# Leveraging Two Types of Global Graph for Sequential Fashion Recommendation

Yujuan Ding  Shenzhen University<EMAIL_ADDRESS>,  Yunshan Ma
National University of Singapore<EMAIL_ADDRESS>,  Wai Keung Wong  The
Hong Kong Polytechnic University<EMAIL_ADDRESS>and  Tat-Seng Chua
National University of Singapore<EMAIL_ADDRESS>
(2021)

###### Abstract.

Sequential fashion recommendation is of great significance in online fashion
shopping, which accounts for an increasing portion of either fashion retailing
or online e-commerce. The key to building an effective sequential fashion
recommendation model lies in capturing two types of patterns: the personal
fashion preference of users and the transitional relationships between
adjacent items. The two types of patterns are usually related to user-item
interaction and item-item transition modeling respectively. However, due to
the large sets of users and items as well as the sparse historical
interactions, it is difficult to train an effective and efficient sequential
fashion recommendation model. To tackle these problems, we propose to leverage
two types of global graph, i.e., the user-item interaction graph and item-item
transition graph, to obtain enhanced user and item representations by
incorporating higher-order connections over the graphs. In addition, we adopt
the graph kernel of LightGCN (He et al., 2020) for the information propagation
in both graphs and propose a new design for item-item transition graph.
Extensive experiments on two established sequential fashion recommendation
datasets validate the effectiveness and efficiency of our approach.

Fashion Recommendation, Sequential Recommendation, Graph Neural Network

††copyright: acmcopyright††journalyear: 2021††copyright:
acmcopyright††conference: Proceedings of the 2021 International Conference on
Multimedia Retrieval; August 21–24, 2021; Taipei, Taiwan.††booktitle:
Proceedings of the 2021 International Conference on Multimedia Retrieval (ICMR
’21), August 21–24, 2021, Taipei, Taiwan††price: 15.00††isbn:
978-1-4503-8463-6/21/08††doi: 10.1145/3460426.3463638††ccs: Information
systems Multimedia and multimodal retrieval

##  1\. Introduction

Recommendation system has become an essential feature in many online
platforms, especially for those that connect users and items. For online
fashion shopping, fashion recommender system can improve users’ shopping
experience and retailers’ sales volume by routing users to their preferred
fashion items. Therefore, it is of great value to develop powerful fashion
recommendation models, and sequential fashion recommendation is one of the key
techniques to achieve this goal.

Figure 1. An illustration of the sequential fashion recommendation task, which
aims to predict the user’s next interaction by exploring both the long-term
(u-i interaction) and short-term (i-i transition) fashion preference.

The key to build an effective sequential recommender system for fashion lies
in capturing both the user’s personalized fashion preference patterns and
item’s transitional patterns. User’s actions (e.g., clicking or buying) on the
online fashion shopping platforms naturally form the chronological sequences.
To predict the next interacted item of a user, we should predict not only the
user-item (abbreviated to u-i) interaction probability (related to long-term
user preference) but also the item-item (abbreviated to i-i) transition
probability between his/her previous choice(s) and the next one. As shown in
Figure 1, $u_{1}$ is a young girl who likes skirts and dresses, $u_{2}$ is a
middle-aged business woman who prefers business-style clothes. Such personal
preference is long-term and static, which can be explored from the overall
historical behavior of users. On top of that, users’ short-term interest also
affects their choice at specific time point. We can see from the example that
just before the particular time point of the recommendation, $u_{1}$ bought a
red skirt. Her next action could be highly related to the previous one, for
example, she might want to find an item to match with the skirt, which makes
the shirt a proper recommendation. Similarly, the two items interacted by
$u_{2}$ are also related with each other, where she would like a black suit to
substitute the previous grey one. To sum up, both the u-i interaction and i-i
transition patterns are prevalent in users’ online shopping experience, and
how to properly model both of them within one unified model is a key research
problem.

To properly model both the u-i interaction and i-i transition, there are
several challenges. First, the large set of items and sparse historical
interactions result in severe data sparsity in fashion domain. As shown by the
real-world fashion datasets in Table 1, the number of items is over hundreds
of thousands, while the number of interactions per item is extremely small. As
a consequence, traditional matrix factorization-based methods, such as MF
(Rendle et al., 2012) and FPMC (Rendle et al., 2010), are unable to
effectively model the u-i interaction and i-i transition patterns. Even worse,
for methods that require a sequence of interacted items as input, such as
GRU4REC (Hidasi et al., 2015) and Caser (Tang and Wang, 2018), the number of
available training samples will be further reduced. Therefore, it is difficult
for those models to capture the inherent patterns on such sparse datasets.
Second, most existing approaches that models i-i interactions as graphs are
inefficient due to either inappropriate construction of the graph or
complicated graph kernels. For example, SR-GNN (Wu et al., 2019a) only models
the session-level i-i transition graph while fails to take into account the
effect between items from different sessions. Moreover, the graph kernels that
have been widely applied in many existing methods, such as Gated Graph Neural
Network (GGNN) (Li et al., 2015; Wu et al., 2019a) or Graph Attention Network
(GAT) (Veličković et al., 2017; Qiu et al., 2019), are complicated, resulting
in more computational costs. In summary, how to tackle the problems of data
sparsity and design an effective yet efficient i-i transition graph are the
most critical considerations when designing the models.

In this paper, to deal with the above mentioned challenges, we propose the
Dual-Graph Sequential Recommender (DGSR) method. First, to counter the data
sparsity problem, we leverage two types of graph based on the global u-i
interactions and i-i transitions. By performing information propagation over
the two global graphs, both the user and item representations will be enhanced
by the global u-i collaborative filtering (CF) signals and the i-i transition
contexts. In addition, higher-order propagation extends the connections in the
current graph and further relieves the data sparsity problem. Second, we
propose a new design which formulates the i-i transition as a bipartite graph.
The graph assigns each item with two nodes – one for the situation when the
item serves as an anchor and another for the situation when the item serves as
a target. We drop the session-level graph and purely utilize the global graph
for efficiency consideration. We adopt the LightGCN (He et al., 2020) as the
graph kernel to further reduces the computational costs. LightGCN revises the
typical Graph Convolutional Network (GCN) (Kipf and Welling, 2016) model by
removing the feature transformation layer and the non-linear activation layer,
which improves the performance and also reduce the computational cost. The
main contributions of this work are summarized as follows:

  * •

We leverage two types of global graph to relieve the data sparsity problem and
enhance the user and item representations. To the best of our knowledge (Wu et
al., 2020), this is the first work to leverage both u-i and i-i global graphs
for sequential fashion recommendation.

  * •

We propose a new design for the i-i transition graph construction and adopt
LightGCN as the kernel in both the u-i and i-i graphs, which lead to great
improvement in performance and efficiency.

  * •

Extensive experiments on two established fashion sequential recommendation
datasets (i.e., Taobao iFashion and Amazon Fashion) demonstrate the
effectiveness of our proposed method.

Table 1. Dataset Statistics Dataset | iFashion-SR | Amazon-Fashion
---|---|---
Min Seq Len | Seven | Ten | Seven | Ten
#User | 36,752 | 36,797 | 48,427 | 19,362
#Item | 458,642 | 460,596 | 137,650 | 106,256
#Actions | 1,624,643 | 1,639,006 | 509,352 | 284,385
#Train sample | 1,474,640 | 1,489,000 | 364,071 | 226,299
#Test sample | 50,001 | 50,002 | 48,427 | 19,362
#Valid sample | 50,001 | 50,002 | 48,427 | 19,362
avg. #act/user | 44.2 | 44.54 | 10.52 | 14.69
avg. #act/item | 3.54 | 3.56 | 3.70 | 2.68

##  2\. Related Work

###  2.1. Sequential and Fashion Recommendation

Personalized fashion recommendation aims to model the personalized fashion
preference of users. Most previous works (He et al., 2016; He and McAuley,
2016b; Yu et al., 2018; He and McAuley, 2016c; Kang et al., 2017; Liu et al.,
2017) focus on emphasizing visual representation of fashion items in building
the recommender system as visual information is considered much more important
in fashion domain than in other domains. Despite the effectiveness of
incorporating visual feature, existing works widely overlook the unique user
behaviors in fashion domain and fail to explore more effective behavior
patterns from the interaction history of users. The sparsity issue is also not
properly addressed in previous works. However, the issue is particularly
significant in fashion domain as the item set is way larger compared to other
domains such as books or music (Hu et al., 2015).

In literature, matrix factorization (MF) (Rendle et al., 2012) is one of the
most simple and effective non-sequential recommendation methods. However, MF,
as well as other non-sequential methods (Wang et al., 2019; He et al., 2020,
2017), only models the u-i interactions but is not able to take i-i transition
into account. In comparison, session-based methods usually solely explore the
item transition patterns for the recommendation. In recent years, Deep Neural
Networks (DNNs) have been widely applied in session-based recommendation for
its capability of modeling sequential data. Various types of DNNs, e.g.,
Recurrent Neural Networks (RNNs), Convolutional Neural Networks (CNNs), have
been applied in developing advanced session-based recommenders (Hidasi et al.,
2015; Li et al., 2017; Quadrana et al., 2017; Tang and Wang, 2018). In the
recent years, GNNs have drawn special attention and some GNN-based methods
have achieved state-of-the-art performance in session-based recommendation
tasks (Wu et al., 2020).

Compared with above two types of methods, sequential recommendation methods
model the user’s general preference and also analyze the latest action(s) of
him (Fang et al., 2019; Quadrana et al., 2018). Markov Chain (MC) is an
effective tool to model the action sequence of users and infer the next one.
Combined with Matrix Factorization (MF), Rendel et al. (Rendle et al., 2010)
propose the Factorized Personalized Markov Chain (FPMC) to capture both the
sequential patterns and the long-term user preference. Despite of its
simplicity and efficiency (Feng et al., 2015; Wang et al., 2015; He and
McAuley, 2016a), it only applies the first-order MC and fail to model any
high-order user-item or item-item dependency or connectivity, which still
limits the overall recommendation performance.

Figure 2. An illustration of the user-item interaction graph and item-item
transition graph in sequential recommendation.

###  2.2. Graph Neural Networks for Recommendation

With the rapid development and tremendous success of GNNs in many application
domains (Scarselli et al., 2008; Kipf and Welling, 2016; Ding et al., 2021),
recommendation approaches based on GNNs (Wu et al., 2020; Guo et al., 2020)
have achieved state-of-the-art performance in various sub-tasks, such as
implicit feedback-based general recommendation and session-based
recommendation (He et al., 2020; Wang et al., 2020). Graph is a natural data
structure for most of data in recommender systems. For example, the user and
item interactive relationship can be modeled with a bipartite graph. Another
main contribution of GNN in recommender system is its ability of capturing the
high-order connectivity, which can help inject the CF signal into the
embedding learning process, thereby achieving significant improvements on
performance (Wang et al., 2019; He et al., 2020). Wang et al. (Wang et al.,
2019; He et al., 2020) proposed the Neural Graph Collaborative Filtering
(NGCF) method for the implicit feedback-based recommendation. NGCF builds the
user-item interaction graph first and then conducts multi-layer embedding
propagation on the graph to refine the embeddings of users (or items). It has
achieved very competitive performance over all CF-based recommendation
methods, as well as its variant LightGCN (He et al., 2020).

GNNs have also been applied in session-based recommendation to capture the
transition patterns in sessions. The majority of existing methods build the
graphs based on the sequence of items within the same session and then apply
GNNs to capture transitions among items, which are claimed to be complex and
difficult to be captured by previous conventional sequential methods (Wu et
al., 2019a). Methods with such a framework include SR-GNN (Wu et al., 2019a),
FGNN (Qiu et al., 2019), GC-SAN (Xu et al., 2019), A-PGNN (Wu et al., 2019b).
In summary, different efforts have been made in modeling the high-order
connectivity of either user-item interaction or item-item transition. However,
so far no work has tried to modeling both yet. Since the sparsity issue is
particularly severe in sequential fashion recommendation, leveraging more
contextual information by high-order connectivity, for both u-i interaction
and i-i transition, would be significantly valuable.

##  3\. Approach

In this section, we introduce the proposed Dual-Graph Sequential Recommender
(DGSR) method. We first give the problem formulation. Then, the basic
sequence-aware factorization framework of DGSR is introduced. After that, we
explain how to build two types of graph and incorporate them for user and item
embedding enhancement. Finally, we introduce the prediction and optimization
of the proposed method.

###  3.1. Problem Formulation

The problem studied in this paper is sequential fashion recommendation. Let
$\mathcal{U}=\\{u_{1},u_{2},...u_{N_{U}}\\}$ denote the whole user set and
$\mathcal{I}=\\{i_{1},i_{2},...i_{N_{I}}\\}$ denote the whole fashion item
set, where $N_{U}$ and $N_{I}$ are the total number of users and fashion items
respectively. Each user $u$ is interacted with a sequence of fashion items in
chronological order, denoted as
$\textbf{s}^{u}=[s_{1}^{u},s_{2}^{u},...,s_{t}^{u},...,s_{|s^{u}|}^{u}]$,
$s_{t}^{u}\in\mathcal{I}$. The objective of sequential fashion recommendation
is to predict the next action and make recommendations accordingly, in other
words, to predict the probability of item $i$ to be the next pick of $u$ after
picking $l$: $y_{u,l,i}:=p(i=s_{t}^{u}|l=s_{t-1}^{u},u)$.

###  3.2. Basic Sequential Recommendation Framework

Personalized sequential recommendation aims to predict the triplet score among
the user, previously interacted item and target item $y_{u,l,i}$. It can be
formulated as a personal transition cube prediction problem (Rendle et al.,
2010), where one own transition matrix is learned for each user. Due to the
limited observations for estimating the transition cube, factorizing methods
are adopted to factorize the transition cube into a linear combination of both
user-item (u-i) interaction and item-item (i-i) transition (Rendle et al.,
2010): $y_{u,l,i}=y_{u,i}+y_{l,i}$. Following the typical sequential
recommendation approach FPMC (Rendle et al., 2010), we describe a user (or an
item) with an embedding vector and model the u-i interaction and i-i
transition with inner-product as:

(1)
$y_{u,l,i}=\boldsymbol{e}^{U}_{u}\cdot\boldsymbol{e}^{IU}_{i}+\boldsymbol{e}^{L}_{l}\cdot\boldsymbol{e}^{IL}_{i}.$

$\boldsymbol{e}^{U}_{u}\in\mathbb{R}^{d}$ is the embedding of user $u$,
$\boldsymbol{e}^{IU}_{i}\in\mathbb{R}^{d}$ is the embedding of item $i$
specifically for the modeling of the interaction with users.
$\boldsymbol{e}^{U}_{u}$ and $\boldsymbol{e}^{IU}_{i}$ are looked up from the
embedding table of users $\boldsymbol{E}^{U}\in\mathbb{R}^{N_{U}\times d}$ and
that of items $\boldsymbol{E}^{IU}\in\mathbb{R}^{N_{I}\times d}$, where $d$,
$N_{U}$ and $N_{I}$ are the the embedding dimensionality, user set length, and
item set length respectively. Likewise,
$\boldsymbol{e}^{L}_{l}\in\mathbb{R}^{d}$ is the embedding of item $l$, to
specifically represent the anchor (last interacted) items,
$\boldsymbol{e}^{IL}_{i}\in\mathbb{R}^{d}$ is the embedding of item $i$ that
is specifically for the item transition modeling. The corresponding embedding
tables are $\boldsymbol{E}^{L}\in\mathbb{R}^{N_{I}\times d}$ and
$\boldsymbol{E}^{IL}\in\mathbb{R}^{N_{I}\times d}$. Note that although all the
$\boldsymbol{E}^{IU}$, $\boldsymbol{E}^{L}$ and $\boldsymbol{E}^{IL}$ are for
item embedding lookup, they are individually initialized and optimized for
different purposes.

After the factorization operation, the overall prediction score is divided
into two parts: 1) the interaction probability score between the given user
and the target item, corresponding to the user’s personalized long-term static
preference, and 2) the transition probability score between the previously
interacted item and the target item, corresponding to the user’s short-term
dynamic preference.

Even though FPMC is a concise and effective method, it has the following
inherent limitations. First, the user and item representative capability is
limited since the model learns the user/item representations solely based on
the dot-product score of specific interaction (transition) pair while
overlooking the global contextual information (i.e., all interaction or
transition pairs). For the u-i interaction, all the items (users) a user (an
item) has interacted with can be treated as the features of the it (Wang et
al., 2019). Such features can enhance the user (item) representations.
Likewise, for the i-i transition, all the items that an item connected (either
as predecessors or successors) can be treated as the contextual features,
which can be used to enhance the short-term preference modeling.

Second, FPMC only considers first-order relations, i.e., the direct u-i
interaction and first-order Markov Chain transition between item and item,
while overlooking the higher-order relations. In fact, higher-order relations
are prevalent and meaningful in modeling both u-i interaction and i-i
transition. As shown in Figure 2 (we will present the details of the graph
construction later), $u_{1}$ and $u_{2}$ have a second-order connection since
both of them have interacted with item $i_{1}$. Consequently, $u_{1}$ and
$u_{2}$ may share some common preferences and could serve as CF features for
each other. Similarly, the higher-order Markov Chain transitions also provide
rich contextual information to improve the modeling of the i-i transition.
Based on above considerations of learning better user and item
representations, we propose to leverage two types of global graph to exploit
more higher-order relations.

###  3.3. User-Item Interaction Graph

Graph Construction:  We demonstrate a toy example of sequential fashion
recommendation in Figure 2 (a), where there are two users ($u_{1}$ and
$u_{2}$) and each of them has a sequence of interacted fashion items. The
following (both u-i and i-i) graph construction illustrations are based on
this example. To build the u-i interaction graph, we follow the previous GNN-
based recommendation approaches (Wang et al., 2019; He et al., 2020) and build
a bipartite graph, as shown in Figure 2 (b). Two types of nodes, namely user
nodes and item nodes, as well as the interactions (edges) between the users
and items form the graph. The first-order connection is built upon the
interaction relationship between users and items. Higher-order connectivity
can be derived by combining two or more edges consecutively. For example,
$u_{1}$ and $u_{2}$ can be connected in a second-order relation through their
connection with item $i_{1}$. Such a second-order connection is meaningful as
it suggests common choice and preference. Similarly, items $i_{1}$ and $i_{4}$
are also connected in second-order as they are both interacted with $u_{2}$,
which means that the two items may be related in some dimensions, such as with
similar style.

Graph Convolution:  To enhance the user and item embeddings, we perform
information propagation over the u-i interaction graph. We adopt the
implementation of LightGCN (He et al., 2020), which drops the feature
transformation, non-linear activation and the self-connection while just keeps
the simple weighted sum aggregator. The $k$-th order information propagation
is denoted as:

(2) $\left\\{\begin{aligned}
\boldsymbol{e}_{u}^{(k)}=\sum_{i\in\mathcal{N}_{u}}{\frac{1}{\sqrt{|\mathcal{N}_{u}|}\sqrt{|\mathcal{N}_{i}|}}\boldsymbol{e}^{(k-1)}_{i}},\\\
\boldsymbol{e}_{i}^{(k)}=\sum_{u\in\mathcal{N}_{i}}{\frac{1}{\sqrt{|\mathcal{N}_{i}|}\sqrt{|\mathcal{N}_{u}|}}\boldsymbol{e}^{(k-1)}_{u}},\end{aligned}\right.$

where $\mathcal{N}_{u}$ and $\mathcal{N}_{i}$ denote the item set connected
with user $u$ and the user set connected with item $i$. Note that the
$\boldsymbol{e}_{i}$ here is a simplification of $\boldsymbol{e}_{i}^{IU}$.
The symmetric normalization term
$\frac{1}{\sqrt{|\mathcal{N}_{u}|}\sqrt{|\mathcal{N}_{i}|}}$ follows the
design of standard GCN (Kipf and Welling, 2016), which prevents the
embeddings’ scale accumulation after the information propagation (He et al.,
2020).

Layer Combination:  We aggregate the information propagated from different
order’s neighbors by a simple sum operation and obtain the final user and item
representations as follows:

(3) $\boldsymbol{e}^{U*}_{u}=\sum^{K}_{k=0}{\boldsymbol{e}^{(k)}_{u}};\ \ \ \
\boldsymbol{e}^{IU*}_{i}=\sum^{K}_{k=0}{\boldsymbol{e}^{(k)}_{i}}.$

$\boldsymbol{e}^{(k)}_{u}$ and $\boldsymbol{e}^{(k)}_{i}$ are the propagated
information from the $k$-th layer of graph convolution for user and item
respectively, and $K$ is the number of graph convolution layers (highest
connection orders).

###  3.4. Item-Item Transition Graph

Graph Construction:  To build the i-i transition graph, several designs have
been proposed before (Xu et al., 2019; Wu et al., 2019a, 2020). For example,
Wu et al. build a session-level graph for each session to model the higher-
order transitions, i.e., SR-GNN (Wu et al., 2019a). However, such session
graphs cannot model the cross-session transitions and overlook the global
contextual information. In this paper, we propose a new design of i-i
transition graph. Similar with the u-i interaction graph, we also formulate
the i-i transition graph as a bipartite graph, as shown in Figure 2 (c). For
each item, we have two types of nodes $l$ and $i$, corresponding to different
situations of items for being the anchor or the target respectively. The
connections (edges) are the first-order transitions between two adjacent items
in the interaction sequence. We perform information propagation from anchor
nodes to target nodes, resulting in the enhanced anchor representations by
incorporating all of its global successors. Similarly, we also perform
information propagation from target nodes to anchor nodes, resulting in the
enhanced target representations by incorporating all of its global
predecessors.

Figure 2 (c) illustrates the constructed i-i transition graph for the toy
example and is associated with the first-order and second-order adjacent
matrices. Higher-order connectivity can be derived by combining multiple
consecutive connections. For example, $i_{1}$ and $i_{3}$ are connected in
second-order by the middle node $i_{2}$ since $[i_{1},i_{2},i_{3}]$ is a
sequence of $u_{i}$. Moreover, $i_{4}$ and $i_{2}$ also have a second-order
connection by the middle node $i_{1}$ since $i_{4}$ transits to $i_{1}$ in the
interaction sequence of $u_{2}$ and $i_{1}$ transits to $i_{2}$ in the
sequence of $u_{1}$. This example indicates that our global graph can model
cross-session i-i transitions. For simplicity, we just demonstrate the partial
transitions from anchor to target, and the transitions from target to anchor
are similar. Note that our design not only models the transition directions
but also has better representative capability since we further specify the
item representation with respect to its different situations.

Graph Convolution:  Several graph kernels for i-i transitions are utilized by
previous methods, such as GGNN in SR-GNN (Wu et al., 2019a). However, existing
widely applied kernels, e.g., GGNN (Wu et al., 2019a) or GAT (Qiu et al.,
2019), introduce extra computational costs, which makes it harder to
effectively train the models. Moreover, inspired by the LightGCN (He et al.,
2020), removing the redundant modules of GCN may boost the recommendation
performance. Therefore, in this paper, we adopt the same graph convolution
kernel of LightGCN for information propagation over the i-i transition graph.
The $k$-th order information propagation is conducted by:

(4) $\left\\{\begin{aligned}
\boldsymbol{e}_{l}^{(k)}=\sum_{i\in\mathcal{N}_{l}}{\frac{1}{\sqrt{|\mathcal{N}_{l}|}\sqrt{|\mathcal{N}_{i}|}}\boldsymbol{e}^{(k-1)}_{i}},\\\
\boldsymbol{e}_{i}^{(k)}=\sum_{l\in\mathcal{N}_{i}}{\frac{1}{\sqrt{|\mathcal{N}_{i}|}\sqrt{|\mathcal{N}_{l}|}}\boldsymbol{e}^{(k-1)}_{l}},\end{aligned}\right.$

where $\mathcal{N}_{l}$ and $\mathcal{N}_{i}$ denote the item set that transit
from item $l$ and the item set that transit to item $i$ (the $\mathcal{N}_{i}$
here is different from that in Equation 2). Note that the $\boldsymbol{e}_{l}$
and $\boldsymbol{e}_{i}$ here are simplifications of $\boldsymbol{e}_{l}^{L}$
and $\boldsymbol{e}_{i}^{IL}$ respectively. The symmetric normalization term
$\frac{1}{\sqrt{|\mathcal{N}_{l}|}\sqrt{|\mathcal{N}_{i}|}}$ follows the
design of standard GCN (Kipf and Welling, 2016).

Layer Combination:  Similar to the u-i graph, to obtain the final anchor item
and target item representations for item-item transition, we aggregate the
propagated information from neighbors in different orders by a simple sum
operations:

(5) $\boldsymbol{e}^{L*}_{l}=\sum^{K}_{k=0}{\boldsymbol{e}^{(k)}_{l}};\ \ \ \
\ \boldsymbol{e}^{IL*}_{i}=\sum^{K}_{k=0}{\boldsymbol{e}^{(k)}_{i}},$

where $\boldsymbol{e}^{(k)}_{l}$ and $\boldsymbol{e}^{(k)}_{i}$ are the
propagated information from the $k$-th layer of graph convolution for the
anchor item and the target item respectively, and $K$ is the number of graph
convolution layers.

###  3.5. Prediction and Optimization

After the information propagation over two graphs, we therefore obtain the
updated user and item representations. The prediction of the score for the
target item $i$ to be the next pick by user $u$ after item $l$ can be computed
as:

(6)
$y^{*}_{u,l,i}=\boldsymbol{e}^{U*}_{u}\cdot\boldsymbol{e}^{IU*}_{i}+\boldsymbol{e}^{L*}_{l}\cdot\boldsymbol{e}^{IL*}_{i}.$

We apply the pairwise BPR loss (Rendle et al., 2012) to train the model,
treating all observed triplets as positive samples and unobserved triplets as
negatives. For each positive sample $(u,l,i)$, we randomly sample one negative
triplet $(u,l,j)$ with same user $u$ and anchor item $l$. The BPR loss is
specifically calculated by:

(7)
$Loss=\sum_{(u,l,i,j)\in\mathcal{O}}{-\text{ln}\sigma(y^{*}_{u,l,i}-y^{*}_{u,l,j})}+\lambda\|\Theta\rVert,$

where
$\mathcal{O}={(u,l,i,j)|u\in\mathcal{U},l=s^{u}_{t-1},i=\textbf{s}^{u}_{t},t\in[0,|\textbf{s}^{u}|]},j\notin\textbf{s}^{u}$.
$\sigma(\cdot)$ is the sigmoid function; $\Theta$ denotes all trainable
parameters in the model, which include user and item embeddings. $\lambda$ is
the hyper-parameter controlling the regularization strength.

##  4\. Experiments

Table 2. The properties of the chosen methods in terms of (a) P: personalized, (b) S: sequence-aware, (c) $\text{IP}_{ui}$: considering information propagation between user and items, and (d) $\text{IP}_{ii}$: information propagation between items. Type |  Model |  P |  S |  $\text{IP}_{\text{ui}}$ |  $\text{IP}_{\text{ii}}$
---|---|---|---|---|---
MF-based |  MF |  ✓ |  |  |
FMC |  |  ✓ |  |
FPMC |  ✓ |  ✓ |  |
Non-sequential with GNN |  NGCF |  ✓ |  |  ✓ |
LightGCN |  ✓ |  |  ✓ |
Session-based with DNN |  GRU4REC |  ✓ |  ✓ |  |
Caser |  ✓ |  ✓ |  |
SR-GNN |  |  ✓ |  |  ✓
Ours |  DGSR |  ✓ |  ✓ |  ✓ |  ✓

In this section, we conduct experiments on two real-world fashion e-commerce
datasets to evaluate the effectiveness of the proposed method in sequential
fashion recommendation. We particularly focus on the following three research
questions:

  * •

RQ1:  Does the proposed DGSR method outperform state-of-the-art sequential and
non-sequential fashion recommendation methods?

  * •

RQ2:  Does each technical component in the model work, and how does the hyper-
parameters and specific settings affect the performance of the model?

  * •

RQ3:  How does the proposed method perform on data with different sparsity,
and how does the incorporated graphs affect the recommendation results?

Table 3. Overall recommendation performance | iFashion-SR-7 | iFashion-SR-10 | Amazon-Fashion-7 | Amazon-Fashion-10
---|---|---|---|---
Model | Recall | MRR | NDCG | Recall | MRR | NDCG | Recall | MRR | NDCG | Recall | MRR | NDCG
MF | 0.5929 | 0.4421 | 0.4778 | 0.5938 | 0.4434 | 0.4791 | 0.3382 | 0.2044 | 0.2357 | 0.2606 | 0.1444 | 0.1716
FMC | 0.4691 | 0.3316 | 0.3641 | 0.4735 | 0.3338 | 0.3673 | 0.2362 | 0.1376 | 0.1606 | 0.1534 | 0.0764 | 0.0942
FPMC | 0.5894 | 0.4421 | 0.4771 | 0.6006 | 0.4372 | 0.4762 | 0.3436 | 0.2078 | 0.2397 | 0.2643 | 0.1513 | 0.1777
GRU4REC | 0.5149 | 0.3526 | 0.3911 | 0.4942 | 0.3402 | 0.3768 | 0.3663 | 0.2301 | 0.2622 | 0.2599 | 0.1317 | 0.1615
Caser | 0.4410 | 0.3179 | 0.3471 | 0.4275 | 0.3012 | 0.3311 | 0.4000 | 0.2338 | 0.2730 | 0.2772 | 0.1633 | 0.1898
LightGCN | 0.5928 | 0.4414 | 0.4775 | 0.5767 | 0.4240 | 0.4580 | 0.3803 | 0.2373 | 0.2769 | 0.3097 | 0.1784 | 0.2092
NGCF | 0.5897 | 0.4186 | 0.4593 | 0.5923 | 0.4182 | 0.4595 | 0.4081 | 0.2634 | 0.2974 | 0.3334 | 0.1982 | 0.2299
SR-GNN | 0.5485 | 0.3862 | 0.4248 | 0.5494 | 0.3890 | 0.4271 | 0.3900 | 0.2566 | 0.2884 | 0.3125 | 0.1956 | 0.2224
DGSR | 0.6478 | 0.5027 | 0.5373 | 0.6522 | 0.5045 | 0.5398 | 0.3851 | 0.2390 | 0.2733 | 0.3125 | 0.1822 | 0.2127

###  4.1. Dataset

We evaluate our proposed model based on two real-world e-commerce datasets:
iFashion (Chen et al., 2019) and Amazon review datasets (McAuley et al.,
2015).

iFashion is a large-scale fashion dataset generated based on the e-commerce
platform Taobao111www.taobao.com. The original dataset contains over three
million users and four million items, where each user is interacted with tens
of items in chronological order. To make the datasets applicable to all
sequential recommendation methods, we crop two sub-datasets which consist of
different minimal fixed-length user interaction sequences of 7 and 10
respectively. For each sub-dataset, we randomly sample 50,000 sequences from
the interaction sequence list, whose length must be longer than the predefined
minimal sequence length. Since one user may have multiple interaction
sequences in the dataset, the user number is less than the sequence number.
The generated dataset is named as iFashion-SR-7 and iFashion-SR-10
respectively, where iFashion-SR denotes iFashion for Sequential
Recommendation.

Amazon review dataset is a large-scale review dataset which consists of the
purchase records and reviews of users on Amazon222www.amazon.com. We use the
Clothing-Shoes-Jewelry subset data (2014 version) to generate our dataset for
sequential recommendation. Since the long-tail situation is severe in this
dataset, we filter out the items with less than five interactions at the very
first step. Similar with the preprocessing for iFashion dataset, we generate
two sub-datasets for users with interacted sequence length longer than the
minimal predefined length of 7 and 10 respectively.

For each data setting, we split the interaction sequences into three parts:
(1) the last interaction in each sequence is used for testing; (2) the second
to last interaction in each sequence is used for validation; and (3) all
remaining interactions are used for training. The statistics of the datasets
are shown in Table 1. For methods modeling one-step transitions (such as
FPMC), the previous one item of each interaction is employed to build a pair.
For methods need to model the whole historical sequence before the target item
(such as SR-GNN), we generate short sub-sequences with the sliding window
strategy (Tang and Wang, 2018) from the original sequences.

###  4.2. Experimental settings

Baselines: We compare the proposed methods with several competitive and
relevant baselines:

  * •

MF (Rendle et al., 2012) factorizes the u-i interaction matrix and is
optimized with the BPR loss.

  * •

FMC (Rendle et al., 2010) focuses on modeling the sequential dynamics by
factorizing the i-i transition matrix.

  * •

FPMC (Rendle et al., 2010) models both the personalized u-i interaction and
the ‘global’ i-i transition by MF and FMC respectively.

  * •

NGCF (Wang et al., 2019) leverages a bipartite graph to model the u-i
interaction, which is a typical GCN-based recommendation model.

  * •

LightGCN (He et al., 2020) is the light version of NGCF and utilizes a light
graph convolution kernel.

  * •

GRU4REC (Hidasi et al., 2015) is an RNN-based session-based recommendation
method which models the interaction sequences with GRUs.

  * •

Caser (Tang and Wang, 2018) is a session-based recommendation method which
treats the embedding of fixed length of historical interacted items as an
“image” and models the interaction sequences with CNNs.

  * •

SR-GNN (Wu et al., 2019a) is a GNN-based method which leverages the session-
level i-i transition graph to enhance the session representation.

Table 2 lists the properties of these methods in terms of whether being
personalized or sequence-aware and whether considering the user-item or the
item-item information propagation. It offers an intuitive illustration of the
difference of those methods.

Implementation details:  We perform grid search on the embedding size of users
and items, which is within [5, 10, 20, 50] . In terms of the number of
propagation layers of the u-i graph and i-i graph, we perform grid search
within [1, 2, 3] for each type of graph respectively. The learning rate during
training is set to 0.01 and the batch size is set to 5000 for all methods. The
weight decay is set to $10^{-5}$ and the maximum number of training epoches is
250. We implement all the baseline methods on these two datasets, and for fair
comparison, we also do grid search for the user and item embeddings within [5,
10, 20, 50] to achieve the best performance. The hidden size of GRU4REC is
chosen from [10, 20, 50, 100]; the number of vertical filters and horizontal
filters of Caser are set to 4 and 8 respectively.

Evaluation metrics: We evaluate the performance of all compared recommendation
methods with the mainstream top-$n$ ranking evaluation. Considering the
computational cost during the evaluation, we generate a negative set with 100
negative samples for each testing samples (positive) and rank the positive
sample along with negative samples based on the predicted scores. All negative
items are not interacted with the corresponding user and the anchor item. We
apply three commonly used metrics for the quantitative evaluation: Recall@$n$,
MRR@$n$, and NDCG@$n$. We set $n=10$.

Table 4. Comparison between models with/without two types of graph. Embedding size is set to 50. | iFashion-SR-7 | iFashion-SR-10 | Amazon-Fashion-7 | Amazon-Fashion-10
---|---|---|---|---
Model | Recall | MRR | NDCG | Recall | MRR | NDCG | Recall | MRR | NDCG | Recall | MRR | NDCG
DGSR-UI/II | 0.5894 | 0.4421 | 0.4771 | 0.6006 | 0.4372 | 0.4762 | 0.3436 | 0.2078 | 0.2397 | 0.2643 | 0.1513 | 0.1777
DGSR-II | 0.6146 | 0.4734 | 0.5070 | 0.6165 | 0.4757 | 0.5092 | 0.2984 | 0.1652 | 0.1963 | 0.2350 | 0.1218 | 0.1481
DGSR-UI | 0.6339 | 0.4583 | 0.5207 | 0.6380 | 0.4891 | 0.5247 | 0.3525 | 0.2169 | 0.2487 | 0.2772 | 0.1551 | 0.1837
DGSR | 0.6478 | 0.5027 | 0.5373 | 0.6522 | 0.5045 | 0.5398 | 0.3851 | 0.2390 | 0.2733 | 0.3125 | 0.1822 | 0.2127

###  4.3. Overall performance (RQ1)

Table 3 shows the overall performance of all compared methods on the iFashion-
SR and Amazon-Fashion datasets. We have the following observation based on the
results.

Performance on iFashion-SR:  (1) Our method outperforms all the compared
methods in both settings in terms of all three metrics by a large margin.

(2) Compared to the basic FPMC, which also models both user-item interaction
and item-item transition, our method achieves around 10% improvement in terms
of NDCG for both settings due to the incorporation of two types of global
graph.

(3) LightGCN shows the best performance among all baselines on both settings,
while the simple MF and FPMC are competitive too according to the results.
Such results may imply that the collaborative signals (CF) in this dataset are
quite significant. It also shows that modeling u-i interaction is effective on
this dataset.

(4) Session-based methods, including GRU4REC, Caser and SR-GNN, do not show
superior performance as expected. The reasons are multi-fold. First, most of
them (except Caser) ignore user information in the model. Second, the training
samples are less for them as they require to input multiple historical
interactions. Third, they ignore the effect among the connected users and
items in higher orders.

Performance on Amazon-Fashion:  (1) DGSR shows competitive performance on both
settings and outperforms most CF-based methods, demonstrating the
effectiveness of it to some extent.

(2) Overall, session-based methods perform better than methods such as FMC,
which suggests that the i-i transition signals are harder to explore for this
dataset. Since session-based methods are better in exploring the dependency
among items by considering the item transition sequences rather than the pairs
in the model, they achieve more desired performance.

(3) As the i-i transition signals are less effective to model than the u-i
interaction, our DGSR, exploring more high-order i-i transitions, might affect
the exploring o u-i patterns instead, which degrades the overall performance
of DGSR.

Figure 3. Performance of models with various graph layers. Up: iFashion-SR-7;
Down: iFashion-SR-10. $k$ denotes the number of the layers for information
propagation. FPMC+UI+II is the DGSR method.

###  4.4. Ablation study (RQ2)

In this part, we conduct several ablation studies to discuss more detailed
technical components in DGSR. The ablation study focuses on three aspects: 1)
the effect of incorporating two types of graph; 2) the effect of the layer
numbers ($k$) in each graph; and 3) the effect of embedding size.

Effect of global graphs: We first investigate the effectiveness of the two
types of graph, namely, the u-i interaction graph and the i-i transition
graph. We conduct the comparison on the variant of DGSR in which one or both
of the graph are removed. The experimental results on four data settings are
listed in Table 4.

From the results we can observe that: First, either incorporating u-i graph or
i-i graph can improve the performance on iFashion-SR dataset. On Amazon-
Fashion, the u-i graph seems not helpful from the comparison between the
models with/without u-i graph (the first two rows), while the i-i graph brings
significant improvement (comparing first and third rows). As discussed in the
above section, modeling i-i transition is hard on Amazon-Fashion, which may
even degrade the performance when combining with the u-i interaction modeling
(comparing results of MF, FMC and FPMC in Table 3). When we further strengthen
the u-i modeling, it leads to more conflicts between u-i and i-i modeling.
However, when we apply both graphs, the performance of the method on all
settings boosts; this is obvious on Amazon-Fashion that the i-i transition
modeling significantly improve the overall recommendation performance.

Figure 4. Performance of DGSR with different embedding sizes. Left: iFashion-
SR-7; Right: iFashion-SR-10.

Number of propagation layers: We further investigate the effect of the number
of propagation layers when the two types of graph are applied in various
models. We study three basic models, MF which only explores u-i interaction,
FMC which only exolores i-i transition, and FPMC which explores both. We apply
u-i graph and i-i graph on three models and generate five improved models with
graph in total. We set different graph layers for each model from 0 (without
graph) to 3, resulting in 15 experimental settings for each dataset. The
NGCG@10 results of all compared models on the iFashion-SR dataset are shown in
Figure 3.

From the results we have the following observations. 1) The performance of all
three basic models are improved by leveraging various graphs. The best layer
number setting for different models are different. 2) For the FMC model, the
performance increases with the increase of graph layers. This demonstrates
that higher-order connectivity is important to improve the i-i transition
pattern modeling. 3) For MF+UI and FPMC+UI, the best performance is achieved
when one-layer information propagation is conducted, which shows that stacking
more graph layers may over-smooth the representation of users and items and
degrade the performance instead. 4) When leveraging both graphs, we can see
that the performance steadily improves with the increase in layer number,
which shows that the u-i graph and i-i graph organically corporate with each
other and contribute to the final interaction prediction modeling.

Figure 5. Performance comparison w.r.t interaction sparsity. The comparison is
based on the NDCG results on iFashion-SR-7. The distribution of the items in
terms of the interaction density is also shown by the bar chart in the
background.

Effect of embedding size:  In Figure 4, we illustrate the performance of the
proposed model with different embedding sizes. From the results we can see
that larger embedding size does bring increase in performance. However, the
rate of performance boost keeps decreasing when the embedding size gets
larger. In the meantime, using large embedding size inevitably results in
large computational cost, which reduces the efficiency of the model.
Therefore, we think the embedding size of 10 is quite an ideal setting when
considering both the effectiveness and efficiency.

###  4.5. Discussion on Sparsity and Higher-order Connectivity (RQ3)

In this section, we first discuss the sparsity problem by showing the
performance of DGSR and other three baselines on testing samples with
different levels of sparsity. From Figure 5, we can see that generally, all
methods perform better on dense samples and worse on sparse ones, which is
consistent with our hypothesis. The DGSR method outperforms the others in the
whole density range, but the superiority is more significant on sparse data
(items interacted lower than 10). Such a result demonstrates that our proposed
DGSR method can effectively tackle the data sparsity problem as claimed.

We further analyze the higher-order connectivity in the data and the specific
effect of it on the prediction and recommendation. We illustrate two cases in
Figure 6 and show the target user, the previously interacted item, the target
item, as well as the multiple connectivities related to the three subjects in
each case. From the examples, we can see that our model is able to rank the
target item higher in both cases with the two graphs. By analyzing more
details, we find that the target items in both cases are connected with other
user and items by interaction or transition relationships. In the first case,
the target item b5b2ab is connected to another user 0d0f6a with the u-i graph,
who picks item 232012. As item 232012 is also picked by the target user
f6e920, the target user and target item are connected in third-order. With the
message passing and aggregation operations, the representation of the target
user and item will be closer, so that the final interaction probability
predicted by the model will be higher. The higher-order connectivity in i-i
graph works in a similar way, which can help improve the prediction of the
transition probability from the anchor item to the target item. In general, we
can see that with two graphs, the target item in two cases can be ranked
higher.

Figure 6. Examples of test samples and the connectivity in two graphs.

##  5\. Conclusion

We worked on the problem of sequential fashion recommendation in this paper,
aiming to model both the interaction between user-item and the transition
between items. To tackle the specific challenges of data sparsity and make the
model simple to learn, we proposed a DGSR model. DGSR leverages two types of
graphs, namely the user-item interaction graph and the item-item transition
graph, to better model the CF signals and the item transitional patterns and
enhance the user and item embeddings. Extensive experiments on two datasets
demonstrated the effectiveness of the proposed method and all technical
contributions.

In future work, we shall improve this work in the following directions. First,
we plan to incorporate additional information besides the implicit feedback to
enrich the graph building. By considering more content information such as
attributes or visual features, the connectivity between the user and items or
item and items can be richer and thus further help to alleviate the
interaction sparsity issue. Second, more fashion domain knowledge can be
introduced in the model to further enhance the user and item representation
learning to achieve better recommendation performance.

## acknowledgement

This research is supported in part by the National Research Foundation,
Singapore under its International Research Centres in Singapore Funding
Initiative. Any opinions, findings and conclusions or recommendations
expressed in this material are those of the author(s) and do not reflect the
views of National Research Foundation, Singapore. It is also supported in part
by the Natural Science Foundation of China under Grant 61703283, in part by
the Guangdong Natural Science Foundation under Project 2021A1515011318, in
part by the Shenzhen Municipal Science and Technology Innovation Council under
the Grant JCYJ20190808113411274.

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