A reliable joint neural collaborative filtering recommendation system
By integrating reliability into a joint neural collaborative filtering recommendation system, the problems of information loss and noise influence in deep learning models are solved. By generating a rating reliability matrix and optimizing the recommendation list, the accuracy and reliability of the recommendation system are improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-06-29
- Publication Date
- 2026-03-13
AI Technical Summary
Existing deep learning-based recommendation models struggle to effectively capture collaborative information within the data, neglect historical interaction information between users and items, and may experience information loss during neural network propagation, resulting in insufficient recommendation accuracy.
A joint neural collaborative filtering recommendation system with fusion reliability is adopted. Through data acquisition and preparation modules, natural noise detection modules based on intuitionistic fuzzy sets, bilinear aggregation modules, fully connected neural network modules, rating and rating reliability prediction modules, and recommendation list acquisition modules, a user-item rating reliability matrix is generated. During the recommendation process, unreliable items are removed and high-reliability items are added to improve the recommendation quality.
By identifying and removing noise, a unified deep neural network is used to fit the rating matrix and reliability matrix, outputting the user's predicted rating and reliability for items, thus improving the accuracy and reliability of the recommendation results.
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Figure CN116881552B_ABST
Abstract
Description
[0001] This invention belongs to the field of recommendation technology, and mainly introduces a neural collaborative filtering recommendation method and system that integrates reliability. Background Technology
[0002] With the popularization of the internet and the deepening of digitalization, the amount of data generated has exploded, making information retrieval more difficult for users. Accurately pushing content of interest to users has become a major battleground for industrial internet research and innovation. Personalized recommendation systems can effectively alleviate overload problems and reduce the time cost for users to filter out irrelevant information, thus finding widespread application in e-commerce, social networks, and search engine ranking.
[0003] While the introduction of deep learning methods has effectively enhanced the model's ability to perform non-linear modeling of data, these models struggle to effectively capture the intrinsic value information within the data. This is because they simply map user and item features into low-dimensional dense vectors, failing to emphasize the underlying mechanisms guiding recommendation applications and the effective mining of historical user-item interactions. Many models use user-item interaction information only for optimizing model parameters, ignoring potential collaborative information in the data that could reveal behavioral similarities between users, severely hindering further performance improvements. Secondly, existing deep learning-based recommendation models primarily utilize vector concatenation combined with neural networks to extract high-order features. However, as the number of neural network layers increases, information loss may occur during forward propagation. Furthermore, neural networks typically perform feature crossing implicitly, a process that is difficult to control, potentially leading to situations where they cannot effectively learn multiple feature combinations. Summary of the Invention
[0004] To address the above problems, this invention proposes a joint neural collaborative filtering recommendation system with fusion reliability, comprising:
[0005] The data acquisition and preparation module is used to clean and reconstruct user data to obtain the user-item rating matrix required by the system. ;
[0006] The natural noise detection module based on intuitionistic fuzzy sets divides the rating matrix according to user and item preferences. Ratings that do not conform to user and item preferences are identified as natural noise, and an initial 0-1 reliability matrix is generated based on the identification results.
[0007] The bilinear aggregation module is used to introduce a parameter-updateable weight matrix on the basis of the original embedded vector, and further consider the importance of the interaction vector in each potential dimension.
[0008] The fully connected neural network module is used to further learn higher-order feature information from user ratings and rating reliability data using a fully connected neural network on top of the aggregation layer;
[0009] The scoring and scoring reliability prediction module is used to output the predicted score value and the prediction reliability corresponding to the score value;
[0010] The recommendation list retrieval module is used to find the set of the top K items with the highest predicted ratings for target user i.
[0011] The recommendation list removal and filling module is used to remove items from the recommendation list whose prediction reliability is less than a set threshold, and to fill the positions of the removed items with items with high prediction scores and high prediction reliability for personalized recommendations, so as to improve the recommendation quality.
[0012] The data acquisition and preparation module is used to generate an explicit feedback matrix with numerical values as specific ratings based on user feedback information about the items. , Indicates the number of users. To represent the number of items, user ID and item ID are represented as one-hot vectors. and And through the mapping matrix The high-dimensional vector is mapped to an embedding vector in a low-dimensional space, where m, n, and k represent the number of users, items, and latent factors, respectively. The specific mapping process is as follows:
[0013]
[0014] The natural noise detection module based on intuitionistic fuzzy sets is used to classify user and project preferences using intuitionistic fuzzy set correlation theory, and to determine the reliability of user ratings based on the classification results, thereby generating an initial reliability matrix.
[0015] S1: Assumption and These are collections of users and projects, with quantities of... and Each user i in user set I rates each item j in item set J from 1 to 5, and the average rating of user i is . Membership degree of user i Non-membership degree and hesitation The specific conversion rules are as follows:
[0016]
[0017]
[0018]
[0019] S2: The intuitive fuzzy numbers for user i and project j obtained from the above formula. and Users and projects are categorized according to the following rules:
[0020]
[0021] S3: Based on the user and project classification results, perform noise discrimination on the ratings of each user and generate a reliability matrix. The rules for generating the initial reliability matrix are as follows:
[0022]
[0023] The bilinear aggregation module is used to fully explore the low-order interactions between user and item embedding vectors, and its expression is as follows:
[0024]
[0025] in, Let J be the weight matrix of item j. This represents finding the dot product of vectors. The Hadamard product is calculated for the vectors. Simultaneously, to preserve the information contained in the original embeddings, the bilinear aggregation layer is concatenated with the original user and item embedding vectors.
[0026] The fully connected neural network module is used to calculate the prediction score and prediction reliability within the same neural network, thereby achieving bidirectional enhancement of both tasks. Specifically, it includes:
[0027]
[0028] Where e represents the number of layers in the neural network, and the initial... Represents the output of the pooling layer. ...
[0029] The rating and rating reliability prediction module is used to output the user's predicted rating for the item and the reliability level corresponding to the predicted rating in the same neural network, and its expression is as follows:
[0030]
[0031] in, and Let these represent the predicted ratings of user i for item j and... Corresponding prediction reliability, activation function The sigmoid function has the following expression:
[0032]
[0033] The recommendation list acquisition module is used to combine explicit and implicit feedback for optimization, and its processing steps are as follows:
[0034] S1: Construct the loss function, whose expression is as follows:
[0035]
[0036] in, and These represent positive and negative samples in the training data, respectively. and These represent the actual value and the predicted value corresponding to the actual value, respectively. These represent the weight parameters of the model's embedding layer, aggregation layer, and fully connected neural network, respectively.
[0037] S2: To calculate the implicit prediction reliability loss, use the predicted value according to the above formula. and the true value Calculate the loss value;
[0038] S3: To calculate the explicit rating loss, first calculate the true rating using the following formula. Normalization :
[0039]
[0040] Where min(y) and max(y) represent the user-item rating matrix, respectively. The minimum and maximum values are then used. The predicted values are then used again. and the normalized true value The loss value is calculated, thus avoiding the impact of value range differences on the optimization process;
[0041] S4: Update model parameters using the Adam optimizer;
[0042] S5: Iterate through the set of positive and negative samples until the set number of iterations is reached or the loss value no longer decreases;
[0043] S6: Use the trained model parameters to make predictions, sort the predicted scores in descending order, and take the top K scores for item recommendation.
[0044] The recommendation list removal and filling module is used to remove unreliable items from the recommended items and select items with high predictive reliability from items that the user has not interacted with to fill the list. The specific steps are as follows:
[0045] S1: Assume the reliability threshold is... Remove recommendations with ratings less reliable than The items are identified, and their corresponding positions p and removal quantities q are recorded.
[0046] S2: Divide the items that user i has not interacted with into a set, which includes two factors: item rating and corresponding reliability;
[0047] S3: Use the K-means algorithm based on Euclidean distance to further refine the partitioning of the set. The specific formula is as follows:
[0048]
[0049] Select the cluster with the largest centroid value from the K-means clustering results as the candidate filling list. Based on the previously removed item positions p and quantities q, in Randomly selected reliability Greater than the threshold Uninteracted items are then filled in descending order of predicted item ratings.
[0050] S4: Score item j based on the overall filling result. With reliability If the filling item Less than the candidate list Centroid and reliability threshold If the product is multiplied, the item is considered to have missed; otherwise, it is considered to have hit.
[0051] The beneficial effects of this invention are that, compared to traditional recommendation algorithms, this model considers the impact of user rating noise on the prediction accuracy of the recommendation system. First, it uses the concept of intuitionistic fuzzy sets to identify natural noise, classifying users and items using intuitionistic fuzzy numbers and generating a 0-1 rating reliability matrix. In calculating the reliability matrix, only the original rating matrix is used, thereby improving the model's versatility and scalability. Second, during training, a unified deep neural network is used to fit the rating matrix and reliability matrix, finally outputting the user's predicted rating for the item and the reliability of the predicted rating. During the recommendation process, a predefined reliability threshold is used to remove predicted ratings with low reliability probabilities, and a K-means imputation strategy is used to add high-reliability items for recommendation, further improving the accuracy and reliability of the recommendation results. Attached Figure Description
[0052] Figure 1 This is a schematic diagram of the process of the present invention;
[0053] Figure 2 This is a system framework diagram of the present invention;
[0054] Figure 3 This is a schematic diagram of the reliability matrix generation of the present invention;
[0055] Figure 4 This invention applies to three datasets. and The changes in value; Detailed Implementation
[0056] To make the objectives, technical solutions, and advantages of the present invention clearer, the specific embodiments and working principles of the present invention will be further described in detail below with reference to the accompanying drawings.
[0057] Figure 1 This is a schematic diagram of a joint neural collaborative filtering recommendation method and system that integrates reliability. The process includes collecting and cleaning data from a database, transforming the data into a rating matrix based on user interaction information, using an intuitionistic fuzzy set-based noise detection method to calculate the intuitionistic fuzzy numbers of users and items, classifying users and items based on these numbers, identifying rating noise based on the classification results, and generating an initial reliability matrix. Finally, this reliability matrix and the initial rating matrix are fed into the same multilayer perceptron for training, sharing user embedding vectors during training. The output includes the user's predicted rating and the corresponding predicted rating reliability. In the subsequent Top-n recommendation process, a reliability threshold is set based on the training results of the rating reliability. Remove recommendations with lower reliability. The project is selected, and according to the set rules, the same number of projects are extracted and removed from the projects that the user has not interacted with to fill the recommendation list, thus obtaining the recommended item list for different users.
[0058] Figure 2 This is a framework diagram of the reliability-integrated recommendation system of the present invention. From Figure 2 As can be seen, the recommendation method and system based on intuitionistic fuzzy sets proposed in this invention include a data acquisition and preparation module, a natural noise detection module based on intuitionistic fuzzy sets, a bilinear aggregation module, a fully connected neural network module, a rating and rating reliability prediction module, a recommendation list acquisition module, and a recommendation list removal and filling module. The data acquisition and preparation module extracts data from the database, performs cleaning and preprocessing operations on the data, and transforms it into a user-item rating matrix. The natural noise detection module based on intuitionistic fuzzy sets calculates the intuitionistic fuzzy numbers of users and items according to the theory of intuitionistic fuzzy sets, classifies users and items according to these intuitionistic fuzzy numbers, and, based on the classification of user and item preferences, divides the rating matrix... Ratings that do not conform to user and item preferences are classified as natural noise, and an initial 0-1 reliability matrix is generated based on the classification results. The bilinear aggregation module introduces a parameter-updatable weight matrix on the basis of the original embedding vector Hadamard product, further considering the importance of interaction vectors in each potential dimension. The shared fully connected neural network module is used to further learn higher-order, nonlinear feature interactions in user ratings and rating reliability data using a fully connected neural network on the basis of the aggregation layer. The rating and rating reliability prediction module is used to output the user's predicted rating preference for non-interactive items and the predicted reliability magnitude corresponding to the rating preference. The recommendation list acquisition module is used to generate a set of items with the highest ranking results for the user based on the rating preference prediction results. The recommendation list elimination and filling module is used to eliminate items with predicted reliability lower than a set threshold based on the predicted reliability of items in the recommendation set, and fill the positions of the eliminated items with items with high predicted ratings and high predicted reliability for personalized recommendations to improve recommendation quality.
[0059] Figure 3 This paper presents an example of noise discrimination based on intuitionistic fuzzy sets. According to the definition of intuitionistic fuzzy sets, this paper transforms user preferences for items in the recommendation system—like, dislike, and uncertain preferences—into membership (M), non-membership (N), and hesitation (H) within an intuitionistic fuzzy set. Based on the relationship between these three attributes in the user and item, these preferences are categorized into three levels: strong preference, weak preference, and unknown preference. The rating of user i for item j is then re-evaluated based on the classification levels of user i and item j to determine whether it is noise. This method transforms the explicit rating matrix into an implicit reliability matrix, ensuring that the subsequent neural network can more fully learn the higher-order interactions between features.
[0060] Membership degree of user i Non-membership degree and hesitation The specific conversion rules are as follows:
[0061]
[0062]
[0063]
[0064] Assume I and J are sets of users and items, respectively, with sizes m and n. Each user i in user set I rates each item j in item set J from 1 to 5, and the average rating of user i is... The process of calculating the intuitive fuzzy number of an item is similar to that of a user.
[0065] Based on the obtained users and items Intuitive fuzzy numbers and Users and items are categorized into three groups: strong preference, neutral preference, and unknown preference. When a user and item belong to the same category, but the rating belongs to a different category, that rating value is considered natural noise.
[0066] Furthermore, the following example illustrates this further:
[0067] Assume there is individual users and Items The user rating matrix for items is used This indicates that the reliability matrix of user ratings for items is represented by... express, Indicates the number of users. To represent the number of items, use This represents the rating value of user i for item j. The value range is 1-5.
[0068] First, standardized information that meets the system requirements is obtained through the data acquisition and processing module. The specific implementation steps of the proposed recommendation system are as follows:
[0069] S1: Obtain the data information required by the system, including user ID, item ID, and user ratings for items, and construct a user-item rating matrix based on the above information. .
[0070] S2: Convert user IDs into one-hot vectors Convert item IDs into one-hot vectors. Initialize the mapping matrix of users, items, and reliability using a Gaussian distribution. Where m, n, and k represent the number of users, the number of projects, and the number of latent factors, respectively. The embedding vector mapping process is as follows:
[0071]
[0072] S3: The bilinear aggregation module combines the inner product and Hadamard product operations, and then concatenates the original embedding vectors to obtain the information contained in the original embeddings. The specific implementation of the module is as follows:
[0073]
[0074] in, Let J be the weight matrix of item j. This represents finding the dot product of vectors. This describes the Hadamard product of vectors. Assume the input is a pair of user items. The first layer is the item embedding vector. and weight matrix First perform the inner product, then combine it with the user embedding vector. Calculate the Hadamard product and then concatenate it with the original user and item embedding vectors. Aggregation of user and item additional attributes follows a similar process.
[0075] S4: In the fully connected neural network module, user-item group And User-Item Additional Factors Group Using the same hidden layer, the combined information vector output by the bilinear aggregation module is... Building upon this foundation, higher-order features in the data are further learned through a multi-layer nonlinear neural network. Furthermore, user-item groups and user-item additional factor groups share user embedding vectors. This enables bidirectional augmentation during training with two sets of data, as shown in the following expression:
[0076]
[0077] Where e represents the number of layers in the neural network, and the initial... Represents the output of the aggregation layer. and ...
[0078] S5: The output of the hidden layer is processed by the final output layer and transformed into the prediction result. The transformation process is as follows:
[0079]
[0080] in, and Let these represent the predicted ratings of user i for item j and... Corresponding prediction reliability, activation function The sigmoid function has the following expression:
[0081]
[0082] S6: The recommendation list acquisition module uses binary cross-entropy error to construct the loss function, and combines explicit and implicit feedback for optimization. The loss function is as follows:
[0083]
[0084] in, and These represent positive and negative samples in the training data, respectively. and These represent the actual value and the predicted value corresponding to the actual value, respectively. These represent the weight parameters of the model's embedding layer, aggregation layer, and fully connected neural network, respectively. To ensure that explicit scoring also applies to cross-entropy error, this paper uses minimum-maximum normalization to normalize the true values of the scoring matrix. The value range is mapped to the range of 0-1, and the specific formula is as follows:
[0085]
[0086] Here, min(y) and max(y) represent the minimum and maximum values in the rating matrix, which are 1 and 5 in this paper, respectively, thus realizing the optimization of the predicted rating and prediction reliability by using the shared binary cross-entropy loss function.
[0087] After obtaining the loss, the Adam optimizer is used to update the model parameters, and the optimized model is used to predict the user's preference value for items. Finally, the initial recommendation list is generated by sorting the predicted preference values.
[0088] S6: The recommendation list removal module uses the reliability results of the prediction score to set different reliability thresholds according to the model's predicted reliability ratio. When the reliability of item rating prediction is less than When the item is removed from the recommendation list, its position p and the number of items removed q are recorded.
[0089] S7: The recommendation list population module divides items that user i has not interacted with into a set, which includes two factors: the user's predicted rating for the item and its corresponding reliability. Then, the K-means algorithm is used to further refine the set, and Euclidean distance is used to update the classification clusters. The specific formula is as follows:
[0090]
[0091] in, and These represent the horizontal and vertical coordinates of the categorical data and the centroid in two-dimensional space, respectively. For point With point The Euclidean distance between them.
[0092] Select the cluster with the largest centroid value from the K-means clustering results as the candidate filling list. At this time This refers to the set of predictions from the model that have high scores and score reliability. Based on the previously removed item locations p and quantities q, in... Randomly select items that the user has not interacted with, and then fill in the remaining items in descending order of their predicted ratings. The filling results are evaluated by considering both the item ratings and reliability. If the item... The higher the value, the earlier the recommended position. Therefore, if filling items... Less than the reliability threshold or Less than the candidate list Centroid and reliability threshold If the product is not found, the item is considered a miss; otherwise, it is considered a hit. This filling method provides users with items that have high scores and reliability in the model's prediction results.
[0093] Figure 4 The model's performance was measured in two metrics: recall ( ) and normalized loss cumulative gain ( Its definition is as follows:
[0094]
[0095] Where k represents the number of items recommended by the model. The set of items that the model recommends to the user. This represents the set of items that users actually interacted with in the test set, i.e., the correctly recommended items in the recommended item set. The proportion of.
[0096] The NDCG metric is used to assess the impact of the location of recommended items; the higher the position of a highly relevant result, the higher its score.
[0097]
[0098]
[0099]
[0100] in This represents the cumulative gain from recommending k items to user i. It is the result of sorting all possible outcomes according to their relevance, and then calculating the cumulative gain and loss based on the ranking from highest to lowest. It represents the ideal state. . This represents the relevance between the p-th item in the recommendation list and the items that user i actually interacted with. If this item is one of the items that was actually interacted with, then... It is 1 if it is true, otherwise it is 0.
[0101] It should be noted that the above description of the embodiments is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions, alterations, or substitutions made by those skilled in the art within the scope of the present invention should be covered by the claims of the present invention.
Claims
1. A joint neural collaborative filtering recommendation system with fusion reliability, characterized by: The data acquisition and preparation module is used to clean and reconstruct user data to obtain the matrix required by the system. The specific steps are as follows: S1: Obtain the data information required by the system, including user ID, item ID, and user ratings for items, and construct a user-item rating matrix based on the above information. ; S2: Convert user ID into a one-hot vector X i Convert the item ID into a one-hot vector X. j Initialize the mapping matrix of users, items, and reliability using a Gaussian distribution. , , Where m, n, and k represent the number of users, the number of projects, and the number of potential factors, respectively, the mapping process is as follows: ; The natural noise detection module based on intuitionistic fuzzy sets generates intuitionistic fuzzy numbers for each user and item using the theory of intuitionistic fuzzy sets. It then classifies users and items into three categories based on the comparison of these intuitionistic fuzzy numbers. Based on the classification of user and item preferences, it identifies ratings in the rating matrix R that do not conform to user and item preferences as natural noise. Finally, it generates an initial 0-1 reliability matrix based on the identification results. The bilinear aggregation module is used to introduce a weight matrix into the embedded vector, resulting in: ; in, Let J be the weight matrix of item j. This represents finding the dot product of vectors. The Hadamard product of the vectors is calculated; simultaneously, to preserve the information contained in the original embedding vectors, the bilinear aggregation layer is combined with the user embedding vector U. i and item embedding vector V j By splicing the parts together, we obtain H0; A fully connected neural network module is used for user-item groups (U i V j ) and User-Item Additives Group (U i Z j Using the same hidden layers and based on H0, the output of the bilinear aggregation module, a fully connected neural network is used to learn high-order feature information from user ratings and rating reliability data. The rating and rating reliability prediction module is used to output the user's predicted rating for the item and the reliability level corresponding to the predicted rating in the same neural network. Its expression is as follows: ; in, and Let these represent the predicted ratings of user i for item j and... Corresponding prediction reliability, activation function The sigmoid function has the following expression: ; The recommendation list retrieval module is used to find the set of the top K items with the largest predicted ratings for target user i. The recommendation list removal and filling module is used to remove items from the recommendation list whose prediction reliability is less than a set threshold, and to fill the positions of the removed items with items with high prediction scores and high prediction reliability for personalized recommendations, so as to improve the recommendation quality.
2. The neural collaborative filtering recommendation system with fusion reliability as described in claim 1, characterized in that, The natural noise detection module based on intuitionistic fuzzy sets classifies user and item rating preferences using the concept of intuitionistic fuzzy sets, and determines the reliability of user ratings based on the classification results, generating an initial reliability matrix. The specific steps are as follows: S1: Assume I and J are sets of users and items, respectively, with sizes m and n. Each user i in user set I rates each item j in item set J from 1 to 5, and the average rating of user i is... Membership degree M of user i ui Non-membership degree N ui And hesitation level H ui The specific conversion rules are as follows: ; ; ; S2: The intuitive fuzzy number (M) of user i and project j obtained according to the above formula. ui , N ui H ui ) and (M vj , N vj H vj Users and projects are categorized according to the following rules: ; S3: Based on the user and project classification results, perform noise discrimination on the rating of each user and generate a reliability matrix B. The initial reliability matrix is generated according to the following rules: ; Among them, B ij This indicates the reliability of user i's rating of item j.
3. The neural collaborative filtering recommendation system with fusion reliability as described in claim 1, characterized in that, The fully connected neural network module is used in user-item groups (U i V j ) and User-Item Additives Group (U i Z j Using the same hidden layers and based on H0, the output of the bilinear aggregation module, a fully connected neural network is used to learn high-order feature information from user rating and rating reliability data, thereby achieving bidirectional enhancement of both tasks, specifically including: ; Where e represents the number of layers in the neural network, ...
4. The neural collaborative filtering recommendation system with fusion reliability as described in claim 1, characterized in that, The recommendation list acquisition module is used to combine explicit and implicit feedback for optimization, and its processing steps are as follows: S1: Construct the loss function, whose expression is as follows: ; in, and These represent the positive and negative samples in the training data, y. ij and These represent the actual value and the predicted value corresponding to the actual value, respectively. These represent the weight parameters of the model's embedding layer, aggregation layer, and fully connected neural network, respectively. S2: To calculate the implicit prediction reliability loss, use the predicted value according to the above formula. and the true value y ij Calculate the loss value; S3: To calculate the explicit rating loss, first calculate the true rating y using the following formula. ij Normalized to Y ij : ; Where min(y) and max(y) represent the minimum and maximum values in the user-item rating matrix R, respectively; then the predicted values are used. and the normalized true value y ij The loss value is calculated, thus avoiding the impact of value range differences on the optimization process; S4: Update model parameters using the Adam optimizer; S5: Iterate through the set of positive and negative samples until the set number of iterations is reached or the loss value no longer decreases; S6: Use the trained model parameters to make predictions, sort the predicted scores in descending order, and take the top K scores for item recommendation.
5. The neural collaborative filtering recommendation system with fusion reliability as described in claim 1, characterized in that, The recommendation list removal and filling module is used to remove unreliable items from the recommended items and select items with high predictive reliability from items that the user has not interacted with for filling. The specific steps are as follows: S1: Assume the reliability threshold is... Remove recommendations with ratings less reliable than The project is identified, and its corresponding location p and removal quantity q are recorded. S2: Divide the items that user i has not interacted with into a set, which includes two factors: item rating and corresponding reliability. S3: Use the K-means algorithm based on Euclidean distance to further refine the partitioning of the set. The specific formula is as follows: ; Select the cluster with the largest centroid value from the K-means clustering results as the candidate filling list C for user i. i Based on the previously removed item location p and quantity q, in C i Random selection Greater than the threshold The uninteracted items are then filled in descending order of the predicted item ratings. S4: Considering all aspects of the filling results for item j and If filling in the items * Less than candidate list C i Centroid and reliability threshold If the product is calculated, the item is considered not to have been selected; otherwise, it is considered to have been selected, and the filled result is used as the final recommendation list.