A recommendation method based on an interpretable generalized logistic transformation matrix decomposition

Abstract

The application discloses a recommendation method based on an interpretable generalized logistic transformation matrix decomposition, and comprises the following steps: converting an original score matrix into normally distributed data through a generalized logistic transformation function; constructing a similarity-based index and a ranking-based index; calculating a probability distribution of a similar user's score on a recommended item and an expected score, and combining the similarity index to generate an interpretability index; integrating the interpretability index into a matrix decomposition target function for optimization; solving a user feature matrix and an item feature matrix through an alternating least squares method or a stochastic gradient descent; calculating a predicted score and mapping back to an original score interval through a generalized logistic inverse transformation; and generating a recommendation list; the application has wider applicability and higher performance in practical application.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of recommendation systems, and in particular to a recommendation method based on an interpretable generalized logistic transformation matrix factorization. BACKGROUND

[0002] With the rapid development of information technology, recommendation systems have become an important bridge connecting users with massive amounts of information. However, traditional recommendation algorithms often ignore the interpretability of the recommendation results while pursuing high accuracy, leading to users' difficulty in understanding the logic behind the recommendations, and thus reducing the trust and satisfaction of the recommendation system. Existing technologies can be mainly summarized into three categories: content-based recommendation systems mainly rely on users' historical selection records or preference records to recommend relevant items, and the core lies in accurately calculating the similarity between different items and recommending new items similar to the preferred items based on these similarities. The advantage of this scheme is that it can mine users' potential interests, but it has the problem of cold start, i.e., when a new type of user appears, the system is difficult to provide recommendations that meet their needs due to the lack of preference records. In addition, content-based recommendation mainly relies on the content features of items, and for items with unclear or difficult-to-extract content features, the recommendation effect may be limited. Collaborative filtering recommendation systems are based on a large amount of historical data of users and items, and recommend items by calculating the similarity between unknown target pairs. Among them, matrix factorization (MF) is one of the most common and popular algorithms in collaborative filtering, which represents the association between users and items by decomposing the user rating matrix into two low-dimensional feature vectors. Although the matrix factorization model has the advantages of scalability and ease of implementation, it has the problems of insufficient expression ability and lack of interpretability. In order to improve the 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, these algorithms still need to be improved in terms of interpretability. Hybrid recommendation systems aim to combine the advantages of different recommendation technologies and avoid their disadvantages by integrating multiple algorithms to provide more accurate and comprehensive recommendations. Hybrid recommendation mainly includes pre-fusion, post-fusion and intermediate fusion. Pre-fusion integrates the results of different algorithms at the data input stage; post-fusion integrates the results after the recommendation results are generated; and intermediate fusion combines the advantages of different algorithms during the recommendation process. Hybrid recommendation systems can fully utilize 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 hybrid recommendation systems is high, and the fusion method and weight distribution between different algorithms are also key factors affecting the recommendation effect. SUMMARY

[0003] Invention purposes: The purpose of the present application is to provide a recommendation method based on interpretable generalized logistic transformation matrix decomposition, which combines advanced representation learning methods, interpretability techniques and flexible data distribution models to solve the problems of insufficient expression ability and lack of interpretability of traditional matrix decomposition models in recommendation systems.

[0004] Technical solutions: The recommendation method based on interpretable generalized logistic transformation matrix decomposition comprises the following steps:

[0005] (1) Convert the original rating matrix to normally distributed data through a generalized logistic transformation function;

[0006] (2) Build an interpretability index: calculate the similarity between users based on the Tanimoto coefficient, and generate a similarity index of users to items; calculate the probability distribution of similar users to the rating of the recommended item and the expected rating, and combine the similarity index to generate an interpretability index;

[0007] (3) Integrate the interpretability index into the matrix decomposition objective function for optimization; solve the user feature matrix and the item feature matrix by the alternating least squares method or the stochastic gradient descent method;

[0008] (4) Calculate the predicted rating and map it back to the original rating interval through the generalized logistic inverse transformation;

[0009] (5) Generate a recommendation list according to the predicted rating.

[0010] Further, in step (2), the calculation formula of the similarity between users is:

[0011] ;

[0012] Wherein, and represent the rating vectors of users and to items;

[0013] The similarity index formula of users to items is as follows:

[0014] ;

[0015] Wherein, represents the user set with similarity higher than the preset threshold to user , represents the rating of user to item .

[0016] Further, in step (2), the calculation formula of the rating probability distribution is:

[0017] ;

[0018] wherein, denotes a set of users with high similarity to the user , denotes a set of users with rating to the item ;

[0019] The calculation formula of the expected rating is:

[0020] ;

[0021] wherein, denotes a set of all possible rating values.

[0022] Further, in step (2), the generation method of the explainability index is:

[0023] ;

[0024] wherein, denotes the explainability degree of the user to the item ; is a preset threshold value for controlling the sensitivity of the explainability index; is a control parameter for adjusting the influence degree of the explainability index on the recommendation result.

[0025] Further, in step (3), the optimization formula is as follows:

[0026] ;

[0027] wherein, denotes a set of known ratings in the rating matrix; is the true value; is a control parameter for removing the influence of invalid values such as missing values or abnormal values; and are regularization parameters for preventing overfitting; and respectively denote the low-dimensional feature vectors of the user and the item ; denotes the explainability index of the user and the item .

[0028] Further, in step (4), the calculation formula of the predicted rating is as follows:

[0029] ;

[0030] wherein, denotes the final user feature embedding, denotes the final item feature embedding.

[0031] Further, the mapping back to the original rating interval by the generalized logistic inverse transform is as follows:

[0032] ;

[0033] wherein, is the mean of the rating matrix after GLT transform.

[0034] The electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the computer program realizes the optimization method of the single-phase transducer when loaded into the processor.

[0035] The storage medium stores a computer program, and the computer program realizes the optimization method of the single-phase transducer when executed by the processor.

[0036] Advantages: Compared with the prior art, the present application has the following obvious advantages: by introducing the generalized logistic transform function and constructing a new interpretability index, the present application has achieved remarkable advantages in improving recommendation accuracy and enhancing recommendation interpretability. At the same time, the present application also has good adaptability and robustness, and can process data sets of different sizes and distribution characteristics, and cope with the influence of data noise and outliers on the recommendation results. These advantages make the GEMF algorithm have wider applicability and higher performance in practical application. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is the flowchart of the present application. DETAILED DESCRIPTION

[0038] The technical solutions of the present application will be further described below in combination with the drawings.

[0039] As Figure 1As shown, the embodiment of the application is a recommendation method based on an interpretable generalized logistic transformation matrix decomposition. First, a generalized logistic transformation function is introduced to convert the original rating data into a nearly normal distribution to meet the needs of subsequent algorithms. Then, by mining the similarity between items and the user rating ranking information, a new interpretability index is constructed to reflect the inherent relationship between users and items. Then, these interpretability indexes are integrated into the matrix decomposition model, a new objective function is designed, and the user and item low-dimensional feature vectors are obtained by optimization. Finally, the prediction rating matrix is calculated using these feature vectors, and the predicted rating is mapped back to the original rating interval through the inverse function of the generalized logistic transformation, thereby realizing the recommendation of the target item. This research scheme not only improves the accuracy of the recommendation system, but also enhances the interpretability of the recommendation results, providing more transparent and reliable recommendation services for users. Including the following steps:

[0040] (1) Generalized logistic transformation (GLT) includes the following steps:

[0041] (11) In order to solve the problem of unreasonable data distribution assumption, the generalized logistic transformation (GLT) function is introduced. GLT function can convert the original rating data into a nearly normal distribution, so as to adapt to the needs of subsequent algorithms. Its definition is as follows:

[0042] ;

[0043] Where, represents the rating after GLT transformation, represents the original rating, and represent the maximum and minimum values of the original rating matrix respectively, is a scaling parameter used to control the range of transformed data, is a logarithmic function parameter used to adjust the distribution shape of transformed data. By adjusting and , the transformed rating data can be approximately normally distributed, thus meeting the requirements of subsequent algorithms on data distribution.

[0044] (12) Generalized logistic transformation is performed on the experimental data.

[0045] (2) Construction of interpretability index

[0046] In order to enhance the interpretability of the recommendation system, two new interpretability indexes are constructed: similarity-based index and ranking-based index. Including the following steps:

[0047] (21) Similarity-based index

[0048] First, the similarity between different items is calculated using the Tanimoto coefficient. The Tanimoto coefficient is a commonly used similarity measure that can reflect the degree of association between items. Its calculation formula is as follows

[0049] ;

[0050] wherein, and represent the rating vectors of users and to items.

[0051] Then, according to the similarity between users, the similarity of users to items is calculated. Specifically, for users and items , the weighted average of the ratings of all users in the user set with high similarity to user to item is calculated as the similarity index of users to items. Its calculation formula is as follows:

[0052] ;

[0053] wherein, represents the user set with similarity higher than the preset threshold to user , represents the rating of user to item .

[0054] (22) Rank-based index

[0055] The similarity-based index can reflect the degree of association between users and items, but cannot fully consider the influence of personal preferences of users. In order to make up for this deficiency, the present application introduces a rank-based index. Specifically, the probability that user rates item as is defined, i.e. the probability that similar users rate the recommended item as a certain specific value. Its calculation formula is as follows:

[0056] ;

[0057] wherein, represents the user set with high similarity to user , represents the user set that rates item as .

[0058] Then, the probability that similar users rate the recommended item the expected rating of the recommendation item by similar users, i.e., the weighted average of the ratings of the recommendation item by similar users. Its calculation formula is as follows:

[0059] ;

[0060] wherein, denotes the set of all possible rating values.

[0061] Finally, based on the similarity-based indicator and the ranking-based indicator, the final explainability indicator is constructed. Specifically, when the similarity between the user and the item is high and the expected rating of the recommendation item by similar users is also high, it is considered that the recommendation item is explainable to the user. Its calculation formula is as follows:

[0062] ;

[0063] wherein, denotes the explainability of the user to the item ; is a preset threshold value for controlling the sensitivity of the explainability indicator; is a control parameter for adjusting the influence degree of the explainability indicator on the recommendation result.

[0064] (3) The explainability matrix decomposition model is as follows:

[0065] After constructing the explainability indicator, it is integrated into the matrix decomposition model, and a new objective function is designed. The objective function is defined as follows:

[0066] ;

[0067] wherein, denotes the set of known ratings in the rating matrix; is the true value; is a control parameter for removing the influence of invalid values (such as missing values or abnormal values); and are regularization parameters for preventing overfitting; and respectively denote the low-dimensional feature vectors of the user and the item ; denotes the explainability indicator of the user and the item . The first term of the objective function is the squared error term between the predicted rating and the actual rating, aiming to minimize the prediction error; the second term is the regularization term of the user feature vector and the item feature vector, aiming to prevent overfitting; the third term is the explainability regularization term, which introduces the explainability indicator of the user to the item and item feature vectors The purpose of this item is to consider the explainability factor in the optimization process, so that the recommendation result is not only accurate, but also meets the user's explainability expectation.

[0068] In order to solve this optimization problem, commonly used optimization algorithms such as alternating least squares (ALS) or stochastic gradient descent (SGD) are adopted. These algorithms update the user feature vector and item feature vector by iteration, so that the objective function gradually converges to the minimum value.

[0069] (4) Predicted score and inverse transformation, including the following steps:

[0070] (41) After obtaining the low-dimensional feature matrix of users and items, the predicted score matrix is calculated:

[0071] ;

[0072] (42) However, since the predicted score matrix is calculated based on the score data after GLT transformation, it is necessary to map it back to the original score interval through the inverse transformation function of GLT:

[0073] ;

[0074] Where, is the mean of the score matrix after GLT transformation. Finally, according to the predicted score, the user is recommended for the project. Specifically, for each user, the projects are sorted in descending order of predicted score, and the top projects are selected as the recommendation result. In this way, the user can get personalized recommendation service that meets his interest and explainability expectation.

[0075] The present application selects the classic Jester data set as the verification set of the experiment. The Jester data set is composed of record data of three different time periods, which provides rich experimental materials for comprehensive verification of the performance of the recommendation algorithm. Among them, the data set contains the score information of users on jokes, and the score range is usually -10 to 10, reflecting the user's preference for jokes, as shown in Table 1.

[0076] Table 1 Statistical information of experimental data

[0077] ;

[0078] Typical matrix factorization-based algorithms are selected and compared 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, their impact on prediction accuracy and time consumption can be achieved. In this experiment, we will mainly explore the impact of GEMF prediction accuracy and runtime. Three of the most typical indicators were selected as the evaluation metrics for prediction results: MSE (mean squared error), MAE (mean absolute error), and RMSE (root mean square error).

[0079] ;

[0080] ;

[0081] ;

[0082] Based on technical solutions 1 to 4, and with fixed comparison schemes, evaluation indicators, and parameter settings, the values ​​of the method proposed in this invention and the comparison schemes on three sets of data are evaluated, as shown in Table 2.

[0083] Table 2. Prediction errors of the seven algorithms

[0084]

[0085] The experimental results in Table 2 show that the proposed solution 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, and target recommendation based on this index can better mine the inherent information of the data, thereby obtaining more accurate recommendation results. To further verify the impact of parameters, restrictions were imposed. Explore different The impact of the chosen value on the scheme.

Claims

1. A recommendation method based on an interpretable generalized logistic transformation matrix factorization, characterized in that, The method comprises the following steps: (1) converting the original rating matrix into normally distributed data through a generalized logistic transformation function; (2) constructing an explainability index: a similarity-based index calculates the similarity between users through a Tanimoto coefficient and generates a similarity index of users to items; a ranking-based index calculates the probability distribution of similar users to the rating of a recommended item and an expected rating, and combines the similarity index to generate an explainability index; the calculation formula of the similarity between users is as follows: ； wherein, and represent a vector of ratings of items by users and a vector of ratings of items by users The similarity index of users to items is as follows: ； wherein, denotes a set of users with a similarity higher than a pre-set threshold to the user, denotes a rating of the user to the item . The calculation formula of the rating probability distribution is as follows: ； wherein, represents a set of users with high similarity to the user , represents a set of users who rated the item with a rating of . The calculation formula of the expected rating is as follows: ； wherein, denotes the set of all possible score values; The generation method of the explainability index is as follows: ； wherein, represents the degree of explainability of the user to the item ; is a preset threshold value for controlling the sensitivity of the explainability index; is a control parameter for adjusting the degree of influence of the explainability index on the recommendation result; (3) integrating the explainability index into a matrix decomposition target function for optimization; solving a user feature matrix and an item feature matrix through an alternating least squares method or a stochastic gradient descent method; (4) calculating a predicted rating and mapping back to the original rating interval through a generalized logistic inverse transformation; (5) generating a recommendation list according to the predicted rating.

2. The recommendation method based on interpretable generalized logistic transformation matrix factorization according to claim 1, characterized in that, In step (3), the optimization formula is as follows: ； where, denotes a set of known ratings in the rating matrix; is a true value; is a control parameter for removing the influence of invalid values such as missing values or abnormal values; and is a regularization parameter for preventing overfitting; and respectively denote a low-dimensional feature vector of a user and an item ; denotes an explainability index of a user and an item . 3.The recommendation method based on interpretable generalized logistic transformation matrix factorization of claim 1, wherein, In step (4), the calculation formula of the predicted rating is as follows: ； wherein, denotes the final user feature embedding, denotes the final item feature embedding.

4. The recommendation method based on interpretable generalized logistic transformation matrix factorization according to claim 1, characterized in that, The formula for mapping back to the original rating interval through the generalized logistic inverse transformation is as follows: ； wherein, is the mean of the GLT transformed score matrix, L is the lower bound of the score; H is the upper bound of the score; the transformation range is (L, H).

5. An electronic device, comprising: A memory and a processor are included, the memory stores a computer program, and the processor implements the steps of the method in any one of claims 1-4 when executing the program.

6. A computer readable storage medium characterized by, A computer program is stored, and the program is executed by the processor to implement the steps of the method in any one of claims 1-4.

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