Against Filter Bubbles: Diversified Music Recommendation via Weighted Hypergraph Embedding Learning

In this study, our focus is on music recommender systems. With the proliferation of digital music, the evolution of music recommendation proves beneficial for users in picking desirable music pieces from an extensive repository [47]. The various music recommendation methods developed thus far can be broadly classified into two fundamental categories: content-based and collaborative-filtering approaches.

Music is an artistic presentation of sound and is characterized by numerous acoustic features [48, 49, 6, 34, 45]. Huang [19] initially extracted audio signatures as music features from audio data, rated new music by utilizing a vector quantization method, and ultimately generated music recommendations. In contrast to recommendations that solely focus on the music content itself, Bu [5] incorporated features extracted from the Mel-frequency cepstral coefficients as a bridge to compare similarities between tracks, embedding them into a unified hypergraph architecture.

Music typically conveys some form of emotion in addition to its acoustic characteristics. Shan [47] explored the discovery of affinity in film music and proposed a generalized framework for implementing emotion-based music recommendations. To tailor recommendations to better suit the user’s current context, Hariri [13] mined popular tags for tracks from social media websites, employed a topic modeling approach to learn latent topics representing various contexts from these tags, and then transformed each track into a set of latent topics capturing the general characteristics of that track.

Another strategy, which is the focus of our attention in this study, relies solely on the past behavior of the user, excluding the content of the music itself, often difficult to access. The direct approach refers to detecting associations between users, tracks, albums and artists through available information, uncovering the latent structure between them, and deducing the tracks that users may be attracted to, providing recommendations [46]. Mao [28] corrected user preference relations found from users’ ratings with a quality model and proposed a regularization framework to calculate the recommendation probability of tracks. Knowledge graphs, as tools to reason on data to extract new and implicit information, were naturally applied to music recommendations that mine associations between users and tracks [35]. La Gatta et al. [22] suggested that hypergraph data models might be more capable of seamlessly representing all possible and complex interactions between users and tracks with related characteristics. Furthermore, music play has a natural characteristic, i.e., sequence. Specifically, Cheng [7] exploited this property to seek the relevance of tracks and attempted to leverage the information encoded in music play sequence into the matrix factorization methods [21, 25] to improve the recommendation performance.

In summary, content-based music recommendation aims to establish similarities between tracks, with less consideration for personalization, while collaborative filtering-based recommendation pays more attention to detecting potential associations between users and tracks, being more inclined to match the users’ historical preferences.

Over the years, numerous recommendation algorithms have been developed to construct recommender systems that process massive amounts of data, aiming to identify potential user preferences and provide optimal recommendations [42, 2, 10, 62]. Ongoing studies on recommender systems often prioritize accuracy as the sole objective [53, 51, 61]. However, most personalized recommender systems compromise the accuracy of recommended items in their pursuit of increased diversity in recommendations [12, 16]. Simultaneously, it has been pointed out that accuracy may not be the exclusive goal of a recommender system [30, 26, 54]. Recommender systems would benefit from giving more consideration to other crucial aspects, such as diversity and novelty. Research has shown that, frequently, the diversity of recommendations is significant, and traditional recommender systems tend to exhibit poor diversity characteristics [4, 1, 18, 16].

Diversified recommendations can enhance the diversity and serendipity of a recommendation list, providing surprises and satisfaction to users, as these items can remain highly relevant to users [24, 43]. Furthermore, diversified recommendations can assist in exploring long-tail items, which is another challenging area and hot spot within recommender systems research [24].

Many current diversity-oriented recommender systems adopt a fixed strategy to adjust the diversity degree for all users. Typically, they define a score function that balances diversity and accuracy with a hyper-parameter. Subsequently, the generated recommendation list is re-ranked based on the calculated scores [26, 43]. For instance, Bradley [4] focused on a variation of a quality metric achieved through a linear combination of similarity and diversity, where the relative weight of the similarity and diversity factors can be altered by adjusting a hyper-parameter. Simultaneously, a non-linear alternative form of the quality metric, computed as the simple harmonic mean of similarity and diversity, has been proposed.

Beyond the pre-defined score function mentioned above, multi-objective optimization technology offers a viable alternative for balancing accuracy and diversity [27]. Unlike single-objective optimization, which can optimize only one objective function, multi-objective optimization can concurrently optimize several objective functions to obtain the Pareto optimal solution set. Two indicators, intra-user diversity and mean absolute error were selected to evaluate recommended diversity and accuracy, respectively [27].

Taken together, this simple way of defining diversity does not apply to more complex scenarios, such as music recommendation, where relationships between multiple entities need consideration.

Recently, numerous studies have delved into hypergraphs [57, 37, 59]. For instance, Bu [5] introduced a unified hypergraph framework for music recommendation, incorporating diverse social media information and acoustic-based content into the algorithm. Theodoridis [50] extended Bu’s framework [5] to include group sparsity constraints, enabling the exploitation of the group structure within the data. Treating music recommendation as a hypergraph-based ranking problem, Tan [49] integrated rich social media information to identify music tracks tailored to individual user preferences. A novel music recommendation framework that leverages a hypergraph data model and hypergraph embedding techniques was delivered by La Gatta [22]. By reexamining user mobility and social relationships, a hypergraph embedding method is specifically designed for a large-scale location-based social network dataset, facilitating automatic feature learning [57]. Introducing a generic user-item-attribute-context data model summarizing various information resources and higher-order relationships for constructing a multipartite hypergraph fulfilling multi-objective recommendation needs, a solution was proposed, utilizing hypergraph ordering [29].

While these approaches have garnered considerable success in resource recommendation applications, they have yet to establish a centralized hypergraph. Our goal is to construct a hypergraph with items at the center, surrounded by other resources, aiming to enhance the strength of connections between resources.

We summarize the notation in Table 1. The graph comprises two essential components: vertices and edges. A hypergraph, denoted as $\mathcal{G}=(\mathcal{V},\mathcal{E})$, consists of a vertex set $\mathcal{V}$ and a hyperedge set $\mathcal{E}$. Each hyperedge $e\in\mathcal{E}$ encompasses an arbitrary number of vertices $v\in\mathcal{V}$. For a weighted hypergraph, represented as $\mathcal{G}=(\mathcal{V},\mathcal{E},\rm{w})$, the vertices $\mathcal{V}$ and hyperedges $\mathcal{E}$ are accompanied by a weighting function $f_{\rm{w}}(e)$: $\mathcal{E}\rightarrow\mathbb{R}$, indicating the strength of connections. A higher weight signifies closer proximity between the connected vertices. Additionally, each hyperedge $e\in\mathcal{E}$ is linked to a non-negative number $\rm{w}(e)$, referred to as the weight of the hyperedge $e$.

A hyperedge $e$ is said to contain a vertex $v$ when $v\in e$. The degree of a hyperedge $e$, denoted by $\delta(e)$, is defined as the cardinality of $e$, i.e., $\delta(e)=\left|e\right|$. If every hyperedge has a degree of $2$, the hypergraph reduces to a normal graph. A hyperpath between vertices $v_{1}$ and $v_{k}$ exists when there is an alternative sequence of distinct vertices and hyperedges $v_{1}$, $e_{1}$, $v_{2}$, $e_{2}$, $\dots$, $e_{k-1}$, $v_{k}$ such that $\left\{v_{i},v_{i+1}\right\}\subseteq e_{i}$ for $1\leq i\leq k-1$. A hypergraph is connected if there is a path for every pair of vertices.

Finally, we obtain the vertex-hyperedge incidence matrix, $\mathbf{H}$. The hypergraph $\mathcal{G}$ can be succinctly represented by $\mathbf{H}$ of size $\left|\mathcal{V}\right|\times\left|\mathcal{E}\right|$ matrix. Let $h(v,e)=1$ indicate that a vertex $v$ is part of a hyperedge $e$, and $h(v,e)=0$ otherwise. The incidence matrix, $\mathbf{H}$, is defined by its elements:

Logically, we define the degree of a vertex as

and the degree of a hyperedge as the number of connected vertices, denoted as,

The hypergraph structure is a fundamental component of our proposed algorithm. Consequently, it is essential to furnish a detailed configuration explanation for the elements within the hypergraph.

We consider five types of objects and four types of relationships. Specifically, the objects comprise users $U$, three resource types (i.e., tracks $Tr$, albums $Al$ and artists $Ar$) and tags $Ta$ that users attach to them. The relationships within the constructed hypergraph are partitioned into actions on resources and inclusion relationships among resources. Actions relations on resources engage two types of interactions: users listening to tracks ($R_{1}$) and users tagging tracks ($R_{2}$). It is worth noting that the relationship between users and the tagging of tracks represents the collective annotation of a particular track by all users, rather than a specific user. Inclusion relationships among resources are defined by connections between tracks and releases and between tracks and artists, signified by $R_{3}$ and $R_{4}$, respectively.

The hypergraph $\mathcal{G}$ is defined as a collection of vertices $\mathcal{V}$ and hyperedges $\mathcal{E}$. The vertex set, $\mathcal{V}$, comprises distinct entities, specifically:

(1) Users ($U$): the set of users;

(2) Albums ($Al$): the set of albums;

(3) Artists ($Ar$): the set of artists;

(4) Tracks ($Tr$): the set of tracks;

(5) Tags ($Ta$): the set of tags that users attach to tracks.

So, the set of vertices $\mathcal{V}$, is defined as the union of $U$, $Al$, $Ar$, $Tr$ and $Ta$, i.e., $\mathcal{V}=U\cup Al\cup Ar\cup Tr\cup Ta$. Hyperedges are introduced to represent the four relationships among the aforementioned objects. In the unified hypergraph, there exist four types of hyperedges, each corresponding to a specific relationship type. To correspond with the relation set $R_{i}$, we define the set of hyperedges as $e^{(i)}$, ($i\in[1,4],i\in\mathcal{R}^{+}$). For convenience and better comprehension, we provide an illustrative representation of these relationships in Table 2.

The construction of the four types of relations and hyperedges is listed as follows.

Figure 1 vividly and succinctly depicts the entire workflow of the DWHRec algorithm, as detailed in Algorithm 1, which outlines the core framework of the system. DWHRec takes two inputs: data and hyper-parameters. The data includes the user’s listening history $Le$, tracks $Tr$, tags $Ta$ associated with the tracks, albums $Al$ and artists $Ar$. DWHRec receives and processes these inputs through a series of steps to generate lists of recommendations $L$ for all users. The hyper-parameters consist of the iteration counts $r$ and the number of steps $k$ in the random walks stage, as well as the vector dimension $s$ and window size $w$ in the embedding stage and the recommended list length $n$.

DWHRec can be segmented into four stages (Algorithm 1). Firstly, a weighted hypergraph $\mathcal{G}$ is constructed based on information from $Le$, $Tr$, $Ta$, $Al$ and $Ar$ (line $1$). A more detailed description of this process is presented in Algorithm 2. Secondly, utilizing the constructed hypergraph, the random walks method is designed to detect potential associations between users $U$ and candidate tracks $Tr$ (line $2$). A more detailed explanation of this process is provided in Algorithm 3. Thirdly, considering the paths left by the vertex walks as sentences and the vertices as words, the skip-gram word embedding model is applied to vectorize the users and tracks vertices, obtaining their vector representations (line $3$). Finally, the designed scoring function takes the vectors of users and tracks as input, calculating the scores for candidate tracks. These candidate tracks are graded, and the recommendation list is generated by ranking them according to the highest rating (lines $4$). Through these steps, DWHRec achieves the goal of providing users with as diversified recommendations as possible.

Last.fm¹¹1http://www.last.fm/ is a well-known data gathering site widely used in the field of music recommendation research [5, 50, 35, 43]. It builds a detailed profile of each user’s musical tastes by recording the tracks they have historically interacted with. Last.fm collects these tracks from Internet radio stations or the user’s computer, for example, by transferring (“scrubbing”) them to Last.fm’s database via a music player (e.g. Spotify²²2https://open.spotify.com/) or a plug-in installed in the user’s music player.

Users were discovered by crawling the Last.fm social graph using the “user.getFriends” endpoint and by crawling the listening users of a certain group of artists, which were obtained via chart.getTopArtists endpoint [43]. After removing duplicates from the approximately $1,100,000$ crawled user names, a grand total of almost $400,000$ unique users were harvested. Due to the substantial number of listening records per user, $10,000$ unique users were randomly chosen. Through other Last.fm Application Programming Interfaces (APIs), a significant number of unique listening events (LEs) from these users were available.

Play count measures how frequently the observed user engages in music listening [11]. For tracks with a high play count, we can assume that the user has likely enjoyed them. However, tracks that are played rarely or have not been played cannot be easily dismissed as unappealing to users. Some tracks that users cannot access have a play count of $0$. Additionally, there are tracks that users do not currently prefer, but it does not imply that they will not prefer them in the long run as their preferences evolve. The interaction between a user and a track (or artist, album) is reflected in the fact that the user has listened to a particular track, i.e., such a listening event exists. Referring to the article [43], we also use a simple key consisting of artist and track name tuples to distinguish individual tracks.

The basic statistical information contained in the dataset is shown in Table 3. For this experiment, two Last.fm datasets were utilized, named lastfm-100k and lastfm-200k, according to the approximate size of the datasets. In the filtered datasets, lastfm-100k contains $501$ users with close to $100,000$ entries for listening events (LEs). In comparison, the number of users and LEs in lastfm-200k is almost twice as large, with $1,001$ users and more than $200$ thousand LEs. The number of tracks in the two datasets is $25,279$ and $42,668$, respectively. Regarding the average actions per user, average actions per track and sparsity, the two datasets are quite similar, with values of $199.3$ vs $200.0$, $4.0$ vs $4.7$, and $99.2$% vs $99.5$%, respectively.

The algorithm DWHRec generates the recommendation list by initially calculating the scores of users and candidate tracks according to the customized scoring function, and then ranking the candidate tracks depending on the scores. To ensure that each user and each track in the testset carries its own vector representation, extra care is required in constructing the dataset. For each user, we ranked their listening records and spanned the top $200$ records (it was observed that the vast majority of the users’ listening records ranked above $200$ had single-digit listening times). In the experimental section, we stochastically split the dataset into training and test sets, with the training set comprising $90\%$ and the testset containing the remaining $10\%$. We conducted ten experiments, iterating over all ten permutations, and the final result displayed is the mean of the ten outcomes. For baselines in our experiment, we evaluated their performance using the RecBole toolkit [64, 63, 55].

DWHRec contains six hyper-parameters, the number of iterations $r$ for random walks, the number of steps $k$ for the walks, the representation dimension $s$ of the vector, the word embedding window size $w$, the length of the recommendation list $n$ and the weighting factor $\alpha$ of the scoring function. In the experiment, the first five hyper-parameters are assigned values using a manually set approach, sequentially set as $r\text{=}5$, $k\text{=}200$, $s\text{=}50$ and $w\text{=}5$. Regarding the diversity weighting factor $\alpha$, an adaptive weight is employed, where the diversity weight for the $i$-th item to be recommended is given by $\alpha_{i}=(1-\frac{1}{i+1})$.

Five evaluation metrics, categorized into accuracy and diversity, were applied to compare different algorithms [60]. Recall and Hit Ratio, two accuracy metrics unrelated to ordering, measured the fundamental accuracy. Ranking accuracy was assessed using two metrics: Mean Average Precision (MAP) and Normalized Discounted Cumulative Gain (NDCG). The Aggregate Diversity (AGGR-DIV) metric was utilized to measure the diversity of recommendations.

The AGGR-DIV metric measures the degree of diversity among items in the recommendation list across all users. It is computed as the total number of unique genres on tracks in the recommendation list, considering all users. AGGR-DIV is defined as follows:

Where $L_{u}$ represents the recommendation list for user $u$, and $Ta(L_{u})$ represents the set of tags annotated to the tracks in $L_{u}$. In Equation (10), $p(ta)$ is the cumulative discounted probability of $ta$ over $L_{u}$, and $D(ta)$ represents the number of occurrences of $ta$ in $L_{u}$. The notation $d(tr,ta)$ represents the number of occurrences of $ta$ in $tr$, taking a value of $1$ if $ta$ is present in $tr$ and $0$ otherwise. $D(ta)$ and $d(tr,ta)$ are defined as follows:

For the track $tr\in L_{u}$, if $tr$ contains the tag $ta$, the count of $ta$ is denoted as $c(tr,ta)$; otherwise, the count is zero. Then, the proportion of $ta$ in the tags associated with $tr$ is equal to the frequency of occurrence of $ta$, denoted as $q(tr,ta)$. The probability of $ta$ in $tr$, expressed as $p(tr,ta)$, is calculated in a discounted form of $q(tr,ta)$,

where $j$ represents that $tr$ is the $j$-th track in $L_{u}$ that contains $ta$. By traversing $L_{u}$ and accumulating $p(tr,ta)$, we obtain the probability $p(ta)$ for $ta$. A higher AGGR-DIV value indicates better diversity in the recommended results.

We compared our approach with several state-of-the-art recommendation algorithms. Below is a brief description of these algorithms.

• 1.

  Popularity Based (PB) [39]: The popularity-based recommender always recommends to users the $n$ most frequently listened-to tracks by all users in the dataset.

• 2.

  Bayesian Personalized Ranking (BPR) [40]: It is the most widely used method for recommendation based on matrix factorization with pairwise ranking loss.

• 3.

  Neural Collaborative Filtering–Matrix Factorization (NeuMF) [15]: The author is dedicated to developing neural network-based techniques to tackle the critical issue in recommendation, specifically collaborative filtering based on implicit feedback.

• 4.

  Deep Matrix Factorization (DMF) [56]: The algorithm constructs a user-item matrix that incorporates explicit ratings and non-preference implicit feedback. It introduces a novel matrix factorization model with a neural network architecture to learn a generic low-dimensional space representation of users and items.

• 5.

  Light Graph Convolution Network (LightGCN) [14]: LightGCN learns user and item embeddings by linearly propagating them on the user-item interaction graph. It uses the weighted sum of embeddings learned at all layers as the final embedding.

• 6.

  Diversified GNN-based Recommender System (DGRec) [58]: It is currently the state-of-the-art diversified recommendation algorithm. The authors suggest diversifying GNN-based recommender systems by directly improving the embedding generation procedure.

• 7.

  Hypergraph Embeddings for Music Recommendation (HEMR) [22]: It is a recommendation algorithm specifically designed for music recommendations, which is the most similar baseline to our method by utilizing hypergraphs.

Seven advanced algorithms, namely PB, BPR, NeuMF, DMF, LightGCN, HEMR and DGRec, are employed as comparative models. DWHRec is compared with these models using the same experimental datasets, lastfm-100k and lastfm-200k (Table 3). The quality of the recommendation results is evaluated based on metrics, including accuracy indicators such as map, recall, hit ratio and ndcg, as well as diversity metrics represented by aggr-div.

Table 4 shows the results of the eight recommendation algorithms on two datasets utilizing evaluation metrics such as map, recall, hit ratio, ndcg and aggr-div. The table is divided into two sections: the upper half showcases results for the lastfm-100k dataset, while the lower half displays results for the lastfm-200k dataset. Both datasets share identical row and column names. The row names correspond to the abbreviations for eight comparative models, while the column names represent metrics for a recommended length of $20$. The values in the table indicate the performance of each model under specific metrics. Bold entries highlight the best results, entries with an underline (“_”) signify the second-best results, and entries with a wavy underline (“~”) indicate the third-best results.

On the lastfm-100k dataset in Table 4, it is evident that DWHRec outperformed other algorithms significantly by a considerable margin across the five metrics provided. DWHRec consistently occupied a leading position under these metrics. LightGCN also demonstrated strong performance, securing the second position in four other metrics except for aggr-div@20. HEMR attained the second position in ndcg@20, while PB secured the third position in the same metric. For NeuMF, its performance closely approached that of DMF. The remaining algorithms distinctly lagged behind both DMF and NeuMF in performance.

On the lastfm-200k dataset in Table 4, changes in trends were observed. DWHRec exhibited outstanding performance, notably excelling in map@20, ndcg@20 and aggr-div@20 metrics, surpassing other algorithms by a significant margin. In terms of map@20 and recall@20 metrics, DWHRec, NeuMF and BPR occupied the top tier, securing the first three positions. The performance of NeuMF and DWHRec on recall@20 was remarkably close, with minimal differences. LightGCN’s performance, however, was not as robust on this dataset. The distinction between DGRec and LightGCN was relatively small. In terms of four accuracy metrics, BPR outperformed both LightGCN and DGRec, with the exception of the aggr-div@20 metric.

Figure 2 proclaims a brief overview of the comparative results, featuring two key metrics: ndcg for accuracy and aggr-div for diversity. The horizontal axis of the figure depicts the length of the recommendation list ($n$), spanning ten data points from $10$ to $100$. To enhance visibility, all lines are uniformly represented with dashed lines (“--”), each accompanied by distinct colors and point shapes. Notably, the color of each line matches the color of the points along it. Blue-gray triangles denote PB (“\trianglepafill”). Light pink stars represent BPR (“\starletfill”). NeuMF is marked with red cross symbols (“$\times$”). DMF is identified by olive circular points (“\circletfill”). Light blue colored squares fill the LightGCN (“\squadfill”). The golden pentagons make up the HEMR (“\pentagofill”). Purple plus signs characterize the DGRec (“\linevh”). DWHRec is adorned with orange diamonds (“\rhombusfill”).

Figure 2 is composed of four parts labeled a, b, c and d. Figures 2(a) and 2(b) depict the ndcg and aggr-div results for the lastfm-100k dataset, while Figures 2(c) and 2(d) portray the corresponding results for the lastfm-200k dataset. All four figures share a common horizontal axis representing the values of $n$. The vertical axis is organized into two groups: the ndcg metric for Figures 2(a) and 2(c), and the aggr-div metric for Figures 2(b) and 2(d).

Across the $n$ range from $10$ to $100$, the ndcg results for all algorithms increased as $n$ grew (Figures 2(a) and 2(c)). However, the growth rates of ndcg values varied among the algorithms. In the lastfm-100k dataset (Figure 2(a)), HEMR exhibited the fastest growth rate. DWHRec, DMF, NeuMF, LightGCN and PB accelerated at comparable rates, forming the second tier. The remaining algorithms demonstrated slower growth rates. Whereas in the lastfm-200k dataset (Figure 2(c)), NeuMF displayed the sharpest growth rate, with HEMR closely following its pace and showing a commendable growth spurt. Over the range of $n$ from $10$ to $100$, the aggr-div results for all algorithms decreased with the increase in $n$ (Figures 2(b) and 2(d)). As $n$ increases, the aggr-div values for all algorithms remain closely aligned, except for HEMR and DWHRec.

Throughout the entire experiment, DWHRec consistently achieved favorable results in evaluation metrics such as map@20, recall@20, ndcg@20 and aggr-div@20, yielding significant differences from the other seven algorithms (Table 4 and Figure 2). Notably, DWHRec delivered commendable aggr-div outcomes, which is an encouraging result.

The DWHRec model includes multiple hyper-parameters, roughly categorized into two main types. The hyper-parameter $r$ represents the number of iterations for random walks, and $k$ denotes the number of steps a vertex can take in a single iteration. Hyper-parameters $r$ and $k$ control the random walks state of vertices in the hypergraph. Hyper-parameter $w$ is the size of the sliding window, and $s$ is the dimension of the representation vector in the word embedding process. Hyper-parameters $s$ and $w$ intervene in the word embedding process, thereby influencing the generation of vertex vectors. Through sensitivity experiments on these hyper-parameters, we aim to explore how their variations impact the final recommendation performance.

For the sensitivity experiments on hyper-parameters, some preparatory work was undertaken. Specifically, the lastfm-100k dataset was selected as the experimental subject. Four recommendation lengths were chosen, namely $n\text{=}10$, $40$, $70$ and $100$. Here, $n\text{=}100$ represents a scenario with a sufficiently long recommendation length, $n\text{=}10$ signifies an extremely short length, while $n\text{=}30$ and $70$ represent typical scenarios. During the testing of a specific hyper-parameter, other hyper-parameters were kept constant. Two metrics, recall and aggr-div, were used to characterize the performance of the recommendations. The experimental results are shown in Figures 3–6.

In practice, when conducting sensitivity experiments for hyper-parameters, attention to certain details is crucial. Both $k$ and $r$ are hyper-parameters that affect the random walks process (Algorithm 3). To investigate the impact of $k$, $r$ is kept constant at a value of $1$. Likewise, when testing $r$, $k$ is fixed at $100$. The other two hyper-parameters, $s$ and $w$, are set to values of $100$ and $5$, respectively. Both $s$ and $w$ are hyper-parameters that influence the word embedding process. To explore the impact of $s$ on performance, $w$ is set to a common value of $5$. Conversely, when investigating the influence of $w$, $s$ is set to a constant value of $100$. As for the remaining two hyper-parameters, $r$ and $k$, they are kept as small as possible and constant, with specific values of $1$ and $100$, respectively. The aforementioned configurations are designed to objectively and accurately assess the impact of hyper-parameters on model performance.

The experimental results illustrate that the choice of $k$ has a noticeable impact on the model’s performance (Figure 3), whether in terms of recall (Figure 3(a)) or aggr-div (Figure 3(b)). Under the recall metric (Figure 3(a)), a longitudinal view reveals that for the same set of $k$ values, a larger $n$ value corresponds to a larger recall value. Observing along the horizontal axis shows that, for the four selected values of $n$, as $k$ increases, the recall values also increase. However, different values of $n$ result in varying degrees of improvement in recall. Given a change of $100$ in $k$ as one unit, when $n$ takes the minimum, intermediate and maximum values, the average increase in recall metric values is $18.07$%, $10.68$% and $9.0$%, respectively, for each unit increase in $k$. For the aggr-div metric (Figure 3(b)), a similar trend is observed on the horizontal axis as in the recall metric. When $n$ is set to $10$, $40$, $70$ and $100$, the aggr-div values increase by $6.47$%, $12.49$% and $15.90$%, respectively, as $k$ increases by one unit. In contrast to the recall metric, in the aggr-div indicator, the average growth rate tends to increase with larger $n$ values. Additionally, in the vertical direction, the pattern of aggr-div values is opposite to that of the recall metric. For the same $k$ value, smaller $n$ values result in larger aggr-div values.

The impact of the hyper-parameter $r$ on the model’s recommendation performance is very similar to that of $k$ (Figure 4). The effects of changing $n$ within the same set of $r$ values and the influence of different $r$ values on the metrics are consistent with the conclusions under $k$ values. The main difference introduced by the two hyper-parameters is reflected in the rate of change of the metric values. Compared to $k$, $r$ yields a greater increase in recall values (Figure 4(a)) when $n$ is at its minimum, with a growth rate of $23.42$%. However, when $n$ takes intermediate and maximum values, the growth rates of recall values are lower than the performance under $k$, at $7.93$% and $4.16$%, respectively. Alternatively, concerning the aggr-div metric (Figure 4(b)), the impact of $r$ values is more profound than that of $k$ values. The growth rates are $9.68$%, $30.13$% and $23.91$% for the three different scenarios of $n$ values, respectively.

The impact of hyper-parameter $s$ on the model’s performance is quite intricate (Figure 5). Let $s$ vary by $50$ as a unit. When $s$ increases by one unit, it brings an average negative growth of $10.11$% to the recall metric (Figure 5(a)) for a recommended list length of $10$. However, when $n$ is $100$, it brings an average positive growth rate of $3.95$%. In the scenario where $n$ takes the middle value, the improvement of $s$ has a minimal impact on the recall value, with an average growth change of only $1.39$%. Across different values of $n$, the changing trend of $s$ on the aggr-div metric remains consistent (Figure 5(b)). Among them, the impact of $s$ is very close when $n$ takes the minimum and maximum values. With each unit increase in $s$, aggr-div values decrease by $19.25$% and $18.38$%, respectively. The effect of $s$ is most pronounced when $n$ takes the middle value, causing a decrease of $23.55$% in aggr-div for each additional unit.

The impact of $w$ on the model is reflected differently in recall and aggr-div (Figure 6). Overall, with the increase of $w$, the recall metric experiences a negative impact (Figure 6(a)), while aggr-div receives a positive influence (Figure 6(b)). The impact of $w$ on the recall metric strengthens with the increase of the recommended list length. Assuming $w$ varies in units of $50$, when $n$ is equal to $100$, an increase of one unit in $w$ leads to an average decrease of $16.4$%. On the aggr-div metric, an increase in $w$ results in more diversified recommendations. The average growth rate of aggr-div, induced by the variation in $w$, exhibits an inverted U-shaped trend with the increase in $n$. When $n$ takes values within the middle range, the average growth rate reaches $27.75$%.

Throughout the entire sensitivity experiment, we aim to uncover certain patterns: (1) In conclusion, all four hyper-parameters can influence the model’s performance, impacting either the recall or aggr-div metrics, or both. Specifically, when $r$, $k$, $s$ or $w$ are small, increasing their values leads to noticeable changes. However, as the hyper-parameter values continue to increase and reach a certain threshold, the model’s performance tends to plateau, and in some cases, it may even produce the opposite effect. (2) To summarize, increasing the value of $k$ and $r$ can enhance the predictive performance of the model within a certain range. A larger improvement is observed in the recall metric when $n$ is smaller, while a greater enhancement is seen in the aggr-div metric when $n$ is larger. (3) The impact of $s$ on the recall metric is complex and overall quite subtle. However, increasing the value of $s$ has a noticeable negative impact on the aggr-div metric. Conversely, $w$ can balance the recall and aggr-div metrics. Increasing $w$ can lead to a decrease in recommendation accuracy while simultaneously enhancing the diversity of recommendations. (4) Under the same set of hyper-parameter values, the larger $n$ is, the larger the recall metric value is. This is because guessing the user’s preferred items in a shorter list is more challenging. As the recommended list lengthens, it undoubtedly increases the likelihood of the recommended items within the user’s preferences. (5) When each parameter surpasses its respective threshold, the model exhibits strong stability.

DWHRec model is divided into three key steps: hypergraph construction, random walks and word vector embedding. Among them, random walks and word vector embedding are designed to obtain computationally convenient user and track vectors. The core of the model lies in its hypergraph structure. Investigating the roles of various types of hyperedges can help clarify their relationships and contributions to the model.

In Section 3.2, four types of hyperedges are introduced in the DWHRec algorithm, denoted as $e^{(1)}$, $e^{(2)}$, $e^{(3)}$ and $e^{(4)}$. The primary objective of DWHRec is to recommend a more diverse set of tracks to users. Users and tracks are the two most important atoms. While the listening events of users to tracks, represented by $e^{(1)}$, serving as a crucial bridge connecting the two, is indispensable. Therefore, to examine the roles of various types of hyperedges in the model, an ablation study was conducted on the lastfm-100k dataset by alternatively eliminating one of $e^{(2)}$, $e^{(3)}$ and $e^{(4)}$.

The concise experimental results are presented in Table 5, while Figure 7 offers a performance comparison of the model based on the recall and aggr-div metrics for all $n$ values. Table 5 is a subset of Figure 7, specifically representing the case when $n=50$. The prefix symbol “-” in both Table 5 and Figure 7 signifies “remove” or “subtract”, meaning the action of elimination or deletion.

Observing Table 5 and Figure 7, we made several findings: (1) Regarding the recall@50 metric, removing $e^{(3)}$ and $e^{(4)}$ led to a decrease in performance, but removing $e^{(2)}$ resulted in a significant improvement. The experiments indicated that compared to the DWHRec model with all types of hyperedges as a baseline, removing $e^{(2)}$, $e^{(3)}$ and $e^{(4)}$ resulted in an increase of $84.60$%, $-30.56$% and $-49.49$%. In which case, the model’s performance, after removing $e^{(3)}$ and $e^{(4)}$ respectively, was only $69.44$% and $50.51$% of the full model’s performance. (2) In the case of the aggr-div@50 metric, removing any type of hyperedge seemed to have a clear impact. Experiments revealed that after removing $e^{(2)}$, $e^{(3)}$ and $e^{(4)}$, the model provided $15.31$%, $82.66$% and $58.99$% of the complete model’s performance, with gaps of $84.69$%, $17.34$% and $41.01$%, respectively. (3) Removing any hyperedge resulted in an apparent drop in aggr-div values, while interventions on recall remained relatively complex.

The ablation experiments analyzed the impact of different types of hyperedges on the model. The experiments indicated that both the album hyperedge $e^{(3)}$ and the artist hyperedge $e^{(4)}$ could improve the model’s performance, whether in terms of recommendation accuracy or diversity. Comparatively, the impact of $e^{(4)}$ was slightly higher than that of $e^{(3)}$. Artists might not have released albums but would certainly create tracks. Therefore, the information captured by $e^{(4)}$ was more comprehensive, while $e^{(3)}$ might have missed some important information. The tagging hyperedge $e^{(2)}$ tended to interfere with the model’s ability to make accurate predictions. Since tags are directly related to the category of tracks, they could lead to a significant increase in diversity. Overall, all four types of hyperedges contributed to achieving a balance between recommendation accuracy and diversity.