CN113590976A - Recommendation method of space self-adaptive graph convolution network - Google Patents

Recommendation method of space self-adaptive graph convolution network Download PDF

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CN113590976A
CN113590976A CN202110809640.7A CN202110809640A CN113590976A CN 113590976 A CN113590976 A CN 113590976A CN 202110809640 A CN202110809640 A CN 202110809640A CN 113590976 A CN113590976 A CN 113590976A
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叶阳东
钟李红
吴宾
孙中川
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Abstract

In recent years, the recommendation method based on the graph neural network has been greatly successful in academia and industry, some researchers model social influence of recursive propagation in a social network by modeling high-order relations among users through the graph convolutional neural network, and constrain feature vectors of target users by using feature vectors of high-order neighbors. In order to improve the accuracy of social recommendation, the invention further captures the influence propagation of the collaborative similarity between the user and the item hidden in the user item interaction network, and the preference of the user changes along with the propagation of the social influence and the collaborative similarity influence. By combining different characteristics of information expression of the user social domain and the user article interaction domain in an actual recommendation scene, the method and the system can adaptively initialize the user potential feature vectors in different semantic spaces to reflect the characteristics that the social relationship among users and the interaction relationship among user articles have different influences on the constraint user feature vectors. In addition, in order to enable the model to be more suitable for practical application, the invention discloses a rapid non-sampling optimizer to learn model parameters, and the model optimization efficiency is improved.

Description

Recommendation method of space self-adaptive graph convolution network
Technical space
The invention relates to the technical field of machine learning and recommendation, in particular to a method for recommending articles by a space self-adaptive graph convolution network model.
Background
With the continuous expansion of the scale of users and networks, the internet information shows explosive growth, which brings the problem of information overload, and further leads people to face the problem that mass data can not timely and accurately mine target information. The recommendation system is one of the most effective methods for solving the problem of information at present as an important means for information filtering. Among them, the widely adopted recommendation technology is based on Collaborative Filtering (CF), and its task is to mine the user's preference and finally recommend personalized items to the user through the user-item historical interaction (e.g., clicking, purchasing, checking in, etc.) information. Although the CF method is simple and effective, the conventional collaborative filtering recommendation system often faces two major challenges of data sparseness and cold start. With the appearance of social media such as facebook, twitter, microblog and the like, people can pay attention to each other on a social platform and can forward, comment or share favorite articles or information. Inspired by the principle of social homogeneity, users who are adjacent in a social network often have similar preferences. Researches show that the social information is integrated into a collaborative filtering algorithm, so that recommendation accuracy is improved, and the problems of data sparseness and cold start are effectively relieved. Thus, social network-based recommendations, i.e., social recommendations, have emerged.
With the great success of the neural network technology in academia and industry in recent years, some researchers integrate the technology into social recommendation research to more clearly describe the social relationship between users. The propagation of inter-user preferences is explicitly modeled from considering only first-order friends of the user to considering the dynamic propagation of user preference effects of friends (indirect friends), thereby significantly effectively constraining the user's vector representation learning. However, the inventors found that there are two key problems that have not been sufficiently studied in the past:
(1) the method does not consider the influence of different characteristics of information expression of a social domain and a user article domain on user feature learning, generally initializes user potential feature representation in the same semantic space, and simultaneously does not further capture collaborative similarity propagation between users and articles in a user article interactive network as a supplement to the user preference learning.
(2) They typically rely on negative sampling to optimize the recommended model, which makes the model highly sensitive to the quality of the negative sampler when training, making it difficult to take full advantage of the computational power of the Graphics Processor (GPU).
Disclosure of Invention
Aiming at the problems, the invention discloses a recommendation method of a space self-adaptive graph convolution network, which comprises 4 modules: the system comprises a data input module, a space self-adaptive embedding module, a bilinear map convolution module and a score prediction module. Firstly, respectively inputting a social domain of a user and an interaction domain of a user item, which influence the preference of the user, in the form of a user-user social network diagram and a user-item interaction diagram; secondly, in order to learn different information characteristics from a user social domain and a user article interaction domain, a self-adaptive initialization scheme is provided for potential characteristic representation of each user through a spatial self-adaptive embedding module; then, combining the advantages of the graph convolution neural network model in a bilinear graph convolution module, and aggregating the neighborhood nodes by using the information of the edges so as to update the representation of the target node. Therefore, the vector representation learning of the user not only models the user preference in the social network for a transfer process, but also further captures the propagation of the collaborative similarity influence between the user and the object in the interactive domain; and finally, performing self-adaptive fusion on two user feature representations generated by the user social domain and the user article interaction domain by adopting a gate control unit, and performing inner product operation with the output article feature vector to obtain a prediction score. In order to enable the model to be more suitable for practical application, the invention discloses a rapid non-sampling optimizer to learn model parameters and improve the model optimization efficiency. In order to enable the model disclosed by the invention to meet the actual environment requirement and aim at the problem of optimization efficiency, the invention discloses a rapid non-sampling optimizer to learn model parameters, and a Graphics Processing Unit (GPU) is better utilized to perform matrix operation related to the model.
Compared with the prior art, the invention has the following effective effects:
(1) the invention provides a recommendation method of a space self-adaptive graph convolution network, aiming at the characteristic that a user expresses different information characteristics in a user social domain and a user article interaction domain, the method provides a self-adaptive initialization scheme for potential characteristic expression of each user; by combining the advantages of the graph convolution network, the neighborhood nodes are aggregated by using the edge information so as to update the representation of the target node, the user preference in the social network is modeled to carry out the transmission process, and the propagation of the collaborative similarity influence between the user and the object in the interactive domain is further captured;
(2) in order to enable the model disclosed by the invention to meet the requirements of the actual environment, the invention designs a rapid non-sampling optimizer to optimize the parameters of the model. The non-sampling strategy reduces the time complexity of the model in the training process and improves the training efficiency.
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In order to more clearly illustrate the technical solution of the present invention, the drawings used in the description of the embodiment or the prior art will be briefly described below.
FIG. 1 is a schematic diagram of a recommendation scenario in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of an EAGCN model according to an embodiment of the present invention;
FIG. 3 is a graph comparing the results of different evaluation indexes of EAGCN according to the embodiment of the present invention;
FIG. 4 is a comparison graph providing a normalized depreciation cumulative gain for the ranking of items in a recommendation list according to an embodiment of the present invention;
FIG. 5 is a graph comparing the accuracy of items in a recommendation list provided by embodiments of the present invention;
FIG. 6 is a graph illustrating the accuracy of items in different user groupings according to an embodiment of the present invention;
FIG. 7 is a graph comparing training times of the present invention and comparison algorithm.
Detailed description of the invention
With the popularization of smart phones and the development of mobile positioning technologies, social networks based on location attract a large number of users. Assuming a Point-of-Interest (POI) recommendation-based social networking site used during travel in a city, a user can check in at the POI and comment on and share with their friends.
As shown in fig. 1, a social network is formed by a user and his/her friend relationship, and a connection line between the user and a POI indicates that the user has a check-in behavior at a point of interest. In this scenario, the user's opinion may be propagated through their social relationships. For example, although user u2Has not gone to gymnasium i1But can also be a gym i1Trust user u recommended to her3Because of user u2By a trusted user u1Go to gymnasium i1. Experience shows that factors such as personal information and social influence of a user play an important role in purchasing decisions or opinions of website users. In the user-item interaction network, although user u5Is not at the point of interest i4Check-in, but the model may pass through 2 "paths of interest" (i) of the user to the item4→u2→i2→u5And i4→u2→i3→u5) The hidden collaborative signal of (1) learns the potential preference characteristics of the user. Therefore, when the recommendation model is constructed, the influence of the social communication of the user information in the social network on the user is considered, and the influence of the collaborative similarity between the user reflecting the user preference and the article in the interest network is also considered.
1. Problem definition:
graph-based models have gained increasing attention as network representation learning has evolved. For the recommendation problem, user-item interactions may be described as a bipartite graph, where the user and item are two isolated sets of nodes and the edges represent the interactions between the user and the item. The social network may be represented as a user-user directed graph, where the edges represent trust between the user and the user. Order to
Figure BDA0003167742520000041
And
Figure BDA0003167742520000042
respectively representing M users and N objectsA collection of articles. If let ruiIf the user u has interaction with the item i, otherwise, the user u has 0, and a scoring matrix R of the item by the user R is obtainedui]M×NE {0,1 }. Accordingly, S ═ Suv]M×ME {0,1} represents a social neighbor matrix, if user u trusts user v, then suvOtherwise, it is 0. The input data of the invention is social network
Figure BDA0003167742520000043
Interaction diagram with user's object is a bipartite diagram
Figure BDA0003167742520000044
Wherein
Figure BDA0003167742520000045
Wherein
Figure BDA0003167742520000046
Representing the user u's rating of item i. Accordingly, we represent the social network of the user as
Figure BDA0003167742520000047
Wherein,
Figure BDA0003167742520000048
user v is trusted by user u in the social network. In addition, examples of the invention are
Figure BDA0003167742520000049
A matrix of potential features of the user is represented,
Figure BDA00031677425200000410
representing a latent characteristic matrix, p, of an articleuPotential feature vector, q, representing user uiRepresenting potential feature vectors for item i. Where D represents the dimension of the vector.
In the present invention, a scalar or index is represented by lower case letters, a vector is represented by lower case bold, and a matrix is represented by bold upper case letters. So far, the social recommendation task of the invention aims to: in thatNetwork map of given user interest
Figure BDA00031677425200000411
Social networking graph with users
Figure BDA00031677425200000412
On the premise, the two network graphs can be defined as a heterogeneous graph
Figure BDA00031677425200000413
The goal is to predict the user's score for the item unknown, i.e.
Figure BDA00031677425200000414
Wherein
Figure BDA00031677425200000415
Representing a prediction of a user's preference for an item.
2. And (3) overall model architecture:
fig. 2 shows the overall architecture of the EAGCN model. The model comprises 4 modules, a data input module, a space self-adaptive embedding module, a bilinear graph convolution module and a grading prediction module. The model architecture to which the present invention relates will be explained in detail below:
2.1 data input module:
taking the user item interaction graph and the user social network graph as input data of a model, wherein the specific representation form is as follows:
(1) user-item interaction diagram:
Figure BDA00031677425200000416
wherein the nodes are users and articles, and the edges represent the interaction between the users and the articles. Scoring matrix R ═ Rui]M×NE is {0,1}, and if the user u accesses the item i, r isui＝1；
(2) User-user social network diagram:
Figure BDA0003167742520000051
the nodes are users, and the directed edges represent trust relationships between the users. Social matrix S ═ Suv]M×ME is e {0,1}, if user u trusts user v, then suv＝1。
2.2 spatial adaptive embedding module:
first, let
Figure BDA0003167742520000052
And
Figure BDA0003167742520000053
representing user and item latent feature matrices, respectively. One-hot representation v for a given user u and item iuAnd viPerforming index operation at an embedding layer, and outputting a free user potential vector P from a user potential feature matrix P and an article potential feature matrix QuAnd free item latent vector qi：
pu＝PTvu,qi＝QTvi (1)
The information of the user social domain and the user article interaction domain shows different characteristics, and the potential feature vectors of the user are initialized in a self-adaptive mode in different semantic spaces. And (4) introducing two weight matrixes, and adaptively generating user embedded representations with different characteristics. Wherein the embedding of user u in these two spaces is modeled by a common user feature vector puAnd two weight matrices transform to obtain:
eu＝WIpu,mu＝WSpu (2)
wherein
Figure BDA0003167742520000054
And the weight matrixes respectively represent the user item interaction domain and the user social domain. This means that the present invention adaptively generates the embedded vector e for the user using two projection matrices according to two spaces of different featuresuAnd muWill be the input to the bilinear map convolution module.
2.3 bilinear graph convolution module:
as shown in fig. 2, the module simulates propagation processes of collaborative similarity influence in a user interaction network and friend preference in a social network respectively by using a Graph Convolution (GCN) network, and extracts collaborative signal embedding characteristics and social friend embedding characteristics of a user, the core idea of the GCN is to iteratively update feature vector representation of a target user (item) by using feature vectors of aggregated neighbor nodes, and such neighborhood aggregation can be abstracted as:
Figure BDA0003167742520000055
studies demonstrate two operations of graph convolution: feature propagation and nonlinear activation contribute little to improving recommendation performance, and even degrade recommendation performance. The invention adopts a simple weighting and aggregator, abandons the use of feature transformation and nonlinear activation, learns the feature vectors of users and articles by linear propagation on a user-article interaction graph and a user social network graph, and uses the learned feature vectors on all layers to output the feature vectors by an average aggregation strategy. As will be described in detail below:
for each user in the user social network graph, set
Figure BDA0003167742520000061
Layer I output representing social influence propagation
Figure BDA0003167742520000062
Inputting the information into the (l + 1) th layer of social influence propagation, aggregating the (l + 1) layer neighbor node information, and expressing the updated user characteristics as
Figure BDA0003167742520000063
Figure BDA0003167742520000064
Wherein, | SuI represents user u letterAny number of users;
in the user and article interaction graph, neighbor nodes of l +1 are aggregated, and the updated characteristic representation of the user and the article is obtained
Figure BDA0003167742520000065
And
Figure BDA0003167742520000066
Figure BDA0003167742520000067
wherein,
Figure BDA0003167742520000068
indicating the number of items that interacted with user u,
Figure BDA0003167742520000069
representing the number of users who interacted with item i.
In the social domain of the user, after the influence process of neighbor information on the user characterization learning process is processed by L layers by using a graph convolutional network, the characteristic representation of each user in the social domain can be obtained, namely the characteristic representation of each user in the social domain is obtained
Figure BDA00031677425200000610
Similarly, multiple user feature representations obtained in the user-item interaction domain
Figure BDA00031677425200000611
And a plurality of item feature representations
Figure BDA00031677425200000612
To avoid over-smoothing and capture rich semantics, the output of the bilinear module is needed to combine the node representations obtained in the different layers to generate a single user (item) feature representation. In the present example, various combination schemes were attempted, including long and short term memory networks, attention mechanisms. Experience has shown that a simple averaging operation can be performed atAnd better performance is obtained on the premise of keeping lower complexity. Examples of the invention:
for user u and item i, a single characterization is obtained by:
Figure BDA0003167742520000071
in the Tensorflow environment of actual model training, the embodiment of the invention adopts efficient sparse matrix operation to perform coding calculation, and then the bilinear chart convolution module is realized in a matrix form as follows:
wherein
Figure BDA0003167742520000072
Is an interaction matrix of user-item, the element r in the matrixuiWhen 1, it means that user u has an interaction with item i, otherwise r ui0. User item interaction network
Figure BDA0003167742520000073
The adjacency matrix of (a) is:
Figure BDA0003167742520000074
order to
Figure BDA0003167742520000075
A 0-layer embedded matrix representing the convolution module of the input graph, wherein
Figure BDA0003167742520000076
Figure BDA0003167742520000077
Matrix form of user-item collaborative similarity influence propagation:
Figure BDA0003167742520000078
wherein,
Figure BDA0003167742520000079
is a symmetric normalized adjacency matrix,
Figure BDA00031677425200000710
the representation regularizes the adjacency matrix A and D represents
Figure BDA00031677425200000711
The degree matrix of (c).
Finally, an embedded matrix E of the user and the object in the user-object interaction domain can be obtained*Comprises the following steps:
Figure BDA00031677425200000712
by analogy, the embedding matrix M of end-user nodes in the social influence space*Comprises the following steps:
Figure BDA00031677425200000713
wherein
Figure BDA00031677425200000714
A social proximity matrix is a matrix of social connections,
Figure BDA00031677425200000715
is a symmetric normalized adjacency matrix, D is
Figure BDA00031677425200000716
The degree matrix of (c).
2.4 score prediction module:
for each user, 2 user embedded representations of an interaction domain and a social domain respectively output from a bilinear chart convolution module
Figure BDA00031677425200000717
And
Figure BDA00031677425200000718
in constructing end-user representations
Figure BDA00031677425200000719
Time of day, user embedded representation
Figure BDA00031677425200000720
And
Figure BDA00031677425200000721
the contribution ratio is different. Inspired by a gating mechanism in a long-term and short-term memory network, the invention adopts a self-adaptive gating unit strategy aiming at the fusion of users to control the influence of different characteristics of a user interaction domain and a social domain on user representation learning, and carries out joint embedding on output 2 different user characteristic vectors, specifically:
Figure BDA0003167742520000081
where σ (-) is an activation function, the invention selects sigmoid function to model the nonlinear capability,
Figure BDA0003167742520000082
is a weight parameter in the gate control unit; an element level multiplication is indicated.
And performing inner product operation on the output user feature vector and the article feature vector, wherein the prediction score is expressed as:
Figure BDA0003167742520000083
3. the optimization process comprises the following steps:
in a recommendation system, two strategies are generally adopted for model optimization: 1) a negative sampling strategy, 2) a non-sampling strategy. The negative sampling strategy is to extract a part of all the user unmarked samples as negative examples, and the non-sampling strategy is to take all the user unmarked samples as negative examples.These two strategies have respective advantages and disadvantages: the negative-sampling-based strategy improves training efficiency by reducing negative samples in the training set, but may reduce model performance, while the full-sampling strategy utilizes full-sample data to improve data coverage, but reduce model training efficiency. In order to optimize all parameters in the EAGCN algorithm, such as the user latent feature matrix P, the item latent feature matrix Q, in the gate control unit
Figure BDA0003167742520000084
The invention discloses a fast non-sampling optimizer to effectively optimize the EAGCN. Following other full sampling strategies, the invention also adopts a weighted square loss function to learn model parameters, and simultaneously allocates a confidence super-parameter c to each predictionui：
Figure BDA0003167742520000085
The time complexity of the loss function of the above formula is O (MND). In the actual recommendation scenario, the number of users and articles can easily reach the billion level optimization process, and in order to reduce complexity, the following loss inference is made:
Figure BDA0003167742520000086
wherein r isuiE {0,1} represents whether there is an interaction between the user and the item, replacing r with a constant CuiRelated terms, further simplifying the above equation:
Figure BDA0003167742520000091
the first term of the formula is only related to the number of user and article interactions, and the time complexity is less
Figure BDA0003167742520000092
The computational bottleneck is the second term of the formula
Figure BDA0003167742520000093
According to the property tr (xy) tr (yx) of the matrix trace, the second term continues to be calculated as:
Figure BDA0003167742520000094
by derivation of the above formula, the time complexity of the second term of the loss function is reduced from O (MND) to O ((M + N) D2) Substituting the formula (16) into the formula (15), removing the constant term part, and adding a regularization term for preventing overfitting to obtain a final fast non-sampling objective function as follows:
Figure BDA0003167742520000095
wherein, λ is a regularization parameter,
Figure BDA0003167742520000096
are the learnable model parameters. The model parameters are divided into two parts: theta1＝{P,Q}，
Figure BDA0003167742520000097
3.1 complexity analysis:
(1) spatial complexity: theta is the same as the other embedded representation recommendation models1The spatial complexity of { P, Q } is linearly related to the number of users and items, i.e., (M + N) D;
Figure BDA0003167742520000098
has a spatial complexity of 4D2. Compared with the mainstream recommendation model, the extra storage cost of the invention is almost negligible, and the super parameter D is far lower than the quantity of users and articles.
(2) Time complexity: the calculation cost of the invention mainly comes from the calculation of a space self-adaptive embedding module, a bilinear graph convolution module and a non-sampling loss function. The first part has a temporal complexity of O ((M + N))D2) (ii) a Studies demonstrate two operations of graph convolution: feature propagation and nonlinear activation contribute little to improving recommendation performance, and even degrade recommendation performance. Based on this second module time complexity is:
Figure BDA0003167742520000101
the time complexity of calculating the loss function refers to the loss inference process results. Thus, the total temporal complexity of the EAGCN model is
Figure BDA0003167742520000102
Fig. 3 is a comparison graph of item accuracy for a recommendation list of 10 in length provided by an embodiment of the present invention. Fig. 4 is a comparison graph of accuracy of items in a recommendation list provided in an embodiment of the present invention, fig. 5 is a comparison graph of normalized breaking and loss accumulation gain of item sorting in the recommendation list provided in the embodiment of the present invention, in the graph, an abscissa is a length of the item recommendation list, and an ordinate is an evaluation index of recommendation performance, where EAGCN is a spatial adaptive graph rolling model method disclosed in the present invention. As can be seen from comparative experiments, the recommendation method disclosed by the invention achieves the best performance under the balance of two recommendation indexes. Fig. 6 is a comparison graph of normalized depreciation cumulative gain of item sorting under different user groupings, with user grouping according to the number of user interactions on the abscissa, provided by an embodiment of the present invention. FIG. 7 is a graph comparing efficiency and time provided by the embodiment of the present invention, and the recommendation method disclosed by the present invention has higher efficiency in model training.
The embodiments of the present invention will be readily understood by those skilled in the art. The foregoing is merely an example of the basic implementation of the present invention and is not intended to limit the invention thereto.

Claims (7)

1. A recommendation method of a spatial adaptive graph convolution network is characterized in that (1) a user preference transfer process in a modeling social network is mainly concerned, and influence propagation of collaborative similarity between users and items in a user item interaction domain is further captured; (2) the model comprises 4 modules which are a data input module, a space self-adaptive embedding module, a bilinear map convolution module and a grading prediction module respectively; (3) a rapid non-sampling optimizer is designed to learn model parameters, and model optimization efficiency is improved.
2. The model of claim 1, wherein the latent feature vectors of the user are adaptively initialized in different semantic spaces in consideration of the fact that the user may exhibit different feature information in the social domain and the interactive domain. Two weight matrixes are introduced, and the transformation form is specifically as follows:
eu＝WIpu,mu＝WSpu
3. the model of a spatially adaptive graph-convolution network of claims 1 and 2, characterized by aggregating neighborhood nodes with edge information in a bilinear graph convolution module, in combination with the advantages of a graph-convolution neural network, to update the representation of the target node. Abandoning the traditional graph convolution characteristic propagation and nonlinear activation operation, adopting a simple linear propagation rule, specifically:
for each user, aggregating neighbor node information on the user's social network graph, the update vector is represented in the form of:
Figure FDA0003167742510000011
for each user (item), aggregating neighbor node information on the user item interaction graph, the update vector is represented in the form:
Figure FDA0003167742510000012
the final representation of the users and items of the social domain and the interaction domain is obtained by:
Figure FDA0003167742510000013
4. the spatial adaptive graph convolution network model of claims 1 and 3, wherein a gating unit is used for adaptively fusing two user feature representations generated by a user social domain and a user item interaction domain to obtain a single user potential feature vector.
Figure FDA0003167742510000014
Figure FDA0003167742510000015
5. The spatial adaptive graph convolution network model of claims 1, 3 and 4, wherein an inner product operation is performed on an output user feature vector and an item feature vector, and a model prediction score is defined as:
Figure FDA0003167742510000021
6. the spatially adaptive graph convolution network model of claims 1 and 5, wherein the weighted square loss function of the model with respect to scored and predicted scores is:
Figure FDA0003167742510000022
7. the model of a spatially adaptive graph convolution network of claims 1 and 6, characterized by a non-sampling optimizer designed through rigorous mathematical reasoning to efficiently learn model parameters.
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