Semantic asymmetric similarity recommendation system considering user preference consistency
By considering the consistency of user preferences in a semantic asymmetric similarity recommendation system, the similarity between items and neighbor selection are comprehensively evaluated, which solves the problem of inaccurate similarity calculation in existing technologies and improves the prediction and recommendation performance of the recommendation system.
Patent Information
- Application Number
- CN202211555099.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-12-06
- Publication Date
- 2025-11-25
- Estimated Expiration
- 2042-12-06
AI Technical Summary
Existing similarity calculation methods mainly rely on user rating information, ignoring the consistency of user preferences and interactions between items. This leads to inaccurate similarity calculation results and inappropriate neighbor selection, affecting the prediction results of the recommendation system.
A semantic asymmetric similarity recommendation system that considers user preference consistency is adopted. Through modules such as data collection, rating conversion, semantic similarity calculation, user consistency calculation, asymmetric relationship calculation and similarity integration, the system comprehensively evaluates the similarity between items and selects the best neighbor items.
This improves the accuracy of similarity calculation results and the reliability of neighbor selection, thereby enhancing the prediction and recommendation capabilities of the recommender system.
Smart Images
Figure CN116108246B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the recommendation technical field, and particularly relates to a semantic asymmetric similarity recommendation system considering user preference consistency. BACKGROUND
[0002] Decision-making is an important activity involved in all aspects of people's daily life, which is usually a process of ranking or selecting the most interesting scheme according to the corresponding decision-making criteria. However, with the increase of complexity, the frequency of making reliable and satisfactory decisions according to personal experience is reduced. The rise of recommendation system makes it possible to select the most suitable product or service from the overloaded information to support the online user's decision-making. An effective recommendation system can greatly improve user satisfaction and purchase experience, and enhance their stickiness to the platform, thereby increasing the influence of the platform. Collaborative filtering is one of the most widely used technologies in recommendation systems, and its basic idea is to use the "wisdom of the crowd" to filter and screen a large amount of information in the system to produce a series of items that the target user may be interested in. Among them, the similarity calculation method is the most important link in the recommendation link, and the quality of the similarity result will directly affect the selection of the nearest neighbor, thereby affecting the rating prediction and recommendation result. Therefore, how to design a reliable similarity method to improve the performance of the recommendation system is particularly important.
[0003] At present, most similarity calculation methods mainly use user rating information for subsequent recommendation, and do not measure the similarity between items from the perspective of language information. In the actual decision-making process, because the cost of obtaining specific and accurate quantitative information is high, people usually prefer to express their opinions or preferences qualitatively. Language information can fully reflect the preference degree of users for a specific item in the decision-making process. Therefore, it is necessary to evaluate the similarity between items from the qualitative perspective.
[0004] The inventor found that the existing item similarity-based recommendation method only uses user rating data to measure the similarity between items, ignores the user preference consistency between items, and does not consider the interaction between items in neighbor screening, which will make the similarity calculation result inaccurate and the neighbor screening unsuitable, thereby leading to poor prediction results. SUMMARY
[0005] In view of the above problems, the present application provides a semantic asymmetric similarity recommendation system considering user preference consistency, which comprises:
[0006] A data acquisition and preparation module is used for acquiring and cleaning user data to obtain the information required by the system.
[0007] a score conversion module for converting user score information into fuzzy semantic information to form a fuzzy semantic matrix S.
[0008] a semantic similarity calculation module for calculating semantic similarity sim(i,j) between each pair of items by means of a related definition of a probability language term set. PLTS .
[0009] a user consistency calculation module for obtaining positive and negative preferences of a user for items and calculating user preference consistency sim(i,j) between items from the perspective of a probability distribution by means of a Bhattacharyya coefficient. BCIT .
[0010] an asymmetric relation calculation module for obtaining common score user items between two items and the number of scores of a target item and calculating asymmetric similarity sim(i,j) between each pair of items by means of a Sigmoid function. AR .
[0011] a similarity integration module for integrating results of the above-mentioned calculation modules to obtain sim(i,j) PLTS-BCIT and sim(i,j) PLTS-BCIT-AR .
[0012] a neighbor search module for searching for a set of K nearest neighbor items of a target item i by means of the three integrated similarity results.
[0013] a score prediction acquisition module for calculating a predicted score value p of a target user u on an un-scored item i. ui .
[0014] a recommendation result acquisition module for finding a set of items with the top n predicted score values for a target user u to make personalized recommendation.
[0015] The similarity recommendation system provided by the application, the score conversion module is used for converting each value in a user-item score matrix R into a corresponding term s α in a language term set S={s α , where alpha is an ordinal number, used for representing a level of a semantic category.
[0016] The similarity recommendation system provided by the application, the semantic similarity calculation module is used for calculating semantic similarity sim(i,j) between each pair of items by means of a related definition of a probability language term set. PLTS , specifically comprising:
[0017] (1) a probability language term set construction module for constructing a probability language term set of a target item i.
[0018] where I (r) (p i (r) ) represents the language term I (r) and its corresponding probability M is the number of all users in the recommendation system, #r i is the number of users who rated item i as r, r max is the maximum value of the rating interval. According to the value, the elements in the language term set are sorted in descending order, and the reordered probability language term set of item i is obtained Repeat the operation to build the probability language term set of all items.
[0019] (2) Semantic deviation acquisition module, used for calculating the deviation degree of the probability language term set between two items.
[0020] where k represents the reordered position of the element in the probability language term set, r i is the subscript of the language term s r of item i, is the number of language terms in .
[0021] (3) Semantic similarity acquisition module, used for calculating the semantic similarity between items based on the probability language term set
[0022] The similarity recommendation system described in the application, the user consistency calculation module, is used to calculate the user preference consistency sim(i,j) between two items by the Bhattacharyya coefficient method BCIT , specifically comprising:
[0023] (1) User preference acquisition module, used for acquiring the evaluation preference information of users on items. The positive and negative preferences of users on target item i are calculated, and the formula is as follows:
[0024] where m is the number of times that item i is evaluated by users, I(r) is the number of users who rate item i as r, is the upward rounding mathematical symbol.
[0025] (2) User consistency acquisition module, used for calculating the user preference consistency result between two items by the Bhattacharyya coefficient method, and the formula is as follows:
[0026] where t represents the positive P or negative N user preference, p i,t is the probability of the user's preference t for item i, calculated as follows:
[0027]
[0028] The similarity recommendation system, the asymmetric relation calculation module is used for obtaining the common scoring item quantity and target item scoring quantity, and obtains the asymmetric similarity sim(i,j) between two items through a Sigmoid function AR , specifically comprising:
[0029] The asymmetric similarity of target item i and item j Wherein U(i,j) represents the user set which has scored both item i and item j, that is, the common scoring item; U i represents the user set which has scored item i.
[0030] The similarity recommendation system, the similarity integration module is used for integrating the results of the above-mentioned calculation modules to obtain sim(i,j) PLTS-BCIT and sim(i,j) PLTS-BCIT-AR . Specifically comprising:
[0031] (1) The first similarity integration module is used for obtaining the semantic similarity sim(i,j) PLTS-BCIT = sim(i,j) PLTS · sim(i,j) BCIT considering the consistency of user preferences. The similarity result is used for the scoring prediction acquisition module.
[0032] (2) The second similarity integration module is used for obtaining the asymmetric semantic similarity sim(i,j) PLTS-BCIT-AR = sim(i,j) PLTS-BCIT × sim(i,j) AR considering the consistency of users. The similarity result is used for the neighbor search module.
[0033] The similarity recommendation system, the neighbor search module is used for finding the best nearest neighbor item set of target item i Specifically comprising:
[0034] (1) The similarity sorting module is used for descendingly sorting the results obtained by the second similarity integration module to obtain the relevance degree sorting of target item i and other items.
[0035] (2) The neighbor acquisition module is used for obtaining the nearest neighbor set of target item i; wherein the number K of the nearest neighbors selected by the system is set, and the first K items with the highest similarity degree with target item i are obtained from the similarity sorting module to form the K nearest neighbor item set of target item i
[0036] The similarity recommendation system, the score prediction acquisition module is used to calculate and acquire the predicted score value p of target user u on the un-scored item i through a score prediction method ui The calculation formula is as follows:
[0037] Among them The average score value of item i is r uj The score value of user u on item j is r The nearest neighbor set of target item i is.
[0038] The similarity recommendation system, the recommendation result acquisition module is used to acquire the recommendation list of target user u; wherein the number n of items recommended by the system for the target user is set, the predicted score set of target user u on the un-scored item is acquired from the score prediction acquisition module, and the predicted score values in the set are sorted from large to small; the first n items with the largest predicted values are selected to recommend to target user u, so as to form the personalized recommendation list of target user u.
[0039] The similarity recommendation method and system provided by the application measure the similarity between items from both qualitative and quantitative angles, consider the user preference consistency between items and the asymmetric relationship between items, which has a very positive effect on improving the accuracy and reliability of the similarity calculation result and finding the best neighbor item for the target item in the neighbor screening stage, thereby further strengthening the prediction and recommendation ability of the recommendation system. BRIEF DESCRIPTION OF DRAWINGS
[0040] Figure 1 It is a method process schematic diagram of the application;
[0041] Figure 2 It is a system framework diagram of the application;
[0042] Figure 3 It is the MAE value change condition of the application under different nearest neighbor set quantities in two data sets;
[0043] Figure 4 It is the F1 value change condition of the application under different nearest neighbor set quantities in two data sets. DETAILED DESCRIPTION
[0044] In order to make the purposes, technical solutions and advantages of the present application clearer, the following will describe in detail a semantic asymmetric similarity recommendation method and system considering user preference consistency according to the present application with reference to the accompanying drawings. It should be understood that the specific implementation methods described herein are only used to explain the present application and should not be used to limit the present application. Changes, modifications, additions, or replacements made by those skilled in the art within the scope of the present application should be covered by the claims of the present application.
[0045] Figure 1 is a process schematic diagram of the similarity recommendation method of the present application. From Figure 1 It can be seen that the similarity recommendation method proposed in the present application includes obtaining and cleaning data information from a database to obtain a standardized data format; converting the obtained score information to obtain corresponding fuzzy language terms; calculating the semantic similarity between items with the help of the related definition of the probability language term set; from the obtained standardized data, the preference characteristics of the user to the items are counted, and the user preference consistency between the items is calculated by using the Bayes system method; from the obtained standardized data, the number of times of being rated of the common rating items and the target items is counted, and the asymmetric relationship between the items is calculated by using the Sigmoid function; the obtained user consistency result is integrated into the semantic similarity to obtain the weighted semantic similarity; the obtained weighted semantic similarity result and the asymmetric relationship between the items are integrated together, and according to the integrated value, the nearest neighbor set of the target item is screened out; the obtained nearest neighbor set and the weighted semantic similarity result are used as input, and the predicted rating value of the target user on the unrated items is calculated by using the rating prediction method; the obtained predicted rating set is sorted to produce a series of items that the target user is most likely interested in for pushing.
[0046] Figure 2 is a framework diagram of the similarity recommendation system of the present application. From Figure 2It can be seen that the similarity recommendation method and system proposed in the application includes a data acquisition and preparation module, a score conversion module, a semantic similarity calculation module, a user consistency calculation module, an asymmetric relationship calculation module, a similarity integration module (including a first and a second similarity integration submodule), a neighbor search module (including a similarity sorting module and a neighbor acquisition module), a score prediction acquisition module, and a recommendation result acquisition module. The data acquisition and preparation module is used to extract data from a database and perform cleaning and preprocessing operations on the data, and process the data into a format required by the score conversion module; the score conversion module is used to convert the score information provided by the data acquisition and preparation module into fuzzy language information; the semantic similarity calculation module calculates the semantic similarity between items according to the data information obtained by the score conversion module; the user consistency calculation module calculates the user preference consistency between items according to the data information obtained by the data acquisition and preparation module; the asymmetric relationship calculation module calculates the asymmetric result between items according to the data information obtained by the data acquisition and preparation module. The similarity integration module integrates the results obtained by the three calculation modules, wherein the first similarity integration module is used to integrate the results of the semantic similarity module and the user consistency module, and the second similarity integration module is used to integrate the results of the three calculation modules; the neighbor search module uses the similarity sorting module to internally sort the results obtained by the second similarity integration module, and then uses the neighbor acquisition module to generate a nearest neighbor set; the score prediction acquisition module performs item score prediction according to the results obtained by the first similarity integration module and the nearest neighbor set obtained by the neighbor search module; and the recommendation result acquisition module internally sorts the item score prediction set obtained by the score prediction acquisition module, and recommends the items with high rankings to a target user.
[0047] Further, the following cases are taken as examples for illustration:
[0048] Suppose there are M users U = {u1, u2,..., uM} and N items I = {i1, i2,..., iN}, and the user-item score matrix is represented as [R]M×N, where r M represents the score value of the user on the item i, U(i,j) represents the user set that has scored both the item i and the item j, i.e., the co-scoring item; and U(i) represents the user set that has scored the item i. N M×N ui i
[0049] First, the data acquisition and preparation module is used to acquire and clean the system data to obtain the variables in the hypothesis. The specific implementation steps of the entire similarity recommendation system are as follows:
[0050] S1: The data collection and preparation module obtains the required data information from the database, including user ID, project ID and score information;
[0051] S2: The score conversion module converts user score information into fuzzy semantic information;
[0052] The language term set is the basis of language decision, and decision makers usually use the term set to express their opinions or preferences for a particular project. The language term set is limited and ordered, and its expression is as follows:
[0053] S={s α |α=0,1,...,τ}
[0054] Where s α represents the possibility value of a certain language term at the αth position, s0and s τ represent the lower and upper limits of the language term, respectively, and τ represents a positive integer. Common language term sets are:
[0055] S={s0=none, s1=very low, s2=low, s3=medium, s4=high, s5=very high, s6=perfect}
[0056] If the score interval in the recommendation system is 1-5, then two language terms s0and s6need to be removed, so that each score value in R is converted to the corresponding language term in S.
[0057] S3: The semantic similarity calculation module calculates the semantic similarity sim(i,j) PLTS between projects according to the converted language term information and the related definitions of the probabilistic language data set.
[0058] First, construct the probabilistic language term set of the target project i, as follows:
[0059]
[0060] Where represents the language term I (r) and its corresponding probability M is the number of all users in the recommendation system, #r i is the number of users who rated project i as r, and r max is the maximum value of the rating interval. According to the value of , the elements in the language term set are sorted in descending order, and the reordered probabilistic language term set of project i is obtained
[0061] Secondly, the deviation degree of the probability language term set between projects is calculated, and the formula is as follows:
[0062]
[0063] Where k represents the reordering position of the element in the probability language term set, r i is the subscript of the language term s r of the project i, is the number of language terms in .
[0064] Finally, the inter-project semantic similarity based on the probability language term set is calculated, and the formula is as follows:
[0065]
[0066] Where e -x is the exponential function, and its similarity image is similar to the forgetting curve, which can better distinguish two projects with small deviation degrees.
[0067] S4: The user consistency calculation module calculates the inter-project user preference consistency sim(i,j) BCIT based on the obtained score information using the Bhattacharyya coefficient method.
[0068] The semantic similarity calculation module only considers the semantic similarity between projects and ignores the user's rating preference (positive or negative) for the project, which may lead to inaccurate similarity results. This module first evaluates the positive and negative preferences of the user for the target project i, and the formula is as follows:
[0069]
[0070] Where m is the number of times the project i is evaluated by the user, I(r) is the number of users who rate the project i as r, is the upward rounding mathematical symbol.
[0071] Then, the Bhattacharyya coefficient method is used to measure the inter-project user preference consistency from the perspective of probability distribution, and the formula is as follows:
[0072]
[0073] Where t represents the positive P or negative N user preference, p i,t is the probability of the user's certain preference t for the project i, and is calculated as follows:
[0074]
[0075] S5: The asymmetric relationship calculation module first counts the number of common rating items |U(i,j)| and the number of times the target item i is rated |U(i,j)| according to the obtained rating information, and then calculates the asymmetric similarity sim(i,j) of the target item i and the item j using the Sigmoid function, as follows: i AR
[0076]
[0077] Compared with the traditional symmetric similarity method, the asymmetric similarity method emphasizes the mutual influence between items and the importance of common rating items, which plays a crucial role in subsequent selection of suitable neighbors for the target item.
[0078] S6: The similarity integration module effectively integrates the similarity results obtained in S3, S4 and S5 to obtain sim(i,j) PLTS-BCIT and sim(i,j) PLTS-BCIT-AR .
[0079] This includes the first similarity integration module, which integrates the results of S3 and S4 to improve the accuracy and reliability of the similarity calculation results.
[0080] sim(i,j) PLTS-BCIT = sim(i,j) PLTS · sim(i,j) BCIT
[0081] The second similarity integration module integrates the results of S3, S4 and S5 to break the symmetry of the similarity results between items, thereby finding a more suitable set of nearest neighbor items for the target item.
[0082] sim(i,j) PLTS-BCIT-AR = sim(i,j) PLTS-BCIT × sim(i,j) AR
[0083] S7: The neighbor search module first uses the similarity sorting module to internally sort the results from the second similarity integration module from large to small to obtain the relevance degree ordering of the target item i and other items, and then obtains the top K items with the highest similarity to the target item i from the similarity sorting module according to the system-set number of nearest neighbors K, to form a K-nearest neighbor item set for the target item i
[0084] S8: The score prediction acquisition module calculates the predicted value p of the target user u on the un-rated item i according to the similarity result obtained by the first similarity integration module and the nearest neighbor item set found by the neighbor search module ui , and the formula is as follows:
[0085]
[0086] wherein, is the average rating value of the item i, and r uj is the rating value of the user u on the item j, is the nearest neighbor set of the target item i.
[0087] S9: The recommendation result acquisition module sorts the rating values in the predicted item set from large to small according to the series of predicted rating item sets calculated in S8 and the number n of recommended items set by the system, and then selects the first n items with the largest predicted values to recommend to the target user u to form the personalized recommendation list of the target user u.
[0088] Figures 2-3 The performance of the proposed method in two aspects is measured respectively, and the two measurements are: mean absolute error (MAE) and F1 value. Their calculation methods and measurement contents are as follows:
[0089] Mean absolute error: In the present application, the prediction accuracy of the recommendation method is measured to test the deviation between the predicted value and the true value of the method, which can better reflect the actual situation of the prediction value error. The smaller the mean absolute error, the better the prediction ability of the method. The calculation method is as follows:
[0090]
[0091] wherein, m represents the number of users tested in the system, and n represents the number of predicted items; r ui and p ui are the true rating value and the predicted rating value of the user u on the item i respectively.
[0092] F1 value: is an index combined by precision (Precision) and recall (Recall), which is used to evaluate the comprehensive performance of the recommendation system accuracy. The precision in the present application measures the proportion of items that the user really likes in the item list recommended to the user; and the recall in the present application measures the proportion of the number of items that the user really likes in the item list recommended to the user to the total number of items that the user likes. Their calculation formulas are as follows:
[0093]
[0094] wherein, Iar and I pr respectively represent the number of items of real recommendations and predicted recommendations.
Claims
1. A semantic asymmetric similarity recommendation system that considers user preference consistency, characterized in that, include: The data acquisition and preparation module is used to acquire and clean user data to obtain standardized data information required by the system. The rating conversion module is used to convert user rating information into fuzzy semantic information to form a fuzzy semantic matrix S; The semantic similarity calculation module, using relevant definitions from the probabilistic language terminology set, is used to calculate the semantic similarity sim(i,j) between any two items. PLTS ; The user consistency calculation module is used to obtain users' positive and negative preferences for projects, and to calculate the consistency of user preferences between projects, sim(i,j), from the perspective of probability distribution using the Bach coefficient. BCIT ; The asymmetric relationship calculation module is used to obtain the number of user items that share ratings between two items and the number of ratings for the target item, and to calculate the asymmetric similarity sim(i,j) between each pair of items. AR ; The similarity integration module is used to integrate the similarity results of the aforementioned calculation modules to obtain sim(i,j). PLTS-BCIT and sim(i,j) PLTS-BCIT-AR ; The neighbor search module is used to find the K nearest neighbor itemsets for the target item i based on the results of three similarity aggregations. The rating prediction module is used to calculate the predicted rating value p for the target user u on the unrated item i. ui ; The recommendation result acquisition module is used to find the set of the top n items with the largest predicted ratings for the target user u and make personalized recommendations.
2. The similarity recommendation system as described in claim 1, characterized in that, The scoring conversion module is used to convert the language term set S = {s} α The values in the user-item rating matrix R (|α=0,1,...,τ}) are transformed into terms s corresponding to the linguistic term set. α , where α is an ordinal number used to represent the hierarchy of the semantic category.
3. The similarity recommendation system as described in claim 1, characterized in that, The semantic similarity calculation module is used to calculate the semantic similarity sim(i,j) between each pair of items by using the relevant definitions in the probabilistic language terminology set. PLTS Specifically, it includes: (1) A probabilistic language terminology set construction module, used to construct the probabilistic language terminology set for the target item i: in Represented as linguistic term I (r) and their corresponding probabilities M represents the total number of users in the recommendation system, #r i Let r be the number of users who rated project i. max It is the maximum value of the scoring interval; according to The value of is used to sort the elements in the language term set in descending order, resulting in the probability of the reordered item i in the language term set. Repeated operations can build a probabilistic language terminology set for all items; (2) Semantic deviation acquisition module, used to calculate the degree of deviation between pairs of probabilistic language term sets: Where k represents the reordering position of an element in the probabilistic language terminology set, r i For the language terminology of project i r subscript, In order to be in The number of Chinese language terms; (3) Semantic similarity acquisition module, used to calculate the semantic similarity between items based on the probabilistic language term set.
4. The similarity recommendation system as described in claim 1, characterized in that, The user consistency calculation module is used to calculate the user preference consistency sim(i,j) between each pair of items using the Bach coefficient method. BCIT Specifically, it includes: (1) User preference acquisition module, used to acquire user evaluation preference information for projects; calculate the user's positive and negative preferences for target project i, as follows: Where m is the number of times item i is rated by users, and I(r) is the number of times users rate item i with a score of r. The mathematical symbol for rounding up; (2) User Consistency Acquisition Module, which is used to calculate the user preference consistency results between pairs of items using the Bach coefficient method, as follows: Where t represents positive P or negative N user preference, p i,t The probability of a user having a certain preference t for item i is calculated as follows:
5. The similarity recommendation system as described in claim 1, characterized in that, The asymmetric relationship calculation module is used to obtain the number of common rating items and the number of target item ratings, and to calculate the asymmetric similarity sim(i,j) between each pair of items using the Sigmoid function. AR Specifically, it includes: Asymmetric similarity between target project i and project j Where U(i,j) represents the set of users who have rated both item i and item j, i.e., the shared rating items; U i This represents the set of all users who have rated item i.
6. The similarity recommendation system as described in claim 1, characterized in that, The similarity integration module is used to integrate the results of the aforementioned calculation modules to obtain sim(i,j) respectively. PLTS-BCIT and sim(i,j) PLTS-BCIT-AR Specifically, it includes: (1) The first similarity integration module is used to obtain the semantic similarity sim(i,j) considering the consistency of user preferences. PLTS-BCIT =sim(i,j) PLTS ·sim(i,j) BCIT This similarity result is used in the score prediction acquisition module; (2) The second similarity integration module is used to obtain the asymmetric semantic similarity sim(i,j) that takes into account user consistency. PLTS-BCIT-AR =sim(i,j) PLTS-BCIT ×sim(i,j) AR The similarity result is used in the neighbor search module.
7. The similarity recommendation system as described in claim 1, characterized in that, The neighbor search module is used to find the best set of nearest neighbor items for target item i. Specifically, it includes: (1) Similarity ranking module, used to sort the results obtained by the second similarity integration module in descending order to obtain the ranking of the degree of association between target item i and other items; (2) Neighbor acquisition module, used to obtain the set of nearest neighbors of target item i; including setting the number K of nearest neighbors selected by the system, and then obtaining the top K items with the highest similarity to target item i from the similarity ranking module to form the set of K nearest neighbor items of target item i.
8. The similarity recommendation system as described in claim 1, characterized in that, The rating prediction acquisition module is used to calculate and obtain the predicted rating value p of the target user u on the unrated item i using a rating prediction method. ui The calculation formula is as follows: in r is the average score of item i. uj The rating score given by user u for item j. Let i be the set of nearest neighbors of the target item i.
9. The similarity recommendation system as described in claim 1, characterized in that, The recommendation result acquisition module is used to acquire a recommendation list for the target user u. This includes setting the number of items n recommended by the system to the target user, acquiring the predicted rating set of the target user u on unrated items from the rating prediction acquisition module, sorting the predicted rating values in the set from largest to smallest, and selecting the top n items with the largest predicted values to recommend to the target user u, so as to form a personalized recommendation list for the target user u.