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CN113836397B - Recommendation method for personalized feature modeling of shopping basket - Google Patents

Recommendation method for personalized feature modeling of shopping basket Download PDF

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CN113836397B
CN113836397B CN202111025959.7A CN202111025959A CN113836397B CN 113836397 B CN113836397 B CN 113836397B CN 202111025959 A CN202111025959 A CN 202111025959A CN 113836397 B CN113836397 B CN 113836397B
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shopping basket
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CN113836397A (en
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包旭光
李淼
常亮
古天龙
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Guilin University of Electronic Technology
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Abstract

The invention discloses a recommendation method for personalized feature modeling of shopping baskets, which comprises the steps of forming triples according to features of historical shopping basket transaction data sets, mapping the triples to a feature vector space, introducing different association types to calculate and associate, finally modeling low-order feature combinations and high-order feature combinations among different entities by utilizing a neural network technology, predicting target article items, enabling a model to capture more association combinations from a user historical data set by using the triples, relieving the data sparsity problem in shopping basket recommendation tasks, enabling recommendation results to have reliability and accuracy, and solving the problems of low recommendation accuracy and low personalization degree of recommendation results based on the shopping basket recommendation method in the prior art.

Description

Recommendation method for personalized feature modeling of shopping basket
Technical Field
The invention relates to the technical field of big data analysis, in particular to a recommendation method for personalized feature modeling of shopping baskets.
Background
The rapid development of internet technology has led to tremendous changes in people's lifestyles from physical groceries to online electronic malls. The data volume of many applications is growing at a high rate, and the extraction of available information by rich user data presents a great challenge, and recommendation systems have long been an effective tool for alleviating information overload and improving user experience. The shopping basket recommendation problem is that given an item currently purchased by a user, other items to be added to the user's shopping basket are predicted. Under the application scene, the retail platform needs to consider collaborative filtering information between users and articles in the historical data and also needs to be recommended by combining the article information currently held by the users. Previous work has solved tasks through association rule mining. However, these works have difficulty in acquiring the characteristic representation and the high-order characteristic interaction of each item in the shopping basket transaction, and thus cannot well meet the personalized needs of the user, and also do not consider the own characteristics of the item to be recommended, and thus cannot accurately provide the user with a suitable commodity.
The currently published invention patent 'an association rule recommendation method integrating user interest weights', publication number CN 112100483A, is used for recommending interest points for users by constructing a scoring matrix of the users on the articles and calculating the interest weights of the users on the articles and obtaining frequent item combinations based on FP-tree. The method does not balance the complementarity and compatibility among different articles in the shopping basket transaction, ignores complex characteristic interaction, obtains the article combination only according to the interest weight of the user on the articles, and hardly accurately recommends another article to be added into the shopping basket.
Disclosure of Invention
The invention aims to provide a recommendation method for shopping basket personalized feature modeling, and aims to solve the problems that in the prior art, recommendation accuracy is low and recommendation result individuation degree is low based on a shopping basket recommendation method.
In order to achieve the above purpose, the invention adopts a recommendation method for modeling personalized features of shopping baskets, which comprises the following steps:
Extracting triples in the historical shopping basket transaction data set;
mapping the triples to a feature vector space;
The association calculation obtains a low-order feature combination result;
operating to obtain a high-order feature combination result;
And carrying out affine transformation on the low-order feature combination result and the high-order feature combination result to obtain a final recommendation value of the commodity, and forming a recommendation list.
The historical shopping basket transaction data set is user transaction data and a public data set with high credibility.
The triple comprises a user item, a shopping basket item and a target item, and three association types among the user item, the target item, the shopping basket item, the target item and the shopping basket item exist in transaction data.
In the process of mapping the triples to the feature vector space, a representation learning method is used for mapping the triples to the feature vector space, aggregation operation is carried out on shopping basket article entities currently held by a user, and the entities in the triples are converted into a vector representation form.
In the process of obtaining a low-order feature combination result by association calculation, sequentially carrying out first-order association calculation and second-order association calculation on three association types in transaction data to obtain the low-order feature combination result, wherein the first-order association calculation captures feature information which is mutually independent, and the second-order association calculation captures dependency relations among features.
And in the process of obtaining a high-order feature combination result by operation, performing serial operation on the mapped feature vectors, and inputting the feature vectors into a neural network layer to obtain the high-order feature combination result.
And carrying out affine transformation on the low-order feature combination result and the high-order feature combination result to obtain a final recommended value of the commodity, and carrying out affine transformation by using a linear function to obtain the final recommended value of the commodity in the process of forming a recommended list, and arranging the final recommended value according to a score descending order to obtain the recommended list.
According to the recommendation method for personalized feature modeling of the shopping basket, the triples are formed according to the features of the historical shopping basket transaction data set, the triples are mapped to the feature vector space, different association types are introduced to calculate and associate, finally, a neural network technology is utilized to model low-order feature combinations and high-order feature combinations among different entities, a target item is predicted, the use of the triples enables the model to capture more association combinations from the historical data set of a user, the problem of data sparsity in shopping basket recommendation tasks is relieved, meanwhile, recommendation results are enabled to have reliability and accuracy, and the problems of low recommendation accuracy and low individuation degree of recommendation results based on the shopping basket recommendation method in the prior art are solved.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow diagram of a recommendation method for personalized feature modeling of shopping baskets of the present invention.
FIG. 2 is a data acquisition and processing flow diagram of an embodiment of the present invention.
FIG. 3 is a flow chart of hidden vector representation of a shopping basket item set in accordance with an embodiment of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
Referring to fig. 1, the invention provides a recommendation method for personalized feature modeling of shopping basket, comprising the following steps:
S1: extracting triples in the historical shopping basket transaction data set;
S2: mapping the triples to a feature vector space;
S3: the association calculation obtains a low-order feature combination result;
s4: operating to obtain a high-order feature combination result;
S5: and carrying out affine transformation on the low-order feature combination result and the high-order feature combination result to obtain a final recommendation value of the commodity, and forming a recommendation list.
The historical shopping basket transaction data set is a public data set with higher user transaction data and reliability.
The triples comprise user items, shopping basket item items and target item items, and three association types between the user items and the target item, between the shopping basket item items and the target item and between the shopping basket item items exist in the transaction data.
In the process of mapping the triples to the feature vector space, a representation learning method is used for mapping the triples to the feature vector space, aggregation operation is carried out on shopping basket article entities currently held by a user, and the entities in the triples are converted into a vector representation form.
And in the process of obtaining a low-order feature combination result by association calculation, sequentially carrying out first-order association calculation and second-order association calculation on three association types in transaction data to obtain the low-order feature combination result, wherein the first-order association calculation captures feature information which is mutually independent, and the second-order association calculation captures the dependency relationship among features.
And in the process of obtaining a high-order feature combination result by operation, carrying out serial operation on the mapped feature vectors, and inputting the feature vectors into a neural network layer to obtain the high-order feature combination result.
And carrying out affine transformation on the low-order feature combination result and the high-order feature combination result to obtain a final recommended value of the commodity, carrying out affine transformation by using a linear function to obtain the final recommended value of the commodity in the process of forming a recommended list, and arranging the final recommended value according to a score value descending order to obtain the recommended list.
Further, the invention describes a specific embodiment of the method by taking the commodity of the online grocery shopping platform as an example of a recommended article, and the method specifically comprises the following steps:
Step 1, acquiring a historical shopping basket transaction data set of a user by utilizing a web crawler technology and a method for searching a reliable public data set, and preprocessing. For each user, all of his/her transaction records will be represented chronologically. For each shopping basket transaction record, sequentially selecting each item as a target item to be predicted, wherein the rest items are automatically regarded as shopping basket items;
And 2, representing the transaction record by using a triplet. Examples: the writing case can be expressed by the triple < user A, (schoolbag, notebook and pencil), wherein the writing case is expressed by the triple < user A > (schoolbag, notebook and pencil), the user A is a user entity, the schoolbag, notebook and pencil are shopping basket article collection entities currently held by the user, and the writing case is a target article entity of the user. Converting all user history shopping basket transaction data into the triples;
Step 3, mapping the triples into a feature vector space by using a representation learning method, and carrying out aggregation operation on shopping basket article entities currently held by a user to convert the entities in the triples into a vector representation form;
step 4, sequentially performing first-order association calculation and second-order association calculation on three association types in the transaction data to obtain a low-order feature combination result;
step 5, inputting the feature vectors in the step 3 into a neural network layer after serial operation to obtain a high-order feature combination result;
And 6, carrying out affine transformation on the results in the step 4 and the step 5 by using a linear function to obtain final recommended values of the commodity, and arranging the score values in a descending order to obtain a recommended list.
Further, referring to fig. 2, fig. 2 is a flowchart illustrating data acquisition and processing in this example, and the specific steps include:
2.1, using the existing web crawler technology, crawling user transaction data on electronic mall websites such as Beijing dong websites and Taobao websites, and searching public data sets with higher credibility on open source websites. The fields of the dataset include: user identity, time of shopping transaction, purchase of items, purchase behavior, etc. Because the original data cannot completely meet the requirement of subsequent calculation of the method, necessary processing and conversion are needed. Part of the initial shopping basket transaction data is shown in table 1, the transaction number is a transaction invoice number, each transaction is assigned a unique 6-bit integer, and part of the code of the return order starts with the letter 'c'. The item description is a brief description of each product.
The purchase amount refers to the total purchase amount of the product by the user in the transaction. The transaction date records the invoice date and time. The customer number assigns a unique 5-digit integer to each customer. The country is the name of the country/region in which each customer is located;
table 1 initial shopping basket transaction data
Transaction numbering Description of the article Purchase quantity Transaction date Customer numbering Country of China
536365 White heart-shaped lamp holder 6 12/1/20108:26 17850 British UK
536365 White metal lantern 6 12/1/20108:26 17850 British UK
536365 Red clothes hanger 8 12/1/20108:26 17850 British UK
536365 Hot water bag 6 12/1/20108:26 17850 British UK
536365 White heart-shaped pattern thermos bottle 6 12/1/20108:26 17850 British UK
536365 Nest box 2 12/1/20108:26 17850 British UK
536365 Glass star-shaped frosted lamp holder 6 12/1/20108:26 17850 British UK
536366 Mi-shaped hand warmer 6 12/1/20108:28 17850 British UK
536366 Red dot pattern hand warmer 6 12/1/20108:28 17850 British UK
536367 Ornament 32 12/1/20108:34 13047 British UK
536367 Toy bedroom 6 12/1/20108:34 13047 British UK
536367 Toy kitchen 6 12/1/20108:34 13047 British UK
2.2 Renumbering the attributes of user identity, shopping transaction time, purchasing articles, purchasing behavior and the like according to the quantity and the size of the attributes, and setting a unique ID to represent a certain object. For example, for a dataset with a number of users of 5000, the user ID number ranges from 0001 to 5000;
2.3, all the articles in the same transaction record of the user form a shopping basket. The purchase items in each shopping basket transaction of the user are divided into a currently held shopping basket item set and a target item, and the currently held shopping basket item set is represented by the item composition items of the shopping basket item set and the number of the shopping basket item set. For example, as shown in table 1, the transaction number "536365" includes the items "white heart-shaped lamp holder, white metal lantern, red clothes rack, hot water bag, white heart-shaped pattern hot water bottle, nest box, glass star-shaped frosted lamp holder", and when the target item is "white heart-shaped lamp", the rest items will automatically become shopping basket item set. Furthermore, negative records need to be created, since training data acquired from the dataset contains only positive records. For each positive record, its corresponding negative record is generated by randomly selecting a target item from the set of items P that the user has never selected;
2.4, deleting less than 10 items purchased by the user from the record. After the representative item is obtained, a record of the purchase transaction containing more than two items is maintained. In order to avoid excessive categories in shopping basket items, the number of items in each shopping basket should not exceed about 15. A user having at least 3 purchase transaction records is selected. For example, as shown in table 1, the transaction number "536566" of the user with the customer number "17850" only contains two commodities of "rice-shaped hand warmer and red dot pattern hand warmer", and therefore the transaction record is discarded. In addition, the user only has 2 purchase transaction records in the data set, so all transaction records corresponding to the user are also discarded;
2.5 for each user, all his/her transaction records are expressed chronologically as { r1, r2,... The first n-1 records are used as training sets, and the last record is used as testing set.
Further, constraint conditions need to be introduced in shopping basket recommendation tasks, and the specific steps comprise:
3.1 for the given series of item sets p= { P 1,...,pt } and user set u= { U 1,...,um }, assume that each item P k is associated with a set of attributes And (5) associating. For example, a product attribute may be size, color, brand, manufacturer, etc., and a sight attribute may be geographic location, ticket price, etc.;
And 3.2, providing recommended goods or services for the user by the recommendation model according to the association between the category of the goods and the goods. In general, there will be a set of associations between category sets c= { C 1,...,Cm } Wherein s (C i,Cj) represents that C j is a subclass of C i. One hierarchy h= { C 1,C2,...,Cn-1,Cn } consists of a set of classes with the same subclass, where C 1 is the root class, e.g., h= { clothing, women's overcoat, women's wind-coat } and h= { scenic spot, natural landscape, water landscape } etc.;
3.3, H represent a set of hierarchies. Each item p k is explicitly assigned to a hierarchy. Given a shopping basket currently held by a user Wherein B i is a set of hierarchical structures For example, shopping basket item set G i={p1,p2,...,pn-1,pn,pk e P, k=1..n }, the goal of the shopping basket recommendation is to predict that a hierarchical structure can be formed with the shopping basket item set To the user. Let f be a general utility function for measuring the scores of the target items, the user, and the shopping basket item set, the shopping basket recommendation task attempts to find the target item P' ∈p satisfying:
because the representation mode of the triples cannot effectively calculate recommended values and construct portraits of users, the invention needs to convert entities and relationship attributes in the triples into the representation mode of vectors. The step of triad vectorization and calculation of recommended values comprises the following steps:
4.1, converting discrete features in the data set into digital features by using one-hot coding. As shown in table 2:
table 2 records one-hot data
Distinguishing positive and negative tuples in a training set of transactions with θ: when θ=1, it means that the user selects the target item v i; when θ= -1, this indicates that the user has not selected the target item v i. Thus, the representation of the transaction < u i,Bi,vi > may be further represented as < u i,Bi,vi, θ >. Wherein each record of T e T corresponds to a vector of length d+1, wherein the first e positions represent users, the last f positions represent shopping basket items, the last f positions represent target items, and the (e+2f+1) th position represents whether the transaction is a positive tuple;
4.2, after the discrete features are subjected to one-hot coding, the data features are very sparse, and the feature space is enlarged. For example, if there are 5000 categories of merchandise, then the discrete features of one category of merchandise will be converted into 5000-dimensional numerical features, and the feature space will be enlarged. A hidden representation of features is learned using a cryptogenomodel. Mapping one-hot coded representations of the user and the item to a low-dimensional hidden space, each item and the user obtaining a hidden vector that can be used as a feature;
4.3, adopting different pooling strategies to aggregate hidden vectors of all the shopping basket articles in the article set to obtain fixed representation;
4.4, modeling three association types (between the user item and the target item, between the shopping basket item and the target item and between the shopping basket item) in the transaction data, and obtaining a characteristic combination result to model the personalized intention. Both the user and the target item are the primary entities of the recommendation, and considering this type of association helps to understand the relationship between the user preferences and the target item entities. Considering the association between shopping basket item and target item facilitates personalization of model recommendations. Items in a shopping basket item set do not always have a strong association, and the association between individual items can also affect the selection of a target item. Let pj be the hidden vector of each item pj in the shopping basket item set, uk be the hidden vector of the user uk, vt be the hidden vector of the target item vt, and the recommendation score f is proportional to the three correlations:
In the formula (2), bi is a hidden vector formed by p j and describing the currently held shopping basket article set Bi, w is a parameter of the whole model, and w is an inner product operation of two vectors.
4.5 The set of shopping basket items held by the user will exhibit different complementarity with respect to the target items. For example, the platform should recommend a piece of business suit to a user who purchased business suit jacket rather than a fleece jacket. Multiple categories of items may be present in each shopping basket transaction record, for example, the shopping basket may contain item lights, lamp holders, jackets, and hangers; each shopping basket transaction record may also contain items that cannot be associated with other items, for example, the shopping basket may contain an item light, a light holder, an outer sleeve, a clothes hanger, and a battery. The first-order correlation model can capture characteristic information independent of each other, and the second-order correlation modeling can capture dependency relations among the characteristics. The first-order correlation calculation formula is:
the calculation formula of the second order correlation becomes:
the parameters of the second-order characteristics of the polynomial model share n (n-1)/2, and any parameters are mutually independent, so that a large number of non-zero samples are needed to solve. Introducing the thought of a factor decomposition machine, and decomposing the coefficient matrix of the cross terms as follows:
wij=<hi,hj> (5)
calculating a first-order association calculation and a second-order association to obtain a low-order feature combination result:
Wherein w 0 and w i are global bias and weight of each feature xi, respectively, hi e R d×k represents the hidden vector corresponding to the ith feature. The first order part in equation (2) can be regarded as a linear regression, and the second order part is a second order correlation between features, thereby improving the correlation between features and labels.
4.6, Obtaining low-order feature interaction:
The size of each shopping basket item set is not fixed, and in theory one shopping basket item set may consist of shopping basket items of any length. The present invention utilizes hidden representations of potential factor model learning features. To obtain a fixed representation of the shopping basket item set, the hidden vectors for each shopping basket item need to be aggregated. Comparative experiments were performed using different polymerization methods, the flow chart is shown in figure 3. The method specifically comprises the following steps:
5.1, carrying out aggregation operation by adopting a max-pooling method, wherein shopping basket article items with the maximum corresponding hidden vector values in the collection represent a shopping basket article set;
5.2, carrying out aggregation operation by adopting a min-pooling method, wherein shopping basket article items with the minimum corresponding hidden vector values in the collection represent a shopping basket article set;
5.3, carrying out aggregation operation by adopting a mean-pooling method, wherein the average value of all hidden vectors in the collection represents a shopping basket article set;
5.4, performing aggregation operation by adopting a Factorized Attention Network method, wherein different hidden vectors in the set are allocated with different weights;
5.5, using accumulation method to aggregate operation example, for every shopping basket transaction record, its number of domains is 5, then the value of only one position of record on the same domain is 1. In the process of obtaining the hidden vector by input, the input layer only has one neuron to act, and the obtained hidden vector is the weight value corresponding to the hidden representation layer by all neurons with the value of 1 in the input layer, and is represented by thickened connecting lines in fig. 3.
Methods such as max-pooling, mean-pooling and random-pooling can all convert multiple vector sets into one vector. max-pooling and min-pooling select the maximum or minimum value from the set, resulting in other levels of information being ignored. The underlying assumption is that a shopping basket set contains only one category. The random pool gives different selection probabilities depending on the element values of the vector, but essentially only the hierarchical structure of one item is considered. Each component in mean-pooling is given the same weight, so the policy cannot reflect the different effects of different items. For example, in a shopping basket business consisting of a camera, a tripod, floodlights, the camera takes the dominant position of this shopping basket, as it affects the user's choice of other accessories. The Factorized Attention Network model considers the different effects of different projects and is a self-adaptive method for parameterizing project weights. Comparing experimental results under different methods, the invention adopts an accumulation method to carry out polymerization operation.
Both the order feature combination and the higher order feature combination are very important, and learning the two types of features is better than considering only one feature. The high-order feature interaction modeling part is introduced, and specific steps and descriptions are as follows:
6.1, establishing a Deep component. The Deep component is a feed-forward neural network that learns the higher order feature crossings. The network adopts a full connection mode, as shown in the right part of fig. 2;
6.2, each data record (each vector of d+1 length) is fed back to the DNN. The input vectors of the shopping basket recommendation predictions are typically highly sparse and grouped by domain, such as gender, country, time of purchase, etc., as compared to the neural network input data of images and audio. Because the input data is quite sparse after one-hot operation, the hidden representation layer is added for reducing the dimension and the model parameter learning burden.
6.3, Using the hidden feature vector in the low-order feature interaction model as the weight of the Deep component;
6.4, obtaining that the input of the neural network part is a serial representation of hidden vectors of all features:
h(0)=[euser,etarget item,ebasket] (8)
wherein e basket is a fixed-length hidden vector set obtained by aggregating hidden vectors of shopping basket articles of a user;
6.5, h (0) are fed back to DNN and the forward processing is as follows:
hl=α(W(l)h(l-1)+b(l)) (9)
Where Wl and bl are weights and biases of the first layer of the MLP and α is relu activation function. The recommendation score should be as high as possible when t is a positive tuple and as low as possible when t is a negative tuple, the score of the higher order combined part being expressed as:
6.6, the final predicted recommended value is a combination of the low-order feature combination and the high-order feature combination part:
where {, } is a concatenation of two components, ω and ψ represent the weight and bias, respectively. For positive tuples, the score value should be as high as possible; for negative tuples, its score value should be as low as possible. Combining the results of the low-order feature interaction part and the high-order feature interaction part by adopting a linear function instead of a sigmoid function;
6.7, loss function is:
Wherein, sigma is a sigmoid function, t.theta.epsilon.1, 1, lambda μ is the L2 regularization coefficient of each parameter. The loss function quantifies the distance between the positive and negative tuples. The Adam optimization algorithm was used to minimize losses. After updating the parameters, a list of recommended objects can be created based on the predictive score given a user ui holding shopping basket item set Bi.
A great improvement of the method is that compared with the recommendation method of the prior association rule mining, the method firstly learns the representation of the shopping basket by mapping the characteristics to a low-dimensional hidden space, and then fits recommendation scores by factorization and MLP. The invention overcomes two limitations of most shopping basket recommendation systems: 1) Representing the shopping basket item set from the ID only perspective; 2) Other higher order feature interaction patterns are not considered. Therefore, on the basis of meeting the individuation of the user, more accurate recommended articles can be provided for the user.
The above disclosure is only a preferred embodiment of the present invention, and it should be understood that the scope of the invention is not limited thereto, and those skilled in the art will appreciate that all or part of the procedures described above can be performed according to the equivalent changes of the claims, and still fall within the scope of the present invention.

Claims (5)

1. A recommendation method for personalized feature modeling of shopping baskets, comprising the steps of:
Extracting triples in the historical shopping basket transaction data set;
mapping the triples to a feature vector space;
The association calculation obtains a low-order feature combination result;
In the process of obtaining a low-order feature combination result by association calculation, sequentially carrying out first-order association calculation and second-order association calculation on three association types in transaction data to obtain the low-order feature combination result, wherein the first-order association calculation captures feature information which is mutually independent, and the second-order association calculation captures dependency relations among features;
The first-order correlation calculation formula is:
the calculation formula of the second order correlation becomes:
Introducing the thought of a factor decomposition machine, and decomposing the coefficient matrix of the cross terms as follows:
Calculating a first-order association calculation and a second-order association to obtain a low-order feature combination result:
Wherein w 0 and w i are global bias and weight of each feature xi, respectively, hi e R d×k represents hidden vectors corresponding to the ith feature, and < is the inner product operation of two vectors;
operating to obtain a high-order feature combination result;
In the process of obtaining a high-order feature combination result by operation, carrying out serial operation on the mapped feature vectors, and inputting the feature vectors into a neural network layer to obtain the high-order feature combination result;
And carrying out affine transformation on the low-order feature combination result and the high-order feature combination result to obtain a final recommendation value of the commodity, and forming a recommendation list.
2. The recommendation method for shopping basket personalized feature modeling of claim 1, wherein the historical shopping basket transaction data set is a public data set with high confidence and user transaction data.
3. The recommendation method for shopping basket personalized feature modeling of claim 1, wherein the triples comprise a user item, a shopping basket item and a target item, and three association types exist between the user item and the target item, between the shopping basket item and the target item, and between the shopping basket item in the transaction data.
4. The recommendation method for personalized feature modeling of shopping baskets of claim 1, wherein in the process of mapping the triples to feature vector space, the triples are mapped into feature vector space by using a method of representation learning, and aggregation operation is performed on shopping basket article entities currently held by a user, and the entities in the triples are converted into a form of vector representation.
5. The recommendation method of shopping basket personalized feature modeling according to claim 1, wherein in performing affine transformation on the low-order feature combination result and the high-order feature combination result to obtain final recommendation values of commodities, in forming a recommendation list, affine transformation is performed using a linear function to obtain final recommendation values of commodities, and the recommendation list is obtained in descending order according to score values.
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