Recommendation method based on interpretable generalized logical transformation matrix decomposition

Abstract

The invention discloses a recommendation method based on interpretable generalized logic transformation matrix decomposition. The recommendation method comprises the following steps: converting an original scoring matrix into normal distribution data through a generalized logic transformation function; constructing indexes based on similarity and indexes based on ranking; calculating probability distribution and expected scores of scores of the recommended items by the similar users, and generating interpretability indexes in combination with the similarity indexes; integrating the interpretability index into a matrix decomposition objective function for optimization; solving a user feature matrix and a project feature matrix through an alternating least square method or stochastic gradient descent; calculating a prediction score and mapping the prediction score back to an original score interval through generalized logic inverse transformation; generating a recommendation list; the method provided by the invention has wider applicability and higher performance in practical application.

Description

Technical Field

[0001] The present invention relates to the technical field of recommendation systems, and in particular to a recommendation method based on interpretable generalized logical transformation matrix decomposition. Background Art

[0002] With the rapid development of information technology, recommendation systems have become a vital bridge connecting users with vast amounts of information. However, traditional recommendation algorithms often pursue high accuracy while neglecting the interpretability of recommendation results. This makes it difficult for users to understand the logic behind the recommendations, which in turn reduces their trust in and satisfaction with the recommendation systems. Existing technologies can be broadly categorized into three main types: Content-based recommendation systems primarily rely on users' historical selection or preference records to recommend relevant items. Their core approach is to accurately calculate the similarity between different items and, based on this similarity, recommend new items similar to those already preferred. This approach has the advantage of tapping into users' potential interests, but it also suffers from the cold start problem: when new users emerge, the system struggles to provide recommendations tailored to their needs due to a lack of preference records. Furthermore, content-based recommendations primarily rely on item features, which can be limited for items with unclear or difficult-to-extract content features. Collaborative filtering recommendation systems, on the other hand, rely on extensive historical data on users and items to recommend items by calculating similarities between unknown pairs of targets. Matrix Factorization (MF) is one of the most common and popular algorithms in collaborative filtering. It represents the associations between users and items by decomposing the user rating matrix into two low-dimensional feature vectors. While MF models offer the advantages of scalability and ease of implementation, they suffer from limited expressiveness and interpretability. To improve recommendation performance, various improved matrix factorization algorithms have been proposed, such as regularized matrix factorization (RMF), non-negative matrix factorization (NMF), and probabilistic matrix factorization (PMF). However, the interpretability of these algorithms still needs to be improved. Hybrid recommender systems aim to combine the strengths of different recommendation techniques while mitigating their weaknesses. By integrating multiple algorithms, they can provide more accurate and comprehensive recommendations. Hybrid recommendation systems are mainly categorized into three types: pre-fusion, post-fusion, and intermediate fusion. Pre-fusion combines the results of different algorithms during the data input stage; post-fusion combines the recommendation results after they are generated; and intermediate fusion combines the strengths of different algorithms during the recommendation process. Hybrid recommender systems can fully leverage the characteristics of different algorithms to improve the accuracy and diversity of recommendations. However, due to the need to integrate multiple algorithms, the implementation complexity of the hybrid recommendation system is relatively high, and the fusion method and weight distribution between different algorithms are also key factors affecting the recommendation effect. Summary of the Invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a recommendation method based on interpretable generalized logical transformation matrix decomposition, which will combine advanced representation learning methods, interpretability techniques and flexible data distribution models to solve the problems of insufficient expressive power and lack of interpretability of traditional matrix decomposition models in recommendation systems.

[0004] Technical solution: The recommendation method based on interpretable generalized logical transformation matrix decomposition described in the present invention includes the following steps: (1) The original rating matrix is ​​converted into normal distribution data through the generalized logistic transformation function; (2) Constructing interpretability indicators: Similarity-based indicators calculate the similarity between users through the Tanimoto coefficient and generate similarity indicators for users to items; ranking-based indicators calculate the probability distribution and expected ratings of similar users for recommended items, and combine similarity indicators to generate interpretability indicators; (3) Integrate the interpretability index into the matrix decomposition objective function for optimization; solve the user feature matrix and item feature matrix by alternating least squares method or stochastic gradient descent; (4) Calculate the predicted score and map it back to the original score interval through the generalized inverse logistic transformation; (5) Generate a recommendation list based on the predicted score.

[0005] Furthermore, in step (2), the formula for calculating the similarity between users is: ; in, and Represents users and Rating vector for the items; The formula for the user-item similarity index is as follows: ; in, Represents user Similarity is higher than the preset threshold The user collection, Represents a user About the project 's rating.

[0006] Furthermore, in step (2), the formula for calculating the scoring probability distribution is: ; in, Represents user A set of users with high similarity, Express your support for the project Rating The user collection of The formula for calculating the expected rating is: ; in, Represents the set of all possible rating values.

[0007] Furthermore, in step (2), the interpretability index is generated as follows: ; in, , indicating that the user About the project the degree of interpretability; is a preset threshold used to control the sensitivity of the interpretability indicator; It is a control parameter used to adjust the influence of the explainability index on the recommendation results.

[0008] Furthermore, in step (3), the optimization formula is as follows: ; in, represents the set of known ratings in the rating matrix; is the true value; It is a control parameter used to remove the influence of invalid values ​​such as missing values ​​or outliers; and is a regularization parameter used to prevent overfitting; and Represents users and projects The low-dimensional feature vector of Represents a user and projects interpretability indicators.

[0009] Furthermore, in step (4), the formula for calculating the predicted score is as follows: ; in, represents the final user feature embedding, represents the final item feature embedding.

[0010] Furthermore, the formula for mapping back to the original score interval through generalized inverse logical transformation is as follows: ; in, is the mean of the rating matrix after GLT transformation.

[0011] An electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, any one of the methods for optimizing a single-phase converter is implemented.

[0012] The storage medium of the present invention stores a computer program, and when the computer program is executed by a processor, it implements any one of the methods for optimizing a single-phase converter.

[0013] Beneficial Effects: Compared with existing technologies, this invention offers the following significant advantages: By introducing a generalized logistic transformation function and constructing a new interpretability metric, it significantly improves recommendation accuracy and enhances interpretability. Furthermore, it exhibits excellent adaptability and robustness, capable of handling datasets of varying sizes and distribution characteristics, and addressing the impact of data noise and outliers on recommendation results. These advantages make the GEMF algorithm more widely applicable and more performant in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0015] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0016] like Figure 1 As shown, an embodiment of the present invention is a recommendation method based on interpretable generalized logical transformation matrix decomposition. First, a generalized logical transformation function is introduced to convert the original rating data into an approximate normal distribution to meet the needs of subsequent algorithms. Then, by mining the similarity between projects and user rating ranking information, a new interpretability index is constructed to reflect the intrinsic relationship between users and projects. Then, these interpretability indicators are integrated into the matrix decomposition model, a new objective function is designed, and the low-dimensional feature vectors of users and projects are obtained through optimization. Finally, these feature vectors are used to calculate the predicted rating matrix, and the predicted rating is mapped back to the original rating interval through the inverse function of the generalized logical transformation, thereby realizing the recommendation of the target project. This research scheme not only improves the accuracy of the recommendation system, but also enhances the interpretability of the recommendation results, providing users with a more transparent and reliable recommendation service. It includes the following steps: (1) The generalized logical transformation (GLT) includes the following steps: (11) In order to solve the problem of unreasonable data distribution assumptions, the present invention introduces the generalized logistic transformation (GLT) function. The GLT function can transform the original scoring data into an approximate normal distribution, thereby meeting the needs of subsequent algorithms. It is defined as follows: ; in, represents the score after GLT transformation, represents the original score, and Represent the maximum and minimum values ​​of the original score matrix, is the scaling parameter used to control the range of the transformed data. It is the logarithmic function parameter, which is used to adjust the distribution of the transformed data. and The value of can make the transformed scoring data approximately obey the normal distribution, thus meeting the requirements of subsequent algorithms for data distribution.

[0017] (12) Perform generalized logical transformation on experimental data.

[0018] (2) Constructing interpretability indicators To enhance the interpretability of recommendation systems, this paper constructs two new interpretability metrics: similarity-based and ranking-based. The process involves the following steps: (21) Similarity-based indicators First, the Tanimoto coefficient is used to calculate the similarity between different items. The Tanimoto coefficient is a commonly used similarity measurement method that can reflect the degree of association between items. Its calculation formula is as follows ; in, and Represents users and Rating vector for the items.

[0019] Then, based on the similarity between users, the similarity between users and items is calculated. Specifically, for user and projects , computing and users A set of users with high similarity All users in the project The weighted average of the scores is used as the similarity index of users to items. The calculation formula is as follows: ; in, Represents user Similarity is higher than the preset threshold The user collection, Represents a user About the project 's rating.

[0020] (22) Ranking-based indicators Similarity-based indicators can reflect the degree of association between users and items, but cannot fully consider the influence of user preferences. To make up for this deficiency, the present invention introduces ranking-based indicators. Specifically, define user About the project Rating The probability of similar users rating the recommended item as a certain value is calculated as follows: ; in, Represents user A set of users with high similarity, Express your support for the project Rating A collection of users.

[0021] Then, calculate the similar user pairs recommended items The expected rating of is the weighted average of similar users’ ratings on the recommended items. The calculation formula is as follows: ; in, Represents the set of all possible rating values.

[0022] Finally, we construct the final interpretability index based on similarity and ranking. Specifically, when the similarity between the user and the item is high and the expected rating of the recommended item by similar users is also high, the recommended item is considered interpretable to the user. The calculation formula is as follows: ; in, , indicating that the user About the project the degree of interpretability; is a preset threshold used to control the sensitivity of the interpretability indicator; It is a control parameter used to adjust the influence of the explainability index on the recommendation results.

[0023] (3) The interpretability matrix decomposition model is as follows: After constructing the interpretability index, we integrate it into the matrix decomposition model and design a new objective function. The objective function is defined as follows: ; in, represents the set of known ratings in the rating matrix; is the true value; It is a control parameter used to remove the influence of invalid values ​​(such as missing values ​​or outliers); and is a regularization parameter used to prevent overfitting; and Represents users and projects respectively The low-dimensional feature vector of Represents a user and projects The first term of the objective function is the square error term between the predicted rating and the actual rating, which aims to minimize the prediction error; the second term is the regularization term of the user feature vector and the item feature vector, which aims to prevent overfitting; the third term is the interpretability regularization term, which introduces the user-item interpretability index. , to adjust the user feature vector and the item feature vector The purpose of this item is to consider the interpretability factor in the optimization process, so that the recommendation results are not only accurate but also meet the user's interpretability expectations.

[0024] In order to solve this optimization problem, commonly used optimization algorithms such as alternating least squares (ALS) or stochastic gradient descent (SGD) are used. These algorithms iteratively update the user feature vector and the item feature vector , so that the objective function gradually converges to the minimum value.

[0025] (4) Prediction score and inverse transformation, including the following steps: (41) After obtaining the low-dimensional feature matrix of users and items, calculate the predicted rating matrix: ; (42) However, since the predicted rating matrix is ​​calculated based on the rating data after GLT transformation, it is necessary to map it back to the original rating interval through the inverse transformation function of GLT: ; in, is the mean of the rating matrix after GLT transformation. Finally, project recommendations are made to users based on the predicted ratings. Specifically, for each user, the projects are sorted from high to low according to the predicted ratings, and the top projects are selected. Items are used as recommendation results. In this way, users can get personalized recommendation services that meet their interests and interpretability expectations.

[0026] We used the classic Jester dataset as the validation set for this experiment. The Jester dataset, consisting of data recorded over three different time periods, provides rich experimental material for comprehensively validating the performance of the recommendation algorithm. This dataset contains user ratings of jokes, typically ranging from -10 to 10, reflecting the user's preference for the jokes, as shown in Table 1.

[0027] Table 1 Experimental data statistics ; Typical matrix factorization algorithms are selected for comparison with other algorithms: GEMF, GPMF, EMF, PMF, EGMF, SVD, and BSMF. GEMF mainly includes four hyperparameters: the dimensions of X and Y, the iteration step size, the regularization parameter of the interpretable term, and the regularization coefficient. By adjusting these parameters, the impact on prediction accuracy and time consumption can be achieved. In the experiment, we will mainly explore the impact of and on the GEMF prediction accuracy and running time. We selected three most typical indicators as the metrics for evaluating the prediction results, namely MSE (mean square error), MAE (mean absolute error) and RMSE (root mean square error).

[0028] ; ; ; Based on technical solutions 1 to 4, and with fixed comparison schemes, evaluation indicators, and parameter settings, the values ​​of the method proposed in the present invention and the comparison schemes on three sets of data are evaluated, as shown in Table 2.

[0029] Table 2 Prediction errors of seven algorithms

[0030] From the experimental results in Table 2, we can see that the proposed method outperforms the other six algorithms on the jester 1, jester 2, and jester 3 datasets. This fully demonstrates that the interpretable index constructed by GEMF is reasonable. The target recommendation based on this index can better mine the intrinsic information of the data, thereby obtaining a more accurate recommendation effect. To further verify the influence of the parameters, the restriction , explore different The impact of the value on the solution.

Claims

1. A recommendation method based on interpretable generalized logical transformation matrix decomposition, characterized in that: The following steps are involved: (1) The original rating matrix is ​​converted into normal distribution data through the generalized logistic transformation function; (2) Constructing interpretability indicators: Similarity-based indicators calculate the similarity between users through the Tanimoto coefficient and generate similarity indicators for users to items; ranking-based indicators calculate the probability distribution and expected ratings of similar users for recommended items, and combine similarity indicators to generate interpretability indicators; (3) Integrate the interpretability index into the matrix decomposition objective function for optimization; solve the user feature matrix and item feature matrix by alternating least squares method or stochastic gradient descent; (4) Calculate the predicted score and map it back to the original score interval through the generalized inverse logistic transformation; (5) Generate a recommendation list based on the predicted score.

2. The recommendation method based on interpretable generalized logical transformation matrix decomposition according to claim 1, characterized in that: In step (2), the formula for calculating the similarity between users is: ； in, and Represents users and Rating vector for the items; The formula for the user-item similarity index is as follows: ； in, Represents user Similarity is higher than the preset threshold The user collection, Represents a user About the project 's rating.

3. The recommendation method based on interpretable generalized logical transformation matrix decomposition according to claim 1, characterized in that: In step (2), the calculation formula for the scoring probability distribution is: ； in, Represents user A set of users with high similarity, Express your support for the project Rating The user collection of The formula for calculating the expected rating is: ； in, Represents the set of all possible rating values.

4. The recommendation method based on interpretable generalized logical transformation matrix decomposition according to claim 1, characterized in that: In step (2), the interpretability index is generated as follows: ； in, , indicating that the user About the project the degree of interpretability; is a preset threshold used to control the sensitivity of the interpretability indicator; It is a control parameter used to adjust the influence of the explainability index on the recommendation results.

5. The recommendation method based on interpretable generalized logical transformation matrix decomposition according to claim 1, characterized in that: In step (3), the optimization formula is as follows: ； in, represents the set of known ratings in the rating matrix; is the true value; It is a control parameter used to remove the influence of invalid values ​​such as missing values ​​or outliers; and is a regularization parameter used to prevent overfitting; and Represents users and projects The low-dimensional feature vector of Represents a user and projects interpretability indicators.

6. The recommendation method based on interpretable generalized logical transformation matrix decomposition according to claim 1, characterized in that: In step (4), the formula for calculating the predicted score is as follows: ； in, represents the final user feature embedding, represents the final item feature embedding.

7. The recommendation method based on interpretable generalized logical transformation matrix decomposition according to claim 1, characterized in that: The formula for mapping back to the original score interval through generalized inverse logistic transformation is as follows: ； in, is the mean of the rating matrix after GLT transformation.

8. An electronic device, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium, characterized in that A computer program is stored, and when the program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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