# Improving Implicit Feedback-Based Recommendation
through Multi-Behavior Alignment

Xin Xin  0000-0001-6116-9115 Shandong UniversityQingdaoChina<EMAIL_ADDRESS>,  Xiangyuan Liu  0009-0005-8513-0879 Shandong UniversityQingdaoChina
<EMAIL_ADDRESS>,  Hanbing Wang  0000-0002-5198-8085 Shandong
UniversityQingdaoChina<EMAIL_ADDRESS>,  Pengjie Ren
0000-0003-2964-6422 Shandong UniversityQingdaoChina<EMAIL_ADDRESS>,
Zhumin Chen  0000-0003-4592-4074 Shandong UniversityQingdaoChina
<EMAIL_ADDRESS>,  Jiahuan Lei  0000-0002-5170-8645 MeituanBeijingChina
<EMAIL_ADDRESS>,  Xinlei Shi  0000-0002-0733-5757 MeituanBeijingChina
<EMAIL_ADDRESS>,  Hengliang Luo  0000-0001-8597-8873
MeituanBeijingChina<EMAIL_ADDRESS>,  Joemon M. Jose
0000-0001-9228-1759 University of GlasgowLondonUK<EMAIL_ADDRESS>,
Maarten de Rijke  0000-0002-1086-0202 University of AmsterdamAmsterdamThe
Netherlands<EMAIL_ADDRESS>and  Zhaochun Ren† 0000-0002-9076-6565 Shandong
UniversityQingdaoChina<EMAIL_ADDRESS>
(2023)

###### Abstract.

Recommender systems that learn from implicit feedback often use large volumes
of a single type of implicit user feedback, such as clicks, to enhance the
prediction of sparse target behavior such as purchases. Using multiple types
of implicit user feedback for such target behavior prediction purposes is
still an open question. Existing studies that attempted to learn from multiple
types of user behavior often fail to:  (i) learn universal and accurate user
preferences from different behavioral data distributions, and  (ii) overcome
the noise and bias in observed implicit user feedback.

To address the above problems, we propose multi-behavior alignment (MBA), a
novel recommendation framework that learns from implicit feedback by using
multiple types of behavioral data. We conjecture that multiple types of
behavior from the same user (e.g., clicks and purchases) should reflect
similar preferences of that user. To this end, we regard the underlying
universal user preferences as a latent variable. The variable is inferred by
maximizing the likelihood of multiple observed behavioral data distributions
and, at the same time, minimizing the Kullback–Leibler divergence (KL-
divergence) between user models learned from auxiliary behavior (such as
clicks or views) and the target behavior separately. MBA infers universal user
preferences from multi-behavior data and performs data denoising to enable
effective knowledge transfer. We conduct experiments on three datasets,
including a dataset collected from an operational e-commerce platform.
Empirical results demonstrate the effectiveness of our proposed method in
utilizing multiple types of behavioral data to enhance the prediction of the
target behavior.

Implicit feedback recommendation, Multi-behavior recommendation,
Recommendation denoising, Transfer learning

††submissionid: 7389††journalyear: 2023††copyright: acmlicensed††conference:
Proceedings of the 46th International ACM SIGIR Conference on Research and
Development in Information Retrieval; July 23–27, 2023; Taipei,
Taiwan††booktitle: Proceedings of the 46th International ACM SIGIR Conference
on Research and Development in Information Retrieval (SIGIR ’23), July 23–27,
2023, Taipei, Taiwan††price: 15.00††doi: 10.1145/3539618.3591697††isbn:
978-1-4503-9408-6/23/07††ccs: Information systems Recommender systems††ccs:
Information systems Personalization

##  1\. Introduction

Recommender systems aim to infer user preferences from observed user-item
interactions and recommend items that match those preferences. Many
operational recommender systems are trained from implicit user feedback (Gu et
al., 2020; Huang et al., 2019). Recommender systems that learn from implicit
user feedback are typically trained on a single type of implicit user
behavior, such as clicks. However, in real-world scenarios, multiple types of
user behavior are logged when a user interacts with a recommender system. For
example, users may click, add to a cart, and purchase items on an e-commerce
platform (Tsagkias et al., 2020). Simply learning recommenders from a single
type of behavioral data such as clicks can lead to a misunderstanding of a
user’s real user preferences since the click data is noisy and can easily be
corrupted due to bias (Chen et al., 2020a), and thus lead to suboptimal target
behavior (e.g., purchases) predictions. Meanwhile, only considering purchase
data tends to lead to severe cold-start problems (Pan et al., 2019; Xie et
al., 2020; Zhu et al., 2021) and data sparsity problems (Pan et al., 2010; Ma
et al., 2022b).

Using multiple types of behavioral data. How can we use multiple types of
_auxiliary_ behavioral data (such as clicks) to enhance the prediction of
sparse _target_ user behavior (such as purchases) and thereby improve
recommendation performance? Some prior work (Gao et al., 2019; Chen et al.,
2020b) has used multi-task learning to train recommender systems on both
target behavior and multiple types of auxiliary behavior. Building on recent
advances in graph neural networks, Jin et al. (2020) encode target behavior
and multiple types of auxiliary behavior into a heterogeneous graph and
perform convolution operations on the constructed graph for recommendation. In
addition, recent research tries to integrate the micro-behavior of user-item
interactions into representation learning in the sequential and session-based
recommendation (Zhou et al., 2018; Meng et al., 2020; Yuan et al., 2022).
These publications focus on mining user preferences from user-item
interactions, which is different from our task of predicting target behavior
from multiple types of user behavior.

Figure 1. Distributions of items interacted with by two users in the Beibei
and Taobao datasets (described in §4.2). Item representations are obtained by
a matrix factorization model trained on the purchase behavior data. $u_{i}c$
($u_{i}p$) represents the distribution of items clicked (purchased) by user
$u_{i}$.

Limitations of current approaches. Prior work on using multiple types of
behavioral data to improve the prediction of the target behavior in a
recommendation setting has two main limitations.

The first limitation concerns the gap between data distributions of different
types of behavior. This gap impacts the learning of universal and effective
user preferences. For example, users may have clicked on but not purchased
items, resulting in different positive and negative instance distributions
across auxiliary and target behaviors. Existing work typically learns separate
user preferences for different types of behavior and then combines those
preferences to obtain an aggregate user representation. We argue that:  (i)
user preferences learned separately based on different types of behavior may
not consistently lead to the true user preferences, and  (ii) multiple types
of user behavior should reflect similar user preferences; in other words,
there should be an underlying universal set of user preferences under
different types of behavior of the same user.

The second limitation concerns the presence of noise and bias in auxiliary
behavioral data, which impacts knowledge extraction and transfer. A basic
assumption of recommendations based on implicit feedback is that observed
interactions between users and items reflect positive user preferences, while
unobserved interactions are considered negative training instances. However,
this assumption seldom holds in reality. A click may be triggered by
popularity bias (Chen et al., 2020a), which does not reflect a positive
preference. And an unobserved interaction may be attributed to a lack of
exposure (Chen et al., 2021b). Hence, simply incorporating noisy or biased
behavioral data may lead to sub-optimal recommendation performance.

Motivation. Our assumption is that multiple types of behavior from the same
user (e.g., clicks and purchases) should reflect similar preferences of that
user. To illustrate this assumption, consider Figure 1, which shows
distributions of items that two users ($u_{1}$ and $u_{2}$) interacted with
(clicks $c$ and purchases $p$), in the Beibei and Taobao datasets (described
in Section 4.2 below). For both users, the items they clicked or purchased are
relatively close. These observations motivate our hypothesis that multiple
types of user behavior reflect similar user preferences, which is vital to
improve the recommendation performance further.

Proposed method. To address the problem of learning from multiple types of
auxiliary behavioral data and improve the prediction of the target behavior
(and hence recommendation performance), we propose a training framework called
multi-behavior alignment (MBA). MBA aligns user preferences learned from
different types of behavior. The key assumption behind MBA is that multiple
types of behavior from the same user reflect similar underlying user
preferences.

To address the data distribution limitation mentioned above, we utilize KL-
divergence to measure the discrepancy between user models learned from
multiple types of auxiliary behavior and target behavior, and then conduct
knowledge transfer by minimizing this discrepancy to improve the
recommendation performance.

For the second limitation mentioned above (concerning noise and bias in
behavioral data), MBA regards the underlying universal user preferences as a
latent variable. The variable is then inferred by maximizing the likelihood of
multiple types of observed behavioral data while minimizing the discrepancy
between models trained on different types of behavioral data. In this manner,
MBA denoises multiple types of behavioral data and enables more effective
knowledge transfer across multiple types of user behavior.

To demonstrate the effectiveness of the proposed method, we conduct extensive
experiments on two open benchmark datasets and one dataset collected from an
operational e-commerce platform. Experimental results show that the proposed
MBA framework outperforms related state-of-the-art baselines.

Main contributions. Our main contributions are as follows:

  * •

We argue that multiple types of auxiliary and target behavior should reflect
similar user preferences, and we propose to infer the true user preferences
from multiple types of behavioral data.

  * •

We propose a learning framework MBA to jointly perform data denoising and
knowledge transfer across multiple types of behavioral data to enhance target
behavior prediction and hence improve the recommendation performance.

  * •

We conduct experiments on three datasets to demonstrate the effectiveness of
the MBA method. One of these datasets is collected from an operational
e-commerce platform, and includes clicks and purchase behavior data.
Experimental results show state-of-the-art recommendation performance of the
proposed MBA method.

##  2\. Related work

We review prior work on multi-behavior recommendation and on denoising methods
for recommendation from implicit feedback.

###  2.1. Multi-behavior recommendation

Unlike conventional implicit feedback recommendation models (Koren et al.,
2009; He et al., 2020), which train a recommender on a single type of user
behavior (e.g., clicks), multi-behavior recommendation models use multiple
types of auxiliary behavior data to enhance the recommendation performance on
target behavior (Gao et al., 2019; Wei et al., 2022; Xia et al., 2021; Cheng
et al., 2023; Wang et al., 2020; Jin et al., 2020; Chen et al., 2021a). Recent
studies use multi-task learning to perform joint optimization on learning
auxiliary behavior and target behavior. For example, Gao et al. (2019) propose
a multi-task learning framework to learn user preferences from multi-behavior
data based on a pre-defined relationship between different behavior. Since
different behavioral interactions between users and items can form a
heterogeneous graph, recent studies also focus on using graph neural network
(GNN) to mine the correlations among different types of behavior. For example,
Wang et al. (2020) uses the auxiliary behavior data to build global item-to-
item relations and further improve the recommendation performance of target
behavior. Jin et al. (2020) propose a graph convolutional network (GCN) based
model on capturing the diverse influence of different types of behavior and
the various semantics of different types of behavior. Xia et al. (2021)
incorporate multi-behavior signals through graph-based meta-learning. Chen et
al. (2021a) regard the multi-behavior recommendation task as a multi-
relationship prediction task and train the recommender with an efficient non-
sampling method. Additionally, some studies apply contrastive learning or a
variational autoencoder (VAE) to improve the multi-behavior recommender. Xuan
et al. (2023) propose a knowledge graph enhanced contrastive learning
framework to capture multi-behavioral dependencies better and solve the data
sparsity problem of the target behavior, and Ma et al. (2022a) propose a VAE-
based model to conduct multi-behavior recommendation.

Another related research field is based on micro-behaviors (Zhou et al., 2018;
Meng et al., 2020; Yuan et al., 2022), which utilize the micro-operation
sequence in the process of user-item interactions to capture user preferences
and predict the next item. For example, Yuan et al. (2022) focus on
“sequential patterns” and “dyadic relational patterns” in micro-behaviors, and
then use an extended self-attention network to mine the relationship between
micro-behavior and user preferences. This work focuses on mining user
preferences from the micro-operation sequence.

However, existing studies still neglect the different data distributions
across multiple types of user behavior, and thus fail to learn accurate and
universal user preferences. Besides, prior work does not consider the noisy
signals of user implicit feedback data, resulting in ineffective knowledge
extraction and transfers.

###  2.2. Recommendation denoising

Existing recommender systems are usually trained with implicit feedback since
it is much easier to collect than explicit ratings (Rendle et al., 2009).
Recently, some research (Jagerman et al., 2019; Wang et al., 2021a, b) has
pointed out that implicit feedback can easily be corrupted by different
factors, such as various kinds of bias (Chen et al., 2020a) or users’ mistaken
clicks. Therefore, there have been efforts aimed at alleviating the noisy
problem of implicit recommendation. These efforts include sample selection
methods (Ding et al., 2018, 2019a, 2019b; Gantner et al., 2012; Yu and Qin,
2020; Wang et al., 2021b), re-weighting methods (Wang et al., 2021a; Shen and
Sanghavi, 2019; Wang et al., 2021a, 2022; Chen et al., 2022), methods using
additional information (Kim et al., 2014; Lu et al., 2019; Zhao et al., 2016),
and methods designing specific denoising architectures (Chen et al., 2021c; Wu
et al., 2021; Xie et al., 2021; Gao et al., 2022).

Sample selection methods aim to design more effective samplers for model
training. For example, Gantner et al. (2012) consider popular but un-
interacted items as items that are highly likely to be negative ones, while
Ding et al. (2018) consider clicked but not purchased items as likely to be
negative samples. Re-weighting methods typically identify noisy samples as
instances with higher loss values and then assign lower weights to them. For
example, Wang et al. (2021a) discard the large-loss samples with a dynamic
threshold in each iteration. Wang et al. (2022) utilize the differences
between model predictions as the denoising signals. Additional information
such as dwell time (Kim et al., 2014), gaze pattern (Zhao et al., 2016) and
auxiliary item features (Lu et al., 2019) can also be used to denoise implicit
feedback. Methods designing specific denoising architectures improve the
robustness of recommender systems by designing special modules. Wu et al.
(2021) use self-supervised learning on user-item interaction graphs to improve
the robustness of graph-based recommendation models. Gao et al. (2022) utilize
the self-labeled memorized data as denoising signals to improve the robustness
of recommendation models.

Unlike the work listed above, which does not consider multiple types of user
behavior, in this work, we focus on extracting underlying user preferences
from (potentially) corrupted multi-behavior data and then conducting knowledge
transfer to improve the recommendation performance.

##  3\. Method

In this section, we detail our proposed MBA framework for multi-behavior
recommendation. We first introduce notations and the problem formulation in
Section 3.1. After that, we describe how to perform multi-behavior alignment
on noisy implicit feedback in Section 3.2. Finally, training details are given
in Section 3.3.

###  3.1. Notation and problem formulation

We write $u\in\mathcal{U}$ and $i\in\mathcal{I}$ for a user and an item, where
$\mathcal{U}$ and $\mathcal{I}$ indicate the user set and the item set,
respectively. Without loss of generality, we regard click behavior as the
auxiliary behavior and purchase behavior as the target behavior. We write
$\mathbf{R}_{f}\in\mathbb{R}^{|\mathcal{U}|\times|\mathcal{I}|}$ for the
observed purchase behavior data. Specifically, each item
$r^{f}_{u,i}\in\mathbf{R}_{f}$ is set to 1 if there is a purchase behavior
between user $u$ and item $i$; otherwise $r^{f}_{u,i}$ is set as 0. Similarly,
we denote $\mathbf{R}_{g}\in\mathbb{R}^{|\mathcal{U}|\times|\mathcal{I}|}$ as
the observed click behavior data, where each $r^{g}_{u,i}\in\mathbf{R}_{g}$ is
set as $1$ if there is a click behavior between user $u$ and item $i$;
otherwise $r^{g}_{u,i}=0$. We use $P(\mathbf{R}_{f})$ and $P(\mathbf{R}_{g})$
to denote the user preference distribution learned from $\mathbf{R}_{f}$ and
$\mathbf{R}_{g}$, respectively.

We assume that there is an underlying latent true user preference matrix
$\mathbf{R}_{t}$ with $r^{t}_{u,i}\in\mathbf{R}_{t}$ as the true preference of
user $u$ over item $i$. The probabilistic distribution of $\mathbf{R}_{t}$ is
denoted as $P(\mathbf{R}_{t})$. Both the data observation of $\mathbf{R}_{f}$
and $\mathbf{R}_{g}$ is motivated by the latent universal true user preference
distribution $P(\mathbf{R}_{t})$ plus different kinds of noises or biases.
Formally, we assume that $P(\mathbf{R}_{t})$ follows a Bernoulli distribution
and can be approximated by a target recommender model $t_{\theta}$ with
$\theta$ as the parameters:

(1) $r^{t}_{u,i}\sim\operatorname{Bernoulli}(t_{\theta}(u,i)).$

Since the true user preferences $r^{t}_{u,i}$ are intractable, we need to
introduce the learning signals from the observed $r^{f}_{u,i}$ and
$r^{g}_{u,i}$ to infer $r^{t}_{u,i}$. As a result, we introduce the following
models to depict the correlations between the observed user implicit feedback
(i.e., $r^{f}_{u,i}$ and $r^{g}_{u,i}$ ) and the latent true user preferences
$r^{t}_{u,i}$:

(2) $\begin{split}&r^{f}_{u,i}\mid
r^{t}_{u,i}=0\sim\operatorname{Bernoulli}(h^{f}_{\phi}(u,i))\\\
&r^{f}_{u,i}\mid
r^{t}_{u,i}=1\sim\operatorname{Bernoulli}(h^{f}_{\varphi}(u,i))\\\
&r^{g}_{u,i}\mid
r^{t}_{u,i}=0\sim\operatorname{Bernoulli}(h^{g}_{\phi^{\prime}}(u,i))\\\
&r^{g}_{u,i}\mid
r^{t}_{u,i}=1\sim\operatorname{Bernoulli}(h^{g}_{\varphi^{\prime}}(u,i)),\end{split}$

where $h^{f}_{\phi}(u,i)$ and $h^{f}_{\varphi}(u,i)$ are parameterized by
$\phi$ and $\varphi$ in the observed purchase behavior data, respectively,
while $h^{g}_{\phi^{\prime}}(u,i)$ and $h^{g}_{\varphi^{\prime}}(u,i)$ are
parameterized by $\phi^{\prime}$ and $\varphi^{\prime}$ in the observed click
behavior data respectively.

The target of our task is formulated as follows: given the observed multi-
behavior user implicit feedback, i.e., $\mathbf{R}_{f}$ and $\mathbf{R}_{g}$,
we aim to train the latent true user preference model $t_{\theta}$, and then
use $t_{\theta}$ to improve the prediction performance on target behavior.
More precisely, during model inference, we introduce both $P(\mathbf{R_{f}})$
and $P(\mathbf{R_{t}})$ to perform the target behavior recommendation and use
a hyperparameter $\beta$ to balance the $P(\mathbf{R_{t}})$ and
$P(\mathbf{R_{f}})$, which is formulated as:

(3) $\operatorname{score}=\beta P(\mathbf{R}_{t})+(1-\beta)P(\mathbf{R}_{f}).$

We select items with the highest score as the target behavior recommendation
results.

###  3.2. Multi-behavior alignment on noisy data

The key motivation for MBA is that multiple types of user behavior should
reflect similar user preferences. Hence, Eq. 4 is expected to be achieved with
the convergence of the training models:

(4) $P(\mathbf{R}_{f})\approx P(\mathbf{R}_{g})\approx P(\mathbf{R}_{t}).$

Therefore, $P(\mathbf{R}_{f})$ and $P(\mathbf{R}_{t})$ should have a
relatively small KL-divergence, which is formulated as follows:

(5) $\displaystyle
KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t})]=E_{P(\mathbf{R}_{f})}[\log
P(\mathbf{R}_{f})-\log P(\mathbf{R}_{t})].$

Similarly, we also have the KL-divergence between $P(\mathbf{R}_{g})$ and
$P(\mathbf{R}_{t})$:

(6) $\displaystyle
KL[P(\mathbf{R}_{g})\|P(\mathbf{R}_{t})]=E_{P(\mathbf{R}_{g})}[\log
P(\mathbf{R}_{g})-\log P(\mathbf{R}_{t})].$

However, naively minimizing the above KL-divergence is not feasible since it
overlooks the data distribution gaps and correlations between multiple types
of behavior. To address this issue, we use Bayes’ theorem to rewrite
$P(\mathbf{R}_{t})$ as follows:

(7) $\displaystyle
P(\mathbf{R}_{t})=\frac{P(\mathbf{R}_{f})P(\mathbf{R}_{t}\mid\mathbf{R}_{f})}{P(\mathbf{R}_{f}\mid\mathbf{R}_{t})}=\frac{P(\mathbf{R}_{g})P(\mathbf{R}_{t}\mid\mathbf{R}_{g})}{P(\mathbf{R}_{g}\mid\mathbf{R}_{t})}.$

By substituting the right part of Eq. 7 into Eq. 5 and rearranging erms, we
obtain the following equation:

(8) $\displaystyle E_{P(\mathbf{R}_{f})}[\log P$
$\displaystyle(\mathbf{R}_{g}\mid\mathbf{R}_{t})]-KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t})]$
$\displaystyle=\log
P(\mathbf{R}_{g})-KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t}\mid\mathbf{R}_{g})].$

Since $KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t}\mid\mathbf{R}_{g})]\geq 0$, the
left side of Eq. 8 is an approximate lower bound of the logarithm $\log
P(\mathbf{R}_{g})$. The bound is satisfied if, and only if,
$P(\mathbf{R}_{f})$ perfectly recovers $P(\mathbf{R}_{t}\mid\mathbf{R}_{g})$,
which means $P(\mathbf{R}_{f})$ trained on the observed target behavior can
perfectly approximates the true user preference distribution captured from the
auxiliary behavior data. The above condition is in line with the main
motivation of the MBA, i.e., different behavior data should reflect similar
user preferences.

We see that the left side of Eq. 8 is based on the expectation over
$P(\mathbf{R}_{f})$, which means that we are trying to train
$P(\mathbf{R}_{f})$ with the given corrupted auxiliary behavior data
$\mathbf{R}_{g}$ (i.e., the term $E_{P(\mathbf{R}_{f})}[\log
P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]$) and then to transmit the information
from $P(\mathbf{R}_{f})$ to $P(\mathbf{R}_{t})$ via the term
$KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t})]$. Such a learning process is
ineffective for learning the true user preference distribution
$P(\mathbf{R}_{t})$ and the target recommender model $t_{\theta}$. To overcome
the above issue, according to Eq. 4, when the training process has converged,
the preference distributions $P(\mathbf{R}_{f})$ and $P(\mathbf{R}_{t})$ would
be close to each other. As a result, we can change the expectation over
$P(\mathbf{R}_{f})$ to the expectation over $P(\mathbf{R}_{t})$ to learn
$P(\mathbf{R}_{t})$ more effectively. So we modify the left side of Eq. 8 as

(9) $\begin{split}E_{P(\mathbf{R}_{t})}[\log
P(&\mathbf{R}_{g}\mid\mathbf{R}_{t})]-KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t})]\\\
&\approx\log
P(\mathbf{R}_{g})-KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t}\mid\mathbf{R}_{g})].\end{split}$

Similarly, if we substitute the middle part of Eq. 7 into Eq. 6 and perform
similar derivations, we can obtain:

(10) $\displaystyle E_{P(\mathbf{R}_{t})}[\log P($
$\displaystyle\mathbf{R}_{f}\mid\mathbf{R}_{t})]-KL[P(\mathbf{R}_{g})\|P(\mathbf{R}_{t})]$
$\displaystyle\approx\log
P(\mathbf{R}_{f})-KL[P(\mathbf{R}_{g})\|P(\mathbf{R}_{t}\mid\mathbf{R}_{f})].$

The left side of Eq. 10 is an approximate lower bound of $\log
P(\mathbf{R}_{f})$. The bound is satisfied only if $P(\mathbf{R}_{g})$
perfectly recovers $P(\mathbf{R}_{t}\mid\mathbf{R}_{f})$, which means
$P(\mathbf{R}_{g})$ trained on the observed auxiliary behaviors can perfectly
approximate the true user preference distribution captured from the target
behavior data. Such condition further verifies the soundness of MBA, i.e.,
multiple types of user behavior are motivated by similar underlying user
preferences.

Combining the left side of both Eq. 9 and Eq. 10 we obtain the loss function
as:

(11) $\displaystyle L=$ $\displaystyle-E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]+KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t})]$
$\displaystyle-E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{f}\mid\mathbf{R}_{t})]+KL[P(\mathbf{R}_{g})\|P(\mathbf{R}_{t})].$

We can see that the loss function aims to maximize the likelihood of data
observation (i.e., $P(\mathbf{R}_{g}\mid\mathbf{R}_{t})$ and
$P(\mathbf{R}_{f}\mid\mathbf{R}_{t})$) and minimize the KL-divergence between
distributions learned from different user behavior data. The learning process
of MBA serves as a filter to simultaneously denoise multiple types of user
behavior and conduct beneficial knowledge transfers to infer the true user
preferences to enhance the prediction of the target behavior.

###  3.3. Training details

As described in Section 3.1, we learn the user preference distributions
$P(\mathbf{R}_{f})$ and $P(\mathbf{R}_{g})$ from $\mathbf{R}_{f}$ and
$\mathbf{R}_{g}$, respectively. In order to enhance the learning stability, we
pre-train $P(\mathbf{R}_{f})$ and $P(\mathbf{R}_{g})$ in $\mathbf{R}_{f}$ and
$\mathbf{R}_{g}$, respectively. We use the same model structures of our target
recommender $t_{\theta}$ as the pre-training model.

As the training converges, the KL-divergence will gradually approach 0. In
order to enhance the role of the KL-divergence in conveying information, we
set a hyperparameter $\alpha$ to enhance the effectiveness of the KL-
divergence. Then we obtain the following training loss function:

(12) $\displaystyle L_{MBA}$ $\displaystyle=-E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]+\alpha
KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t})]$ $\displaystyle-
E_{P(\mathbf{R}_{t})}[\log P(\mathbf{R}_{f}\mid\mathbf{R}_{t})]+\alpha
KL[P(\mathbf{R}_{g})\|P(\mathbf{R}_{t})].$

####  3.3.1. Expectation derivation

As described in Section 3.1, both $\mathbf{R}_{f}$ and $\mathbf{R}_{g}$
contain various kinds of noise and bias. In order to infer the latent true
user preferences from the corrupted multi-behavior data, we use
$h^{f}_{\phi}(u,i)$ and $h^{f}_{\varphi}(u,i)$ to capture the correlations
between the true user preferences and the observed purchase data. Similarly,
$h^{g}_{\phi^{\prime}}(u,i)$ and $h^{g}_{\varphi^{\prime}}(u,i)$ are used to
capture the correlations between the true user preferences and the observed
click data, as shown in Eq. 2. Specifically, we expand
$E_{P(\mathbf{R}_{t})}[\log P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]$ as:

(13) $\displaystyle E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]=\sum_{(u,i)}E_{r^{t}_{u,i}\sim
P(\mathbf{R}_{t})}[\log P(r^{g}_{u,i}\mid r^{t}_{u,i})]$
$\displaystyle=\sum_{(u,i)|r^{g}_{u,i}=1}\left[\log
h^{g}_{\varphi^{\prime}}(u,i)t_{\theta}(u,i)+{}\right.$ $\displaystyle\hskip
49.79231pt\left.\log h^{g}_{\phi^{\prime}}(u,i)(1-t_{\theta}(u,i))\right]+{}$
$\displaystyle\phantom{=}\sum_{(u,i)|r^{g}_{u,i}=0}\left[\log(1\\!-\\!h^{g}_{\varphi^{\prime}}(u,i))t_{\theta}(u,i)+{}\right.$
$\displaystyle\hskip
45.52458pt\left.\log(1\\!-\\!h^{g}_{\phi^{\prime}}(u,i))(1\\!-\\!t_{\theta}(u,i))\right].$

Similarly, the term $E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{f}\mid\mathbf{R}_{t})]$ can be expanded as:

(14) $\displaystyle E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{f}\mid\mathbf{R}_{t})]=\sum_{(u,i)}E_{r^{t}_{u,i}\sim
P(\mathbf{R}_{t})}[\log P(r^{f}_{u,i}\mid r^{t}_{u,i})]$
$\displaystyle=\sum_{(u,i)|r^{f}_{u,i}=1}\left[\log
h^{f}_{\varphi}(u,i)t_{\theta}(u,i)\right.+{}$ $\displaystyle\hskip
51.21504pt\left.\log h^{f}_{\phi}(u,i)(1-t_{\theta}(u,i))\right]+{}$
$\displaystyle\mbox{}\hskip
8.5359pt\sum_{(u,i)|r^{f}_{u,i}=0}\left[\log(1\\!-\\!h^{f}_{\varphi}(u,i))t_{\theta}(u,i)\\!\right.+{}$
$\displaystyle\mbox{}\hskip
51.21504pt\left.\log(1\\!-\\!h^{f}_{\phi}(u,i))(1-t_{\theta}(u,i))\right].$

By aligning and denoising the observed target behavior and auxiliary behavior
data simultaneously, the target recommender $t_{\theta}$ is trained to learn
the universal true user preference distribution.

####  3.3.2. Alternative model training

In the learning stage, we find that directly training $t_{\theta}$ with Eq.
12–Eq. 14 does not yield satisfactory results, which is caused by the
simultaneous update of five models (i.e., $h^{g}_{\phi^{\prime}}$,
$h^{g}_{\varphi^{\prime}}$, $h^{f}_{\phi}$, $h^{f}_{\varphi}$ and
$t_{\theta}$) in such an optimization process. These five models may interfere
with each other and prevent $t_{\theta}$ from learning well. To address this
problem, we set two alternative training steps to train the involved models
iteratively.

In the first training step, we assume that a user tends to not click or
purchase items that the user dislikes. That is to say, given $r^{t}_{u,i}=0$
we have $r^{f}_{u,i}\approx 0$ and $r^{g}_{u,i}\approx 0$, so we have
$h^{f}_{\phi}\approx 0$ and $h^{g}_{\phi^{\prime}}\approx 0$ according to Eq.
2. Thus in this step, only the models $h^{f}_{\varphi}$,
$h^{g}_{\varphi^{\prime}}$ and $t_{\theta}$ are trained. Then Eq. 13 can be
reformulated as:

(15) $E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]=L_{CN}+L_{CP},$

where

$\displaystyle L_{CN}$ $\displaystyle=\sum_{(u,i)\mid
r^{g}_{u,i}=0}\log(1-h^{g}_{\varphi^{\prime}}(u,i))\cdot t_{\theta}(u,i),$
$\displaystyle L_{CP}$ $\displaystyle=\sum_{(u,i)\mid r^{g}_{u,i}=1}\log
h^{g}_{\varphi^{\prime}}(u,i)\cdot
t_{\theta}(u,i)-C_{1}\cdot(1-t_{\theta}(u,i)).$

Meanwhile, Eq. 14 can be reformulated as:

(16) $E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{f}\mid\mathbf{R}_{t})]=L_{PN}+L_{PP},$

where

$\displaystyle L_{PN}=\sum_{(u,i)\mid
r^{f}_{u,i}=0}\log(1-h^{f}_{\varphi}(u,i))\cdot t_{\theta}(u,i),$
$\displaystyle L_{PP}=\sum_{(u,i)\mid r^{f}_{u,i}=1}\log
h^{f}_{\varphi}(u,i)\cdot t_{\theta}(u,i)-C_{1}\cdot(1-t_{\theta}(u,i)).$

Here, we denote $C_{1}$ as a large positive hyperparameter to replace $-\log
h^{g}_{\phi^{\prime}}(u,i)$ and $-\log h^{f}_{\phi}(u,i)$.

In the second training step, we assume that a user tends to click and purchase
the items that the user likes. That is to say, given $r^{t}_{u,i}=1$ we have
$r^{f}_{u,i}\approx 1$ and $r^{g}_{u,i}\approx 1$, so we have
$h^{f}_{\varphi}\approx 1$ and $h^{g}_{\varphi^{\prime}}\approx 1$ according
to Eq. 2. Thus in this step, only the models $h^{f}_{\phi}$,
$h^{g}_{\phi^{\prime}}$ and $t_{\theta}$ will be updated. Then Eq. 13 can be
reformulated as:

(17) $E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]=L^{\prime}_{CP}+L^{\prime}_{CN},$

where

$\displaystyle L^{\prime}_{CP}$ $\displaystyle=\sum_{(u,i)\mid
r^{g}_{u,i}=1}\log h^{g}_{\phi^{\prime}}(u,i)(1-t_{\theta}(u,i)),$
$\displaystyle L^{\prime}_{CN}$ $\displaystyle=\sum_{(u,i)\mid
r^{g}_{u,i}=0}C_{2}t_{\theta}(u,i)+\log(1-h^{g}_{\phi^{\prime}}(u,i))(1-t_{\theta}(u,i)).$

Eq. 14 can be reformulated as:

(18) $E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{f}\mid\mathbf{R}_{t})]=L^{\prime}_{PP}+L^{\prime}_{PN}$

where

$\displaystyle L^{\prime}_{PP}$ $\displaystyle=\sum_{(u,i)\mid
r^{f}_{u,i}=1}\log h^{f}_{\phi}(u,i)(1-t_{\theta}(u,i)),$ $\displaystyle
L^{\prime}_{PN}$ $\displaystyle=\sum_{(u,i)\mid
r^{f}_{u,i}=0}C_{2}t_{\theta}(u,i)+\log(1-h^{f}_{\phi}(u,i))(1-t_{\theta}(u,i)).$

$C_{2}$ is a large positive hyperparameter to replace
$-\log(1-h^{g}_{\varphi^{\prime}}(u,i))$ and $-\log(1-h^{f}_{\varphi}(u,i))$.

####  3.3.3. Training procedure

In order to facilitate the description of sampling and training process, we
divide $E_{P(\mathbf{R}_{t})}[\log P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]$ and
$E_{P(\mathbf{R}_{t})}[\log P(\mathbf{R}_{f}\mid\mathbf{R}_{t})]$ into four
parts (see Eq. 15 to Eq. 18), namely click positive loss ($L_{CP}$ and
$L^{\prime}_{CP}$), click negative loss ($L_{CN}$ and $L^{\prime}_{CN}$),
purchase positive loss ($L_{PP}$ and $L^{\prime}_{PP}$), and purchase negative
loss ($L_{PN}$ and $L^{\prime}_{PN}$). Each sample in the training set can be
categorized into one of three situations:  (i) clicked and purchased,  (ii)
clicked but not purchased, and  (iii) not clicked and not purchased.  The
three situations involve different terms in $E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{g}\mid\mathbf{R}_{t})]$ and $E_{P(\mathbf{R}_{t})}[\log
P(\mathbf{R}_{f}\mid\mathbf{R}_{t})]$. In situation (i), each sample involves
the $L_{CP}$ and $L_{PP}$ (or $L^{\prime}_{CP}$ and $L^{\prime}_{PP}$ in the
alternative training step). In situation (ii), each sample involves the
$L_{CP}$ and $L_{PN}$ (or $L^{\prime}_{CP}$ and $L^{\prime}_{PN}$ in the
alternative training step). In situation (iii), each sample involves the
$L_{CN}$ and $L_{PN}$ (or $L^{\prime}_{CN}$ and $L^{\prime}_{PN}$ in the
alternative training step). We then train MBA according to the observed
multiple types of user behavior data in situations (i) and (ii), and use the
samples in situation (iii) as our negative samples. Details of the training
process for MBA are provided in Algorithm 1.

Input: The observed multi-behavior data $\mathcal{D}$, hyperparameter
settings;

Output: All model parameters $\varphi$, $\varphi^{\prime}$,
$\phi$,$\phi^{\prime}$,$\theta$;

1 while  _not coverage_ do

2 Sample ($u$, $i$) from $\mathcal{D}$ ;

3 flag = 0 ;

4 $L_{KL}=\alpha KL[P(\mathbf{R}_{f})\|P(\mathbf{R}_{t})]+\alpha
KL[P(\mathbf{R}_{g})\|P(\mathbf{R}_{t})]$ ;

5 if  _flag=0_ then

6 if  _$r^{f}_{u,i}=1$ and $r^{g}_{u,i}=1$_ then

7 Compute $L_{MBA}=L_{KL}-(L_{CP}+L_{PP})$ ;

8

9 else if  _$r^{f}_{u,i}=0$ and $r^{g}_{u,i}=1$_ then

10 Compute $L_{MBA}=L_{KL}-(L_{CP}+L_{PN})$ ;

11

12 else if  _$r^{f}_{u,i}=0$ and $r^{g}_{u,i}=0$_ then

13 Compute $L_{MBA}=L_{KL}-(L_{CN}+L_{PN})$ ;

14

15 end if

16 Update $\varphi$, $\varphi^{\prime}$, and $\theta$ through $L_{MBA}$ ;

17 flag = 1 ;

18

19 else

20 Compute $L_{MBA}$ similar to line 6–line 12 using
$L_{KL},L^{\prime}_{PP},L^{\prime}_{CP},L^{\prime}_{PN},L^{\prime}_{CN}$;

21 Update $\phi$, $\phi^{\prime}$, and $\theta$ through $L_{MBA}$ ;

22 flag = 0 ;

23

24 end if

25

26 end while

Algorithm 1 Training Process of MBA

##  4\. Experimental settings

###  4.1. Experimental questions

Our experiments are conducted to answer the following research questions:
(RQ1) How do the proposed methods perform compared with state-of-the-art
recommendation baselines on different datasets?  (RQ2) How do the proposed
methods perform compared with other denoising frameworks?  (RQ3) Can MBA help
to learn universal user preferences from users’ multiple types of behavior?
(RQ4) How do the components and the hyperparameter settings affect the
recommendation performance of MBA?

###  4.2. Datasets

To evaluate the effectiveness of our method, we conduct a series of
experiments on three real-world benchmark datasets, including
Beibei111https://www.beibei.com/ (Gao et al., 2019),
Taobao222https://tianchi.aliyun.com/dataset/dataDetail?dataId=649 (Zhu et al.,
2018), and MBD (multi-behavior dataset), a dataset we collected from an
operational e-commerce platform. The details are as follows:  (i) The Beibei
dataset is an open dataset collected from Beibei, the largest infant product
e-commerce platform in China, which includes three types of behavior, _click_
, _add-to-cart_ and _purchase_. This work uses two kinds of behavioral data,
clicks and purchases.  (ii) The Taobao dataset is an open dataset collected
from Taobao, the largest e-commerce platform in China, which includes three
types of behavior, _click_ , _add to cart_ and _purchase_. In this work, we
use clicks and purchases of this dataset.  (iii) The MBD dataset is collected
from an operational e-commerce platform, and includes two types of behavior,
_click_ and _purchase_.  For each dataset, we ensure that users have
interactions on both types of behavior, and we set click data as auxiliary
behavior data and purchase data as target behavior data. Table 1 shows the
statistics of our datasets.

Table 1. Statistics of the datasets. Dataset | Users | Items | Purchases | Clicks
---|---|---|---|---
Beibei | 21,716 | 7,977 | 243,661 | 1,930,069
Taobao | 48,658 | 39,395 | 208,905 | 1,238,659
MBD | 102,556 | 20,237 | 230,958 | 659,914

###  4.3. Evaluation protocols

We divide the datasets into training and test sets with a ratio of 4:1. We
adopt two widely used metrics Recall@$k$ and NDCG@$k$. Recall@$k$ represents
the coverage of true positive items that appear in the final top-$k$ ranked
list. NDCG@$k$ measures the ranking quality of the final recommended items. In
our experiments, we use the setting of $k=10,20$. For our method and the
baselines, the reported results are the average values over all users. For
every result, we conduct the experiments three times and report the average
values.

###  4.4. Baselines

To demonstrate the effectiveness of our method, we compare MBA with several
state-of-the-art methods. The methods used for comparison include single-
behavior models, multi-behavior models, and recommendation denoising methods.

The single-behavior models that we consider are:  (i) MF-BPR(Rendle et al.,
2009), which uses bayesian personalized ranking (BPR) loss to optimize matrix
factorization.  (ii) NGCF(Wang et al., 2019), which encodes collaborative
signals into the embedding process through multiple graph convolutional layers
and models higher-order connectivity in user-item graphs.  (iii) LightGCN(He
et al., 2020), which simplifies graph convolution by removing the matrix
transformation and non-linear activation. We use the BPR loss to optimize
LightGCN.

The multi-behavior models that we consider are:  (i) MB-GCN(Jin et al., 2020),
which constructs a multi-behavior heterogeneous graph and uses GCN to perform
behavior-aware embedding propagation.  (ii) MB- GMN(Xia et al., 2021), which
incorporates multi-behavior pattern modeling with the meta-learning paradigm.
(iii) CML(Wei et al., 2022), which uses a new multi-behavior contrastive
learning paradigm to capture the transferable user-item relationships from
multi-behavior data.

To verify that the proposed method improves performance by denoising implicit
feedback, we also introduce the following denoising frameworks:  (i)
WBPR(Gantner et al., 2012), which is a re-sampling-based method which
considers popular, but un-interacted items are highly likely to be negative.
(ii) T-CE(Wang et al., 2021a), which is a re-weighting based method which
discards the large-loss samples with a dynamic threshold in each iteration.
(iii) DeCA(Wang et al., 2022), which is a newly proposed denoising method that
utilizes the agreement predictions on clean examples across different models
and minimizes the KL-divergence between the real user preference parameterized
by two recommendation models.  (iv) SGDL(Gao et al., 2022), which is a new
denoising paradigm that utilizes self-labeled memorized data as denoising
signals to improve the robustness of recommendation models.

Table 2. Overall performance comparison of purchase predictions on Beibei,
Taobao and MBD with single-behavior methods and multi-behavior methods. R
denotes Recall, and N denotes NDCG. Underscore indicates the best result among
the baseline methods. Boldface means best results. A significant improvement
over the best baseline is marked with * ($p<0.05$).

Datasets | Beibei | Taobao | MBD
---|---|---|---
Method | R@10 | R@20 | N@10 | N@20 | R@10 | R@20 | N@10 | N@20 | R@10 | R@20 | N@10 | N@20
MF | 0.0901 | 0.1438 | 0.0668 | 0.0855 | 0.0303 | 0.0420 | 0.0190 | 0.0224 | 0.3816 | 0.4597 | 0.2490 | 0.2697
NGCF | 0.0987 | 0.1561 | 0.0742 | 0.0939 | 0.0350 | 0.0518 | 0.0219 | 0.0267 | 0.4030 | 0.4892 | 0.2623 | 0.2852
LightGCN | 0.0988 | 0.1541 | 0.0733 | 0.0925 | 0.0460 | 0.0640 | 0.0290 | 0.0342 | 0.3460 | 0.4365 | 0.2205 | 0.2443
MBGCN | 0.1054 | 0.1642 | 0.0784 | 0.0986 | 0.0418 | 0.0621 | 0.0250 | 0.0308 | 0.4625 | 0.5615 | 0.2949 | 0.3213
MBGMN | 0.1046 | 0.1632 | 0.0779 | 0.0981 | 0.0542 | 0.0808 | 0.0330 | 0.0406 | 0.3660 | 0.4810 | 0.2323 | 0.2624
CML | 0.0861 | 0.1382 | 0.0618 | 0.0796 | 0.0318 | 0.0524 | 0.0176 | 0.0234 | 0.3839 | 0.4928 | 0.2200 | 0.2487
MBA | 0.1127 | 0.1742* | 0.0834 | 0.1046* | 0.0579* | 0.0812 | 0.0369* | 0.0435* | 0.4644 | 0.5677* | 0.3012* | 0.3285*

Table 3. Overall performance comparison of purchase predictions on Beibei,
Taobao and MBD with other denoising frameworks. Normal denotes the normal
training. R denotes Recall, and N denotes NDCG. Underscore indicates the best
result among the baseline methods. Boldface indicates best results. A
significant improvement over the best baseline is marked with * ($p<0.05$).

Dataset | Beibei | Taobao | MBD
---|---|---|---
Base model | Method | R@10 | R@20 | N@10 | N@20 | R@10 | R@20 | N@10 | N@20 | R@10 | R@20 | N@10 | N@20
MF | Normal | 0.0901 | 0.1438 | 0.0668 | 0.0855 | 0.0303 | 0.0420 | 0.0190 | 0.0224 | 0.3816 | 0.4597 | 0.2490 | 0.2697
WBPR | 0.0770 | 0.1189 | 0.0586 | 0.0731 | 0.0307 | 0.0440 | 0.0195 | 0.0233 | 0.3554 | 0.4216 | 0.2375 | 0.2551
T-CE | 0.0795 | 0.1262 | 0.0562 | 0.0724 | 0.0261 | 0.0350 | 0.0148 | 0.0174 | 0.1868 | 0.2320 | 0.1195 | 0.1314
DeCA | 0.0898 | 0.1378 | 0.0664 | 0.0831 | 0.0282 | 0.0405 | 0.0183 | 0.0218 | 0.3055 | 0.3654 | 0.1983 | 0.2143
SGDL | 0.0768 | 0.1240 | 0.0561 | 0.0725 | 0.0090 | 0.0137 | 0.0056 | 0.0069 | 0.1833 | 0.2300 | 0.1183 | 0.1307
MBA | 0.1127* | 0.1742* | 0.0834* | 0.1046* | 0.0579* | 0.0812* | 0.0369* | 0.0435* | 0.4644* | 0.5677* | 0.3012* | 0.3285*
LightGCN | Normal | 0.0988 | 0.1541 | 0.0733 | 0.0925 | 0.0460 | 0.0640 | 0.0290 | 0.0342 | 0.4145 | 0.4974 | 0.2719 | 0.2939
WBPR | 0.0879 | 0.1310 | 0.0682 | 0.0832 | 0.0486 | 0.0694 | 0.0307 | 0.0367 | 0.3989 | 0.4772 | 0.2647 | 0.2855
T-CE | 0.0779 | 0.1254 | 0.0526 | 0.0691 | 0.0292 | 0.0416 | 0.0188 | 0.0224 | 0.2761 | 0.3465 | 0.1756 | 0.1941
DeCA | 0.0770 | 0.1230 | 0.0528 | 0.0687 | 0.0412 | 0.0587 | 0.0255 | 0.0305 | 0.2382 | 0.3031 | 0.1544 | 0.1714
SGDL | 0.0944 | 0.1462 | 0.0695 | 0.0874 | 0.0452 | 0.0641 | 0.0281 | 0.0335 | 0.3894 | 0.4707 | 0.2470 | 0.2686
MBA | 0.1078* | 0.1698* | 0.0786* | 0.1002* | 0.0538* | 0.0780* | 0.0327* | 0.0396* | 0.4750* | 0.5926* | 0.3026* | 0.3337*

###  4.5. Implementation details

We implement our method with PyTorch.333Our code is available at
https://github.com/LiuXiangYuan/MBA. Without special mention, we set MF as our
base model $t_{\theta}$ since MF is still one of the best models for capturing
user preferences for recommendations (Rendle et al., 2020). The model is
optimized by Adam (Kingma and Ba, 2015) optimizer with a learning rate of
0.001, where the batch size is set as 2048. The embedding size is set to 32.
The hyperparameters $\alpha$, $C_{1}$ and $C_{2}$ are search from { 1, 10,
100, 1000 }. $\beta$ is search from { 0.7, 0.8, 1 }. To avoid over-fitting,
$L_{2}$ normalization is searched in { $10^{-6}$, $10^{-5}$, …, 1 }. Each
training step is formed by one interacted example, and one randomly sampled
negative example for efficient computation. We use Recall@20 on the test set
for early stopping if the value does not increase after 20 epochs.

For the hyperparameters of all recommendation baselines, we use the values
suggested by the original papers with carefully fine-tuning on the three
datasets. For all graph-based methods, the number of graph-based message
propagation layers is fixed at 3.

##  5\. Experimental Results

###  5.1. Performance comparison (RQ1)

To answer $\rm RQ1$, we conduct experiments on the Beibei, Taobao and MBD
datasets. The performance comparisons are reported in Table 2. From the table,
we have the following observations.

First, the proposed MBA method achieves the best performance and consistently
outperforms all baselines across all datasets. For instance, the average
improvement of MBA over the strongest baseline is approximately 6.3% on the
Beibei dataset, 6.6% on the Taobao dataset and 1.5% on the MBD dataset. These
improvements demonstrate the effectiveness of MBA. We contribute the
significant performance improvement to the following two reasons: (i) we align
the user preferences based on two types of two behavior, transferring useful
information from the auxiliary behavior data to enhance the performance of the
target behavior predictions; (ii) noisy interactions are reduced through
preference alignment, which helps to improve the learning of the latent
universal true user preferences.

Second, except CML the multi-behavior models outperform the single-behavior
models by a large margin. This reflects the fact that adding auxiliary
behavior information can improve the recommendation performance of the target
behavior. We conjecture that CML cannot achieve satisfactory performance
because it incorporates the knowledge contained in auxiliary behavior through
contrastive meta-learning, which introduces more noisy signals. Furthermore,
we compare MBA with the best single-behavior model (NGCF on the Beibei and MBD
datasets, LightGCN on the Taobao dataset), and see that MBA achieves an
average improvement of 12.4% on the Beibei dataset, 26.8% on the Taobao
dataset and 15.3% on the MBD dataset.

To conclude, the proposed MBA approach consistently and significantly
outperforms related single-behavior and multi-behavior recommendation
baselines on the purchase prediction task.

###  5.2. Denoising (RQ2)

Table 3 reports on a performance comparison with existing denoising frameworks
on the Beibei, Taobao and MBD datasets. The results demonstrate that MBA can
provide more robust recommendations and improve overall performance than
competing approaches. Most of the denoising baselines do not obtain
satisfactory results, even after carefully tuning their hyperparameters. Only
WBPR can outperform normal training in some cases. However, MBA consistently
outperforms normal training and other denoising frameworks. We think the
reasons for this are as follows: (i) In MBA, we use the alignment between
multi-behavior data as the denoising signal and then transmit information from
the multi-behavior distribution to the latent universal true user preference
distribution. This learning process facilitates knowledge transfer across
multiple types of user behavior and filters out noisy signals. (ii) In the
original papers of the compared denoising baselines, testing is conducted
based on explicit user-item ratings. However, our method does not use any
explicit information like ratings, only implicit interaction data is
considered.

To further explore the generalization capability of MBA, we also adopt
LightGCN as our base model (i.e., using LightGCN as $t_{\theta}$). The results
are also shown in Table 3. We see that MBA is still more effective than the
baseline methods. We find that LightGCN-based MBA does not perform as well as
MF-based MBA on the Beibei and Taobao datasets. We think the possible reasons
are as follows: (i) LightGCN is more complex than MF, making MBA more
difficult to train; (ii) LightGCN may be more sensitive to noisy signals due
to the aggregation of neighbourhoods, resulting in a decline in the MBA
performance compared to using MF as the base model.

To conclude, the proposed MBA can generate more accurate recommendation
compared with existing denoising frameworks.

###  5.3. User preferences visualization (RQ3)

To answer RQ3, we visualize the distribution of users’ interacted items. We
select two users in the Beibei, Taobao and MBD datasets and draw their
behavior distributions using the parameters obtained from an MF model trained
on the purchase behavior data and the parameters obtained from MBA,
respectively. Figure 2 visualizes the results. From the figure, we observe
that for one user, the clicked items and purchased items distributions of MBA
stay much closer than that of MF. The observation indicates that MBA can
successfully align multiple types of user behavior and infer universal and
accurate user preferences.

Besides, we see that different users in MBA have more obvious separations than
users in MF, which implies that MBA provides more personalized user-specific
recommendation than MF.

###  5.4. Model investigation (RQ4)

Table 4. The performance of MBA after removing KL-divergence and pre-trained models. R denotes Recall, and N denotes NDCG. Boldface indicates best results. A significant improvement over the best baseline is marked with * ($p<0.05$) Datasets | Beibei | Taobao | MBD
---|---|---|---
Method | R@10 | R@20 | N@10 | N@20 | R@10 | R@20 | N@10 | N@20 | R@10 | R@20 | N@10 | N@20
MBA-KL | 0.0897 | 0.1412 | 0.0651 | 0.0831 | 0.0261 | 0.0380 | 0.0151 | 0.0185 | 0.3250 | 0.4185 | 0.1779 | 0.2027
MBA-PT | 0.0687 | 0.1136 | 0.0487 | 0.0642 | 0.0087 | 0.0152 | 0.0054 | 0.0072 | 0.3226 | 0.4138 | 0.1775 | 0.2017
MBA | 0.1127* | 0.1742* | 0.0834* | 0.1046* | 0.0579* | 0.0812* | 0.0369* | 0.0435* | 0.4644* | 0.5677* | 0.3012* | 0.3285*

####  5.4.1. Ablation study.

Regarding RQ4, we conduct an ablation study (see Table 4) on the following two
settings:  (i) MBA-KL: we remove KL-divergence when training MBA; and  (ii)
MBA-PT: we co-train the $P(\mathbf{R}_{f})$ and $P(\mathbf{R}_{g})$ in MBA
instead of pre-training.

Figure 2.  Distributions of items interacted with by two users in the Beibei,
Taobao and MBD datasets. Item representations in the graphs on the left are
obtained by a matrix factorization model trained on the purchase behavior
data, while item representations in the right column graphs are obtained by
MBA. $u_{i}c$ ($u_{i}p$) represents the distribution of items clicked
(purchased) by user $u_{i}$.

The results show that both parts (KL-divergence and pre-trained models) are
essential to MBA because removing either will lead to a performance decrease.
Without KL-divergence, we see the performance drops substantially in terms of
all metrics. Hence, the KL-divergence helps align the user preferences learned
from different behaviors, thus improving the recommendation performance.
Without pre-trained models, the results drop dramatically, especially in the
Taobao dataset, which indicates that it is hard to co-train
$P(\mathbf{R}_{f})$ and $P(\mathbf{R}_{g})$ with MBA. Using a pre-trained
model can reduce MBA’s complexity and provide prior knowledge so that it can
more effectively extract the user’s real preferences from the different types
of behavior distributions.

####  5.4.2. Hyperparameter study

Next, we conduct experiments to examine the effect of different parameter
settings on MBA. Figure 3 shows the effect of $\alpha$, which is used to
control the weight of the KL-divergence in conveying information. On the
Beibei dataset, the performance of MBA is affected when the $\alpha$ is
greater than or equal to 100. Thus, when dominated by KL-divergence, MBA’s
performance will be close to that of the pre-trained models. On the Taobao and
MBD datasets, when $\alpha$ is greater than or equal to 100, MBA will
gradually converge, with a relatively balanced state between the KL-divergence
and the expectation term. Under this setting, MBA achieves the best
performance.

Figure 3. Impact of the hyperparameter $\alpha$.

##  6\. Conclusion

In this work, we have focused on the task of multi-behavior recommendation. We
conjectured that multiple types of behavior from the same user reflect similar
underlying user preferences. To tackle the challenges of the gap between data
distributions of different types of behavior and the challenge of behavioral
data being noisy and biased, we proposed a learning framework, namely multi-
behavior alignment (MBA), which can infer universal user preferences from
multiple types of observed behavioral data, while performing data denoising to
achieve beneficial knowledge transfer. Extensive experiments conducted on
three real-world datasets showed the effectiveness of the proposed method.

Our method proves the value of mining the universal user preferences from
multi-behavior data for the implicit feedback-based recommendation. However, a
limitation of MBA is that it can only align between two types of behavioral
data. As to our future work, we aim to perform alignment on more types of user
behavior. In addition, we plan to develop ways of conducting more effective
and efficient model training.

###### Acknowledgements.

This research was funded by the Natural Science Foundation of China
(62272274,61972234,62072279,62102234,62202271), Meituan, the Natural Science
Foundation of Shandong Province (ZR2022QF004), the Key Scientific and
Technological Innovation Program of Shandong Province (2019JZZY010129),
Shandong University multidisciplinary research and innovation team of young
scholars (No.2020QNQT017), the Tencent WeChat Rhino-Bird Focused Research
Program (JR-WXG2021411), the Fundamental Research Funds of Shandong
University, the Hybrid Intelligence Center, a 10-year program funded by the
Dutch Ministry of Education, Culture and Science through the Netherlands
Organization for Scientific Research, https://hybrid-intelligence-centre.nl.
All content represents the opinion of the authors, which is not necessarily
shared or endorsed by their respective employers and/or sponsors.

## References

  * (1)
  * Chen et al. (2021a) Chong Chen, Weizhi Ma, Min Zhang, Zhaowei Wang, Xiuqiang He, Chenyang Wang, Yiqun Liu, and Shaoping Ma. 2021a.  Graph Heterogeneous Multi-relational Recommendation. In _Proceedings of AAAI_.
  * Chen et al. (2020b) Chong Chen, Min Zhang, Yongfeng Zhang, Weizhi Ma, Yiqun Liu, and Shaoping Ma. 2020b.  Efficient Heterogeneous Collaborative Filtering without Negative Sampling for Recommendation. In _Proceedings of AAAI_.
  * Chen et al. (2022) Huiyuan Chen, Yusan Lin, Menghai Pan, Lan Wang, Chin-Chia Michael Yeh, Xiaoting Li, Yan Zheng, Fei Wang, and Hao Yang. 2022.  Denoising Self-attentive Sequential Recommendation. In _Proceedings of RecSys_.
  * Chen et al. (2021c) Huiyuan Chen, Lan Wang, Yusan Lin, Chin-Chia Michael Yeh, Fei Wang, and Hao Yang. 2021c.  Structured Graph Convolutional Networks with Stochastic Masks for Recommender Systems. In _Proceedings of SIGIR_.
  * Chen et al. (2020a) Jiawei Chen, Hande Dong, Xiang Wang, Fuli Feng, Meng Wang, and Xiangnan He. 2020a.  Bias and Debias in Recommender System: A Survey and Future Directions.  _CoRR_ (2020).
  * Chen et al. (2021b) Jiawei Chen, Xiang Wang, Fuli Feng, and Xiangnan He. 2021b.  Bias Issues and Solutions in Recommender System. In _Proceedings of RecSys_.
  * Cheng et al. (2023) Zhiyong Cheng, Sai Han, Fan Liu, Lei Zhu, Zan Gao, and Yuxin Peng. 2023.  Multi-Behavior Recommendation with Cascading Graph Convolution Networks. In _Proceedings of WWW_.
  * Ding et al. (2018) Jingtao Ding, Fuli Feng, Xiangnan He, Guanghui Yu, Yong Li, and Depeng Jin. 2018\.  An Improved Sampler for Bayesian Personalized Ranking by Leveraging View Data. In _Proceedings of WWW_.
  * Ding et al. (2019a) Jingtao Ding, Yuhan Quan, Xiangnan He, Yong Li, and Depeng Jin. 2019a.  Reinforced Negative Sampling for Recommendation with Exposure Data.. In _Proceedings of IJCAI_.
  * Ding et al. (2019b) Jingtao Ding, Guanghui Yu, Xiangnan He, Fuli Feng, Yong Li, and Depeng Jin. 2019b.  Sampler Design for Bayesian Personalized Ranking by Leveraging View Data.  _TKDE_ (2019).
  * Gantner et al. (2012) Zeno Gantner, Lucas Drumond, Christoph Freudenthaler, and Lars Schmidt-Thieme. 2012.  Personalized Ranking for Non-uniformly Sampled Items. In _Proceedings of KDD_.
  * Gao et al. (2019) Chen Gao, Xiangnan He, Dahua Gan, Xiangning Chen, Fuli Feng, Yong Li, Tat-Seng Chua, and Depeng Jin. 2019\.  Neural Multi-task Recommendation from Multi-behavior Data. In _Proceedings of ICDE_.
  * Gao et al. (2022) Yunjun Gao, Yuntao Du, Yujia Hu, Lu Chen, Xinjun Zhu, Ziquan Fang, and Baihua Zheng. 2022.  Self-guided Learning to Denoise for Robust Recommendation. In _Proceedings of SIGIR_.
  * Gu et al. (2020) Yulong Gu, Zhuoye Ding, Shuaiqiang Wang, and Dawei Yin. 2020\.  Hierarchical User Profiling for E-commerce Recommender Systems. In _Proceedings of WSDM_.
  * He et al. (2020) Xiangnan He, Kuan Deng, Xiang Wang, Yan Li, Yongdong Zhang, and Meng Wang. 2020\.  LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation. In _Proceedings of SIGIR_.
  * Huang et al. (2019) Chao Huang, Xian Wu, Xuchao Zhang, Chuxu Zhang, Jiashu Zhao, Dawei Yin, and Nitesh V Chawla. 2019.  Online Purchase Prediction via Multi-scale Modeling of Behavior Dynamics. In _Proceedings of KDD_.
  * Jagerman et al. (2019) Rolf Jagerman, Harrie Oosterhuis, and Maarten de Rijke. 2019\.  To Model or To Intervene: A Comparison of Counterfactual and Online Learning to Rank from User Interactions. In _Proceedings of SIGIR_.
  * Jin et al. (2020) Bowen Jin, Chen Gao, Xiangnan He, Depeng Jin, and Yong Li. 2020.  Multi-behavior Recommendation with Graph Convolutional Networks. In _Proceedings of SIGIR_.
  * Kim et al. (2014) Youngho Kim, Ahmed Hassan, Ryen W White, and Imed Zitouni. 2014.  Modeling Dwell Time to Predict Click-level Satisfaction. In _Proceedings of WSDM_.
  * Kingma and Ba (2015) Diederik P Kingma and Jimmy Ba. 2015.  Adam: A Method for Stochastic Optimization. In _Proceedings of ICLR_.
  * Koren et al. (2009) Yehuda Koren, Robert Bell, and Chris Volinsky. 2009\.  Matrix Factorization Techniques for Recommender Systems.  _Computer_ (2009).
  * Lu et al. (2019) Hongyu Lu, Min Zhang, Weizhi Ma, Ce Wang, Feng Xia, Yiqun Liu, Leyu Lin, and Shaoping Ma. 2019.  Effects of User Negative Experience in Mobile News Streaming. In _Proceedings of SIGIR_.
  * Ma et al. (2022b) Muyang Ma, Pengjie Ren, Zhumin Chen, Zhaochun Ren, Lifan Zhao, Peiyu Liu, Jun Ma, and Maarten de Rijke. 2022b.  Mixed Information Flow for Cross-domain Sequential Recommendations.  _TKDD_ (2022).
  * Ma et al. (2022a) Wanqi Ma, Xiancong Chen, Weike Pan, and Zhong Ming. 2022a.  VAE++ Variational AutoEncoder for Heterogeneous One-Class Collaborative Filtering. In _Proceedings of WSDM_.
  * Meng et al. (2020) Wenjing Meng, Deqing Yang, and Yanghua Xiao. 2020\.  Incorporating User Micro-behaviors and Item Knowledge into Multi-task Learning for Session-based Recommendation. In _Proceedings of SIGIR_.
  * Pan et al. (2019) Feiyang Pan, Shuokai Li, Xiang Ao, Pingzhong Tang, and Qing He. 2019.  Warm up Cold-start Advertisements: Improving CTR Predictions via Learning to Learn ID Embeddings. In _Proceedings of SIGIR_.
  * Pan et al. (2010) Weike Pan, Evan Xiang, Nathan Liu, and Qiang Yang. 2010\.  Transfer Learning in Collaborative Filtering for Sparsity Reduction. In _Proceedings of AAAI_.
  * Rendle et al. (2009) Steffen Rendle, Christoph Freudenthaler, Zeno Gantner, and Lars Schmidt-Thieme. 2009.  BPR: Bayesian Personalized Ranking From Implicit Feedback. In _Proceedings of UAI_.
  * Rendle et al. (2020) Steffen Rendle, Walid Krichene, Li Zhang, and John Anderson. 2020.  Neural Collaborative Filtering vs. Matrix Factorization Revisited. In _Proceedings of RecSys_.
  * Shen and Sanghavi (2019) Yanyao Shen and Sujay Sanghavi. 2019.  Learning With Bad Training Data via Iterative Trimmed Loss Minimization. In _Proceedings of ICML_.
  * Tsagkias et al. (2020) Manos Tsagkias, Tracy Holloway King, Surya Kallumadi, Vanessa Murdock, and Maarten de Rijke. 2020\.  Challenges and Research Opportunities in Ecommerce Search and Recommendations.  _SIGIR Forum_ (2020).
  * Wang et al. (2021a) Wenjie Wang, Fuli Feng, Xiangnan He, Liqiang Nie, and Tat-Seng Chua. 2021a.  Denoising Implicit Feedback for Recommendation. In _Proceedings of WSDM_.
  * Wang et al. (2020) Wen Wang, Wei Zhang, Shukai Liu, Qi Liu, Bo Zhang, Leyu Lin, and Hongyuan Zha. 2020\.  Beyond clicks: Modeling Multi-relational Item Graph for Session-based Target Behavior Prediction. In _Proceedings of WWW_.
  * Wang et al. (2019) Xiang Wang, Xiangnan He, Meng Wang, Fuli Feng, and Tat-Seng Chua. 2019.  Neural Graph Collaborative Filtering. In _Proceedings of SIGIR_.
  * Wang et al. (2022) Yu Wang, Xin Xin, Zaiqiao Meng, Joemon M Jose, Fuli Feng, and Xiangnan He. 2022\.  Learning Robust Recommenders through Cross-Model Agreement. In _Proceedings of WWW_.
  * Wang et al. (2021b) Zitai Wang, Qianqian Xu, Zhiyong Yang, Xiaochun Cao, and Qingming Huang. 2021b.  Implicit Feedbacks are Not Always Favorable: Iterative Relabeled One-Class Collaborative Filtering against Noisy Interactions. In _Proceedings of ACMMM_.
  * Wei et al. (2022) Wei Wei, Chao Huang, Lianghao Xia, Yong Xu, Jiashu Zhao, and Dawei Yin. 2022\.  Contrastive Meta Learning with Behavior Multiplicity for Recommendation. In _Proceedings of WSDM_.
  * Wu et al. (2021) Jiancan Wu, Xiang Wang, Fuli Feng, Xiangnan He, Liang Chen, Jianxun Lian, and Xing Xie. 2021.  Self-supervised Graph Learning for Recommendation. In _Proceedings of SIGIR_.
  * Xia et al. (2021) Lianghao Xia, Yong Xu, Chao Huang, Peng Dai, and Liefeng Bo. 2021.  Graph Meta Network for Multi-behavior Recommendation. In _Proceedings of SIGIR_.
  * Xie et al. (2021) Ruobing Xie, Cheng Ling, Yalong Wang, Rui Wang, Feng Xia, and Leyu Lin. 2021\.  Deep Feedback Network for Recommendation. In _Proceedings of IJCAI_.
  * Xie et al. (2020) Ruobing Xie, Zhijie Qiu, Jun Rao, Yi Liu, Bo Zhang, and Leyu Lin. 2020.  Internal and Contextual Attention Network for Cold-start Multi-channel Matching in Recommendation.. In _Proceedings of IJCAI_.
  * Xuan et al. (2023) Hongrui Xuan, Yi Liu, Bohan Li, and Hongzhi Yin. 2023\.  Knowledge Enhancement for Multi-Behavior Contrastive Recommendation. In _Proceedings of WSDM_.
  * Yu and Qin (2020) Wenhui Yu and Zheng Qin. 2020.  Sampler Design for Implicit Feedback Data by Noisy-label Robust Learning. In _Proceedings of SIGIR_.
  * Yuan et al. (2022) Jiahao Yuan, Wendi Ji, Dell Zhang, Jinwei Pan, and Xiaoling Wang. 2022.  Micro-Behavior Encoding for Session-based Recommendation. In _Proceedings of ICDE_.
  * Zhao et al. (2016) Qian Zhao, Shuo Chang, F Maxwell Harper, and Joseph A Konstan. 2016.  Gaze Prediction for Recommender Systems. In _Proceedings of RecSys_.
  * Zhou et al. (2018) Meizi Zhou, Zhuoye Ding, Jiliang Tang, and Dawei Yin. 2018\.  Micro Behaviors: A New Perspective in E-commerce Recommender Systems. In _Proceedings of WSDM_.
  * Zhu et al. (2018) Han Zhu, Xiang Li, Pengye Zhang, Guozheng Li, Jie He, Han Li, and Kun Gai. 2018.  Learning Tree-based Deep Model for Recommender Systems. In _Proceedings of KDD_.
  * Zhu et al. (2021) Yongchun Zhu, Kaikai Ge, Fuzhen Zhuang, Ruobing Xie, Dongbo Xi, Xu Zhang, Leyu Lin, and Qing He. 2021\.  Transfer-meta Framework for Cross-domain Recommendation to Cold-start Users. In _Proceedings of SIGIR_.

  *[KL-divergence]: Kullback–Leibler divergence
  *[GNN]: graph neural network
  *[GCN]: graph convolutional network
  *[VAE]: variational autoencoder
  *[BPR]: bayesian personalized ranking