CN113744023A - Dual-channel collaborative filtering recommendation method based on graph convolution network - Google Patents

Dual-channel collaborative filtering recommendation method based on graph convolution network Download PDF

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CN113744023A
CN113744023A CN202110957912.8A CN202110957912A CN113744023A CN 113744023 A CN113744023 A CN 113744023A CN 202110957912 A CN202110957912 A CN 202110957912A CN 113744023 A CN113744023 A CN 113744023A
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宋春花
苗雨欣
牛保宁
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Taiyuan University of Technology
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Abstract

The invention discloses a dual-channel collaborative filtering recommendation method based on a graph convolution network, which divides a vector expression updating process of user nodes and commodity nodes into a local convolution channel and a global convolution channel, and respectively undertakes different information aggregation tasks. In a local convolution channel, a state transition matrix is introduced and a corresponding transition probability threshold is set, so that a high-order neighborhood range of a node is directly positioned in a single-layer network, and a multi-layer network stacking mode is replaced. In the global convolution channel, clustering is carried out on the basis of node characteristics to construct a global interaction graph, and a high-order interaction mode between nodes is modeled from an overall structure and is used as supplement to local information. And finally, acquiring node vector expressions containing different types of high-order relations by integrating the local information and the global information. By the method and the device, modeling and integration of different types of interactive information can be realized, and the recommendation performance of the algorithm is further improved.

Description

Dual-channel collaborative filtering recommendation method based on graph convolution network
Technical Field
The invention relates to the technical field of social recommendation, in particular to a dual-channel collaborative filtering recommendation method based on a graph convolution network.
Background
With the rapid development of the internet, various types of data on the network grow exponentially, the data overload problem is caused by the excessive data volume, and it is difficult for users to efficiently sort out the contents of interest from the massive network data. The recommendation algorithm is used as a reliable and effective means for improving the problem, and personalized pushing is performed according to past historical record data and according to the requirements and interests of the user. To date, recommendation algorithms have been successfully applied to a number of areas, such as online commerce, information retrieval, news push, etc.
The collaborative filtering is an important branch of a recommendation algorithm, the core idea of the collaborative filtering is to represent users and commodities in a digital vector form, the prediction and recommendation processes are completed based on vector calculation, and the collaborative filtering is composed of two key steps in the design process corresponding to a model: 1) vector embedding, namely representing users and commodities by using digital vectors; 2) interactive modeling, calculating scores or similarities based on vector expressions. The traditional collaborative filtering model takes the rows and columns of a user-commodity interaction matrix or hidden vectors extracted from the rows and columns as vector representations of users and commodities, and calculates the similarity between the users and the commodities based on a predefined similarity function so as to recommend the users and the commodities. With the application of the deep learning technology in the recommendation algorithm, the neural network gradually becomes an important tool for building a collaborative filtering model, and the recommendation performance of collaborative filtering is further improved by introducing the nonlinear network in the processes of vector embedding and similarity calculation. However, these methods often only consider the characteristic information of the user and the commodity itself, and do not fully utilize the interaction relationship that has been generated in the historical behavior. The relation between the user and the commodity, such as browsing, purchasing, clicking and other interactive behaviors, can be naturally expressed by using a graph structure, the collaborative filtering model based on the graph convolution network takes the user and the commodity as nodes with the same position in an interactive graph, the characteristics of the nodes are considered when vector expression is updated, and the collaborative signals from neighbor nodes are added, so that the expression capability of the model is improved.
The collaborative filtering model based on the graph convolution network also has the following problems:
1) the inherent over-smooth problem of the graph convolution network can lead the characteristics of the nodes to gradually approach to similarity after multiple graph convolution operations and are difficult to distinguish, so that the preference characteristics in the recommendation process are homogenized, and finally the recommendation performance of the algorithm is reduced;
2) the two interactive graphs derived from historical data are used for constructing an algorithm, limited information can be aggregated only in a local range, and potential interactive modes in the whole structure are ignored.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a dual-channel collaborative filtering recommendation method based on a graph convolution network, wherein different graph convolution operations are constructed according to historical behavior records of a user, so that modeling and integration of different types of interactive information are realized, and the recommendation performance of an algorithm is further improved.
The technical scheme adopted by the invention for solving the technical problems is as follows: a dual-channel collaborative filtering recommendation method based on a graph convolution network is constructed, and comprises the following steps:
s1, initializing a graph structure, and deriving a second interactive graph G, an adjacent matrix A of the second interactive graph and an initial feature matrix X of user nodes and commodity nodes in the second interactive graph from historical behavior data sets of users;
s2, constructing a local convolution channel, and calculating transfer matrixes P of different orders on the two interactive graphs based on the adjacent matrixes A of the two interactive graphs in the local convolution channelkDetermining a first-order neighborhood range of nodes in the two interactive graphs by the adjacency matrix A, and determining a high-order neighborhood range of the nodes in the two interactive graphs by the transfer matrix; in each order neighborhood, aggregating corresponding neighborhood information for each user node or commodity node, and adding the neighborhood information of each order to obtain an average value to obtain a local neighborhood characteristic XN(ii) a Adding the initial characteristic of each user node or commodity node and the local neighborhood characteristic thereof to obtain the local characteristic X of each user node or commodity nodelocal；
S3, constructing a global convolution channel, wherein in the global convolution channel, initial points based on user nodes and commodity nodesA starting characteristic matrix X and an adjacent matrix A, adding first-order neighborhood information for each user node or commodity node in the two interactive graphs to obtain a new user node or commodity node characteristic matrix XC(ii) a With XCOn the basis, all user nodes and commodity nodes are reclassified by a KMeans clustering algorithm, if two nodes in all the user nodes and the commodity nodes are classified into the same class, a connecting edge is considered to exist between the two nodes, and a global interaction graph G is constructed according to the principleglobal(ii) a To ensure the validity of the information, the global interaction graph G is appliedglobalAnd performing secondary screening on neighborhoods of all user nodes and commodity nodes, selecting a fixed number of neighbor nodes with the most similar characteristic expressions in the global neighborhood for each of all user nodes and commodity nodes, aggregating corresponding neighborhood information, and adding the corresponding neighborhood information and the initial characteristics to obtain the global characteristic X of each user node or commodity nodeglobal；
S4, interactive prediction is carried out based on local feature XlocalAnd global feature XglobalAdding the two parts of characteristics to obtain the final vector representation X of each user node or commodity nodeFAnd predicting the grade of the user for the commodity in the form of vector inner product.
Parameters in the local convolution channel and the global convolution channel are optimized by using a paired BPR loss function, and training is carried out in a mode of maximizing the difference between the positive sample and the negative sample.
Wherein, the first-order neighborhood range of each user node or commodity node is determined by using the adjacency matrix A, and the transfer matrix P is usedkIn the step of determining the high-order neighborhood range of each user node or commodity node, when the local neighborhood range of the user node or commodity node is determined, the first-order neighborhood is determined by the adjacency matrix A; for the high-order neighborhood, a transition threshold P is set based on the corresponding transition matrixΘ0.5 if the component [ P ] in the matrix is transferredk]ij>PΘThen, it is considered that a connecting edge exists between the node i and the node j in the neighborhood of the corresponding k-th order. Defining between nodes in higher order neighborhoodsInteraction matrix Qk(k.gtoreq.2): in the same-order neighborhood, if the component [ P ] of the corresponding position of the matrix is transferredk]ij>PΘThen there is [ Q ]k]ij1, otherwise 0; by the method, the neighborhood composition of each user node or commodity node in different orders is obtained.
Compared with the prior art, the technical scheme of the invention can obtain the following beneficial effects:
1. aiming at the problem of over-smoothness existing in the characteristic iteration process of the conventional graph recommendation model, the aggregation mode of local neighborhood information is improved by introducing a transfer matrix, and the local neighborhood information is aggregated and updated by adopting a single-layer graph convolution network, so that the over-smoothness problem is solved;
2. aiming at the defect that the existing graph recommendation model depends on a bipartite graph structure, all nodes are reclassified by a clustering algorithm on the basis of vector characteristics of users and commodities, a new interaction graph is constructed from the global perspective, and a potential interaction mode is modeled;
3. the invention represents users and commodities from two aspects of local structure and global interaction by constructing two different convolution channels. Then, during prediction interaction, vector expressions representing two different types of high-order relations are integrated, and recommendation precision is effectively improved.
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The invention will be further described with reference to the accompanying drawings and examples, in which:
fig. 1 is a schematic flow diagram of a dual-channel collaborative filtering recommendation method based on a graph convolution network according to the present invention.
Fig. 2 is a schematic structural diagram of a dual-channel collaborative filtering recommendation method based on a graph convolution network provided by the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described are only for illustrating the present invention and are not to be construed as limiting the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 and fig. 2, the dual-channel collaborative filtering recommendation method based on the graph convolution network provided by the present invention includes:
and S1, initializing a graph structure, and deriving a second interactive graph G, an adjacent matrix A of the second interactive graph and an initial feature matrix X of user nodes and commodity nodes in the second interactive graph from the historical behavior data set of the user.
The user's historical behavior records are organized as [ UserID1, [ ItemID1, ItemID2, …]]The form of the method is that each record in the data set corresponds to a user, the representative meaning is the number sequence of the user and the commodity interacted with the user, the interaction can be various behaviors such as purchasing, browsing, clicking, collecting and sharing, and two interaction graphs G (V, E) between the user and the commodity and the initial vector expression of the nodes in the graphs are derived from historical interaction data. The interaction graph G (V, E) is a two-part undirected graph, where V represents a set of nodes in the graph, and is defined by a set of user nodes VUserAnd commodity node set VItemComposition is carried out; e represents the set of connected edges in the graph.
If the User usesnAnd commodity ItemmWhen the interaction is generated, a connecting edge e exists between the twonmE.e, the interaction graph is an undirected graph, so Enm＝emn. On the basis, an interaction matrix R can be obtained, wherein the interaction matrix R is a matrix with N rows and M columns, N represents the number of users, M represents the number of commodities, and for each component [ R ] in the interaction matrix R]nmIf its corresponding edge exists, enmE, then the component of the current position R]nm1, and conversely 0. Further, the adjacency matrix a of the interaction graph may be represented as:
Figure BDA0003220923480000051
where 0 represents a zero matrix and T represents a transpose operation. The adjacency matrix represents the interaction situation of the nodes in the graph, but since there is no direct interaction relationship between users and between commodities in the two interaction graphs, the corresponding positions are all 0.
And respectively obtaining initial vector expressions of user nodes and commodity nodes by dimensionality reduction of rows and columns in the interaction matrix R, and unifying the initial vector expressions to a fixed dimensionality d:
Figure BDA0003220923480000052
Figure BDA0003220923480000053
XUser、XItemand the initial characteristic matrixes respectively represent user nodes and commodity nodes.
S2, constructing a local convolution channel, and calculating transfer matrixes P of different orders on the two interactive graphs based on the adjacent matrixes A of the two interactive graphs in the local convolution channelkDetermining a first-order neighborhood range of nodes in the two interactive graphs by the adjacency matrix A, and determining a high-order neighborhood range of the nodes in the two interactive graphs by the transfer matrix; in each order neighborhood, aggregating corresponding neighborhood information for each user node or commodity node, and adding the neighborhood information of each order to obtain an average value to obtain a local neighborhood characteristic XN(ii) a Adding the initial characteristic of each user node or commodity node and the local neighborhood characteristic thereof to obtain the local characteristic X of each user node or commodity nodelocal。
The task of the local convolution channel is to aggregate local neighborhood information for the nodes in the graph, and the invention directly positions the high-order neighborhood range of the nodes in a single-layer network by introducing a transition matrix and setting a corresponding transition probability threshold value to complete the information aggregation process, thereby replacing the form of multilayer network stacking and solving the problem of over-smoothness.
If the structure of the interaction graph is known, the calculation method of the transition matrix on the graph is as follows:
P＝D-1A
a is the adjacency matrix of the two interaction graphs, and D is the degree matrix of the adjacency matrix (a diagonal matrix whose diagonal components represent the number of edges each associated with that vertex). Each component [ P ] in the transfer matrix P]ijRepresenting the transition probability from node i to node j in the graph, a high-order transition matrix PkEach component [ P ] of (k ≧ 2)k]ijRepresenting the probability of node i walking k steps to reach node j in the graph.
In the local convolution channel, when determining the neighborhood range of a node in the graph, the first order neighborhood is still determined by the adjacency matrix a. For higher-order neighborhoods (greater than or equal to the second order), a transition threshold value P is set based on the corresponding transition matrixΘ0.5 if the component [ P ] in the matrix is transferredk]ij>PΘThen, it is considered that a connecting edge exists between the node i and the node j in the neighborhood of the corresponding k-th order. To this end, an interaction relation matrix Q between nodes in a high-order neighborhood can be definedk(k.gtoreq.2): in the same-order neighborhood, if the component [ P ] of the corresponding position of the matrix is transferredk]ij>PΘThen there is [ Q ]k]ij1, and conversely 0. By the method, the neighborhood structure of different orders of each node is obtained.
In the transition matrix, if a plurality of information transmission paths exist between two nodes, the transition paths are continuously overlapped along with the expansion of the neighborhood, and the corresponding transition probability is higher. By setting a transition threshold PΘAnd selecting the neighbor nodes with higher transition probability in each order of neighborhood, thereby playing the role of information screening.
And in each order of neighborhood, aggregating neighborhood information of the user nodes and the commodity nodes, adding the neighborhood information of each order to obtain an average value to obtain local neighborhood characteristics of the nodes, and then adding the initial characteristics of the nodes and the local neighborhood characteristics to obtain the output of a local convolution channel.
Specifically, in each level of neighborhood, taking user node u and commodity node i as an example, the corresponding neighborhood information x isN(u)-k、xN(i)-kThe polymerization method of (A) is as follows:
Figure BDA0003220923480000071
Figure BDA0003220923480000072
k represents the neighborhood order, N(·)-kK-th order neighborhood, | N, of the representative node(·)-kAnd | represents the number of nodes that the node neighbors within the current neighborhood.
Adding neighborhood information of each order and then averaging to obtain local neighborhood characteristics x of the nodeN(U)、xN(i)；
Figure BDA0003220923480000074
Figure BDA0003220923480000075
Adding the initial characteristics of the nodes and the local neighborhood characteristics to obtain the output of a local convolution channel:
Figure BDA0003220923480000076
Figure BDA0003220923480000077
xu、xithe characteristics of the user node u and the commodity node i, and the characteristic updating process of other users and commodities follows the above process.
In order to better implement the local convolution channel update procedure described in the above step S2, a matrix-form feature calculation procedure is given here:
Figure BDA0003220923480000078
Figure BDA0003220923480000079
Xlocal＝X+XN
x is an initial characteristic matrix of nodes in the graph, XNIs a local neighborhood feature matrix, XlocalIs a local feature matrix of the nodes in the graph. Wherein:
Figure BDA00032209234800000710
Figure BDA00032209234800000711
L、Lkrespectively representing an adjacency matrix A and a high-order relation matrix QkLaplacian matrix of D, DkIs a corresponding degree matrix.
S3, constructing a global convolution channel, and adding first-order neighborhood information of each user node or commodity node in the two interaction graphs to obtain a new user node or commodity node feature matrix X based on the initial feature matrix X and the adjacent matrix A of the user node and the commodity node in the global convolution channelC(ii) a With XCOn the basis, all user nodes and commodity nodes are reclassified by a KMeans clustering algorithm, if two nodes in all the user nodes and the commodity nodes are classified into the same class, a connecting edge is considered to exist between the two nodes, and a global interaction graph G is constructed according to the principleglobal(ii) a In order to ensure the positivity of high-order neighbor information transmission, a global interaction graph G is adoptedglobalThe neighborhoods of all the user nodes and the commodity nodes are screened for the second time, a fixed number of neighbor nodes with the most similar characteristic expressions are selected for each of the user nodes and the commodity nodes in the global neighborhood, and the neighbor nodes are aggregatedAdding the corresponding neighborhood information and the initial characteristics to obtain the global characteristics X of each user node or commodity nodeglobal。
In the global convolution channel, the method models potential high-order relations by constructing a new interaction graph, and is not limited to a pair-wise bipartite graph connection mode which is observed in historical data. Specifically, a global interaction graph G is constructed in a clustering modeglobalTo represent the interaction of all nodes in the global structure and utilize the structure of GglobalAnd constructing graph convolution operation by the derived related information to finish the information aggregation task in the global channel.
In order to embody the structural property of the nodes in the process of constructing the interactive graph, neighborhood information of all the nodes is added before clustering, namely the characteristics of the nodes are spliced with first-order neighborhood characteristics:
XC＝concat(X,LX)
by node characteristics X carrying first-order neighborhood informationCOn the basis, all nodes are reclassified by a kMeans clustering algorithm, and if two nodes are classified into the same class, a connecting edge is added between the two nodes, so that an interaction graph G on the global structure is obtainedglobalThe algorithm pseudo code is as follows:
Figure BDA0003220923480000081
Figure BDA0003220923480000091
interaction graph G representing global interaction relationshipglobalIn the method, two nodes generating an interaction relationship may belong to the same local structure, or may be separated from each other in a spatial distance, so that the global property of the nodes is embodied.
In order to ensure the positivity of high-order information, the global interaction graph G is used for the momentglobalSecondary screening is carried out on the neighborhoods of all the nodes in the network, and each node is selected in the global neighborhoodA fixed number of neighbor nodes with the most similar characteristics are selected.
And in the global neighborhood, aggregating neighborhood information corresponding to the user nodes and the commodity nodes to obtain global neighborhood characteristics, and adding the initial characteristics of the nodes and the global neighborhood characteristics to obtain the output of a global convolution channel.
Specifically, taking the user node u and the commodity node i as an example, the information aggregation mode in the global neighborhood is as follows:
Figure BDA0003220923480000092
Figure BDA0003220923480000093
Figure BDA0003220923480000094
is a global neighborhood characteristic of a node, N(·)-globalGlobal neighborhood of a representative node, | N(·)-globalAnd | represents the number of nodes that the node neighbors within the global neighborhood.
Adding the global neighborhood characteristics of the nodes and the original characteristics to obtain the output of a global convolution channel
Figure BDA0003220923480000095
Figure BDA0003220923480000096
Figure BDA0003220923480000097
In order to better realize the updating process of the partial convolution channel, the characteristic calculation process in the form of a matrix is given here:
Xglobal＝X+LHX
Figure BDA0003220923480000101
Xglobalis a global feature matrix of nodes in the graph, and H is a global interaction graph GglobalDerived incidence matrix L representing the interaction of nodes in the global structureHLaplace matrix, D, being the correlation matrix HHIs a matrix of degrees of correspondence.
S4, interactive prediction is carried out based on local feature XlocalAnd global feature XglobalAdding the two parts of characteristics to obtain the final vector representation X of each user node or commodity nodeFAnd predicting the grade of the user for the commodity in the form of vector inner product.
After completing the feature updating process of the local convolution channel in step S2 and the global convolution channel in step S3, the local feature and the global feature of the node are obtained respectively, and the two pieces of information are added to obtain the final vector expression of the node:
Figure BDA0003220923480000102
Figure BDA0003220923480000103
at this time, the score of the user u for the commodity i can be expressed by the vector of the two
Figure BDA0003220923480000104
Inner product between:
Figure BDA0003220923480000105
parameters in the local convolution channel and the global convolution channel are optimized by using a paired BPR loss function, and training is carried out in a mode of maximizing the difference between the positive sample and the negative sample. The formula is expressed as:
Figure BDA0003220923480000106
wherein O { (u, i, j) | (u, i) ∈ O+,(u,j)∈O-Represents the training data, which includes both positive samples O+I.e. the interaction that actually occurred, also contains the negative example O-The fictitious interactions come from the commodity set which does not generate the interactions with the corresponding users in the data set; σ (-) represents the Sigmoid activation function. An Adam optimizer is used to optimize the model and update the parameters.
Compared with the prior art, the technical scheme of the invention can obtain the following beneficial effects:
1. aiming at the problem of over-smoothness existing in the characteristic iteration process of the conventional graph recommendation model, the aggregation mode of local neighborhood information is improved by introducing a transfer matrix, and the local neighborhood information is aggregated and updated by adopting a single-layer graph convolution network, so that the over-smoothness problem is solved;
2. aiming at the defect that the existing graph recommendation model depends on a bipartite graph structure, all nodes are reclassified by a clustering algorithm on the basis of vector characteristics of users and commodities, a new interaction graph is constructed from the global perspective, and a potential interaction mode is modeled;
3. the invention represents users and commodities from two aspects of local structure and global interaction by constructing two different convolution channels. Then, during prediction interaction, vector expressions representing two different types of high-order relations are integrated, and recommendation precision is effectively improved.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (3)

1. A dual-channel collaborative filtering recommendation method based on a graph convolution network is characterized by comprising the following steps:
s1, initializing a graph structure, and deriving a second interactive graph G and an adjacent matrix of the second interactive graph from a historical behavior data set of a userAAnd initial feature matrixes of user nodes and commodity nodes in the two interactive graphsX；
S2, constructing a local convolution channel, wherein in the local convolution channel, an adjacent matrix based on two interactive graphsACalculating the transition matrix of different orders on the two interactive graphsP kDetermining a first-order neighborhood range of nodes in the two interactive graphs by the adjacency matrix A, and determining a high-order neighborhood range of the nodes in the two interactive graphs by the transfer matrix; in each order of neighborhood, aggregating corresponding neighborhood information for each user node or commodity node, and adding the neighborhood information of each order to obtain the local neighborhood characteristicsX N(ii) a Adding the initial characteristic of each user node or commodity node and the local neighborhood characteristic thereof to obtain the local characteristic of each user node or commodity nodeX local；
Step S3, a global convolution channel is constructed, and in the global convolution channel, initial characteristic matrixes based on user nodes and commodity nodesXAnd a adjacency matrixAAdding first-order neighborhood information of each user node or commodity node in the two interactive graphs to obtain a new user node or commodity node feature matrixX C(ii) a To be provided withX COn the basis, all user nodes and commodity nodes are reclassified by a KMeans clustering algorithm, if two nodes in all the user nodes and the commodity nodes are classified into the same class, a connecting edge is considered to exist between the two nodes, and a global interaction graph G is constructed according to the principleglobal(ii) a To ensure the validity of the information, the global interaction graph G is appliedglobalAnd performing secondary screening on neighborhoods of all user nodes and commodity nodes, and selecting a fixed number of neighbors with most similar characteristic expressions in the global neighborhood for each of all user nodes and commodity nodesThe nodes and corresponding neighborhood information are aggregated and added with the initial characteristics to obtain the global characteristics of each user node or commodity nodeX global；
S4, interactive prediction is carried out based on local featuresX localAnd global featuresX globalAdding the two parts of characteristics to obtain the final vector representation of each user node or commodity nodeX FAnd predicting the grade of the user for the commodity in the form of vector inner product.
2. The graph convolution network-based two-channel collaborative filtering recommendation method according to claim 1, wherein parameters in a local convolution channel and a global convolution channel are optimized using a pairwise BPR penalty function, and are trained in a manner that maximizes a gap between positive samples and negative samples.
3. The dual-channel collaborative filtering recommendation method based on graph convolution network as claimed in claim 1, wherein a transition matrix is used to determine a first-order neighborhood range of each user node or commodity node using an adjacency matrix AP kIn the step of determining the high-order neighborhood range of each user node or commodity node, when the local neighborhood range of the user node or commodity node is determined, the first-order neighborhood is adjacent to the adjacent matrixATo determine; for the high-order neighborhood, a transition threshold P is set based on the corresponding transition matrixΘ=0.5 if the component in the transition matrix is [ 2 ]P k]ij>PΘIf so, a connecting edge exists between the node i and the node j in the corresponding k-order neighborhood; defining an interaction relation matrix between nodes in a high-order neighborhoodQ k(k.gtoreq.2): in the neighborhood of the same order, if the component of the corresponding position of the transition matrix is [ 2 ]P k]ij>PΘWhen the value is "2Q k]ij=1, otherwise 0; by the method, the neighborhood composition of each user node or commodity node in different orders is obtained.
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