A neural collaborative filtering recommendation algorithm based on attention mechanism and contrastive learning

Jianqiao Liu

doi:10.1515/nleng-2025-0137

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A neural collaborative filtering recommendation algorithm based on attention mechanism and contrastive learning

Jianqiao Liu

Published/Copyright: July 16, 2025

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From the journal Nonlinear Engineering Volume 14 Issue 1

Abstract

The neural collaborative filtering recommendation algorithm widely serves as personalized recommendations of users, which further applies deep learning to a recommendation system. It is a universal framework in the neural collaborative filtering recommendation algorithm; however, it does not regard the impact of important features on recommendation results, nor does it regard the issues of data sparsity and long tail distribution of items. To settle these issues, this article proposes a recommendation algorithm based on the attention mechanism and contrastive learning, which focuses on more important features through the attention mechanism and increases the quantity of samples to achieve data augmentation through contrastive learning; therefore, it enhances recommendation performance. The experimental results on two benchmark datasets show that the algorithm proposed in this article has further enhanced recommendation performance compared to other benchmark algorithms.

Keyword: attention mechanism; contrastive learning; deep learning; neural collaborative filtering; recommendation algorithm

1 Introduction

With the rapid development of information technology, today’s community has accessed the age of informatization, generating a large amount of data every moment. How to quickly and accurately obtain messages that the user is interested in from these data is a challenge, and recommendation systems can effectively settle this problem. At present, recommendation systems have been used in e-business, social networks, news communication, and other domains [1,2,3]. Recommendation algorithms are an important component of recommendation systems, and the performance of recommendation algorithms has a significant impact on recommendation results. Currently, collaborative filtering recommendation algorithms are a widely used recommendation algorithm that recommends items of interest to users by calculating their user's similarity and item’s similarity [4]. Among various collaborative filtering recommendation algorithms, matrix factorization is one of the popular ones. Matrix factorization decomposes user and item interaction data into two low-dimensional user matrices and item matrix, obtains the latent contact among users and items, and recommends items of interest to the user through the product of the user matrix and item matrix [5]. Recently, deep learning has also developed promptly, and neural networks in deep learning have realized enormous success in many domains. Many studies have attempted to employ neural networks in the domain of recommendation and have realized some good results, among which the neural collaborative filtering recommendation algorithm is one of them [6]. The neural collaborative filtering recommendation algorithm is a recommendation algorithm that applies neural networks to matrix factorization. It is a universal recommendation algorithm framework with both linear and nonlinear modeling abilities, which can learn stronger user and item representation abilities and has good recommendation performance.

Recently, with the continuous increase in data, it has been difficult to label data, and many data do not have labels. Contrastive learning belongs to self-supervised learning, which can learn from unlabeled data and extract important features from unlabeled data. Contrastive learning has made tremendous achievements in many application domains [7,8,9]. In the domain of the recommendation system, contrastive learning can transform positive samples, add new samples to the sample space, and enhance the representation of data. The self-supervised graph learning model proposed by Wu et al. [10] generates contrastive views on user–item interaction graphs using three methods: node dropout, edge dropout, and random walk and maximizes the consistency of different views of the same node. The SimGCL proposed by Yu et al. [11] creates contrastive views by adding noise to the embedding space, rather than directly modifying the graph structure. This strategy does not change the original user–item interaction graph but improves recommendation performance by enhancing node representation. By using contrastive learning, the performance of the recommendation system can be effectively enhanced. The attention mechanism simulates human attention, focusing more on important things and less on unimportant things. In the recommendation system, utilizing the attention mechanism can provide more attention and weight to important users and items, rather than treating all users and items equally [12,13,14]. Wang et al. [15] proposed a product recommendation model based on self-attention mechanism and attribute heterogeneous information network embedding. The model learns low-dimensional embedding representations of users and items through attribute heterogeneous information network embedding and uses a self-attention mechanism to consider the varying degrees of influence of different attribute information on recommendation results, overcoming the limitations of traditional attribute heterogeneous information network embedding recommendation models. He et al. [1] proposed a recommendation model based on a dual-layer attention mechanism, which improves the interpretability of recommendation results by introducing local attention and mutual attention to learn the potential correlations between users and comments. The attention mechanism can obtain important messages, grasp key sections, better train models, and enhance models’ performance. Therefore, we propose an improved neural collaborative filtering recommendation algorithm, which integrates attention mechanism and contrastive learning on the foundation of the neural collaborative filtering algorithm. This algorithm uses an attention mechanism to adjust the weights of important items, concentrate more attention on important items, and use contrastive learning to add new samples for data augmentation. Experiments were guided on benchmark datasets, and the results showed that the proposed algorithm in this article is effective. Compared with other recommendation algorithms, the proposed algorithm has better performance of recommendation.

The contributions of this article can be concluded as follows:

This article proposes an improved neural collaborative filtering recommendation algorithm, which integrates attention mechanism and contrastive learning on the foundation of the neural collaborative filtering algorithm. Use an attention mechanism to adjust the weights of important items and focus more attention on important items. Use contrastive learning to add new samples for data augmentation.
Experiments were conducted on public datasets, and the experimental results showed that the proposed algorithm in this article is effective. Compared with other benchmark algorithms, our proposed algorithm has better recommendation performance.

The rest of this article is organized as next. In Section 2, we introduced the neural collaborative filtering model. In Section 3, we provided a detailed introduction to our proposed algorithm. In Section 4, we guide experiments on two public datasets to validate the validity of our proposed algorithm. In Section 5, we gave a summary of this article.

2 Neural collaborative filtering (NCF)

Recently, neural networks have developed promptly and realized enormous prosperity in image processing, voice recognition, natural language processing, and other domains. NCF is a collaborative filtering commendation algorithm based on neural network technology, which replaces traditional vector inner product operations with neural networks to achieve matrix factorization and calculate user ratings for items, and provide personalized commendations to users. NCF is a general framework based on neural networks for personalized recommendations, consisting of two sections: generalized matrix factorization (GMF) and multi-layer perceptron (MLP). It has the linear modeling ability of GMF and the nonlinear modeling ability of MLP, which can finer learn the latent contact among users and items. In GMF, users and items are encoded into user and item vectors, and the linear latent contact among users and items is described through the inner product operation of user and item vectors. In the MLP, users and items are encoded, and neural networks are used to learn the deep nonlinear latent contacts among users and items. GMF has linear modeling ability, while MLP has nonlinear modeling ability. The combination of these two models has stronger study ability and can finer learn the deep latent contact among users and items [16–18].

In the NCF framework, the matrix factorization model can be easily extended and learned from data, resulting in a variant of matrix factorization. Therefore, matrix factorization is widely served as practical applications. There is also an extension method that uses nonlinear functions to set the nonlinearity of matrix factorization and learn the latent contact among users and items from logarithmic loss data. By using nonlinear functions, not only the model can be represented nonlinearly, but also its expressive power can be enhanced, thereby obtaining the nonlinear contact between users and items and improving the performance of the model. The linear model is generally difficult to obtain deep latent contacts between users and items; therefore, matrix factorization is not very effective in improving collaborative filtering. In the NCF framework, MLP has nonlinear modeling capabilities and enormous flexibility, enabling them to learn the deep latent contacts among users and items. MLP is discriminative from GMF, which can only use the inner product of fixed user and item features. A MLP can gradually reduce the quantity of neurons from the import layer to the export layer, using fewer neurons at the higher layer to learn more abstract features of users and items. MLP generally has multiple hidden layers, each with a discriminative quantity of neurons, so that they can process information and complete various tasks. MLP has nonlinear modeling abilities and can learn nonlinear contacts in data. The combination of nonlinear and linear models can further enhance the performance of the recommendation.

3 Methodology

3.1 Problem definition

The main notations and their descriptions used in the article are shown in Table 1.

Table 1

Notations and descriptions

Notations	Descriptions
U	User set
I	Item set
u	User
i	Item
a ⌢ u , i	Attention value
τ	Temperature coefficient
y u i	True value
y ˆ u i	Prediction value
f	Prediction function

Generally, U = { u } is represented as a set of users, I = { i } is represented as a set of items, and the historical interaction among user u and item i is represented as y u i , which is explained as follows:

(1) y u i = 1 , interation between u and i 0 , otherwise,

where y u i = 1 represents the interaction between user u and item i, and y u i = 0 represents the interaction that does not exist between user u and item i. The quantity of user sets U is represented by m, the quantity of item sets I is represented by n, and the historical interaction matrix between the user and the item is denoted as Y, where Y is a matrix of m × n . The recommendation algorithms mainly predict user ratings for items without interaction based on the historical interaction records among users and items and recommend high-rated items without interaction with the user. This process can be abstracted into the form of a learning function, which is used to calculate the score of user u for item i. The function is represented as

(2) y ˆ u i = f ( u , i ) ,

where y ˆ u i represents the prediction score of user u for item i and f represents the prediction function.

3.2 Framework diagram

The proposed algorithm in this article is a recommendation algorithm that applies neural networks to collaborative filtering and has realized enormous success. However, the neural collaborative filtering algorithm handles all items equally and does not regard the important impacts of important items on the recommendation results. The neural collaborative filtering recommendation algorithm also did not regard the sparsity of user and item interaction data and the long tail effect. Therefore, we integrate attention mechanism and contrastive learning based on the neural collaborative filtering recommendation algorithm to enhance the performance of the recommendation algorithm. By using an attention mechanism to assign discriminative weights to important items, more attention is given to important items. Through contrastive learning, transform the original samples to construct new ones, achieve data augmentation, and optimize model performance. The framework diagram of the neural collaborative filtering recommendation algorithm based on attention mechanism and contrastive learning (NCF-AC) proposed in this article is shown in Figure 1.

Figure 1

NCF-AC model framework.

The following section provides a detailed introduction to attention mechanisms and contrastive learning.

3.3 Attention mechanism

Attention mechanism is a technique that simulates human attention, which assumes that humans have discriminative levels of attention toward important items, pay more attention to important items, and do not pay too much attention to unimportant items. The attention mechanism believes that important items will have discriminative impacts on the results, and all items should not be treated equally. The important items need to be given higher weights. Attention mechanism can help us select important and useful messages from a large amount of messages, play more weight into these messages, and enhance our work efficiency. In the proposed algorithms, adopting attention mechanism can finer handle the interaction among users and items, focus more attention on important users and items, enhance the accuracy of recommendation results, and achieve personalized recommendations. The attention mechanism can learn from user behavior which items are more important to the user and which items are not important to the user in order to better recommend items that the user is interested in [19,20]. The calculation of attention in this article is explained in formula (3), which assigns higher weights to discriminative vectors to finer match the user’s preference for items. This can enhance the accuracy of recommending items to user and finer meet their personalized needs

(3) a ⌢ u , i = V a ReLU ( W a [ p u ; q i ] + b a ) ,

where W a and b a are the weight matrices and bias vectors from the import layer to the hidden layer, respectively, V a is the attention weight vectors from the hidden layer to the export layer, [ p u ; q i ] represents the concatenation of two feature vectors, and ReLU is the activation function.

The attention mechanism can capture the attention of user u to item i and assign higher weights to discriminative items. When performing feature fusion, the ultimate interaction features among users and items are learned through p u and q i . Adopting attention mechanism, it is possible to finer learn the latent contact among users and items and enhance the performance of the recommendation.

3.4 Contrastive learning

Contrastive learning is a self-supervised learning and has been widely used in domains such as natural language processing, image processing, and computer vision. Contrastive learning constructs variants of the samples that are similar to the samples through transformation processing and adds new samples to the sample space. The enhanced samples should be as close as possible in space, and discriminative samples should be as far apart as possible in space. The core of contrastive learning is data augmentation. In the domain of the recommendation system, user and item features are high-dimensional sparse data, and there are connections among users and items. The interaction data among users and items is a positive sample, and in general, there are relatively few positive samples. Therefore, constructing more positive samples through contrastive learning is a key issue in contrastive learning [21,22]. The contrastive learning served in this article is to add random noise to positive samples to construct new samples and achieve data augmentation. For a sample e i , calculate the sample using formulas (4) and (5) to construct a new sample

(4) e i ′ = e i + Δ i ′ ,

(5) e i ″ = e i + Δ i ″ ,

where add noise vectors Δ i ′ and Δ i ″ to the original sample, following ∥ Δ ∥ 2 = ε and Δ = Δ ¯ ⊙ sign ( e i ) , Δ̄ conforms to a standard normal distribution.

Add noise to the original sample. Rotate the original sample at a small angle, with each rotation corresponding to a new sample. By rotating multiple times, multiple new samples can be obtained, achieving data augmentation. Because the original sample is rotated at a relatively small angle, the resulting sample maintains a certain difference from the original sample after rotation, while also retaining the majority of the message of the original sample. The noise added to the original sample is random and discriminative. The calculation of contrastive loss L cl is explained in the following formula:

(6) L cl = ∑ i − log exp ( e i ′ T e i ″ / τ ) ∑ j exp ( e i ′ T e j ″ / τ ) ,

where 1 / τ is a constant, T is the transposition of vectors, i is a positive sample, and j is a negative sample. The optimization of contrastive loss is to reduce the cosine similarity among discriminative samples obtained through the transformation of the original sample, making the sample distribution more uniform. By optimizing the contrastive loss, similar samples can be made closer in the vector space, while discriminative samples can be further away in the vector space, maximizing useful information from contrastive learning and improving model performance.

3.5 Model optimization

The loss function of the algorithm proposed in this article consists of two parts, one of which is the loss function L n of the neural collaborative filtering recommendation after adding attention mechanism, and the other is the loss function L cl of contrastive learning. The optimization objective of the algorithm proposed in this article is the sum of loss L n , loss L cl , and L2 regularization.

Loss L n : This is a paired loss that maximizes the difference in scores among positive and negative samples. Perform matrix factorization on the user rating matrix and optimize it using Bayesian maximum posteriori probability. The loss calculation is explained as follows:

(7) L n = − ∑ i ∈ B ln ( y p − y n ) ,

where y p represents the score of the positive sample, y n represents the score for the negative sample, and B represents the set of samples.

After obtaining the loss L n and loss L cl , we combine them for joint study, as explained in the following formula:

(8) L = L n + L cl + λ ∥ θ ∥ ,

where λ is the regularization coefficient, which is a hyperparameter used to adjust the severity of punishment. The larger the value, the greater the severity of punishment. Adding regularization terms λ ∥ θ ∥ is to prevent overfitting.

3.6 Algorithm description

Algorithm: An NCF-AC

Step 1: Preprocess the data. Generate embedding vectors for users and items, generate user–item interaction matrices, and divide them into training and testing sets.

Step 2: Build the model. Use attention mechanisms to capture information between users and items, assigning different weights to different features; use contrastive learning for data augmentation to improve recommendation performance.

Step 3: Train the model. Train the model using the training set data, adjust the model parameters by minimizing the loss function, and select an optimizer to optimize the loss.

Step 4: Predict the score. For each user and item pair in the test set, input the test set into the trained model to obtain the predicted score. And sort the scores, returning the top N items with the highest scores as the recommendation results.

Step 5: Model evaluation. Use various evaluation metrics such as hit ratio (HR) and normalized discounted cumulative gain (NDCG) to assess the performance of the model.

4 Experimental results and analysis

In this section, we guide experiments on public datasets to confirm the performance of our proposed algorithm. These experiments mainly answer the following questions:

RQ1: How is the overall performance of our proposed recommendation algorithm compared with other recommendation algorithms?

RQ2: What is the impact of the key parameters of our proposed recommendation algorithm on recommendation performance?

RQ3: What is the impact of adding attention and contrastive learning modules to the neural collaborative filtering recommendation algorithm on recommendation performance?

First, we introduce the datasets, evaluation metrics, and benchmark algorithms we use and then answer the upper questions separately. Analyze the overall performance of the algorithm proposed in this article, analyze the impact of key parameters on recommendation performance, and confirm the impact of different modules on recommendation performance through ablation experiments.

4.1 Datasets

In order to confirm the performance of the recommendation algorithm proposed in this article, the experiments were guided on two public datasets, and the detailed information on these two public datasets are as follows:

Movielens dataset: The Movielens dataset is a commonly used machine study dataset used to assess the performance of recommendation algorithms. This dataset is collected through an online movie rating website, which includes user data, movie data, and user rating data for movies. Regardless of the specific rating given by the user to the movie, a grade of 1–5 will be uniformly marked as 1 (with interaction), and in other cases, it will be marked as 0. The data is preprocessed. We deleted user data with less than 20 interactions among users and movies.
Pinterest dataset: The Pinterest dataset is also a commonly used dataset for evaluating the performance of recommendation algorithms. It is a communal and large-scale image recommendation dataset. This dataset contains approximately 50,000 users and 1.58 million interactions among users and items. In order to ensure the quality of the dataset, we also preprocessed the dataset, retaining only user data with 20 or more interactions among users and items.

4.2 Evaluation metrics

HR is a commonly used metric to assess the performance of recommendation algorithms and used to assess the hit rate of recommendation systems. HR behalf the proportion of items that users actually like in the recommendation list. The range of HR values is generally between 0 and 1. The higher the HR value, the more accurate the recommendation.
NDCG is the normalized discounted cumulative gain, which is also a commonly served indicator to assess the performance of recommendation algorithms. NDCG regards the impact on the ranking order of recommended items by users. Items with higher rankings have higher obtained, while items with lower rankings need to compromise their obtained. Items with discriminative ranking orders have an important impact on recommendation performance, with the top items having a greater impact and the bottom items having a smaller impact. The range of NDCG values is between 0 and 1, and the higher the value, the better the recommendation performance. NDCG is a comprehensive evaluation metric for the performance of recommendation algorithms.

4.3 Benchmark algorithms

Item KNN (Item K-nearest neighbors): is a recommendation algorithm based on collaborative filtering, which obtains a set of similar items to the target item based on the user’s historical behavior interaction of the items. Based on the set of similar items, the algorithm estimates the user’s rating on the target items. The algorithm is simple and efficient.
BPR: BPR (Bayesian personalized ranking) is a recommendation algorithm based on matric factorization, which learns the latent features of users and items through Bayesian analysis, optimizes using stochastic gradient descent, and then recommends to the user based on the ranking consequences of items. The algorithm has advantages in selecting a very small amount of data for recommendation in massive amounts of data.
GMF: This is a GMF recommendation algorithm that behalf user and items as a low-dimensional user matrix and item matrix through matrix factorization. Then, the user matrix and item matrix are dot products, and item recommendations are made based on the dot product calculation results. The algorithm is a relatively effective method in both explicit and implicit feedback recommendations.
MLP: This is a recommendation algorithm based on neural networks, which has a hidden layer or multiple hidden layers. There are multiple neurons in the hidden layer, and the next layer receives import from the previous layer. The layers are converted through nonlinear activation features. The algorithm has good recommendation performance, but its training process is relatively time-consuming.
NCF: This is a recommendation algorithm that applies neural networks to matrix factorization, consisting of two parts: GMF and MLP. It has linear and nonlinear modeling abilities and can finer learn the deep latent contact among users and items, with good recommendation performance. The algorithm is a neural network-based collaborative filtering algorithm for implicit feedback data and is a widely used recommendation algorithm.

4.4 Performance analysis

In order to confirm the validity of the NCF-AC proposed in this article, extensive experiments were guided on two public datasets with other benchmark algorithms to compare the recommendation performance. In the experiments, this article sets the quantity of layers for the MLP to 3, the vector size to 64, the temperature coefficient to 0.1, the Top-K to 10, and the training frequency to 20. The benchmark algorithms are set according to the original references. The experimental results are shown in Table 2. It can be seen from Table 2 that on the Movielens dataset, the recommendation algorithm proposed in this article has a higher evaluation metric HR than other benchmark algorithms, and a higher evaluation metric NDCG than other benchmark algorithms. This indicates that adding attention mechanisms and contrastive learning on the basis of neural collaborative filtering recommendation algorithms is effective in improving the performance of recommendation algorithms. For the Pinterest dataset with a large amount of data, the recommendation algorithm proposed in this article also performs well in terms of recommendation performance, with higher evaluation metrics HR and NDCG than other benchmark algorithms. This indicates that the recommendation algorithm proposed in this article is also effective for other datasets, with wide adaptability and good generalization ability. Compared with the Movielens dataset, the Pinterest dataset is a relatively large dataset, and having more samples can enable the algorithm to finer learn the representation of users and items, and finer filter out items that users may be interested in. The experimental results fully demonstrate that the attention mechanism can enable users to pay more attention to important items, finer predict user behavior, and recommend more suitable items to users. Contrastive learning can optimize models and enhance algorithm performance by changing samples, increasing samples, and enhancing data representation. Therefore, the proposed recommendation algorithm in this article based on the NCF, integrating attention mechanism and contrastive learning, can enhance the recommendation performance to a certain extent.

Table 2

Performance comparison

Dataset	Movielens		Pinterest
Dataset	HR	NDCG	HR	NDCG
ItemKNN	0.701	0.429	0.862	0.536
BPR	0.687	0.418	0.858	0.534
GMF	0.712	0.431	0.860	0.542
MLP	0.720	0.436	0.864	0.547
NCF	0.731	0.442	0.872	0.553
NCF-AC	0.754	0.463	0.915	0.578

4.5 The impact of parameter

In the recommendation algorithm proposed in this article, the temperature coefficient τ is an important parameter. If the temperature coefficient is set relatively large, the distribution of negative samples will be smoother, which will cause the model to treat all negative samples equally, thereby affecting the performance of the recommendation. If the temperature coefficient is set relatively small, the model will pay special attention to those hard negative samples, which may cause the model to think that those negative samples may be latent positive samples, which will make it difficult for the sample to converge and the sample’s generalization ability will be poor. The temperature coefficient τ has a significant impact on the performance of the algorithm; therefore, the setting of the temperature coefficient τ plays an important role in the algorithm. Generally, appropriate temperature coefficient values can be determined through experimental analysis. In order to obtain the appropriate temperature coefficient, we set the temperature coefficients separately τ = {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9}, experiments were guided, and the experimental results are shown in Figures 2 and 3. From the experimental results, it can be seen that in the Movielens dataset, as the temperature coefficient increases, the performance of the model gradually decreases. When the temperature coefficient is equal to 0.1, the performance of the model is optimal. In the Pinterest dataset, the experimental results are basically similar to those in the Movielens dataset. As the temperature coefficient continues to increase, the performance of the model gradually decreases. When the temperature coefficient is equal to 0.2, the performance of the model is optimal. The size and sparsity of different datasets vary, and the temperature coefficient is not entirely the same. Through experimental analysis, it is generally found that the effect is better when the temperature coefficient is set in the range of 0.1–0.2.

Figure 2

The impact of temperature coefficient τ on performance in the Movielens dataset.

Figure 3

The impact of temperature coefficient τ on performance in the Pinterest dataset.

4.6 Ablation experiment

In order to confirm the performance impact of adding an attention module and contrastive learning module on the proposed algorithm based on NCF, we guide ablation experiments on the Movielens dataset and Pinterest dataset. We analyzed the impact of different modules on recommendation performance through ablation experiments, and the experimental results are shown in Figures 4 and 5. We first add only an attention module to the neural collaborative filtering recommendation algorithm, without adding a contrastive learning module, represented as NCF-A. From the experimental results, it can be seen that on the Movielens dataset and Pinterest dataset, both the evaluation metrics HR and NDCG have enhanced recommendation performance, validating that adding the attention module can enhance the performance of recommendation algorithms. Then, we guide the following experiment by adding only a contrastive learning module and not an attention module to the neural collaborative filtering recommendation algorithm, represented as NCF-C. From the experimental results, it can be seen that on the Movielens dataset and Pinterest dataset, both the evaluation metrics HR and NDCG have enhanced recommendation performance, validating that adding the contrastive learning module can enhance the performance of recommendation algorithms. From Figures 4 and 5, it can also be seen that by adding both attention and contrastive learning modules to the neural collaborative filtering recommendation algorithm, the recommendation performance is optimal in terms of evaluation metrics HR and NDCG. Through ablation experiments, we can conclude that using the attention mechanism to adjust the weights of important items, focusing more attention on important items, and using contrastive learning to add new samples for data augmentation can effectively enhance the performance of the recommendation algorithm.

Figure 4

HR values in the ablation tests.

Figure 5

NDCG values in the ablation tests.

5 Conclusions

In this article, we propose an NCF-AC, which integrates attention mechanism and contrastive learning on the basis of the neural collaborative filtering recommendation algorithm. Different items have varying degrees of impact on recommendation results, and attention mechanism adjusts the weights of different items based on their varying degrees of impact on recommendation results. In response to the problem of data sparsity, contrastive learning performs transformation operations on samples, increases the quantity of samples, enhances data representation, and enhances model performance by reducing the distance among similar samples in the projection space through contrastive learning loss. Extensive experiments have been guided on public datasets, and the experimental results show that the algorithm proposed in this article is effective. Compared with other benchmark algorithms, the recommendation performance has been enhanced to a certain extent.

Funding information: The author states no funding involved.
Author contributions: Jianqiao Liu completed the work on this manuscript. The author has accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The author states no conflict of interest.
Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-08-15

Revised: 2024-12-30

Accepted: 2025-04-01

Published Online: 2025-07-16

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/nleng-2025-0137

Keywords for this article

attention mechanism; contrastive learning; deep learning; neural collaborative filtering; recommendation algorithm

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