recommendation decoder

The sequence recommendation decoder evaluates the probabilities of items in
the sequence item set. We first concatenate the sequence representation
$h_{B}$ and the transferred behavioral representation $h_{(A\rightarrow B)}$
into the hybrid representation $c_{S}$, i.e.,
$c_{S}=\begin{bmatrix}h_{B},h_{(A\rightarrow B)}\\\
\end{bmatrix}^{\mathsf{T}}$. Then, the recommendation probability for each
item $B_{j+1}\in\mathbbm{B}$ is computed as follows:

(11) $\begin{split}&P(B_{j+1}|M\\_S_{B},S,\langle
E,R\rangle)=\begin{cases}0&\text{if }{B_{j+1}\notin\mathbbm{B}}\\\
\frac{\exp(W_{j+1}c_{S}+b_{I})}{\sum_{k}^{m}\exp(W_{k}c_{S}+b_{I})}&\text{if
}{B_{j+1}\in\mathbbm{B}},\end{cases}\end{split}$

where $W_{k}\in W_{I}$ is the weight matrix, $b_{I}$ is the bias term. The
recommendation probabilities are set to zero for those items that do not exist
in the item set $\mathbbm{B}$.

###  3.10. Objective function

Our goal is to maximize the prediction probability for each domain given a
hybrid interaction sequence. Therefore, we define the negative log-likelihood
loss function as follows:

(12) $\displaystyle L_{R}(\theta)=L_{R_{A}}(\theta)+L_{R_{B}}(\theta),$

where $\theta$ are all parameters in MIFN. Specifically, $L_{R_{A}}(\theta)$
and $L_{R_{B}}(\theta)$ can be derived as follows:

(13)
$\begin{split}L_{R_{A}}(\theta)&=-\frac{1}{|\mathbb{S}|}\sum_{S\in\mathbb{S}}\sum_{A_{i}\in
S}\log P(A_{i+1}|S,\langle E,R\rangle)\\\
L_{R_{B}}(\theta)&=-\frac{1}{|\mathbb{S}|}\sum_{S\in\mathbb{S}}\sum_{B_{j}\in
S}\log P(B_{j+1}|S,\langle E,R\rangle),\end{split}$

where $\mathbb{S}$ is the set of all hybrid interaction sequences in our
training set, and $P(A_{i+1}|S,\langle E,R\rangle)$ or $P(B_{j+1}|S,\langle
E,R\rangle)$ are the next prediction probabilities, which are as defined in
Eq. 2.

Additionally, MIFN incorporates a mode switch module to calculate the mode
selection probability between sequence mode and graph mode. We assume that if
an item does not exist in item set, it can just be generated under the graph
mode. Here, we can jointly train another mode prediction loss as follows,
which adopts the negative log-likelihood loss:

(14)
$\begin{split}L_{M_{A}}(\theta)&=-\frac{1}{|\mathbb{S}|}\sum_{S\in\mathbb{S}}\sum_{A_{i}\in
S}[(1-\mathbbm{1}(A_{i+1}\in\mathbbm{A}))\log P(M\\_S_{A}|S,\langle
E,R\rangle)]\\\
L_{M_{B}}(\theta)&=-\frac{1}{|\mathbb{S}|}\sum_{S\in\mathbb{S}}\sum_{B_{j}\in
S}[(1-\mathbbm{1}(B_{j+1}\in\mathbbm{B}))\log P(M\\_S_{B}|S,\langle
E,R\rangle)]\\\ L_{M}(\theta)&=L_{M_{A}}(\theta)+L_{M_{B}}(\theta),\\\
\end{split}$

where $\mathbbm{1}(item\in itemset)$ is the indicator function that equals 1
if this item is in the item set and 0 otherwise. $L_{M}(\theta)$ is the total
mode loss for domain $A$ and $B$.

Finally, we adopt a joint-learning strategy, and the final loss combines both
recommendation loss and mode loss:

(15) $\begin{split}&L(\theta)=L_{R}(\theta)+L_{M}(\theta).\\\ \end{split}$

##  4\. Experimental Setup

###  4.1. Research questions

We evaluate MIFN on four e-commerce datasets. We aim to answer the following
questions in our experiments:

  1. (RQ1)

How does MIFN perform compared with the state-of-the-art methods in terms of
Recall and MRR? (See Section 5.1.)

  2. (RQ2)

Does the KTU help to improve the performance of recommendations? And does the
performance differ from the situation when we only allow for the flow of
behavioral information? (See Section 5.2.)

  3. (RQ3)

Does the knowledge graph construction method have a big effect on the overall
recommendation results? (See Section 5.3.)

  4. (RQ4)

Is MIFN able to provide better recommendations by incorporating the flow of
knowledge across domains? (See Section 5.4.)

###  4.2. Datasets

We conduct experiments on the Amazon e-commerce
collection,333https://www.amazon.com/ which consists of user interactions
(e.g., userid, itemid, ratings, timestamps) from multiple domains and some
item meta information (e.g., descriptions, images, product associations).
Compared with other recommendation datasets, the Amazon dataset contains
overlapping user interactions in multiple domains, which is suitable for
cross-domain sequential recommendation (CDSR). Specifically, we pick two pairs
of complementary domains “Movie-Book” domains and “Food-Kitchen” domains for
experiments. For the “Movie-Book” dataset, the “Movie” domain contains movie
watching records. The “Book” domain covers book reading records. For the
“Food-Kitchen” dataset, the “Food” domain contains food purchase records. The
“Kitchen” domain contains furniture purchase records. We follow the settings
of Ma et al. (2019a) to process the data. To satisfy cross-domain
characteristics, we first pick users who have interactions in both domains.
Since we do not target cold-start users or items in this work, we only keep
users who have more than 10 interactions and items whose frequency is larger
than 10. To satisfy sequential characteristics which consists of many user
interactions within a period of time, we first order the interactions by time
for each user, then we split the sequences from each user into several small
sequences with each sequence containing interactions within a period, i.e., a
month for the “Movie-Book” dataset, and a year for the “Food-Kitchen” dataset.
We also require that each sequence contains at least 3 items from each domain.
The statistics of the processed datasets are shown in Table 2.

Table 2. Dataset statistics. Domain | #Items | #Train | #Test | #Valid | Avg_Seq_Len
---|---|---|---|---|---
Movie | 36,845 | 44,732 | 19,861 | 9,274 | 11.98
Book | 63,937
Food | 29,207 | 25,766 | 17,280, | 7,650 | 19.91
Kitchen | 34,886

For knowledge graph construction, we use the Amazon product data to mine the
relations of the items.444https://jmcauley.ucsd.edu/data/amazon The data is
collected from large-scale user logs, which contain the following relations:
(1) “Also_buy” (users also buy item $X$ when buying item $Y$.);  (2)
“Also_view” (users also view item $X$ when viewing item $Y$.);  (3)
“Buy_together” (users buy item $X$ and $Y$ together frequently);  (4)
“Buy_after_viewing” (users buy item $X$ after they buy $Y$);  (5)
“Is_the_same_category” (item $X$ and $Y$ belong to the same category).
Additionally, for the “Movie-Book” dataset, we also crawl the relation
“Adapted_from” between books and movies from
Wikipedia.555https://en.wikipedia.org/ For example, $\langle$movie,
Adapted_from, book$\rangle$ means that the movie is adapted from the book. We
align knowledge entities with Wikipedia titles by fully matching. The
statistics of the knowledge information are shown in Table 3.

Table 3. KG statistics. Domain | #Entities | #Relations | #Triples
---|---|---|---
Movie |  065,418 | 6 |  03,911,284
Book | 315,770 | 40,048,795
Food |  050,273 | 5 |  03,822,123
Kitchen |  082,552 |  07,836,064

For evaluation, we use the last interacted item in each sequence for each
domain as the ground truth item, respectively. We randomly select 80% of each
user’s interactions as the training set, 10% as the validation set, and the
remaining 10% as the test set.

###  4.3. Baseline methods

We compare the proposed model MIFN with baselines from five categories:  (1)
traditional recommendation methods,  (2) cross-domain recommendation methods,
(3) sequential recommendation methods,  (4) cross-domain sequential
recommendation methods, and  (5) knowledge-aware recommendation methods.

####  4.3.1. Traditional recommendation methods.

We adapt three commonly used traditional recommendation methods to SRs:

  * •

POP: This method recommends the most popular items in which items are ranked
based on their popularity. It is a simple baseline, but is commonly used owing
to its simplicity yet effectiveness (He et al., 2017).

  * •

Item-KNN: This method is inspired by the classical KNN model; it looks for
items that are similar to other items that have been clicked by a user in the
past, where similarity is defined as the cosine similarity between the vector
of sequences (Sarwar et al., 2001).

  * •

BPR-MF: This method follows the idea of MF with a pairwise ranking objective
via stochastic gradient descent (Rendle et al., 2009). Following Hidasi et al.
(2016a), we represent a new sequence by the average latent factors of items
that appeared in the sequence so far.

####  4.3.2. Cross-domain recommendation methods.

We use two popular cross-domain recommendation methods for comparison.

  * •

NCF-MLP++: This is a deep learning based method where the model learns the
inner product of the traditional CF by using multilayer perceptron (MLP) in
each domain. The user representations are shared between both domains while
item representations are private in each domain, and the final recommendations
are aggregated from both domain recommendations probabilities. We adopt the
implementation in (Ma et al., 2019a).

  * •

Conet: This method transfers information between different domains by a cross-
stitch network (Misra et al., 2016), where information in each domain is
captured by neural CF model (He et al., 2017).

####  4.3.3. Sequential recommendation methods.

A number of SR methods have been proposed in the last few years. In this work,
we construct/select baselines that are fair (use the same information, similar
architectures, etc.) to compare with:

  * •

GRU4REC: It is the first attempt to use GRU for SRs. It utilizes session-
parallel mini-batch training strategy and employs a ranking-based loss
functions (Hidasi et al., 2016a).

  * •

HRNN: This method combines the extra user’s information into GRU networks and
proposes a hierarchical RNN model based on GRU4REC (Quadrana et al., 2017).

  * •

NARM: This method takes an attention mechanism into consideration to capture
both sequential-level preferences and the user’s main purpose (Li et al.,
2017).

  * •

STAMP: This method constructs two network structures to capture a user’s
general preferences and the current preferences of the last click within the
current sequence (Liu et al., 2018).

####  4.3.4. Cross-domain Sequential recommendation methods.

  * •

$\pi$-Net: This method is the only one that considers cross-domain
characteristics for SRs. We take this as the fairest baseline to compare with.
It designs a new gating mechanism to recurrently extract and share useful
information across different domains (Ma et al., 2019a).

####  4.3.5. Knowledge-aware recommendation methods.

  * •

SRGNN: This method constructs each sequence as a directed graph, where the
items in the sequence are entities and transition relationship between
adjacent items represents edge which is considered as knowledge information.
By modeling the complex transitions, each session graph and item embeddings of
all items involved in each graph can be obtained through gated graph neural
networks (Wu et al., 2019).

  * •

KSR: This method incorporates KGs into SRs, and it combines the sequential
user preference captured by an RNN and attribute-level preferences captured by
Key-Value Memory Networks to get the final representation of user preference
(Huang et al., 2018).

###  4.4. Evaluation metrics

We target the top-K recommendations in this work, so we adopt two widely used
ranking-based metrics (Cheng et al., 2018; He et al., 2018; Mei et al., 2018;
Ren et al., 2019): MRR@K and Recall@K. Specifically, we report $K$ = 5, 10,
20.

  * •

Recall: This measures the proportion of the top-K recommended items that are
in the evaluation set. It does not consider the actual rank of the item as
long as it is amongst the list of recommend items.

  * •

MRR: This is the average of reciprocal ranks of the relevant items. And the
reciprocal rank is set to zero if the ground truth item is not in the list of
recommended items. MRR takes the order of recommendation ranking into account.
Since each sample has only one ground truth item, we choose MRR as the ranking
metric instead of others, e.g., NDCG.

###  4.5. Implementation details

For most of the baseline methods, we find the best settings using grid search
on the validation set. For those with too many hyperparameters, we follow the
reported optimal hyperparameter settings from the original publications that
introduced them. For our model, the embedding size and the hidden size are set
to 256, the hop layer $H$ is set to 2, and the number of entities $N$ in KG is
set to 200. We initialize the model parameters randomly using the Xavier
method. We take Adam as our optimization method. MIFN is implemented in
TensorFlow and trained on a GeForce GTX TitanX GPU. The code and dataset used
to run the experiments in this paper are available at
https://github.com/mamuyang/MIFN.

##  5\. Results and Analysis

###  5.1. Overall performance (RQ1)

We report the results of MIFN compared with the baseline methods on the
“Movie-Book” and “Food-Kitchen” datasets. The results of all methods are shown
in Table 4 and 5, respectively. From the results, we have the following main
observations.

Table 4. Experimental results (%) on the Amazon (“Movie-Book”) dataset. Bold face indicates the best result in terms of the corresponding metric. Significant improvements over the best baseline results are marked with † (t-test, $p<.05$).  Methods | Movie-domain | Book-domain
---|---|---
MRR | Recall | MRR | Recall
@5 | @10 | @20 | @5 | @10 | @20 | @5 | @10 | @20 | @5 | @10 | @20
POP |  00.10 |  00.11 |  00.13 |  00.20 |  00.29 |  00.58 |  00.11 |  00.14 |  00.16 |  00.20 |  00.44 |  00.75
BPR-MF |  00.51 |  00.57 |  00.64 |  00.89 |  01.35 |  02.26 |  01.44 |  01.64 |  01.77 |  02.51 |  03.97 |  05.97
ItemKNN |  01.05 |  01.27 |  01.48 |  02.11 |  03.84 |  06.99 |  01.35 |  01.64 |  01.95 |  02.88 |  05.10 |  09.69
NCF-MLP++ |  01.64 |  01.86 |  02.03 |  02.95 |  04.61 |  07.24 |  01.76 |  01.98 |  02.11 |  03.20 |  04.84 |  07.34
Conet |  01.43 |  01.73 |  02.01 |  02.83 |  05.20 |  09.24 |  01.17 |  01.36 |  01.51 |  02.13 |  03.54 |  05.77
GRU4REC | 12.80 | 12.86 | 12.88 | 13.69 | 14.11 | 14.43 | 13.87 | 13.92 | 13.95 | 14.64 | 15.02 | 15.34
HRNN | 13.38 | 13.43 | 13.45 | 13.95 | 14.25 | 14.58 | 14.57 | 14.61 | 14.62 | 14.99 | 15.25 | 15.46
NARM | 13.80 | 13.85 | 13.86 | 14.20 | 14.53 | 14.80 | 15.25 | 15.26 | 15.27 | 15.57 | 15.66 | 15.78
STAMP | 12.44 | 12.56 | 12.63 | 13.66 | 14.58 | 15.68 | 11.53 | 11.56 | 11.57 | 11.82 | 12.00 | 12.20
$\pi$-Net | 14.49 | 14.52 | 14.54 | 14.88 | 15.10 | 15.37 | 15.75 | 15.76 | 15.77 | 15.94 | 16.02 | 16.09
SRGNN | 11.77 | 11.84 | 11.88 | 12.66 | 13.18 | 13.87 | 15.12 | 15.14 | 15.15 | 15.46 | 15.61 | 15.77
KSR | 14.18 | 14.23 | 14.26 | 14.91 | 15.28 | 15.73 | 15.84 | 15.87 | 15.89 | 16.51 | 16.72 | 16.92
MIFN-KTU | 14.20 | 14.25 | 14.28 | 14.85 | 15.26 | 15.44 | 14.87 | 14.90 | 14.91 | 15.54 | 15.80 | 16.07
MIFN+$L_{M}$ | 14.73 | 14.75 | 14.81 | 14.87 | 15.96 | 16.02 | 15.75 | 15.97 | 15.99 | 16.87 | 16.96 | 17.05
MIFN | 14.84 | 14.87 | 14.88 | 15.13 | 16.34† | 16.56† | 16.05 | 16.16 | 16.23† | 16.99† | 17.03† | 17.13†

First, MIFN outperforms the single-domain SR methods (e.g., STAMP, NARM) and
the knowledge-aware methods (e.g., SRGNN, KSR) on all datasets. Particularly,
on the “Movie-Book” dataset, the largest increase over NARM is 7.5% and 12.4%
in terms of MRR@5 and Recall@10 on the “Movie” domain, and on the “Book”
domain, the largest increase is 6.2% and 9.1% in terms of MRR@20 and Recall@5.
And the increase over KSR on the “Movie” domain is 4.6% and 6.9% in terms of
MRR@5 and Recall@10, on the “Book” domain, the increase is 2.1% and 2.9% in
terms of MRR@20 and Recall@5. On the “Food-Kitchen” dataset, the largest
increase over NARM is 6.5% and 9.3% in terms of MRR@20 and Recall@20 on the
“Food” domain, and on the “Kitchen” domain, the increase is 9.1% and 12.3% in
terms of MRR@5 and Recall@10. And the increase over KSR is 2.7% and 3.9% in
terms of MRR@20 and Recall@10 on the “Food” domain, and on the “Kitchen”
domain, the increase is 1.6% and 4.1% in terms of MRR@20 and Recall@20. These
improvements demonstrate that jointly considering both cross-domain behavior
and knowledge is helpful for SR.

Table 5. Experimental results (%) on the Amazon (“Food-Kitchen”) dataset. Bold face indicates the best result in terms of the corresponding metric. Significant improvements over the best baseline results are marked with † (t-test, $p<.05$).  Methods | Food-domain recommendation | Kitchen-domain recommendation
---|---|---
MRR | Recall | MRR | Recall
@5 | @10 | @20 | @5 | @10 | @20 | @5 | @10 | @20 | @5 | @10 | @20
POP |  00.40 |  00.49 |  00.56 |  00.82 |  01.50 |  02.15 |  00.22 |  00.25 |  00.27 |  00.40 |  00.60 |  01.47
BPR-MF |  00.82 |  00.87 |  00.94 |  01.35 |  01.82 |  02.61 |  00.41 |  00.47 |  00.50 |  00.62 |  01.04 |  01.47
ItemKNN |  01.55 |  01.98 |  02.43 |  03.28 |  06.70 | 12.47 |  01.13 |  01.44 |  01.90 |  02.60 |  04.77 | 11.08
NCF-MLP++ |  02.01 |  02.24 |  02.42 |  03.45 |  05.19 |  08.02 |  00.87 |  01.03 |  01.17 |  01.72 |  03.00 |  04.99
Conet |  03.38 |  03.64 |  03.82 |  05.07 |  07.07 |  09.73 |  03.30 |  03.55 |  03.71 |  05.09 |  07.03 |  09.47
GRU4REC |  08.10 |  08.23 |  08.29 |  09.46 | 10.38 | 11.26 |  08.36 |  08.39 |  08.41 |  08.70 |  08.93 |  09.25
HRNN |  07.22 |  07.35 |  07.45 |  08.49 |  09.47 | 10.93 |  07.81 |  07.86 |  07.88 |  08.29 |  08.61 |  09.12
NARM |  09.43 |  09.54 |  09.62 | 10.34 | 11.86 | 12.23 |  08.41 |  08.44 |  08.46 |  08.69 |  08.91 |  09.21
STAMP |  09.28 |  09.38 |  09.44 | 10.22 | 10.91 | 11.81 |  08.52 |  08.55 |  08.57 |  08.81 |  09.05 |  09.28
$\pi$-Net |  09.56 |  09.67 |  09.75 | 10.59 | 10.46 | 12.54 |  08.57 |  08.60 |  08.62 |  08.89 |  09.12 |  09.42
SRGNN |  07.31 |  07.49 |  07.60 |  08.68 | 10.02 | 11.67 |  07.20 |  07.26 |  07.29 |  07.90 |  08.36 |  08.87
KSR |  09.79 |  09.91 |  09.98 | 10.82 | 11.78 | 12.77 |  09.03 |  09.07 |  09.08 |  09.39 |  09.62 |  09.92
MIFN-KTU |  09.43 |  09.65 |  09.83 | 10.50 | 11.16 | 12.53 |  08.29 |  08.33 |  08.36 |  08.95 |  09.17 |  09.52
MIFN+$L_{M}$ |  09.86 |  09.88 | 10.03 | 10.93 | 11.96 | 13.14 |  09.05 |  09.17 |  09.18 |  09.28 |  09.89 | 10.24
MIFN |  09.91 | 10.16 | 10.25 | 11.20 | 12.25 | 13.27† |  09.18 |  09.21 |  09.23 |  09.72† | 10.01† | 10.33†

Second, MIFN outperforms the cross-domain sequential recommendation baseline
$\pi$-Net, which just makes use of information at user behavior level.
Specifically, MIFN outperforms $\pi$-Net in terms of all metrics on both
domains. It demonstrates that considering both knowledge _and_ user behavior
level information is better than only behavioral information. Meanwhile, it
also proves the effectiveness of the KTU module of MIFN. With this module,
MIFN is able to capture cross-domain knowledge and conduct information
transfer in the KG so as to learn better sequence representations.

Third, we can observe that the results of MIFN in the “Book” domain are better
than those in the “Movie” domain on the “Movie-Book” dataset. We believe that
this is because the data is less sparse in the “Book” domain compared to that
in the “Movie” domain. And the results in the “Food” domain are better than
the “Kitchen” domain on the “Food-Kitchen” dataset. Again, we think it is
because the data sparsity difference as the users have more interactions in
the “Food” domain than in the “Kitchen” domain. With more interaction data,
the models can identify more user preference characteristics in the dense
domain so as to transfer it to the sparse domain through both the user
behavioral information flow and the knowledge information flow.

Fourth, $\pi$-Net outperforms other sequential baselines, which means that
cross domain information is beneficial to both domains. At the same time,
knowledge aware methods outperform other sequential baselines, which also
means that knowledge information can improve recommendation performance.
Furthermore, it seems that considering knowledge is more useful than modeling
cross-domain characteristics, as KSR slightly outperforms $\pi$-Net.

Fifth, the sequential methods achieve much better results than traditional
methods and cross-domain methods. This is because RNN-based methods are able
to capture the sequential characteristics and can obtain the better
representations while the traditional methods neglect this information.
Besides, it seems that STAMP obtains lower results than the sequential method
NARM in the “Movie-Book” dataset, while it performs better in the “Kitchen”
domain of “Food-Kitchen” dataset. We believe that this is because of
differences in the datasets, e.g., we found that the user preferences in the
kitchen domain are relatively more focused. And the knowledge aware method
SRGNN performs worse than most sequential methods. This is because that SRGNN
just employs the transition relation between adjacent items to construct the
graph so as to get the representations of different items, however it does not
consider the relation between the non-adjacent items (the other sequential
methods do consider this), which may also affect item representations.

###  5.2. Ablation study (RQ2)

To verify the effectiveness of the proposed modules, we design the ablation
study to compare several model variants. The results are listed in Table 4 and
Table 5.

  1. (1)

MIFN is the best performing variant, which includes both the BTU and KTU
modules, and trained with the recommendation loss $L_{R}$ only.

  2. (2)

MIFN-KTU is MIFN without the KTU module and performs information transfer only
at the level of behavioral information;

  3. (3)

MIFN+$L_{M}$ is MIFN by adding the mode switch loss.

First, by removing KTU, the performance of MIFN-KTU is dramatically less than
that of MIFN, which confirms that considering knowledge flow can improve the
cross-domain recommendations. In addition, the results of MIFN-KTU are worse
than those of the knowledge-aware method KSR, while MIFN outperforms KSR on
all domains. This indicates that the KTU module is able to make good use of
the cross-domain knowledge and is able to better capture user preferences by
modeling the cross-domain knowledge flow.

Second, if we jointly train the recommendation loss $L_{R}$ and the mode
switch loss $L_{M}$, the performance drops a little but its performance is
still than that of the baselines. The switch loss $L_{M}$ assumes that if the
next item does not exist in the item set, it must be recommended under the
graph mode, which makes the model tend to recommend items existing in the
graph. However, since there already exists a similar supervision signal in
$L_{R}$, which assumes that each item is recommended under the graph mode, the
sequence mode, or a combination of both. Further adding the $L_{M}$ loss
introduces unnecessary bias towards graph mode.

###  5.3. Influence of the knowledge graph construction algorithm (RQ3)

The number of triples in the complete KG is large (see Table 3), so we propose
a knowledge graph construction method as detailed in Algorithm 1 to build KG
for each sequence. To study the effect of the knowledge graph construction
method, we design an experiment aimed at analyzing the effect of the ratios of
the ground truth items in the constructed KG on the final recommendation
performance. We achieve this by simulating and controlling the ratios
artificially. Specifically, we add the ground truth items to the extracted
entities according to the specified ratios in advance. The results are shown
in Table 6 and Table 7.

Table 6. Analysis of the knowledge graph construction algorithm on the Amazon (“Movie-Book”) dataset. The different ratios represent the different proportions of the predicted ground truth items appeared in the KG. Ratios | Movie-domain recommendation | Book-domain recommendation
---|---|---
MRR | Recall | MRR | Recall
@5 | @10 | @20 | @5 | @10 | @20 | @5 | @10 | @20 | @5 | @10 | @20
30% | 16.46 | 16.83 | 16.99 | 21.27 | 24.33 | 28.97 | 18.51 | 18.70 | 18.85 | 25.82 | 27.32 | 31.38
50% | 19.53 | 20.43 | 20.83 | 30.33 | 37.07 | 42.67 | 25.04 | 25.68 | 25.98 | 36.08 | 40.75 | 45.12
70% | 23.41 | 23.43 | 23.45 | 42.54 | 47.99 | 50.61 | 27.12 | 28.31 | 28.41 | 48.93 | 56.64 | 57.31
90% | 33.45 | 34.99 | 35.09 | 65.81 | 76.83 | 77.97 | 40.01 | 40.86 | 43.00 | 79.83 | 80.50 | 83.86
100% | 67.04 | 67.56 | 67.69 | 89.57 | 93.30 | 95.15 | 83.08 | 83.46 | 83.62 | 91.97 | 94.79 | 97.02
Table 7. Analysis of the knowledge graph construction algorithm on the Amazon (“Food-Kitchen”) dataset. The different ratios represent the different proportions of the predicted ground truth items appeared in the KG. Ratios | Food-domain recommendation | Kitchen-domain recommendation
---|---|---
MRR | Recall | MRR | Recall
@5 | @10 | @20 | @5 | @10 | @20 | @5 | @10 | @20 | @5 | @10 | @20
30% | 11.75 | 12.30 | 12.72 | 17.67 | 21.77 | 27.99 | 10.96 | 11.51 | 11.99 | 13.71 | 15.52 | 22.41
50% | 22.14 | 22.61 | 22.74 | 35.21 | 38.51 | 42.47 | 22.75 | 23.20 | 23.74 | 34.56 | 37.86 | 41.64
70% | 26.01 | 26.74 | 27.35 | 41.52 | 47.11 | 56.17 | 25.46 | 26.24 | 26.79 | 37.54 | 43.51 | 51.60
90% | 36.58 | 37.50 | 38.11 | 59.72 | 66.57 | 75.61 | 31.29 | 32.88 | 33.40 | 55.21 | 66.78 | 74.17
100% | 47.40 | 48.51 | 48.60 | 85.15 | 92.89 | 94.13 | 43.78 | 45.57 | 45.77 | 80.16 | 92.68 | 95.45

First, we can see that the performance increases as the ratio of ground truth
item appeared in the KG increases on both datasets. For instance, when the
ratio varies from 30% to 100%, the value of MRR@20 increases from 16.99% to
67.69% in the “Movie” domain and the value of Recall@20 increases from 22.41%
to 95.45% in the “Kitchen” domain. This demonstrates that a good knowledge
graph construction algorithm is of vital importance.

Second, we notice that when the ratio increases linearly, the results do not
increase linearly. On both datasets, the increase is relatively slow from 30%
to 90%. However, when we simulate the ratio from 90% to 100%, the performance
is greatly improved in terms of both MRR and Recall on the “Movie-Book”
dataset. We believe that this is because when the ratios reaches a certain
value, the model can easily capture the characteristics of recommended items
from the graph mode in most cases and relies mostly on the KG to do
recommendations. We also notice that with 100% ratio, Recall is improved
largely on “Food-Kitchen” dataset while MRR is not. We think this is because
of the density of the KG. As shown in Table 3, there are more triples in the
‘Movie-Book” dataset, especially the “Book” domain. The richer knowledge makes
it relatively easier to rank the ground truth items.

Currently, using Algorithm 1, the ratios of the ground truth items in the KG
of the “Movie-Book” and “Food-Kitchen” datasets are 14% and 12%, respectively,
both of which are relatively low. Algorithm 1 is only based on the entity
distance calculated using the pretrained entity representations in the KG,
which is insufficient. To this end, we think an important future research
direction in order to further improve MIFN is to design a more effective
knowledge graph construction algorithm.

###  5.4. Qualitative analysis with case studies (RQ4)

To analyze the recommendation results with and without a flow of knowledge, we
list some examples from the “Movie-Book” dataset. Figure 3 shows
recommendations when the extracted KG is relevant to the current user
preference, and Figure 4 shows recommendations when the extracted KG is
irrelevant. Figure 3(a) and 4(a) are recommendations from MIFN, while Figure
3(b) and 4(b) are recommendations from MIFN-KTU. In each figure, the orange
color represents the interactions in the “Movie” domain, and the blue color
represents the interactions in the “Book” domain. The meaning of the different
colored fonts and lines are explained in the legend. The green tick indicates
that the recommendation is correct, and the red cross indicates it is wrong.

(a) Recommendation from MIFN.

(b) Recommendation from MIFN-KTU.

Figure 3. Case study of MIFN and MIFN-KTU when the extracted KG is relevant to
the current user preference.

(a) Recommendation from MIFN.

(b) Recommendation from MIFN-KTU.

Figure 4. Case study of MIFN and MIFN-KTU when the extracted KG is irrelevant
to the current user preference.

From Figure 3, we can observe that when using the extracted KG (Figure 3(a)),
MIFN can give correct recommendations for both domains, however, the
recommendation is wrong in the “Book” domain when the KG is not used (Figure
3(b)). Furthermore, it should be noted that the mode switch probabilities in
Figure 3(a) are different for the two domains. The probability of sequence
mode is 1.0 in the “Movie” domain, but in the “Book” domain, the probability
of graph mode is 0.75, which means that the recommendation of the “Movie”
domain comes from the item set, while the recommendation mostly relies on the
KG for the “Book” domain. From the KG, the book entity “One Fine Stooge: Larry
Fine’s Frizzy Life In Pictures” gets the highest recommendation score of 0.65
in the “Book” domain. The reason is that there exists a knowledge triple, that
is, people who watch the movie “The Three Stooges Go Around the World in a
Daze” will also view the book “One Fine Stooge: Larry Fine’s Frizzy Life In
Pictures.” This knowledge is well transferred by the flow of knowledge to
obtain a better recommendation for the “Book” domain. In contrast, as shown in
Figure 3(b), the recommendation is wrong because the model only relies on the
flow of behavioral information to recommend items from the item set.

On the other hand, we also found that the flow of knowledge is not always
helpful. As shown in Figure 4(a), MIFN still gives a wrong recommendation even
by modeling knowledge information flow with KTU. MIFN recommends “The
confucian Transformation of Korea” with the graph mode recommendation
probability of 0.77, which means, in this case, it still relies mostly on the
KG to do recommendation. However, we can observe that most of the extracted
entities in the KG are thriller movies or reference books which are not
relevant to the current user preference. As a result, MIFN performs somewhat
worse than MIFN-KTU, because although MIFN-KTU also recommends the wrong item,
the recommended item seems more relevant to the user preference, i.e.,
“children—family.” This suggests that the quality of the extracted KG has a
large impact on the final recommendation performance, which further verifies
the conclusion in Section 5.3.

##  6\. Conclusion and Future Work

In this paper, we study how to incorporate knowledge into the cross-domain
sequential recommendation task. We present MIFN, which jointly models two
types of information flow across domains, i.e., of behavioral information and
of knowledge. To verify the effectiveness of MIFN, we conduct experiments on
datasets from four Amazon domains. The results demonstrate that MIFN
outperforms other state-of-the-art baselines. Through extensive analysis
experiments, we confirm that the flow of knowledge helps improve the
recommendation performance in general, which means mixed flow of information
can be used to enhance the CDSR performance.

As to future work, MIFN can be enhanced from at least two directions. First,
currently we extract KGs with Algorithm 1 currently, which we show can be made
more effective by including as much relevant knowledge as possible. Hence, we
will further study the knowledge graph construction algorithm to improve the
quality of the KG without increasing its size. Second, MIFN is limited to
information flow between two domains in this work. Therefore, we want to study
how to make cross-domain recommendations across multiple domains.

## Data and Code

To facilitate reproduction of the results in the paper, we are sharing the
code and resources used to produce our results at
https://github.com/mamuyang/MIFN.

###### Acknowledgements.

This research was partially supported by the Natural Science Foundation of
China (61972234, 61902219, 61672324, 61672322, 62072279), the Key Scientific
and Technological Innovation Program of Shandong Province (2019JZZY010129),
the Tencent AI Lab Rhino-Bird Focused Research Program (JR201932), the
Fundamental Research Funds of Shandong University, the National Key R&D
Program of China (2020YFB1406700), and the Innovation Center for AI (ICAI).
All content represents the opinion of the authors, which is not necessarily
shared or endorsed by their respective employers and/or sponsors.

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  *[CDSR]: cross-domain sequential recommendation
  *[SR]: sequential recommendation
  *[MIFN]: mixed information flow network
  *[BTU]: behavior transfer unit
  *[KTU]: knowledge transfer unit
  *[KG]: knowledge graph
  *[CF]: collaborative filtering
  *[KNN]: K-Nearest neighbors
  *[MF]: matrix factorization
  *[RNN]: recurrent neural network
  *[RNNs]: recurrent neural network
  *[GRU]: gated recurrent unit
  *[RS]: recommender system
  *[SRs]: sequential recommendation
  *[GCNs]: graph convolutional network
  *[KGs]: knowledge graph
  *[GRUs]: gated recurrent unit
  *[MLP]: multilayer perceptron