# Towards Explainable Collaborative Filtering with Taste Clusters Learning

Yuntao Du  Zhejiang UniversityHangzhouChina<EMAIL_ADDRESS>,  Jianxun Lian
Microsoft Research AsiaBeijingChina<EMAIL_ADDRESS>,  Jing Yao
Xiting Wang  Microsoft Research AsiaBeijingChina jingyao<EMAIL_ADDRESS>,  Mingqi Wu  Microsoft GamingRedmondUnited States<EMAIL_ADDRESS>,
Lu Chen
Yunjun Gao  Zhejiang UniversityHangzhouChina chenlu<EMAIL_ADDRESS>and
Xing Xie  Microsoft Research AsiaBeijingChina<EMAIL_ADDRESS>
(2023)

###### Abstract.

Collaborative Filtering (CF) is a widely used and effective technique for
recommender systems. In recent decades, there have been significant
advancements in latent embedding-based CF methods for improved accuracy, such
as matrix factorization, neural collaborative filtering, and LightGCN.
However, the explainability of these models has not been fully explored.
Adding explainability to recommendation models can not only increase trust in
the decision-making process, but also have multiple benefits such as providing
persuasive explanations for item recommendations, creating explicit profiles
for users and items, and assisting item producers in design improvements.

In this paper, we propose a neat and effective Explainable Collaborative
Filtering (ECF) model that leverages interpretable cluster learning to achieve
the two most demanding objectives: (1) Precise - the model should not
compromise accuracy in the pursuit of explainability; and (2) Self-explainable
- the model’s explanations should truly reflect its decision-making process,
not generated from post-hoc methods. The core of ECF is mining taste clusters
from user-item interactions and item profiles. We map each user and item to a
sparse set of taste clusters, and taste clusters are distinguished by a few
representative tags. The user-item preference, users/items’ cluster
affiliations, and the generation of taste clusters are jointly optimized in an
end-to-end manner. Additionally, we introduce a forest mechanism to ensure the
model’s accuracy, explainability, and diversity. To comprehensively evaluate
the explainability quality of taste clusters, we design several quantitative
metrics, including in-cluster item coverage, tag utilization, silhouette, and
informativeness. Our model’s effectiveness is demonstrated through extensive
experiments on three real-world datasets.

Collaborative Filtering; Explanability; Recommendation; Clustering

††journalyear: 2023††copyright: acmlicensed††conference: Proceedings of the
ACM Web Conference 2023; May 1–5, 2023; Austin, TX, USA††booktitle:
Proceedings of the ACM Web Conference 2023 (WWW ’23), May 1–5, 2023, Austin,
TX, USA††price: 15.00††doi: 10.1145/3543507.3583303††isbn:
978-1-4503-9416-1/23/04††ccs: Information systems Collaborative
filtering††ccs: Information systems Clustering††ccs: Information systems
Recommender systems††ccs: Information systems Web mining††ccs: Information
systems Summarization††ccs: Computing methodologies Learning from implicit
feedback

##  1\. Introduction

Collaborative filtering (CF) is an effective and widely used technique for
recommender systems. The rationale behind CF is that the user’s potential
interests can be inferred from a group of like-minded users’ behaviors
(_e.g.,_ user-based CF), or, a set of similar items to the user’s behavior
history (_e.g.,_ item-based CF). Existing methods for CF can be roughly
categorized into two types: memory-based CF and model-based CF. Memory-based
CF methods (Sarwar et al., 2001) explicitly find the neighborhood of
users/items for preference inference. These methods, although concise and
effective, usually suffer from memory consumption, (inference) computational
cost, and data sparsity issues. In contrast, model-based CF uses machine
learning methods to help model the relationship between users and items. In
the past decades, the research trends have been mainly focusing on model-based
CF, with methods evolving from latent factorization-based methods (such as MF
(Koren et al., 2009) and SVD++ (Koren, 2008)) to neural embedding-based
methods (such as NCF (He et al., 2017) and CDAE (Wu et al., 2016)), and to
recently neural graph-based methods (such as LightGCN (He et al., 2020) and
UltraGCN (Mao et al., 2021)). The foundation model in this direction is to
represent users and items with high-quality latent factor embeddings, so that
users’ preference towards items can be decoded from the latent embeddings.

A notable drawback of latent factor-based CF is the lack of transparency and
explainability. Knowing the decision logic of recommender algorithms rather
than using them as black boxes is important on multiple aspects, such as
assisting developers in model debugging and abnormal case studies or
generating persuasive explanations to promote the recommended items and
increase conversion rates. Many prior attempts have been made to achieve this
goal. To name a few representative works, (McAuley and Leskovec, 2013)
combines a latent matrix factorization model with a latent topic model, then
each dimension of user/item embeddings can be associated with a textual topic
mined from users’ reviews. (Zhang et al., 2014) proposes the Explicit Factor
Model (EFM), which extracts aspect features from textual reviews and makes
predictions by combining scores from a latent factor model and from aspect-
level interest matching. (Pan et al., 2020) proposes a feature mapping
paradigm. By mapping latent embeddings to interpretable aspect features, an
uninterpretable model can now provide explainability. However, we argue that
explainable CF is still an open question, because existing solutions fail to
satisfy at least one of the properties: (P1,flexibility) the dimension of
latent embeddings and the number of interpretable features/topics do not
necessarily match (_e.g.,_(McAuley and Leskovec, 2013) fails on this);
(P2,coherence) a model’s interpretable modules and predictive modules should
be harmoniously integrated for decision making, instead of functioning as
isolated modules, which may lead to divergent outcomes (_e.g.,_(Zhang et al.,
2014) fails on this); (P3, intrinsic explainability) a model is inherently
understandable and interpretable, instead of relying on a post-hoc model for
explanations (_e.g.,_(Pan et al., 2020) fails on this).

In this paper, we propose a neat yet effective Explainable Collaborative
Filtering (ECF) framework with the goal of accurate and explainable
recommendations, while satisfying all three properties. At the core of ECF is
mining various taste clusters. We assume that items have some explicit
features such as tags or aspects (hereinafter we will use tags for
unification). A taste cluster is a group of items which are not only similar
in users’ latent interest space, but also explicitly share some common tags,
so that the overlapping tags can be selected as descriptive interpretation for
the taste cluster. Both users and items are mapped to multiple taste clusters.
On the one hand, item recommendations can be made by measuring the coherence
between users’ and items’ taste cluster affiliations; on the other hand, the
descriptive tags interpret what determines users’ preference towards items. We
also design a new set of quantitative metrics to evaluate the quality of ECF
beyond the accuracy, covering: (1) In-cluster item coverage; (2) Tag
utilization; (3) Silhouette; (4) Tag informativeness, with the goal of
discovering the discriminability of taste clusters as well as the exactitude,
diversity, and uniqueness of clusters interpretability in a holistic manner.
The ECF framework has many more application potentials beyond the user-item
prediction and interpretation. For example, the affiliation of users to taste
clusters can be used for user profiling, empowering web-scale services like
ads audience targeting and audience extension. The affiliation of items to
taste clusters can help missing tags discover for items, automatic item topic
generation and theme-wise item recommendations (such as the playlist
recommendation in online music service).

However, the implementation and optimization of ECF is a non-trivial task.
Main challenges include: (1) how to construct an end-to-end model, so that
taste cluster generation, tags selection, user- and item-cluster affiliations
can be optimized jointly; (2) how to achieve good performance on both accuracy
and explainability simultaneously, instead of sacrificing one for the other;
(3) how to guarantee the diversity of generated taste clusters. To this end,
we design an embedding-based model to generate taste clusters with
discriminative tags and establish the sparse mapping between users/items and
clusters. We further devise the forest mechanism for ECF, which can not only
substantially lift the accuracy, but also provides a diverse set of taste
clusters. For each targeting merit (such as exactitude, diversity, and
uniqueness of clusters interpretability) we design a corresponding objective
function, so that the whole model can be trained in an end-to-end manner.

In summary, our main contributions include:

  * •

We present a neat yet effective explainable collaborative filtering framework,
called ECF 111The codes are available at https://github.com/zealscott/ECF.,
which leverages interpretable taste clusters and sparse user- and item-cluster
affiliations for recommendation in a flexible, coherent, and self-explainable
way.

  * •

We propose an optimization method for ECF to learn high quality taste clusters
with informative tags and sparse affiliations simultaneously in an end-to-end
manner.

  * •

We design a new set of quantitative metrics to evaluate the explainability
quality of taste clusters comprehensively.

  * •

We conduct extensive experiments on three real-world datasets with various
state-of-the-art methods to demonstrate the effectiveness of ECF.

##  2\. Methodologies

In this section, we first outlines the task definition for explainable
recommendations and introduces the framework of Explainable Collaborative
Filtering (ECF). We then delve into the methodology of the end-to-end
optimization process for training ECF and establish a comprehensive set of
metrics to quantitatively evaluate the effectiveness of explainability.

###  2.1. Problem Formulation

User-item Interactions and Item Tags. We focus on the implicit feedback
(Rendle et al., 2009) in recommendation, where a user’s preferences are
inferred through implicit signals such as clicks or play actions. Let
$\mathcal{U}$ be a set of users and $\mathcal{I}$ a set of items. Let
$\textbf{Y}\in\mathbb{R}^{|\mathcal{U}|\times|\mathcal{I}|}$ as the user-item
interaction matrix, where $y_{ui}=1$ means that there is an interaction
between user $u$ and item $i$, otherwise $y_{ui}=0$. Besides, we assume there
is a set of tags $\mathcal{T}$ for items, and each item $i$ has a subset of
tags $\mathcal{T}_{i}\subset\mathcal{T}$ to describe its genre and features.

Task Description. Given the interactions data Y and items’ tags $\mathcal{T}$,
the task of explainable recommendation is to (1) predict how likely user $u$
adopts item $i$, and (2) explain what determines the recommendation of item
$i$ to user $u$ with the descriptions from $\mathcal{T}$.

###  2.2. The Proposed ECF framework

We propose an ECF framework for explainable recommendations with collaborative
filtering. The core of ECF is mining various taste clusters which represent
specific interest patterns. We first give the definition of taste clusters and
show how to leverage them for recommendation and explanation. Then we detail
the proposed method to generate sparse affiliations between users/items and
taste clusters. The pseudocode of ECF is shown in the Appendix A.1.

A Taste Cluster is a group of items $c=\\{i_{1},i_{2},...,i_{c}\\}$ that
uncovers a certain type of underlying interest for users and can be easily
identified through shared tags among the items within the cluster. So, each
taste cluster is associated with a set of tags
$\mathcal{T}_{c}=\\{t_{1},t_{2},...,t_{k}\\}$, which are derived from
corresponding item sets and acts as the descriptive interpretation for the
cluster.

Assuming there is a set of taste clusters $\mathcal{C}=\\{c\\}$, we map
users/items to these taste clusters with sparse affiliation matrix. To be
specific, let $\textbf{A}\in\mathbb{R}^{|\mathcal{U}|\times|\mathcal{C}|}$ and
$\textbf{X}\in\mathbb{R}^{|\mathcal{I}|\times|\mathcal{C}|}$ be the
affiliation matrices between users/items and taste clusters, respectively.
Each entry $a_{uc}$ in A denotes the preference degree of user $u$ to taste
cluster $c$, and each entry $x_{ic}$ denotes the relatedness between item $i$
and taste cluster $c$. To enhance the clarity and persuasiveness of the
explanation, the affiliation matrix should be kept sparse, meaning only the
most pertinent entries have non-zero values, making it possible to clearly
identify a user’s preferences and item affiliations using only a few taste
clusters.

After that, both users and items are mapped to multiple taste clusters, and
ECF can make user-item recommendation and explanation with taste clusters and
affiliations as follows.

Item recommendation. We assume that a user’s decision about whether to make a
purchase/click is based on her preference with taste clusters, as well as the
item’s relatedness with them. Thus, the prediction score of user $u$ and item
$i$ can be calculated by multiplying their affiliations:

(1)
$\displaystyle\hat{y}_{ui}=\mathrm{sparse\\_dot}(\textbf{a}_{u},\textbf{x}_{i}),$

where $\mathrm{sparse\\_dot}(\cdot)$ denotes sparse dot product for
$\textbf{a}_{u}$ and $\textbf{x}_{i}$.

Personalized explanation. For each prediction $\hat{y}_{ui}$, ECF is able to
generate explanation by measuring the coherence between users’ and items’
taste cluster affiliations. Specifically, the overlapped taste clusters are
first derived from affiliation matrix:

(2) $\displaystyle\mathcal{C}_{ui}=S(\textbf{a}_{u})\cap S(\textbf{x}_{i}),$

where $S(\cdot)$ is an index selector to collect corresponding clusters where
the affiliation between users/items and taste clusters exists, and
$\mathcal{C}_{ui}$ denotes the set of overlapped taste clusters for user $u$
and item $i$. Thus, the descriptive tags of taste clusters in
$\mathcal{C}_{ui}$ are used to interpret what determines user $u$ preference
toward item $i$. Moreover, importance score $w_{ui}^{c}$ is introduced to
quantify the contribution of each taste cluster in $\mathcal{C}_{ui}$:

(3) $\displaystyle w_{ui}^{c}=a_{uc}\times x_{ic}.$

Therefore, ECF is able to explain the prediction decision by using the
descriptive tags of overlapped taste clusters $\mathcal{C}_{ui}$ and their
corresponding importance scores $w_{ui}^{c}$. Due to the sparsity of
affiliation matrix, the size of overlapped taste clusters is small, so that we
could easily derive the readable decision logic of ECF by investigating only a
few taste clusters. And the final explanation results can be constructed by
existing methods (_e.g.,_ template-based explanation (Zhang et al., 2014)) or
explanation paths from user to taste clusters and items (demonstrated in
Section 3.5.2).

Despite the simplicity, it is still unclear how to obtain the desired taste
clusters and sparse affiliation matrix. This is a non-trivial task since
performing clustering algorithm (_e.g.,_ K-means) for items or blindly
collecting items with same tags would fail to encode both user interest and
item profiles simultaneously (see Section 3.3 for comparison). Besides,
directly learning the affiliation matrix from data is unable to train due to
its sparsity nature. Instead, we represent items and taste clusters as
embeddings, and measure their affiliations with cosine similarity:

(4) $\displaystyle\tilde{x}_{ic}=\cos(\textbf{v}_{i},\textbf{h}_{c}),$

where $\textbf{v}\in\mathbb{R}^{d}$ and $\textbf{h}\in\mathbb{R}^{d}$ are the
embeddings of items and clusters, and $d$ is the embedding size. To clearly
identify the belongings between items and clusters, we only consider the
Top-$m$ clusters for each item:

(7) $\displaystyle m_{ic}=\left\\{\begin{array}[]{cl}1&\text{ if
}c\in\mathop{\mathrm{argTop{m}}}(\tilde{\textbf{x}}_{i})\\\ 0&\text{ otherwise
}\end{array}\right.$ (8)
$\displaystyle\textbf{x}_{i}=\sigma(\tilde{\textbf{x}}_{i})\odot\textbf{m}_{i},$

where $\odot$ denotes Hadamard product, $\sigma(\cdot)$ is the sigmoid
function. In the above equations, we first make Top-$m$ selection for each
item according to the similarity scores, and apply the sigmoid function to
indicate the relatedness of items and clusters with none-zero probabilities,
then use a binary mask to filter other less relevant clusters and obtain the
final item-cluster affiliation matrix X. However, due to the non-
differentiability and discrete nature of $\mathop{\mathrm{argTop{}}}$
operation, the computation is intractable thus cannot be optimized with
gradients. Therefore, we relax it by tempered softmax:

(9) $\displaystyle
m_{ic}\approx\tilde{m}_{ic}=\frac{\exp({\cos(\textbf{v}_{i},\textbf{h}_{c})/T})}{\sum\nolimits_{c}\exp(\cos(\textbf{v}_{i},\textbf{h}_{c})/T)},$

where $T$ is a hyperparameter called temperature, which controls the entropy
of the distribution. Thus, for back-propagation, the continuous relaxation
$\tilde{m}_{ic}$ is used to approximate $m_{ic}$. However, when calculating
the probability of taste clusters, we should directly use $m_{ic}$ instead of
$\tilde{m}_{ic}$, to be consistent with the real affiliation relationship. To
close the gap between forward pass and backward pass, we follow a similar idea
to reparameterized trick (Jang et al., 2017; Zhang and Li, 2022), and rewrite
$m_{ic}$ as follows:

(10)
$\displaystyle\hat{m}_{ic}=\tilde{m}_{ic}+\mathrm{detach\\_gradient}(m_{ic}-\tilde{m}_{ic}),$

where the detach_gradient will prevent the gradient from back-propagating
through it. In the forward pass, detach_gradient has no effect, thus the
affiliated clusters can be directly computed by $\mathop{\mathrm{argTop{}}}$
operation. In the backward pass, detach_gradient takes effect, so
$\nabla_{\hat{m}_{ic}}\mathbf{\mathop{\mathcal{L}}}=\nabla_{\tilde{m}_{ic}}\mathbf{\mathop{\mathcal{L}}}$.
So the whole computation is fully differentiable and can be smoothly optimized
with the model.

We use the same mechanism to obtain the affiliations between users and
clusters. Specifically, the user-cluster similarity matrix can be computed as
$\tilde{\textbf{A}}=\textbf{Y}\times\tilde{\textbf{X}}$, where Y is the user-
item interaction matrix. Then, we also force each user to connect with Top-$n$
taste clusters to derive the user-cluster affiliation matrix A.

Forest Mechanism. Preference sparsification with taste clusters is an
approximation of latent factor-based collaborative filtering. As a result, ECF
inevitably suffers from sub-optimal performance and limited diversity.To
overcome these two challenges, we introduce a straightforward yet impactful
ensemble approach that improves the expressiveness of taste clusters and
preserves its interpretability. Specifically, for each individual ECF model,
we randomly select $|\mathcal{C}|$ items as the initial taste clusters and use
different random seeds for model training. Then we train $F$ different ECF
instances to form the final ECF model, and the final prediction is based on
the summation of all $F$ models. We find this simple random mechanism can
boost the performance of ECF and provide a comprehensive explanation for
predictions (the impact of different number of models is discussed in Section
3.4.3).

###  2.3. Optimization of ECF

Next, we introduce an end-to-end optimization method to train ECF, with the
aim of constraining the taste cluster from different perspectives to meet its
definition. First, since taste clusters can reveal both the user’s interests
and the similarity between items, it is reasonable to directly predict user
preference for an item through their common taste clusters (as described in
Equation (1)). Therefore, the cluster-based predictions can be optimized with
BPR loss (Rendle et al., 2009):

(11)
$\displaystyle\mathbf{\mathop{\mathcal{L}}}_{\text{CS}}=\sum\nolimits_{(u,i,j)\in\mathcal{O}}-\ln\sigma(\hat{y}_{ui}-\hat{y}_{uj}),$

where $\mathcal{O}=\\{(u,i,j)|y_{ui}=1,y_{uj}=0\\}$ denotes the training set
of user-item interactions. Then we consider the informativeness of tags. We
first calculate the tag distribution of taste clusters:

(12) $\displaystyle\tilde{\textbf{D}}=\textbf{X}^{\top}\textbf{E},$

where $\textbf{E}\in\mathbb{R}^{|\mathcal{I}|\times|\mathcal{T}|}$ is the
multi-hot matrix where each entry $e_{it}$ denotes whether item $i$ has the
tag $t$, and $\tilde{\textbf{D}}$ represents the tag frequency of each taste
cluster. Intuitively, we can directly select the most frequent tags as the
description of taste clusters. However, this naive approach would result in
the indistinguishability between different clusters, since some tags are
commonly shared by most items, and they would dominate the tag distribution
across different taste clusters. Take the game genres at Xbox dataset as an
example. Most of the games are online and allow for mutiplayer, thus selecting
the “Multiplayer-Online” tag fails to provide informative description for
taste clusters. To tackle this problem, we first reweight each tag according
to its frequency of occurrence in items, and then compute the weighted
distribution:

(13) $\displaystyle
d_{ct}=\tilde{d}_{ct}\times\log(\frac{N}{f_{t}+\epsilon}),$

where $N$ is the number of items, $f_{t}$ is the frequency of tag $t$ across
all items, and $\epsilon$ is a small fraction (we set it as $10^{-6}$) to
avoid numerical overflow. Thus, the above equation considers both tag
frequency and items’ affiliations for tag informativeness: the more frequently
the distinctive tag appears, the more informative it is for interpreting the
taste cluster.

To improve the understanding of taste clusters, we advocate for an appropriate
number of tags, not too few or too many. An excessive or inadequate number of
tags makes it difficult to identify users’ true interests and results in a
complex or abstract interpretation of the taste cluster.” To achieve that, we
first normalize their frequencies as:

(14)
$\displaystyle\beta_{ct}=\frac{\exp(d_{ct}/\tau)}{\sum\nolimits_{j\in\mathcal{T}}\exp(d_{cj}/\tau)},$

where $\tau$ is the is the temperature hyperparameter. At low temperatures,
the distribution sharpens, causing only the tag with the highest score to
stand out. As the temperature increases, the distribution becomes more even
and the distinctiveness between tags will decrease. Then, we consider
maximizing the likelihood of the probabilities of Top-$P$ tags so that the
taste clusters can be easily interpreted by those tags:

(15)
$\displaystyle\mathbf{\mathop{\mathcal{L}}}_{\text{TS}}=\sum\nolimits_{c\in\mathcal{C}}\sum\nolimits_{t\in\mathop{\mathrm{argTop{P}}}(\beta_{c})}-\log\beta_{ct},$

where $\mathcal{C}$ denotes the set of taste clusters. We fix the number of
tags $P=4$ for all experiments, since it achieves a good balance between
informativeness and readability.

Moreover, different taste clusters should contain different items and reveal
different user preferences, so that the latent interest space could be better
preserved. Hence, for better model capacity and diversity, we encourage the
embeddings of taste clusters to differ from each other’s. There are many
methods for independence modeling, such as distance correlation (Székely et
al., 2007), orthogonality (Liu et al., 2019b), and mutual information
(Belghazi et al., 2018; Wang et al., 2021). Here we opt for mutual information
for all experiments due to its simplicity and effectiveness:

(16)
$\displaystyle\mathbf{\mathop{\mathcal{L}}}_{\text{IND}}=\sum\nolimits_{c\in
C}-\log\frac{\exp(s(\textbf{h}_{c},\textbf{h}_{c}))}{{\sum\nolimits_{c^{\prime}\in
C}\exp(s(\textbf{h}_{c},\textbf{h}_{c^{\prime}}))}},$

where $s(\cdot)$ is the similarity function to measure the associations of any
two taste clusters, which is set as cosine function here. Finally, we consider
learning taste clusters by putting the above objective functions together:
$\mathbf{\mathop{\mathcal{L}}}_{\text{TC}}=\mathbf{\mathop{\mathcal{L}}}_{\text{CS}}+\mathbf{\mathop{\mathcal{L}}}_{\text{TS}}+\mathbf{\mathop{\mathcal{L}}}_{\text{IND}}$.
For simplicity we do not need to tune any weighting coefficients for each
loss. However, due to the $\mathop{\mathrm{argTop{}}}$ operations in
affiliation selections, the supervised signals are sparse and hard to
converge. Thus, we add auxiliary supervised signals from user-item
predictions:

(17)
$\displaystyle\mathbf{\mathop{\mathcal{L}}}_{\text{CF}}=\sum\nolimits_{(u,i,j)\in\mathcal{O}}-\ln\sigma(\textbf{u}_{u}^{\top}\textbf{v}_{i}-\textbf{u}_{u}^{\top}\textbf{v}_{j}),$

where $\textbf{u}_{u}$ denotes the embeddings of user $u$. We choose inner
product of embeddings to measure the similarity between users and items for
simplicity, but more sophisticated embedding-based models (_e.g.,_ LightGCN
(He et al., 2020)) can also be applied, which will be discussed in Section
3.4.4. By combing the taste clusters loss and collaborative loss, we minimize
the following objective function to learn the model parameters:

(18)
$\displaystyle\mathbf{\mathop{\mathcal{L}}}_{\text{ECF}}=\mathbf{\mathop{\mathcal{L}}}_{\text{TC}}+\lambda\mathbf{\mathop{\mathcal{L}}}_{\text{CF}},$

where $\lambda$ a hyperparameter to control the impact of auxiliary
collaborative signals.

###  2.4. New Metrics for Explainability

Here we aim to design a holistic set of quantitative metrics to qualify the
effectiveness of explanation _w.r.t._ taste clusters:

  * •

In-cluster item coverage denotes the average proportion of items in a taste
cluster that the selected tags can cover. With a slight abuse of notation, we
use $\mathcal{T}_{i}$ to denote the tags of item $i$ and $\mathcal{T}_{c}$ to
denote the tags of cluster $c$:

(19)
$\displaystyle\text{Cov.}=\frac{1}{|\mathcal{C}|}\sum\nolimits_{c\in\mathcal{C}}\sum\nolimits_{i\in
c}\frac{\mathbbm{1}(\left|\mathcal{T}_{i}\cap\mathcal{T}_{c}\right|)}{|c|},$

where $\mathbbm{1}(x)=1$ if and only if $x>0$, otherwise $0$. When the item
coverage ratio is high, we deem that these tags can be properly used as the
descriptive interpretation for the taste cluster.

  * •

Tag utilization represents how many unique tags are used for interpreting
taste clusters:

(20)
$\displaystyle\text{Util.}=\frac{1}{|\mathcal{T}|}\bigcup_{c\in\mathcal{C}}\mathcal{T}_{c},$

where we union all the selected tags from each taste cluster, and a higher tag
utilization indicates a more diverse interpretation of interest patterns.

  * •

Silhouette (Rousseeuw, 1987) is a clustering metric which measures the
similarity difference between intra-cluster and inter-cluster items:

(21)
$\displaystyle\text{Sil.}=\frac{1}{|\mathcal{C}|^{2}}\sum\nolimits_{c_{1}\in\mathcal{C}}\sum\nolimits_{c_{2}\in\mathcal{C}}\frac{b(c_{1},c_{2})-a(c_{1})}{\max\\{a(c_{1}),b(c_{1},c_{2})\\}},$

where $b(c_{1},c_{2})$ is the mean cosine similarity between all disjoint
items in $c_{1}$ and $c_{2}$, and $a(c_{1})$ is the mean cosine similarity of
items in taste cluster $c_{1}$. The high silhouette indicates the items are
similar in the same taste clusters.

  * •

Informativeness measures the distinctiveness of selected tags to represent the
items in the taste cluster:

(22)
$\displaystyle\text{Info.}=\frac{1}{|\mathcal{C}|}\sum\nolimits_{c_{i}\in\mathcal{C}}\frac{|R(\mathcal{T}_{c})\cap
c|}{|c|},$

where $R(\mathcal{T}_{c})$ is an post-hoc discriminator that predicts the most
likely top $|c|$ items given the tags of taste cluster $c$ . We detail the
implementation of the function $R(\cdot)$ in Appendix A.9. A greater
informativeness score implies that those tags more accurately characterize the
items within the taste clusters.

The above four metrics measure the quality of taste clusters from different
aspects. Since ECF depends on taste clusters to make recommendation and
explanation, these metrics can be also viewed as the evaluation of
explanation. We further provide an overall metric by normalizing each metric
with a random approach. In addition, since explainability is a human notion
and cannot be fully evaluated computationally without input from human users,
we also included two user studies as complementary to the metrics, which will
be detailed in Section 3.3.

###  2.5. Complexity Analysis

####  2.5.1. Model Size

We analyze the size of ECF from both training and inference perspectives.
During the training, the model parameters of single ECF consist of (1) ID
embedding of users and items
$\\{\textbf{U},\textbf{V}|\textbf{U}\in\mathbb{R}^{|\mathcal{U}|\times
d},\textbf{V}\in\mathbb{R}^{|\mathcal{I}|\times d}\\}$, which are also used by
all embedding-based methods; and (2) ID embedding of taste clusters
$\\{\textbf{H}|\textbf{H}\in\mathbb{R}^{|\mathcal{C}|\times d}\\}$. We utilize
$F$ different ECF models for training, so that the overall parameters are $F$
times of the single model parameters. During the inference, different from
other embedding-based methods, ECF only needs the sparse affiliations between
users/items and clusters for prediction, and the parameters are
$F(m|\mathcal{I}|+n|\mathcal{U}|)$, where $m$ and $n$ are the number of
affiliations. The size of ECF is similar or even less than typical embedding-
based methods (_i.e.,_ MF need $d(|\mathcal{I}|+|\mathcal{U}|)$ parameters)
when selected affiliations $m,n\ll d$.

####  2.5.2. Time Complexity

Time cost of ECF mainly comes from the taste clusters learning. For
collaborative similarity learning of taste clusters, the computational
complexity of calculating the affiliations is
$O(|\mathcal{C}|(d|\mathcal{I}|+|\textbf{Y}|)$, where $|\mathcal{C}|$,
$|\mathcal{I}|$, $|\textbf{Y}|$ and $d$ denote the number of taste clusters,
items, interactions, and the embedding size. For tag similarity learning, the
computational complexity of tag distribution is
$O(|\mathcal{C}||\mathcal{I}||\bar{t}|)$, where $|\bar{t}|$ is the average
number of tags that items have. As for independence modeling, the cost of
mutual information is $O(d|\mathcal{C}|^{2})$. Besides, computing the
auxiliary collaborative signals would cost $O(d|\mathcal{I}||\mathcal{U}|)$.
Thus, the time complexity of the whole training epoch is
$O(|\mathcal{C}||\textbf{Y}|+d|\mathcal{I}||\mathcal{U}|)$ when the number of
taste clusters is far more less than the number of users/items. Under the same
experimental settings (_i.e.,_ same embeddings size and same number of tags),
ECF has comparable complexity to EFM and AMCF, two representative explainable
methods.

##  3\. Experiments

We design experiments to answer the following research questions: (1) How does
ECF perform in accuracy, compared with related competitive methods? (2) What
is the quality of ECF’s interpretability? (3) What is the impact of various
components and hyperparameters on the effectiveness of ECF? (4) What do the
generated taste clusters resemble and what are the potential uses for ECF?

###  3.1. Experimental Settings

Table 1. Statistics of the datasets used in our experiments.

Dataset | #Users | #Items | #Interactions | #Tags
---|---|---|---|---
Xbox | 465,258 | 330 | 6,240,251 | 115
MovieLens | 6,033 | 3,378 | 836,434 | 18
Last-FM | 53,486 | 2,062 | 2,228,949 | 54

We use three real-world datasets for experiments: Xbox, MovieLens and Last-FM,
which vary in domain, size, tag numbers, and sparsity. The Xbox dataset is
provided by Microsoft Gaming and collected from the GamePass scenario
222https://www.xbox.com/en-US/xbox-game-pass. GamePass is a popular
membership-based service offered by Xbox, with which users can freely play a
few hundreds of high-quality games (that is why in Table 1 Xbox has only 330
items). MovieLens is a widely used dataset which contains user rating history
and the types of movies, we follow (Pan et al., 2020) to get 18 neat tags for
movie description. Last-FM is a public music listening dataset. We use the
official APIs 333https://www.last.fm/api of Last.fm to obtain the tags for
each track and discard rare tags which are annotated by less than 50 people.
Besides, to reduce noise, we adopt the 10-core setting, _i.e.,_ retaining
users and items with at least ten interactions. We use the same data partition
with previous study (Pan et al., 2020) for comparison (i.e., the proportions
of training, validation, and testing set are 80%, 10%, and 10% for all
datasets). Table 1 summarizes the basic statistics of the three datasets.

###  3.2. Evaluation of Accuracy (RQ1)

####  3.2.1. Baselines

We compare ECF with two groups of models:

  * •

MF (Rendle et al., 2009), NCF (He et al., 2017), CDAE (Wu et al., 2016) and
LightGCN (He et al., 2020) are four strong and representative embedding-based
CF methods which learn users’ hidden preference from interactions. But they
suffer from poor explainability.

  * •

EFM (Zhang et al., 2014) and AMCF (Pan et al., 2020) are two strong
explainable recommendation models, but they fail to satisfy all three
explanation merits. We adapt EFM model slightly to make it fit for our
scenario (see Appendix A.2 for details).

We also add the single model version of ECF for variant comparison, denoted as
“ECFsingle”.

####  3.2.2. Evaluation Metrics

We adopt two widely used evaluation protocols (Rendle et al., 2009; Zhang et
al., 2014; Wang et al., 2021) for top-$K$ recommendation: Recall@K and NDCG@K.
Hyper-parameters are reported in Appendix A.3.

####  3.2.3. Performance Comparison

The performance _w.r.t._ Recall@20 and NDCG@20 is reported in Table 2. More
experiments with different $K$ can be found in Appendix A.4. In comparison,
embedding-based methods achieve competitive performance on all datasets.
LightGCN outperforms all other baselines on MovieLens and Last-FM datasets, we
contribute this to the ability of capturing the high-order user-item
relationship in bipartite graph. On the other hand, explainable methods - EFM
and AMCF - only show a slight improvement over MF. As for the ECFsingle, we
can see the performance drops compared with MF, due to the sparsity design of
taste clusters affiliations for interpretability. However, the forest
mechanism in ECF makes up for its shortcomings in accuracy and outperforms all
the baselines by a large margin (including the forest version of MF, see
Appendix A.4 for details). This demonstrates that ECF is not taking a trade-
off between accuracy and interpretability, instead, it can achieve excellent
accuracy performance while providing interpretability.

Table 2. Top-$20$ recommendation results. “${\dagger}$” indicates the
improvement of the ECF over the baseline is significant at the level of 0.05.

| Xbox | MovieLens | Last-FM
---|---|---|---
Recall | NDCG | Recall | NDCG | Recall | NDCG
MF | 0.5048 | 0.3268 | 0.1603 | 0.2416 | 0.0658 | 0.0506
NCF | 0.4746 | 0.2931 | 0.1606 | 0.2406 | 0.0618 | 0.0401
CDAE | 0.5192 | 0.3286 | 0.1627 | 0.2499 | 0.0589 | 0.0534
LightGCN | 0.4933 | 0.3261 | 0.1854 | 0.2698 | 0.0788 | 0.0675
EFM | 0.5070 | 0.3312 | 0.1702 | 0.2525 | 0.0703 | 0.0549
AMCF | 0.5036 | 0.3217 | 0.1604 | 0.2405 | 0.0675 | 0.0516
ECFsingle | 0.4231 | 0.2331 | 0.1068 | 0.1501 | 0.0467 | 0.0380
ECF | 0.5922† | 0.3721† | 0.2124† | 0.2903† | 0.0851† | 0.0773†

###  3.3. Evaluation of Explainability (RQ2)

Then we evaluate the explainability of ECF. As elaborated in Section 2.4, we
utilize four metrics to evaluate the explainability of our model: in-cluster
item coverage, tag utilization, silhouette and informativeness. Since ECF is a
cluster-based CF method, for comparison, we use three strong competitors to
construct the clusters from different perspectives as baselines. Specifically,
TagCluster is a tag-oriented method which groups items with the same tags into
clusters; K-means is a similarity-oriented method which utilizes item
embedding from MF to perform K-means algorithm; Random is a baseline method by
randomly selecting items into clusters. The detailed implementation of
baselines is reported in Appendix A.5.

To have an overall understanding of the explainability, we introduce an
aggregated metric denoted as Overall in Table 3. To overcome the scale
inconsistency issue in different metrics, we first normalize each metric by
calculating the relative gain over the Random baseline, then sum up the
normalized four scores as the Overall metric. In terms of the overall metric,
ECF outperforms all competitors by a large margin. Specifically, all the
baselines can only preserve a certain aspect while ignoring the rest three
aspects. For instance, since TagCluster only considers the explicit tags for
clustering, it fails to preserve the collaborative filtering-related
similarity in the cluster. Furthermore, traditional clustering methods like
K-means suffer from low coverage ratio and poor informativeness, revealing
their inability to form significant taste clusters with descriptive tags. In
contrast, ECF considers all relevant factors, thus preventing significant
shortcomings in any one metric.

Besides, we have included two user studies on the LastFM dataset as
complementary to Table 3. These studies involved 30 volunteers evaluating the
explainability of both taste clusters and user-item recommendations.
Volunteers were asked to participate two tasks as human evaluation. The task
description and results are detailed in Appendix A.6, and ECF also achieved
the best among baselines from human judgements.

Table 3. Explainability Evaluation of ECF.

Method | Cov. | Util. | Sil. | Info. | Overall
---|---|---|---|---|---
Xbox
ECF | 0.8002 | 0.7052 | 0.2604 | 0.3162 | 1.7463
TagCluster | 0.9950 | 0.2878 | -0.1788 | 0.1579 | 0.9262
K-means | 0.5710 | 0.3739 | 0.4286 | 0.0185 | 1.0563
Random | 0.5396 | 0.1450 | -0.3614 | 0.0125 | 0.0000
MovieLens
ECF | 0.7992 | 0.7778 | 0.1964 | 0.3131 | 1.5651
TagCluster | 0.991 | 0.5259 | -0.2573 | 0.1517 | 0.8898
K-means | 0.6877 | 0.4478 | 0.3265 | 0.0168 | 0.9573
Random | 0.5933 | 0.3672 | -0.4452 | 0.0061 | 0.0000
Last-FM
ECF | 0.7648 | 0.6259 | 0.1584 | 0.2996 | 1.5352
TagCluster | 0.9880 | 0.3703 | -0.2511 | 0.1206 | 0.9143
K-means | 0.5667 | 0.4841 | 0.3197 | 0.0182 | 1.0752
Random | 0.5385 | 0.2275 | -0.4673 | 0.0148 | 0.0000

Figure 1. Impact of affiliation number on items (Top-$m$) and on users
(Top-$n$). Figure 2. 5 real examples of learned taste clusters on Last-FM
dataset.

###  3.4. Study of ECF (RQ3)

####  3.4.1. Impact of Top-$m$ and Top-$n$

As described in Section 2.2, we use Top-$m$ and Top-$n$ to select the most
relevant taste clusters for items/users. The experimental results of different
$m$ and $n$ on Xbox and Last-FM dataset are reported in Figure 1, while the
results on MovieLens dataset is omitted due to similar trend and limited
space. We observe that the recommendation performance boosts dramatically when
$m$ and $n$ increase, especially from 10 to 20. This is because when the
affiliations between taste clusters and users/items are sparse, it is unable
to model the complex and latent users’ preference, as well as the multi-
faceted semantics of items. However, large $m$ and $n$ would make the
explanation results hard to understand because of the excessive number of
reachable paths between users, taste clusters and items. Therefore, to balance
the readability and accuracy, we set $m$ and $n$ to 20 for all datasets.

Figure 3. Hyperparameter study on Last-FM dataset. Left: impact of $\lambda$
in Eq.(18). Right: impact of the forest mechanism.

####  3.4.2. Impact of $\lambda$

We then verify the effectiveness of the auxiliary collaborative signals. The
results on Last-FM dataset is illustrated in the left of Figure 3, and the
results on other two datasets are reported in Appendix A.8. We observe that a
small $\lambda$ value results in a significant decline in the performance of
ECF, due to the insufficient supervised signals for the learning of taste
clusters. On the other hand, when $\lambda$ exceeds 0.6, the improvement is
minimal, indicating that ECF can be optimized with adequate collaborative
signals. Thus, we fix $\lambda$ to 0.6 for all of our experiments.

####  3.4.3. Impact of Forest Mechanism

To analyze the effect of the ensemble version of ECF, we gradually increase
the size of forest, and the performance results are reported in the right of
Figure 3. We find that there is a notable performance gain of ECF, compared
with the single ECF model. We contribute the improvement to the holistic
modeling of users’ latent interest space with diverse taste clusters. Besides,
we also find that the performance of ECF is even better than the forest
version of MF (see Figure 3 and Appendix A1 for details), which indicates the
effectiveness of taste cluster learning.

####  3.4.4. Flexibility of ECF

Since the ECF framework only relies on embeddings to learn explainable taste
clusters, it can be viewed as a model-independent explainable paradigm, which
is easily applied with other popular embedding-based methods. Thus, we also
incorporate ECF with LightGCN (He et al., 2020), a competitive graph-based
embedding method, to investigate its flexibility. The results in Figure A.10
indicate that the performance and explainability of ECF would also benefit
from more complex embedding-based methods, which demonstrates the superiority
and universality of ECF (see Appendix A.10 for details).

###  3.5. Case Study and Applications (RQ4)

In this section, we present examples from the Last-FM dataset to provide an
intuitive understanding of taste clusters and demonstrate the explainability
of ECF. Additionally, we showcase the versatility of ECF by highlighting
useful scenarios beyond item recommendations.

####  3.5.1. Learned Taste Clusters

We first illustrate the generated five taste clusters in Figure 2. Each taste
cluster is interpreted with four tags, which are the best description of the
tracks within. For instance, all the tracks in taste cluster $c_{3}$ are
soundtrack, while some are ambient music (_e.g.,_ “Hand Covers Bruise”), and
some are tagged with “alternative” (_e.g.,_ “Only Hope”). Besides, each taste
cluster is able to explicitly represent certain users’ preference. Taking the
taste cluster $c_{2}$ as an example, users who have a high affiliation score
with it tend to favor rap and hip-pop music, especially these tracks that are
accompanied with dancing. Moreover, different taste clusters have different
tags (_e.g.,_ pop music in $c_{1}$ and folk music in $c_{5}$), indicating the
diversity of users’ preference.

As for the relationship between taste clusters and items, we find taste
clusters have the ability to serve as complementary information to the tagging
of items, which we call tag discovery. For instance, folk song “Bubbly” in
taste cluster $c_{5}$ is tagged with “female_vocalists—pop—folk—acoustic—love”
by Last.fm. Thus, we can suspect whether “Bubbly” has the missing tag
“singer_songwriter” since other tags in the taste cluster $c_{5}$ (_i.e.,_
“folk—acoustic—pop”) are perfectly to describe the track. In fact, the singer
of the song, Colbie Caillat, is also a songwriter who wrote the song.
Therefore, taste clusters can be useful for automatic tag completion.

Figure 4. Explanations of the recommendation of user $u_{71}$ to track
$i_{77414}$ (“Bubbly”) on Last-FM dataset. $c$ denotes the taste cluster which
shows in Figure 2. The tags of the track $i_{77414}$ are
“female_vocalists—pop—folk—acoustic—love”.

####  3.5.2. Recommendation Explanation

Next, we demonstrate the explanation ability of ECF. Taking the recommendation
of user $u_{71}$ to track $i_{77414}$ (“Bubbly”) as an example, Figure 4 shows
the listening history of $u_{71}$ as well as the recommendation logic of ECF,
where we have the following observations.

First, ECF maps users as well as items with their corresponding taste
clusters. For user $u_{71}$, since he/she has listened different kinds of
songs from soundtrack to pop and soul music, three different taste clusters
(_i.e.,_ $c_{1}$, $c_{3}$ and $c_{4}$.) have been affiliated to reveal his
interest. Similarly, track $i_{77414}$ is also connected with three taste
clusters (_i.e.,_ $c_{1}$, $c_{4}$ and $c_{5}$), which is able to describe the
song from different aspects. Besides, the weights of affiliation matrix
indicate the relatedness between users/items with taste clusters.

Second, to recommend track $i_{77414}$ to user $u_{71}$, ECF first finds their
interactions of taste clusters according to the affiliations (_i.e.,_ $c_{1}$,
$c_{4}$), which are depicted as red circles in Figure 4. These taste clusters
serve as a bridge to explicitly connect user’s preference and items’
semantics. Then two explanation paths ($i_{71}\rightarrow c_{1}\rightarrow
i_{77414}$ and $i_{71}\rightarrow c_{4}\rightarrow i_{77414}$) are constructed
for recommendation. For each path, we multiply their affiliation weight to
generate the importance score of the taste cluster, according to Equation (3).
At last, by summarizing all the scores over intersected taste clusters, we can
calculate the final prediction score, as well as the explanation paths from
user $u_{71}$ to $i_{77414}$.

####  3.5.3. Taste Cluster Recommendation

Here we propose a new recommendation scenario, called taste cluster
recommendation, which means users are recommended with a bundle of similar
items, and these items can be described with few tags (or features). We find
this task is ubiquitous in real-world applications, like playlist
recommendation in Spotify (Jacobson et al., 2016). Current solutions to tackle
this problem typically rely on manual selection by editors to guarantee the
selected items are similar in tags (or other explicit features). However, this
approach suffers from tedious selection process and poor personality. Our
method could be a substitution for labor selections by learning taste clusters
in an end-to-end manner. To be specific, since each learned taste cluster is a
collection of items with descriptive tags, it can be naturally viewed as a
playlist or game set. Thus, we can directly recommend taste clusters to users
according to their affiliation weights. Taking user $u_{71}$ in Figure 4 as an
example, ECF could recommend him/her with a pop song playlist which is sung by
female artists, since he/she used to listen lots of pop music by female
artists, like Colbie Caillat, Adele and Celine Dion.

####  3.5.4. User Profiling

The user-cluster affiliations discovered by ECF can also be used as user
profiles directly. Take Figure 4 for example, ECF assigns user $u_{71}$ to
three clusters: $c_{1}$, $c_{3}$ and $c_{4}$. Then we can use the tag summary
of these clusters as (part of) her profile. Such kind of clusters as user
profiles can benefit various web applications, including (1) user-level
predictive tasks, such as user demographic attributes prediction and user
churn/uplift prediction (Huang et al., 2012; Diemert et al., 2018), where
cluster profiles can be consumed as auxiliary features; (2) ad audience
targeting (Tang et al., 2011; Provost et al., 2009), where ad platforms or
advertisers can leverage user clusters to reach a certain segment of users
that have targeted interests and habits in an interpretable manner; (3) look-
alike audience extension (Ma et al., 2016; Liu et al., 2019a), where the task
is to reach users similar to a given set of seed users, especially with the
goal of enhancing the performance of cold-start and long tail items and
improving the recommendation diversity. User clusters are naturally suitable
for this task because similar users have already been indexed in the same
clusters.

##  4\. Related Works

Collaborative filtering techniques, especially model-based CF methods, have
achieved great success in personalized recommender systems. Most (if not all)
of those methods rely on the latent factor embeddings to generate rating
predictions, which makes it difficult to give explanations for the
predictions. However, explaining why a user likes an item can be as important
as the accuracy of the prediction itself (Zhang and Chen, 2020), since it can
not only enhance the transparency and trustworthiness of the system, but also
significantly improve user satisfaction. Therefore, varieties of strategies
for rendering explainable recommendations have been proposed. We first review
explainable collaborative filtering methods (Abdollahi and Nasraoui, 2016; Vig
et al., 2009; McAuley and Leskovec, 2013; Zhang et al., 2014; He et al., 2015;
Wu and Ester, 2015; Tan et al., 2016; Cheng et al., 2018; Pan et al., 2020),
then we discuss other recent explainable recommendation works.

Explainable collaborative filtering methods. EMF (Abdollahi and Nasraoui,
2016) adds an explainability regularizer into the objective function of MF to
force user/item hidden vectors to be close if a lot of the user’s neighbors
also purchased the item. HFT (McAuley and Leskovec, 2013) leverages the topic
model to obtain interpretable textual labels for latent rating dimensions. EFM
(Zhang et al., 2014) factorizes a rating matrix in terms of both explicit
phases from textual reviews as well as latent factors, and makes predictions
by combing the scores of both explicit and implicit features. TriRank (He et
al., 2015) models user-item-tag ternary relation as a heterogeneous tripartite
graph and performs vertex ranking for recommendation. ATM (Cheng et al., 2018)
utilizes latent factors to estimate tag importance of a user towards an item,
and makes predictions via a linear combination of tag ratings. More recently,
AMCF (Pan et al., 2020) maps uninterpretable embeddings into the interpretable
aspect features by minimizing both ranking loss and interpretation loss.
Nonetheless, those methods are unable to satisfy all three important
explanation properties: flexible, coherence and self-explainable, resulting in
ineffectiveness to boost the transparency of recommender systems.

Other directions of explainable recommendation. There is also a large
literature that considers other auxiliary information or other methods to
explain recommendations (Abdollahi and Nasraoui, 2016; Chen et al., 2018; Wang
et al., 2018a, b; Peake and Wang, 2018; Wang et al., 2019; Chen et al., 2019;
Fusco et al., 2019; Wang et al., 2021; Geng et al., 2022). For example, NARRE
(Chen et al., 2018) designs an attention mechanism over the user and item
reviews for rating prediction, and leverages the attention weight for
explanation. VECF (Chen et al., 2019) proposes visually explainable
recommendation based on personalized region-of-interest highlights by a
multimodal attention network. PLM-Rec (Geng et al., 2022) learns a language
model over knowledge graph to generate explainable paths. Those methods
leverage more expressive data for explanation, which can be the future
direction of our ECF framework.

##  5\. Conclusion and future work

In this paper, we propose a neat yet effective explainable collaborative
filtering framework, called ECF, which is able to learn informative taste
clusters in an end-to-end manner, and perform both recommendation and
explanation by measuring the intersection between user-/item- cluster
affiliations. ECF is flexible, coherent and self-explainable. Meanwhile, we
design four quantitative metrics and conduct human studies to evaluate the
explainability quality of taste clusters in a comprehensive manner. Extensive
experiments conducted on three real-world datasets demonstrate the superiority
of ECF from both recommendation accuracy and explanation quality. In the
future, we aim to apply ECF to real-world recommendation scenarios with
millions of users and items to improve its scalability. Besides, we plan to
incorporate ECF with more expressive data beyond tags, such as reviews (Chen
et al., 2018), knowledge graphs (Wang et al., 2021; Du et al., 2022) to fully
exploit the power of this framework.

###### Acknowledgements.

This work was supported in part by the NSFC under Grants No. (62025206,
61972338, and 62102351), and the Ningbo Science and Technology Special
Innovation Projects with Grant Nos. 2022Z095 and 2021Z019. Yunjun Gao is the
corresponding author of the work.

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##  Appendix A Appendix

Table A1. Complete Top-$K$ recommendation results. “${\dagger}$” indicates the
improvement of the ECF over the baseline is significant at the level of 0.05.
R and N refer to Recall and NDCG, respectively.

| Xbox | MovieLen | Last-FM
---|---|---|---
R@5 | R@10 | N@5 | N@10 | R@5 | R@10 | N@5 | N@10 | R@5 | R@10 | N@5 | N@10
MF | 0.2615 | 0.3686 | 0.2383 | 0.2824 | 0.0601 | 0.0975 | 0.2738 | 0.2511 | 0.0289 | 0.0446 | 0.0428 | 0.0443
NCF | 0.2372 | 0.3433 | 0.2065 | 0.2503 | 0.0594 | 0.0985 | 0.2701 | 0.2517 | 0.0269 | 0.0456 | 0.0396 | 0.0383
CDAE | 0.2604 | 0.3738 | 0.2346 | 0.2813 | 0.0609 | 0.0946 | 0.2671 | 0.2534 | 0.0286 | 0.0402 | 0.0431 | 0.0518
LightGCN | 0.2684 | 0.3625 | 0.2382 | 0.2837 | 0.0699 | 0.1163 | 0.2979 | 0.2752 | 0.0398 | 0.0578 | 0.0605 | 0.0634
EFM | 0.2647 | 0.3652 | 0.2368 | 0.2873 | 0.0657 | 0.1027 | 0.2866 | 0.2635 | 0.0319 | 0.0482 | 0.0471 | 0.0484
AMCF | 0.2601 | 0.3613 | 0.2355 | 0.2806 | 0.0603 | 0.0986 | 0.2719 | 0.2498 | 0.0295 | 0.0488 | 0.0456 | 0.0457
MFforest | 0.2907 | 0.3983 | 0.2615 | 0.3159 | 0.0787 | 0.1276 | 0.3122 | 0.2911 | 0.0374 | 0.0548 | 0.0562 | 0.0594
ECFsingle | 0.1714 | 0.2763 | 0.1423 | 0.1854 | 0.0352 | 0.0608 | 0.1584 | 0.1505 | 0.0205 | 0.0315 | 0.0339 | 0.0345
ECF | 0.2970† | 0.4299† | 0.2644† | 0.3193† | 0.0788 | 0.1325† | 0.3183† | 0.2952† | 0.0455† | 0.0635† | 0.0782† | 0.0749†

###  A.1. Pseudocode of ECF

To help readers get an intuitive sense of the framework, we provide a
pseudocode in Algorithm 1.

Input: a set of users $\mathcal{U}$ and items $\mathcal{I}$; user-item
interactions Y; tags $\mathcal{T}$ for items

Output: Learned user embeddings U; item embeddings V; taste cluster embeddings
H; sparse affiliation matrix A and X

1

2Randomly initialize all parameters

3 Randomly select $|\mathcal{C}|$ items as the initial taste clusters

4while  _not converge_ do

5 for  _each pair $(u,i,j)$ in Y_ do

6 Calculate the sparse affiliations $\textbf{a}_{u}$, $\textbf{x}_{i}$ and
$\textbf{x}_{j}$ with Eq.(8)

7 Perform cluster-based predictions with Eq. (11)

8 Calculate tags distribution for taste clusters with Eq.(15)

9 Calculate independence of taste clusters with Eq.(16)

10 Update model parameters with Eq.(18)

11

12

Algorithm 1 Training Pipeline for an individual ECF

###  A.2. Adaptation of EFM

Since EFM relies on the phase-level reviews for prediction and explanation, we
make a few modifications to fit our settings where only tags of items are
available. First, we generate the user-feature matrix by counting all the
features of items that users have interacted with, which means that all the
mentioned features are considered as positive. Second, the negative opinions
of item’s features are discarded because no auxiliary information is
available. Third, the item-feature quality matrix is simplified as a 0-1
matrix where 1 denotes the item has the tag in attributes, while 0 denotes
otherwise. After reconstructing the user-feature matrix and item-feature
quality matrix, we run the EFM model as it describes in the paper.

###  A.3. Hyper-Parameter Settings

We optimize all models with Adam (Kingma and Ba, 2015), where the batch size
is fixed at 1024. For CDAE, the hidden size is 100, and the dropout ratio is
set to 0.5. For LightGCN, we set the number of layers to 3, and the dropout
ratio is also set to 0.5. For EFM, we fix the percentage of explicit factors
to 40%, and tune the coefficient of feature-based score for best performance.
For AMCF, we use their official codes (https://github.com/pd90506/AMCF) for
implementation and set the hyperparameter of feature mapping as 0.05. For ECF,
we set $m=20$ and $n=20$, which means that we restrict that each item and item
are associated with only 20 clusters. The temperature hyperparameters $T$ and
$\tau$ are all set as 2. We also set $|\mathcal{C}|=64$ for all datasets,
which indicates each ECF model could generate 64 taste clusters. Besides, the
number of single ECF model $F$ is set as 9 for all experiments. Moreover,
early stopping strategy is performed for all methods, _i.e.,_ premature
stopping if recall@20 on the test set does not increase for 10 successive
epochs. We report the average metrics for all the users in the testing set.

Besides, since ECF utilize sparse affiliations between users/items and taste
clusters instead of embeddings to perform recommendation, we choose two
options for fair comparison: (1) we fix the size of ID embeddings (users,
items and taste clusters) as 64 for all methods; (2) since the affiliation
size of ECF is 180 (top 20 affiliated taste clusters for each users/items, and
we use 9 single ECF model), we align it with the embedding size of all other
methods, and set the size of embeddings as 180. We conduct both experiments
for all baselines and select the best performance for the report.

###  A.4. Complete Recommendation Performance

We report the comprehensive recommendation performance in Table A1, where
$K=20$ is omitted since the results are already reported in Table 2. From the
results we see a similar trend as we discussed in Section 3.2: embedding-based
methods (_e.g.,_ MF and LightGCN) show strong performance across different
datasets yet suffer from poor explanation; explainable methods can only
slightly outperform MF, since they need to balance the trade-off between
accuracy and transparency. However, ECF achieves the best performance in all
ranking metrics (including the forest version of MF). Therefore, our model is
able to not only provide accurate recommendation results, but also intuitive
and clear explanations for each prediction with taste clusters.

###  A.5. Baselines for Explanation Evaluation

  * •

TagCluster is a tag-oriented method which collects items according to their
tags. To be specific, we first randomly sample $|\mathcal{C}|$ items as the
seed of clusters, and search for the items which have the same tags with them.
When there is no item that has the exactly the same tags as the seed, we relax
it by randomly discarding one tag and continue to search. We iteratively
conduct the operations until the size of clusters meets threshold $Z$. And we
choose the 4 most frequent tags in the clusters as the tags of taste clusters.

  * •

K-means is a similarity-oriented method which leverages the item embeddings
from FM to perform K-means clustering algorithm. The result clusters are as
directly used as the taste clusters. And we also select the top-4 most common
tags as the descriptive tags for taste clusters.

  * •

Random is a baseline method which randomly select $K$ items to construct the
clusters. The procedure is repeated until all items are allocated in at least
one cluster. We use the same mechanism as above methods to generate tags for
each clusters.

Table A2. The human evaluation results on Last-FM dataset.

| ECF | TagCluster | K-means | Random
---|---|---|---|---
RankOfTask(1) | 1.73 | 2 | 2.73 | 3.63
RankOfTask(2) | 1.3 | 2.5 | 2.23 | 3.93

###  A.6. Human Evaluation

We conducted two task to evaluate the explanability of ECF from human
perspective. Task(1) is to rank the quality of the clusters’ tags generated by
ECF and three baselines; and Task(2) is to rank the quality of user-item
explanations, with rank 1 representing the best and rank 4 representing the
worst. We randomly select 10 generated clusters for evaluation, and the mean
ranking results of these two tasks are shown in Table A2. We can see that ECF
achieved the best from human judgements, which ranks 1.73 and 1.3 for
clusters’ tags and recommendation explanation, respectively. Since human
evaluation can be time-consuming, expensive, and not scalable, our proposed
computational metrics are important for automatic evaluation.

###  A.7. Ablation Study _w.r.t._ $\lambda$

We also investigate the impact of different $\lambda$ on other two datasets,
and the results are shown in Figure A1. We find that as the increase of
auxiliary collaborative signals, the performance of ECF improves gradually.
However, when the weighting coefficient $\lambda$ reaches beyond 0.6, the
improvement becomes marginal. Thus, we set $\lambda=0.6$ for all experiments.

###  A.8. Ablation Study _w.r.t._ Forest Mechanism

We briefly discuss how the number of single ECF model influences the
performance. Since the single ECF model is unable to model the complex and
hidden users’ interest space at once, more learned taste clusters may help to
alleviate this issue. We confirm this assumption by adding more single ECF
model for ensemble prediction, and the results on Xbox and MovieLens dataset
are illustrated in Figure A2. We can see the huge performance gains when we
increase the number of ECF models, especially from a single model to three
models. However, as the number of single models continuously increases, the
improvements become negligible. We set the number of ECF models to $9$ for all
experiments.

Figure A1. Impact of $\lambda$ on Xbox and MovieLens datsets.

Figure A2. Impact of forest mechanism on Xbox and MovieLens datasets. Table
A3. The recommendation performance and explainability of ECF and ECFLGN on
Last-FM dataset.

| Performance | Explainability
---|---|---
R@20 | N@20 | Cov. | Util. | Sil. | Info. | Overall
ECF | 0.0851 | 0.0773 | 0.7648 | 0.6259 | 0.1584 | 0.2996 | 1.5352
ECFLGN | 0.0876 | 0.0792 | 0.7831 | 0.6430 | 0.1590 | 0.3042 | 1.5758

###  A.9. Implementation of Discriminator

We opt for a simple Multi-Layer Perceptron (MLPs) as the post-hoc
discriminator. Specifically, it is a three-layer MLP (hidden size is 64) with
ReLU as the activate function, cross-entropy as the loss function. We utilize
the tags of items as the input data, and feed them into the MLPs to predict
the item it belongs with. To improve the robustness of the model, we randomly
mask 50% of the item’s tags for training. After training, we use the tags of
taste clusters as the input, and collect top $|c_{i}|$ items as
$R(\mathcal{T}_{c_{i}})$ by ranking their prediction probabilities.

###  A.10. Implementation of ECF with LightGCN

We use the item embeddings of the last layer in LightGCN for taste clusters
learning, and the auxiliary collaborative signal is also replaced with the
prediction loss from LightGCN. We denote this variant as ECFLGN and the
results of both performance and explainability on Last-FM dataset are shown in
Table A3.