CN106777123A - A kind of group based on two-way tensor resolution model recommends method - Google Patents

Abstract

The invention discloses a group recommendation method based on a bidirectional tensor decomposition model, including: 1) defining an interaction relationship D _S representing a group G, a user U and a product I; 2) constructing a tensor decomposition model; 3) using the The Yethian personalized sorting method converts and solves the tensor decomposition model, and obtains the values of each parameter in the tensor decomposition model; 4) Obtains the group preference of the g-th group for the i-th product And traverse all commodities to obtain the group preferences of the gth group for all products; 5) sort the group preferences of the gth group for all products in descending order, and select the first N products as the recommended product list and push them to the gth group. The invention models the individual preference as a two-way process, which can effectively reflect the real formation process of the individual preference, improves the accuracy of group recommendation, and has better robustness.

Description

A Group Recommendation Method Based on Bidirectional Tensor Decomposition Model

technical field

The invention belongs to the field of group recommendation, in particular to a group recommendation (BTF-GR) method based on a bidirectional tensor decomposition model

Background technique

Social networking has long been an important part of the social media environment. Users will spontaneously form groups on social networking platforms, and capturing the preferences of each group will help us conduct in-depth behavioral analysis of user groups, and then recommend target products and Serve. But group recommendation is different from individual recommendation, because groups are usually composed of users with diverse preferences, so group recommendation is not easy to achieve. The core task of group recommendation is to aggregate individual preferences to generate a group recommendation result, but the existing aggregation strategies all model the formation of group preference as a one-way process, although group preference is the result of individual preference aggregation, but in In a real social environment, there is interaction between groups and individuals, and the existing aggregation strategy cannot capture the influence of groups on individual preferences, resulting in low accuracy of group recommendations; the individual characteristics of users and the group characteristics of groups are diverse, so There are differences in the influence of groups on individual preferences, but the existing aggregation cannot describe the difference of this influence, which makes the group recommendation results unsatisfactory; and when the existing group recommendation method is applied to a sparse data set, the recommendation performance drops significantly, so The existing group recommendation methods cannot solve the problem of data sparsity in the big data environment well, and do not have good robustness.

In recent years, decomposition has become the most popular recommendation technique. Through decomposition, the interaction between users and products can be described. Although the application of tensor decomposition to label recommendation, advertisement click prediction and other recommendation problems has achieved good recommendation performance, Zhang Quantitative decomposition has a high time complexity and is limited by the size of the data, so it is not suitable for group recommendation problems in a big data environment.

Contents of the invention

Aiming at the deficiencies of existing group recommendation strategies, the present invention proposes a group recommendation method based on a two-way tensor decomposition model, in order to reflect the interaction between the group and the individual in the individual preference modeling, and to describe the preference of the group to the individual The difference in influence, through the aggregation of accurate individual preferences to form accurate group preferences, thereby improving the accuracy of group recommendations, and is suitable for accurate and stable group recommendations in large-scale and sparse data environments.

In order to achieve the above object, the technical scheme adopted in the present invention is:

A kind of group recommendation method based on the two-way tensor decomposition model of the present invention is characterized in that it proceeds according to the following steps:

Step 1. Define an interaction relationship representing group G, user U and product I: In the interaction relationship D _S , G={G ₁ ,...,G _g ,...,G _|G| } represents a group set, G _g represents any gth group, 1≤g≤|G| ;U＝{U ₁ ,...,U _u ,...,U _|U| } represents the set of users, and U _u represents the uth user; I＝{I ₁ ,...,I _i ,...,I _|I| } represents the product set, I _i represents the i-th product,

Step 2: Use formula (1) to construct the tensor decomposition model of the i-th product for the u-th user in the g-th group

In formula (1), Indicates the individual preference of the u-th user in the g-th group to the i-th product; Indicates the uth user's individual preference for himself Impact, Indicates the individual preference of the g-th group to which the u-th user belongs to the u-th user , b _i represents the deviation of the i-th product; Represents the weight of the individual characteristics of the uth user to the uth user; U _u,l represents the lth hidden variable of the uth user, and k _u represents the number of hidden variables of the uth user; Indicates the l-th latent variable of the i-th product that interacts with the u-th user; Indicates the weight of the group characteristics of the g-th group to which the u-th user belongs to the u-th user; G _g,m represents the m-th hidden variable of the g-th group, and k _g represents the number of hidden variables of the g-th group ; Represents the mth latent variable of the i-th product that interacts with the g-th group;

Step 3, using the Bayesian personalized ranking method to analyze the tensor decomposition model Perform an optimization solution to obtain the tensor decomposition model Each parameter value in;

Step 4. Use formula (2) to obtain the group preference of the g-th group for the i-th product Thus, the group preference of the gth group for all products is obtained:

In formula (2), Δ( ) is the average aggregation function;

Step 4: Sort in descending order the group preferences of all products by the gth group, and select the products corresponding to the top N group preferences as a list of recommended products and push them to the gth group.

The group recommendation method of the present invention is also characterized in that the third step is carried out as follows:

Step 3.1, utilize formula (3) to obtain described tensor decomposition model The objective function of

In formula (3), Indicates the difference between the individual preference of the u-th user in the g-th group for the _i -th product and the individual preference for the _i -th product; Indicates that the _i -th product belongs to the positive feedback set of the u-th user in the g-th group, and the positive feedback set is a set of all products that have interacted with the u-th user in the g-th group; Indicates that the i _b -th product belongs to the negative feedback and missing value set of the u-th user in the g-th group, and the negative feedback and missing value set is the set of all products that have not interacted with the u-th user in the g-th group; Represents the logistic function; Θ represents the tensor decomposition model The set of parameters in and has λ _Θ represents a regularization parameter;

Step 3.2, initialization parameter set Θ and regularization parameter λ _Θ ;

Step 3.3, traversing all the products in the positive feedback set of the uth user in the gth group, and in the process of traversing each product, from the negative feedback and missing feedback of the uth user in the gth group Arbitrarily select a product in the value set;

Step 3.4, utilize stochastic gradient descent method to obtain the parameters in the parameter set Θ Gradient; in parameter with When it is a fixed value, for the parameter Perform iterative updates respectively until convergence, so as to obtain the parameters the optimal value;

Step 3.5, traversing all the products in the positive feedback set of the uth user in the gth group, and in the process of traversing each product, from the negative feedback and missing value set of the uth user in the gth group Choose any product from

Step 3.6, utilize stochastic gradient descent method to obtain the parameters in the parameter set Θ with Gradient; in parameter When it is the optimal value, for the parameters with Perform iterative updates respectively until convergence, so as to obtain the parameters with the optimal value of .

Compared with the prior art, the beneficial effects of the present invention are reflected in:

1. For the first time, the present invention models the formation of group preferences as a two-way process of aggregating individual preferences and the influence of groups on individual preferences. Compared with existing group recommendation methods that model group preferences as a one-way process of aggregating individual preferences, this The modeling idea of the invention is more in line with the real scene of group preference formation. The invention can not only capture the interaction between the group and the individual, but also describe the differences in the influence of the group on the individual preferences of different users, thus effectively improving the group The recommendation accuracy is satisfactory, and a satisfactory group recommendation result is obtained.

2. The present invention solves the high time complexity problem existing in the tensor decomposition model by modeling users, groups, and products as a tensor decomposition of paired interactions. At the same time, the tensor decomposition model proposed by the present invention integrates Group preference can effectively reduce the negative impact of data sparseness, so the present invention enables the tensor decomposition model to be applied to the group recommendation problem in the big data environment, and the tensor decomposition model of pairwise interaction in the present invention can Get higher forecast quality.

3. There is a large amount of sparse implicit feedback data in the big data environment, and there is a large deviation in the individual preference predicted by the method of directly predicting the preference score to solve the model, which leads to a decline in recommendation accuracy and satisfaction. However, the present invention transforms the model solution into For the ranking problem, the ranking method has good adaptability to sparse implicit feedback data, and can obtain accurate preference ranking. The present invention uses the Bayesian personalized ranking method to solve the model to obtain accurate individual preference rankings, and then aggregates them into accurate group preference rankings, thus effectively improving the accuracy and satisfaction of group recommendations.

4. The present invention sets personalized weights for users to capture the differential effects of individual preferences and group influence on different users. The setting of personalized weights makes the model closer to the real situation of individual preferences, which helps to obtain better group recommendation accuracy.

5. In the real group recommendation environment, the usual strategy is to provide a recommendation list as long as possible to cover the preferences of all users in the group as much as possible. When the recommendation list is longer, the group recommendation method proposed by the present invention not only has better robustness, but also has better performance, so the present invention is applicable to the group recommendation environment.

6. Due to the increase in preference diversity of large-scale groups, the recommendation for large-scale groups is very difficult and imprecise, while the group recommendation method proposed by the present invention has better robustness for groups of different sizes.

7. The present invention can be used in a group recommendation system for physical products such as home appliances and food, digital products such as music and movies, service products such as travel routes and vacation arrangements, and can be used on platforms such as webpages and APPs of computers and mobile phones, and has a wide range of applications.

Description of drawings

Fig. 1 is a schematic flow sheet of the present invention;

Fig. 2 is the comparative figure of method proposed by the present invention and traditional method;

Fig. 3 is data representation and solution of the present invention;

Fig. 4 a is the comparison chart of the average accuracy rate mean value of the present invention and the benchmark algorithm;

Fig. 4b is a comparison chart of the recall ratio of the recommendation list length of the present invention and the benchmark algorithm being 5;

Fig. 4c is the comparison chart of the average sorting reciprocal of the present invention and the benchmark algorithm;

Figure 5a is a comparison chart of the average accuracy rate between personalized weights and fixed weights;

Figure 5b is a comparison chart of the recall rate of the recommendation list length of 5 with personalized weight and fixed weight;

Figure 5c is a comparison chart of the average ranking reciprocal of personalized weights and fixed weights.

detailed description

The tensor decomposition model proposed by the present invention is a two-way paired interactive tensor decomposition model, that is, the formation of group preferences is a two-way process, and the user, group, and product are modeled as a paired interaction relationship. The group recommendation method proposed by the present invention is based on the following two assumptions:

1. Each user in a group has an inherent preference for a product. Each user's intrinsic preference for a product may be influenced by the group to which he belongs;

2. The influence of groups on individual preferences is significantly different among users. The user's final preference is the combined result of internal preference and group influence.

In this embodiment, as shown in Figure 1, a group recommendation method based on a two-way tensor decomposition model is performed according to the following steps:

Step 1. Define an interaction relationship representing group G, user U and product I: In the interaction relation D _S , G={G ₁ ,...,G _g ,...,G _|G| } represents the group set, G _g represents any gth group, 1≤g≤|G|; U ＝{U ₁ ,...,U _u ,...,U _|U| } represents the set of users, and U _u represents the uth user; I＝{I ₁ ,...,I _i ,...,I _|I| } represents the product set, I _i represents the i-th product, Traditional group preference modeling only considers the interaction between user U and product I, but the present invention not only considers the interaction between user U and product I, but also considers the interaction between group G and user U, and the interaction between different users There are differences in the strength of the effect. The difference between the group preference modeling idea proposed by the present invention and the traditional group preference modeling idea is shown in FIG. 2 .

Step 2, carry out pairwise interactive decomposition of the interaction relationship between group G, user U and product I, the data representation of group G, user U and product I and the pairwise interactive tensor decomposition model proposed by the present invention are shown in Figure 3 Figure 3 also shows the difference between the tensor decomposition model proposed by the present invention and the traditional tensor decomposition model, and then using formula (1) can construct the tensor of the i-th product for the u-th user in the g-th group Quantitative decomposition model

In formula (1), Indicates the individual preference of the u-th user in the g-th group to the i-th product; Indicates the uth user's individual preference for himself Impact, Indicates the individual preference of the g-th group to which the u-th user belongs to the u-th user , b _i represents the deviation of the i-th product; Represents the weight of the individual characteristics of the uth user to the uth user; U _u,l represents the lth hidden variable of the uth user, and k _u represents the number of hidden variables of the uth user; Indicates the l-th latent variable of the i-th product that interacts with the u-th user; Indicates the weight of the group characteristics of the g-th group to which the u-th user belongs to the u-th user; G _g,m represents the m-th hidden variable of the g-th group, and k _g represents the number of hidden variables of the g-th group ; Represents the mth latent variable of the i-th product that interacts with the g-th group;

Step 3. Use the Bayesian personalized ranking method to decompose the tensor model Perform an optimization solution to obtain the tensor decomposition model Each parameter value in , that is, the direct solution of individual preference is transformed into the ranking of individual preference;

Step 3.1, Solve the tensor decomposition model That is, given the u-th user in the g-th group, the optimal parameters of the u-th user are obtained, so according to the Bayesian personalized ranking method, the learning objective of the tensor decomposition model is to maximize the formula (2) The posterior probability in

In formula (2), Θ represents the tensor decomposition model The set of parameters in and has Indicates the preference ranking of the u-th user in the g-th group for all products; Indicates the individual preference likelihood function of the u-th user in the g-th group for all products obtained from the sample set; Represents prior knowledge of the parameters. where the likelihood function It can be expressed as formula (3):

In formula (3), Indicates that the u-th user in the g-th group has a preference for all products, and the product ranked product front, and the ordering of each pair of products is independent of the ordering of other product pairs; Indicates that the u-th user of the g-th group compares to product i _b for product The individual preference probability of can be expressed as formula (4):

In formula (4), Indicates the difference between the individual preference of the u-th user in the g-th group for the _i -th product and the individual preference for the _i -th product; Represents the logistic function. According to this transformation, and assuming prior knowledge of the parameters Obey the mean value of 0, the covariance matrix is a Gaussian distribution of _ΣΘ , then the logarithmic form of the posterior probability in formula (2) can be simplified to formula (5):

tensor decomposition model The learning objective is transformed into the objective function of minimizing formula (6)

In formula (6), Indicates that the i _a -th product belongs to the positive feedback set of the u-th user in the g-th group, and the positive feedback set is the set of all products that have interacted with the u-th user in the g-th group; Indicates that the i _b -th product belongs to the negative feedback and missing value set of the u-th user in the g-th group, and the negative feedback and missing value set is the set of all products that have not interacted with the u-th user in the g-th group; λ _Θ represents the regularization parameter;

Step 3.2, initialization parameter set Θ and regularization parameter λ _Θ ;

Step 3.3. Traverse all products in the positive feedback set of the uth user in the gth group, and randomly select from the negative feedback and missing value set of the uth user in the gth group during the process of traversing each product select a product;

Step 3.4, using the stochastic gradient descent method to obtain the parameters in the parameter set Θ Gradient; in parameter with When it is a fixed value, for the parameter Perform iterative updates respectively until convergence, so as to obtain the parameters the optimal value;

Step 3.5, traverse all the products in the positive feedback set of the uth user in the gth group, and randomly select from the negative feedback and missing value set of the uth user in the gth group during the process of traversing each product select a product;

Step 3.6, using the stochastic gradient descent method to obtain the parameters in the parameter set Θ with Gradient; in parameter When it is the optimal value, for the parameter with Perform iterative updates respectively until convergence, so as to obtain the parameters with the optimal value of .

Step 4: Use formula (7) to obtain the group preference of the g-th group for the i-th product Thus, the group preference of the gth group for all products is obtained:

In formula (7), Δ( ) is the average aggregation function;

Step 4: Sort the group preferences of all products by the g-th group in descending order, and select the products corresponding to the top N group preferences as a recommended product list and push them to the g-th group.

Carry out experimental demonstration for the inventive method, specifically include:

1) Prepare the standard data set

The present invention uses CiteULike and Last.fm, two widely used data sets in the recommendation field, as standard data sets to verify the performance of the group recommendation method proposed by the present invention. The first dataset, CiteULike, is an online community website for scientific researchers. On CiteULike, scholars can use tags to mark academic articles, and they can also create and join groups to share cited articles. The CiteULike data set used in the experiment contains 130,321 "group-user-product" triples, of which 11,168 articles are annotated by 1310 users from 584 groups, the average group size is 5.4, and selected from each group The first 10 articles are used as a test set, and the remaining data is used as a training set; the second data set Last.fm is an online community website for music fans. On Last.fm, music fans can tag musicians or tracks and create or form groups with people of similar taste. The Last.fm data set used in the experiment contains 317907 "group-user-product" triples, of which 1992 musicians are marked by 3605 users from 2716 groups, and the average group size is 21.2. The top 10 musicians in each group are used as the test set, and the remaining data are used as the training set.

2) Evaluation indicators

The recall rate (Rec@N) with a recommended length of N, mean average precision (MAP) and average rank reciprocal (MRR) are used as the evaluation indicators of this experiment. Recall evaluates the ability of a group recommender system to return all relevant products, mean precision and mean rank reciprocal reveal the accuracy of relevant products in the recommended list. The formula for calculating the recall rate Rec@N with a recommended list length of N is:

In formula (8), N _related is the number of products that appear in both the sorted list and the test set; N is the number of related products in the test set.

The formula for calculating the average accuracy rate is:

In formula (9), where |G| is the number of groups in the test set, is an indicator variable, if the group If the product ranked nth in the recommended list also appears in the test set, the value is 1, and the other cases are 0. The accuracy rate of the recommendation result represented by , the formula is:

In formula (10), where is the number of products that co-occur in the sorted list and the test set, is the number of related products in the recommendation list.

The average sorted reciprocal is the multiplication of the inverse of the first correctly sorted product, calculated as:

3) Experiment on a standard dataset

In order to verify the effectiveness of the proposed model in the present invention, we compared the Bidirectional Tensor Decomposition (BTF-GR) model proposed in the present invention for group recommendation with 4 benchmark methods. The 4 benchmark methods are: user-based collaborative Filtering (UserCF) method - user-based nearest neighbor (UserKNN) algorithm, product-based collaborative filtering (ItemCF) method - product-based nearest neighbor (ItemKNN) algorithm, matrix factorization (IMF) method based on implicit feedback, matrix factorization-based The Bayesian Personalized Ranking (BPRMF) method. Modeling and recommendation are carried out with 5 methods on the CiteULike dataset and Last.fm dataset, and the recommendation results are compared. The experimental results are shown in Figure 4a, Figure 4b, and Figure 4c. Compared with the four benchmark methods, the group recommendation method proposed by the present invention has achieved better recommendation accuracy on both the Last.fm and CiteULike datasets, and the performance advantage of the present invention is more obvious for sparse implicit feedback data.

In order to test the influence of personalized weights on the proposed model of the present invention, we construct a variant model by setting uniform fixed weights for all individuals, and use it as a control experiment. The solid lines in Fig. 5a, Fig. 5b and Fig. 5c represent the results of the bidirectional tensor decomposition (BTF-GR) model of the present invention, and the dashed lines represent the results of the variant model. The results show that the Bidirectional Tensor Factorization (BTF-GR) model always outperforms the variant with fixed weights on both the CiteULike dataset and the Last.fm dataset. This result shows that user preference and group influence play different roles in the formation of individual preference, and the Bidirectional Tensor Factorization (BTF-GR) model can capture this difference to obtain better recommendation accuracy.

In order to verify the robustness of the model proposed in the present invention and understand the robustness comparison with the four benchmark methods, we designed two experimental groups for verification by changing the length of the recommendation list and the group size. The experimental results show that the bidirectional tensor decomposition (BTF-GR) model of the present invention has good robustness in the length of the recommendation list and the size of the group, and the recommendation accuracy is always better than the four benchmark methods. Longer, the better the performance of the bidirectional tensor decomposition (BTF-GR) model of the present invention, that is, the present invention is applicable to the group recommendation environment.

Claims (2)

1. A group recommendation method based on a two-way tensor decomposition model, characterized in that it is carried out according to the following steps: Step 1. Define an interaction relationship representing group G, user U and product I: In the interaction relationship DS, G={G ₁ ,...,G _g ,...,G _|G| } represents a group set, G _g represents any gth group, 1≤g≤|G|; U＝{U ₁ ,...,U _u ,...,U _|U| } represents the set of users, U _u represents the uth user; 1≤u≤|U|; I＝{I ₁ ,.. .,I _i ,...,I _|I| } means the product set, I _i means the i-th product, 1≤i≤|I|; Step 2: Use formula (1) to construct the tensor decomposition model of the i-th product for the u-th user in the g-th group ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ In formula (1), Indicates the individual preference of the u-th user in the g-th group to the i-th product; Indicates the uth user's individual preference for himself Impact, Indicates the individual preference of the g-th group to which the u-th user belongs to the u-th user , b _i represents the deviation of the i-th product; Represents the weight of the individual characteristics of the uth user to the uth user; U _u,l represents the lth hidden variable of the uth user, and k _u represents the number of hidden variables of the uth user; Indicates the l-th latent variable of the i-th product interacting with the u-th user; Indicates the weight of the group characteristics of the g-th group to which the u-th user belongs to the u-th user; G _g,m represents the m-th hidden variable of the g-th group, and k _g represents the number of hidden variables of the g-th group ; Represents the mth latent variable of the i-th product that interacts with the g-th group; Step 3, using the Bayesian personalized ranking method to analyze the tensor decomposition model Perform an optimization solution to obtain the tensor decomposition model Each parameter value in; Step 4. Use formula (2) to obtain the group preference of the g-th group for the i-th product Thus, the group preference of the gth group for all products is obtained: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}}_{\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}}_{\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ In formula (2), Δ( ) is the average aggregation function; Step 4: Sort in descending order the group preferences of all products by the gth group, and select the products corresponding to the top N group preferences as a list of recommended products and push them to the gth group. 2. The group recommendation method according to claim 1, characterized in that, said step 3 is carried out as follows: Step 3.1, utilize formula (3) to obtain described tensor decomposition model The objective function of ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; G</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\underset{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; u</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\underset{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; u</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}\underset{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; \backslash </span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; u</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; \&Theta;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Theta;</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ In formula (3), Indicates the difference between the individual preference of the u-th user in the g-th group for the i- _a -th product and the i- _b -th product; i _a ∈ I _gu means that the _i -th product belongs to the g-th group The positive feedback set of the u-th user, the positive feedback set is the set of all products that have interacted with the u-th user in the g-th group; ib∈I\I _gu means that the i _b -th product belongs to the g-th group The set of negative feedback and missing values of the u-th user, the set of negative feedback and missing values is the set of all products that have not interacted with the u-th user in the g-th group; Represents the logistic function; Θ represents the tensor decomposition model The set of parameters in and has λ _Θ represents a regularization parameter; Step 3.2, initialization parameter set Θ and regularization parameter λ _Θ ; Step 3.3, traversing all the products in the positive feedback set of the uth user in the gth group, and in the process of traversing each product, from the negative feedback and missing feedback of the uth user in the gth group Arbitrarily select a product in the value set; Step 3.4, using the stochastic gradient descent method to obtain the parameters U _u,l in the parameter set Θ, G _g,m , _Gradient of bi; in parameter with When is a fixed value, for the parameter U _u,l , G _g,m , b _i are updated iteratively until convergence, so as to obtain parameters U _u,l , G _g,m , The optimal value of b _i ; Step 3.5, traversing all the products in the positive feedback set of the uth user in the gth group, and in the process of traversing each product, from the negative feedback and missing value set of the uth user in the gth group Choose any product from Step 3.6, utilize stochastic gradient descent method to obtain the parameters in the parameter set Θ with Gradient; in parameter U _u,l , G _g,m , When b _i is the optimal value, for the parameters with Perform iterative updates respectively until convergence, so as to obtain the parameters with the optimal value of .