Application of collaborative filtering algorithm based on time decay function in music teaching recommendation model

Overall design

Figure 1 depicts the architecture of the music resource recommendation module, a comprehensive system designed to provide users with personalized music recommendations. The recommendation model processes primary user and resource information and rating data to generate tailored recommendation results. The customized recommendation process is divided into three key steps: data processing, recommendation calculation, and prediction recommendation.

Step 1: Data processing

In the initial stage, referred to as Part A, the system preprocesses data from three primary sources: the user information database, the resource information database, and the scoring information database. This involves cleaning, organizing, and structuring the data to build a robust model. Key outputs of this stage include user feature vectors, resource attribute vectors, and resource attribute preference vectors. These vectors serve as the foundation for calculating user similarity in later stages.

Step 2: Recommendation calculation

Building on the data processed in Part A, Part B calculates user similarity. This is done using the recommendation model, which identifies the nearest neighbors for each user. The model considers user characteristics and an information bias model to predict preferences for new users. The model utilizes rating data and resource attributes to determine preferences for existing users. The aim is to find users with similar tastes and preferences, facilitating more accurate recommendations.

Step 3: Prediction and recommendation

In the final stage, Part C, the system predicts user scores for various resources. Based on these predicted scores, it compiles a list of each user’s top N recommended resources. This step ensures that users receive the most relevant and appealing recommendations, enhancing their overall experience with the platform.

Recommendation model based on CF

User-music score matrix

In the CF recommendation model, user preference is represented by a vector. A user-music matrix can be constructed by combining the preference vectors of all users. This matrix is the input of the collaborative filtering model. The goal of the model is to calculate the similarity between users, retrieve the neighbor users of all users, generate a neighbor user set, and finally obtain recommended users and recommended music in the neighbor user set. This “preference” level is expressed as the number of repetitions in a music system with no direct music rating mechanism.

Assuming that the music set that the neighboring users like but the target users haven’t heard is M, the implicit scores of all neighboring users on the music in M can be averaged as the predicted score set S of the target users on the music in M. Finally, the music with a TopN score in S can be added to the recommendation list.

One effective method for addressing the cold start problem, particularly for new users, is leveraging implicit feedback from initial interactions. This approach relies on monitoring and analyzing the user’s early behavior within the system, such as the music they listen to, the tracks they skip, or the songs they play repeatedly. By collecting and interpreting these implicit signals, the recommendation system can begin to infer user preferences even when explicit ratings or long-term interaction data are unavailable. This method has the advantage of being non-intrusive, as it does not require users to provide direct input about their preferences. Additionally, implicit feedback reflects genuine behavior more, capturing real-time decision-making processes during music consumption. As the user continues to interact with the system, the accumulated implicit feedback can be used to refine recommendations and gradually personalize the user experience.

To effectively implement this strategy, it is essential to define appropriate metrics for implicit feedback, such as the number of times a user plays a song or the duration they listen to specific tracks. The system can build a more accurate profile of user preferences by assigning weights to different types of interactions—such as treating repeated plays as a more robust signal of interest than a single listen. Moreover, advanced machine learning techniques, such as matrix factorization or collaborative filtering, can be applied to the implicit feedback data to recommend music based on patterns learned from other users with similar behavior. Over time, the recommendation system can enhance its ability to predict user preferences, even without extensive historical data.

Time decay function

Fitting the TD (Chen, Hui & Thaipisutikul, 2021; Huang et al., 2023; Liu et al., 2024) by analogy with the forgetting law of human memory, the TD expresses the weight of users’ interest in items, where the longer a user acts on items, the less it will affect users’ current interest.

Using the forgetting curve to fit the TD factor provides a more realistic representation of memory and relevance in models. Human memory tends to retain new information more clearly, but without regular reinforcement, even recent information fades over time. By applying this principle to the TD factor, algorithms can prioritize newer or frequently reinforced information while gradually diminishing the influence of outdated data. in recommendation systems, recent user interactions would have a more substantial impact on predictions than interactions that occurred further in the past.

The fitting method of the attenuation function can be linear, exponential, and logarithmic. In this paper, the linear time decay function f(|T − t|) is adopted, and its expression is as follows: (4)${\displaystyle f\left(|T-t|\right)=\frac{1}{1+\alpha |T-t|}.}$

Among them, α represents the time decay factor, which decides the attenuation rate of the function. Adjusting the value can simulate the memory curve; if the user interest changes faster, then the decay rate is faster, and the value of α will increase; T indicates the current time, while t is the time of the action; |T − t| represents time difference, and f(|T − t|) decreases as the growth of the time difference, namely value range is (0, 1).

TD-CF needs to increase the weight of users’ recent behaviors, and TD is used as a weight factor to constrain the similarity of users. Compared with previous behaviors, users’ recent behaviors can better reflect their current interests. Considering the influence of time, the traditional similarity calculation of CF is improved, and the optimized cosine similarity calculation formula is as follows: (5)${\displaystyle \text{Tsim}{\left(i,j\right)}_{cos}=\frac{\sum _{u\in N\left(i\right)\cap N\left(j\right)}f\left(|T-t|\right)}{\sqrt{\left|N\left(i\right)\right|\left|N\left(j\right)\right|}}.}$

In addition to incorporating the TD into the similarity calculation, the influence of time information on the preference degree should also be considered. Compared with the long-term behavior of users, the recent behavior of users can better reflect the current interests of users. Therefore, when predicting the user’s current interest, the weight of the recent feedback items should be increased, and the items similar to those that the user likes or has purchased in the near future should be recommended first. The user’s interest preference can be calculated after the time the user acts on the items is obtained. The modified preference degree is shown in Eq. (6), (6)${\displaystyle \mathrm{Tp}\left(u,i\right)=\sum _{j\in S\left(i,N\right)\cap N\left(u\right)}\text{Tsim}{\left(i,j\right)}_{cos}\frac{r_{uj}}{1+\beta |T-t|}}$ where β is the updated time decay factor, which needs to be adjusted according to different data sets.

Model mixing

The model based on CF is sparse and needs a lot of historical data, while the model based on TD does not entirely depend on the new users’ listening history. This paper uses the mixed recommendation model to weigh the two models. When the user’s listening history is rich, the weight of the CF model is increased, and when the user’s listening history is low, the weight of the time decay model is increased. The flow of weighted recommended music is shown in Fig. 2.

The Recommendation degree rec of the weighted mixed music recommendation model is shown in Eq. (7). (7)${\displaystyle \mathrm{Rec}=\alpha \mathrm{Sim}+\left(1-\alpha \right)\mathrm{Tp}\left(u,i\right)}$ where α is the weight. When the user has a rich listening history, the weight of the collaborative filtering model is increased; when the user has a small listening history, the weight of the time decay model is increased.

Data sources

In this experiment, the internationally published music data set “Last.fm Dataset-1k” is used for experimental analysis (https://zenodo.org/records/4589071, doi: 10.5281/zenodo.4589071), which is the representative of implicit feedback data set with context information. By integrating the data of the preprocessed original files into one file, the experimental data set contains 12,293 users, 320 singers, and 18,698 related records. In the experiment, 70% of the data sets are selected for training and 30% for testing. The user interest model is established on the training set, and the method’s performance is verified on the test data set.

Evaluation metrics

The study employs several evaluation metrics to assess the performance of various recommendation models, including root mean square error (RMSE), F1-score (F1), and mean average precision (mAP).

RMSE is a widely used metric for measuring the accuracy of predictions in recommendation systems. It calculates the square root of the average of squared differences between predicted and actual ratings. The lower the RMSE value, the more accurate the model’s predictions are.

The F1-score is a harmonic mean of precision and recall, providing a single measure that balances both. Precision is the fraction of relevant items among the recommended ones, while recall is the fraction of relevant items recommended out of all possible relevant items. The F1-score is particularly useful in cases of an imbalance between precision and recall.

Mean average precision (mAP) is a metric that evaluates the ranking quality of the recommendation model. It calculates the average precision of recommendations across all users and then takes the mean of these values. Precision is computed at every position in the ranked list of recommended items, considering only relevant items. mAP emphasizes the importance of returning relevant items earlier in the list, providing a more nuanced measure of recommendation quality.

Memory usage (in MB) measures the memory each model consumes. User-Item CF scales poorly with data size, requiring more memory as the dataset grows. Computation time (in seconds) measures the time each model takes to generate recommendations. These measures evaluate the computational efficiency of the models.

Model comparison

The CF model, TD model, TD-CF model, the singular value decomposition (SVD++) model, and K-means model are compared and analyzed. RMSE is used for evaluation. The comparison results under different sample sizes are shown in Fig. 3:

According to the experimental results, the RMSE value of the prediction result of the mixed model is lower than that of the single model, SVD++ model, and K-means model, which indicates that the recommendation model considering time decay has a better recommendation effect. As the number of predicted scores increases, the RMSE value decreases. From the above analysis results, it can be seen that in the traditional recommendation process, there are still some problems, such as a sparse rating matrix and complex recommendations for new users. Using the improved CF algorithm to recommend teaching resources can solve the problems of data sparsity, scalability, and cold start of users.

The comparison of experimental results in Fig. 4 shows that the evaluation index values of F1 and mAP of the proposed model on the competition data set are better than those of other methods. Among them, when the length of the recommendation list is 10, 40, 70, and 100, respectively, the maximum F1 value of INCF is 24.59% higher on average than that of the other recommendation models (excluding popular recommendations). The minimum average value is 16.28% higher than the other recommendation models. Mapp is also far ahead, indicating that in the existing experimental data and experimental environment, the recommendation performance of the proposed model is better than that of other recommendation models.

User-item CF is a traditional recommendation method that relies on the historical interaction data between users and items to calculate similarity. It is simple: modeling the relationships between users and items based on their historical ratings. However, it is sensitive to data sparsity and the long-tail effect, which can negatively impact its performance. Additionally, user-item CF struggles with the cold start problem, where it is difficult to recommend items to new users or recommend new items due to the lack of historical data.

Matrix factorization is a more advanced technique that decomposes the user-item rating matrix into two lower-dimensional matrices, capturing the latent features of users and items. Standard methods include singular value decomposition (SVD) and alternating least squares (ALS). This approach effectively handles large-scale datasets and often yields better recommendation results than traditional CF methods. However, it involves complex computations and parameter tuning and remains sensitive to data sparsity.

The latent factor model (LFM) is a specific implementation of matrix factorization that focuses on uncovering latent factors to explain user-item interactions. By mapping users and items into a low-dimensional space, LFM captures underlying preferences and characteristics. It provides good recommendation performance and is suitable for implicit feedback data. Despite these advantages, LFM requires careful parameter tuning and has a high computational complexity.

TD-CF introduces a time decay function into collaborative filtering, accounting for the temporal aspect of user interactions. TD-CF places greater weight on recent user behaviors by integrating the time decay function into similarity calculations and user preference estimation. This enhances the relevance of recommendations, especially for short-term user interests. The time decay mechanism helps mitigate the long-tail effect and data sparsity by reducing the influence of outdated interactions.

We show the computation time (seconds) and memory usage (MB) of each model in Fig. 5. User-item CF performs well on small-scale data, but with the increase of data size, the computation time and memory usage increase significantly, showing the characteristic of O(N $\stackrel{ˆ}{}$2). The computation time and memory usage of matrix factorization and LFM increase with data size growth; despite the high computational complexity, they can effectively handle large-scale data and mine latent features. After introducing the time decay function, the computational complexity of TD-CF is similar to that of user-item CF. Still, considering the time of User behavior improves the timeliness and relevance of recommendation results. Although it increases some computational burden, it is still better than User-Item CF in performance.

The simulation results show that TD-CF maintains a low computational complexity while considering both recommendation accuracy and timeliness and is suitable for datasets of different sizes. Compared with other models, TD-CF has significant advantages in dealing with user dynamic interests and performs reasonably in consuming computing resources, which has high practical value.

The accuracy of the TD-CF model varies with weight α, as shown in Fig. 6.

With the increase in the sample size, the model’s accuracy is improved accordingly. When there are 40 and 50 songs, the accuracy of recommendation is the highest when α is 0.4; When there are 60 songs, the accuracy of recommendation is the highest when α is 0.5; When there are 70 songs, and α is 0.6, the accuracy of recommendation is the highest. This verifies the effectiveness of the mixed music recommendation model. When users have a rich listening history, the weight of the CF model is increased, and when users have less listening history, the weight of the TD model is increased. Thereby obtaining a better recommendation effect.

A linear decay provides a balanced weighting, ensuring that recent interactions are favored without overly diminishing the influence of slightly older preferences. Compared to exponential or logarithmic decay functions, the linear model is more accessible to interpret and control, avoiding scenarios where interest in older items diminishes too sharply (as with exponential decay) or too slowly (as with logarithmic decay). The linear function ensures a smooth and gradual reduction in the weight of past interactions, aligning well with the aim of maintaining a steady focus on recent user preferences in music teaching recommendations.

Figure 7 shows that for Last.fm Dataset-1k, the mixed recommendation algorithm in this paper, is more accurate under different recommended items. This is because the user’s interest changes with time, and the user’s forgetting of items is considered when calculating the similarity, thus improving the accuracy of predicting item scores. At the same time, it shows that the best recommendation effect can be obtained by selecting the appropriate number of recommended items N = 50.

In music teaching, TD-CF is selected to recommend teaching resources. By analogy with the characteristics of human memory and forgetting, the closer the time is, the more the user’s interest can be reflected, and the higher the weight of short-term interest in recommendation is so that the characteristics of music teaching resources and users can be fully utilized to achieve more accurate recommendation.

Discussion

The research tackles one of the primary limitations of traditional CF models: their sensitivity to data sparsity and cold start issues. By integrating the time decay function, TD-CF addresses these limitations by reducing the impact of outdated interactions and placing greater emphasis on recent user behaviors. This temporal aspect proves crucial in contexts like music recommendation, where user interests are highly dynamic and change over time. Figures 4 and 7 show that the TD-CF model consistently outperforms other models across different dataset sizes and recommendation list lengths, underscoring its robustness in handling short-term and long-term user preferences.

From a computational perspective, the results depicted in Fig. 5 highlight the efficiency of the TD-CF model. While matrix factorization techniques such as SVD++ and LFM exhibit superior performance in capturing latent features, they are computationally expensive and require complex parameter tuning. On the other hand, the TD-CF model maintains a low computational complexity (comparable to user-item CF) while improving recommendation timeliness and accuracy. This balance between performance and computational cost makes TD-CF a practical and scalable solution for large-scale recommendation systems, especially in educational environments where real-time recommendations are essential for improving learning outcomes.

Critically, our research advances the field by demonstrating how time-sensitive collaborative filtering can be applied to the domain of music teaching resources. In this area, conventional recommendation systems fall short. Traditional models typically struggle to capture the evolving nature of user interests, which is particularly problematic in educational settings where student preferences and learning needs change over time. By leveraging time decay, the TD-CF model aligns more closely with the natural learning process, where more recent learning interactions are weighted more heavily than older ones. This analogy with human memory and forgetting proves instrumental in enhancing the recommendation of teaching resources, as it reflects the dynamic and temporal aspects of music consumption and education.

However, despite its effectiveness, the TD-CF model is not without limitations. One potential area for further research is the exploration of more sophisticated time decay functions that better capture the nuances of user behavior over extended periods. Additionally, while our model demonstrated high accuracy with an optimal value of α, as shown in Fig. 6, further tuning of this parameter may be required when applying the model to different datasets or recommendation domains. Although mitigated by the time decay function, the model’s reliance on historical data could still be improved by integrating additional contextual information, such as user demographics or content features, to refine recommendations further.

The proposed TD-CF model addresses fundamental limitations in traditional recommendation systems by introducing time decay. It is particularly well-suited for applications involving dynamic user preferences, such as music teaching.