CN111709474A - Graph embedding link prediction method fusing topological structure and node attributes - Google Patents
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Abstract
The invention provides a graph embedding link prediction method fusing a topological structure and node attributes, which comprises the following steps: s1, learning the topological structure information of the network through a graph embedding algorithm, and embedding the topological structure information of the network into a vector space to obtain an embedded structure feature vector based on the node; s2, uniformly coding the node attributes in the network to obtain node attribute feature vectors; and S3, carrying out nonlinear fusion on the structural features and the attribute features by using a deep neural network and outputting a link prediction score. The invention can well integrate the topological structure characteristics and the node attribute information in the network and help the user to obtain more accurate relevance pushing.
Description
Technical Field
The invention relates to a link prediction algorithm, in particular to a graph embedding link prediction method fusing a topological structure and node attributes.
Background
The invention patent with publication number CN109492133A proposes a link prediction method based on motif and network embedding. The method comprises the following specific steps of redefining first-order and second-order similarities of nodes according to a higher-order network structure motif; then a multi-coder model with shared parameters is designed, which inputs the neighbor information of all nodes in one motif at a time and adds a first-order similarity constraint condition at the generated vector representation. The link prediction method only considers the topological structure information of the nodes in the network and ignores rich and diverse attribute information of the nodes.
The invention patent publication CN109214599A proposes an end-to-end link prediction model based on graph attention network. Firstly, inputting a topological structure of an unweighted and undirected homogeneous network, then performing first-order and second-order neighbor sampling on all nodes according to the topological structure of a training set so as to batch the network, then inputting the batched training set into the model to train out model parameters, finally inputting a point pair to be predicted, and outputting the probability that a connecting edge exists between the point pair by the model.
Both methods only consider the topological structure information of the nodes in the network, and particularly depend on the defined structure similarity index, so that the difference of the predicted results in different networks is large, a universal structure similarity index is difficult to provide, and meanwhile, rich and diverse attribute information of the nodes is ignored.
In the network data obtained in the real world, not only the topological structure information of the network exists, but also rich attribute information is included, for example, in the social network, besides the friend relationship among users, the network includes a large amount of user attribute label information, and the information is also important for tasks such as friend recommendation in the social network, and the prediction accuracy can be greatly improved. Therefore, how to fully utilize the structural information and the attribute information in the network is a main research problem in the text.
Disclosure of Invention
The problem to be solved by the present invention is to provide a graph embedding link prediction method fusing topology structure and node attribute for the above-mentioned deficiencies in the prior art, and solve the problem that the topology structure and node attribute information cannot be fused at the same time for link prediction in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a graph embedding link prediction method fusing topological structure and node attributes comprises the following steps: s1, learning the topological structure information of the network through a graph embedding algorithm, and embedding the topological structure information of the network into a vector space to obtain an embedded structure feature vector based on the node; s2, uniformly coding the node attributes in the network to obtain node attribute feature vectors; and S3, carrying out nonlinear fusion on the structural features and the attribute features by using a deep neural network and outputting a link prediction score.
Compared with the prior art, the invention has the following beneficial effects: the link prediction algorithm provided by the invention realizes link prediction by fusing the topological structure and the node attribute information. Firstly, the graph embedding technology is applied to the research of the link prediction problem, aiming at the problem that the structural similarity index is difficult to be universal, the topological structure information of the network is learned through a graph embedding algorithm, and the topological structure information of the network is embedded into a low-dimensional and dense vector space to obtain an embedded structure feature vector based on the nodes. And then carrying out unified coding on the node attributes in the network to obtain a node attribute feature vector, carrying out nonlinear fusion on the structural features and the attribute features by using a deep neural network, and outputting a link prediction score.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
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FIG. 1 is a diagram illustrating attribute encoding of a network node according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a depth feature fusion network according to an embodiment of the present invention;
FIG. 3 is a general flow diagram of one embodiment of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the functions of the invention clearer and easier to understand, the invention is further explained by combining the drawings and the detailed implementation mode:
the link prediction algorithm disclosed by the invention is mainly divided into three steps: firstly, applying a graph embedding technology to a link prediction problem research, and aiming at the problem that a structure similarity index is difficult to be universal, learning the topological structure information of the network through a graph embedding algorithm, and embedding the topological structure information of the network into a low-dimensional and dense vector space to obtain an embedded structure feature vector based on a node. Then, the node attributes in the network are uniformly coded to obtain a node attribute feature vector. And finally, carrying out nonlinear fusion on the structural features and the attribute features by using a deep neural network and outputting a link prediction score.
Before further elaborating on the preferred specific algorithm steps, the basic concepts are first defined: in a simple network without weights and directions, the network may use the G ═ V, E representation, where V represents the set of nodes in the network and E represents the set of connected edges in the network. For a undirected network, consider a node pair (v)i，vj) And (v)j，vi) Representing the same link, a simple weightless undirected network is generally defined by ① nodes having no rings, i.e., the nodes themselves cannot be connected, ② nodes having no side number of 1 and no weight on the side, ③ nodes having no side relation to the direction of connection, i.e., the two nodes are considered to be equivalent in the process of link formation, and an adjacency matrix A is used to represent the connection relation between the nodes of the networkiAnd vjThere is a connecting edge between them, then on the corresponding position of AThe element is 1, and the other elements are 0.
The steps of learning the structural feature vector of the node are shown as follows, and the algorithm mainly comprises three parts:
first, a node sequence is sampled on the network using a truncated random walk approach.
The random walk generator samples a sequence of nodes in the network, and selects a node V in the network G ═ E, ViAs a root node, starting random walk from the root node, randomly selecting a neighbor node from neighbor nodes of the last visited node as a next visited node until the maximum path length t is reached, and taking a path passed by the random walk as a sampling sequence Wvi，|WviI | ═ t. The sampling is repeated λ times at node vi.
And secondly, mapping the nodes into vector representation form.
And (4) taking the sampled node sequence as a sentence, inputting the sentence into a SkipGram model for training, and setting the window size to be w. In the network representation learning task, for the collected node sequence WviA window of size w is set. For each vjMapping to the current vector space phi (v)j) ∈ R. for each given node vjTo maximize its node sequence WvjProbability of neighbor node in middle window:
thirdly, the calculation amount is reduced by using a Softmax mode.
Hierarchical Softmax is used to reduce computational complexity. Given node vk∈ V, calculating conditional probability
Pr(vk|Φ(vj) A large amount of computation is required, and thus this conditional probability is calculated using the hierarchical softmax. The nodes are taken as leaf nodes and placed in a binary tree, for each leaf node, a unique path from a root node to the node is always provided, and the probability of the appearance of the leaf node is estimated according to the unique path.
To node vkThe path of (A) is recorded as
Wherein
Then:
may be at node blA two-classifier model is built on the parent node to estimate Pr (b)l|Φ(vj))，
Wherein
Represents node blA parent node of (a); and after final iterative training, using the weight matrix of the hidden layer of the SkiGram expansion model as potential vector representation of the node. Whereby Pr (v) can be converted tok|Φ(vj) Time complexity is reduced from O (V | to O (log | V |). After iterative training, the weight matrix of the hidden layer of the SkipGram extended model is used as the potential vector representation of the node.
The node attributes comprise discrete attributes and continuous attributes, a general attribute coding mode is provided for the different types of attributes, and the discrete node attributes and the continuous node attributes in the network are coded to obtain a uniform real-value attribute feature vector form, as shown in figure 1.
The attributes of the so-called discrete type are attributes of the category type, such as gender, age, and the like of the user in the social network. For the discrete attribute, one-hot encoded to continuous vector representation may be used. For example, the gender attribute has two values { male, female }, and a vector v ═ 0, 1} can be used to describe the gender of the user, where the value of the first element in the vector is 1 represents gender male and the value of the second element in the vector is 1 represents gender female. The method carries out one-hot coding on all the discrete node attributes in the network. Finally, the coding sequence of each type of attribute is spliced to obtain the final discrete attribute feature vector.
The continuous attribute is commonly present in the social network, such as blog information published by a user in a microblog network, picture data shared by the user on a picture sharing website, and the like. This class of attributes cannot be directly compared, but text-type attributes can be processed through TF-IDF techniques. The specific steps are as follows: calculating word frequency, and normalizing the word frequency in order to facilitate comparison of texts with different lengths; and calculating the frequency of the inverse document. Calculating TF-IDF value, using product of word frequency and inverse document frequency as TF-IDF value; and fourthly, splicing the TF-IDF values of each word in the document to form a feature vector of the text attribute.
After the continuous attributes are expressed into real-value vectors, the attribute final feature vectors of the nodes in the network can be obtained by splicing the attribute coding feature vectors of the nodes from beginning to end. In order to facilitate the input of the attribute feature vectors into a machine learning algorithm and a neural network, the attribute information of each node is processed into feature vectors with equal dimensions. And filling 0 in the corresponding attribute feature position of the node lacking some kind of attribute, thereby obtaining the attribute feature of the node with the same dimension.
When the nonlinear fusion between the features is carried out by establishing a deep learning model, a link prediction task is used as target guidance, and a neural network is established to fuse the network structure features and the attribute features of the nodes. The method can realize the nonlinear fusion of the network structure characteristics and the node attribute characteristics. The structure diagram of the depth feature fusion network is shown in fig. 2.
In particular, f is defined as two nodes vi，vjSimilarity function, using Softmax function to define node viFor vjConditional probability of (2):
wherein, p (v)j|vi) To measure vjAnd viThe possibility of connection. The structural similarity degree between nodes needs to be extracted from the neighbor nodes of the nodes, and the node v is defined based on the assumption of conditional independenceiNode set N adjacent theretoiThe conditional probability between is:
wherein N isiRepresentative node viOf the neighboring node. The likelihood function L of the entire model can be defined as:
taking the likelihood function as a learning target of the model, the structure of the feature depth fusion model is as follows:
inputting a layer: the node structure vector representation is denoted u and includes node structure information, and the node attribute code vector representation is denoted u' and includes node attribute information.
② hidden layer structural characteristic vector u and attribute characteristic vector u are weighted and input into a multi-layer perceptron, and the hidden representation of each layer is marked as h0，h1，...hn. The representation of the hidden layer is defined as follows:
hk＝k(Wkhk-1+bk)，k＝1，2，...，n
wherein gamma represents the weight of the attribute feature,krepresenting the activation function and n the number of layers of the hidden layer.
The hidden layer adopts a tower structure shown in the attached figure 2: the number of neurons in the current layer is halved compared to the previous layer. Such a tower structure can learn more abstract features from the data. u and u' need to be adjusted by a weight coefficient γ when input to the hidden layer.
③ output layer, willThe output h of the last hidden layer is converted into a probability vector o, which contains the input node viLink prediction for other nodes:
o＝[p(v1|vi)，p(v2|vi)，...，p(v|V||vi)]
taking the corresponding row in the weight matrix of the hidden layer and the output layer as a node vjIs an abstract representation of (1), denoted as ujNode vi，vjThe similarity function of (a) is defined as:
further, a formula for calculating the connection probability in the vector o is obtained:
the optimization objective function of the entire model is then denoted as Θ
From the formula for calculating the connection probability, one can obtain:
the optimization objective function is to make the similarity of nodes in the neighbor nodes larger and the similarity of nodes not in the neighbor nodes smaller.
After obtaining the model, the flow chart is shown in fig. 3, and then the constructed depth model is trained. During the network training process, the Adam optimization framework model is preferably used. The Adam optimizer designs independent adaptive learning rates for different parameters by computing first and second order moment estimates of the gradient, for infrequently updated parametersA higher learning rate is used and frequently updated parameters are used with a lower learning rate. And finally, outputting the probability value of the connection between the node and other nodes in the network at the output layer of the neural network. Therefore, the invention embeds the network topological structure information into a low-dimensional and dense vector space, uniformly encodes the node attributes in the network to obtain the node attribute feature vector, and performs nonlinear fusion on the structure features and the attribute features by using the deep neural network of the tower structure. The invention meets the requirements that the interaction between the individuals of the social network is more convenient and frequent under the large environment along with the rapid development of the internet technology, better researches on the interaction relationship between the individuals in the network are greatly helpful for understanding the social network evolution mechanism and improving the communication experience between the individuals, the link prediction provided by the invention can help the user to obtain more accurate recommendation,orFind back missing friendsEtc. of. In addition, the method can be widely and practically applied in the fields of biology, electric power, communication and the like, and has great economic value and good social benefit.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.
Claims (10)
1. A graph embedding link prediction method fusing a topological structure and node attributes is characterized by comprising the following steps: s1, learning the topological structure information of the network through a graph embedding algorithm, and embedding the topological structure information of the network into a vector space to obtain an embedded structure feature vector based on the node; s2, uniformly coding the node attributes in the network to obtain node attribute feature vectors; and S3, carrying out nonlinear fusion on the structural features and the attribute features by using a deep neural network and outputting a link prediction score.
2. The graph-embedded link prediction method fusing topology and node attributes according to claim 1, wherein a simple weightless undirected network G ═ V, E, where V represents a set of nodes in the network and E represents a set of connected edges in the network, and there is no ring between nodes, the number of connected edges between nodes is at most 1, there is no weight on connected edges, and the edges between nodes do not consider the connection direction.
3. The method for predicting graph-embedded links fusing topology and node attributes according to claim 2, wherein the step of obtaining the node-based embedded structure feature vector in step S1 is as follows: s11, sampling the node sequence on the network by using a cut-off random walk mode; s12, mapping the nodes into vector representation forms; and S13, using Softmax to participate in the optimization calculation of the probability under the condition of the given node.
4. The graph-embedded link prediction method fusing topology and node attributes according to claim 3, wherein in step S11, the random walk generator samples a node sequence in the network, and selects a node V in the network G ═ (E, V)iAs a root node, starting random walk from the root node, randomly selecting a neighbor node from neighbor nodes of the last visited node as a next visited node until the maximum path length t is reached, and taking a path passed by the random walk as a sampling sequence Wvi，|WviAt node v | ═ tiIs repeatedly sampled x times.
5. The graph-embedded link prediction method fusing topology and node attributes according to claim 4, wherein in step S12, the sampled node sequence is regarded as a sentence and input into a SkipGram model for training, and the window size is w; in the network representation learning task, for the collected node sequence WviSetting a window of size w for each vjMapping to the current vector space phi (v)j) ∈ R, for each given node vjIs shown in the drawing (a) and (b),maximizing its node sequence WvjProbability of neighbor node in middle window:
6. the graph-embedded link prediction method fusing topology and node attributes according to claim 5, wherein in the step of S13, the nodes are placed in a binary tree as leaf nodes, the probability of the occurrence of the leaf nodes is estimated according to the unique paths of the leaf nodes, and the nodes are connected to the node vkThe path of (A) is recorded as
Wherein the content of the first and second substances,
then there are:
then at node blA two-classifier model is built on the parent node to estimate Pr (b)l|Φ(vj))，
Wherein
Represents node blA parent node of (a); and after final iterative training, using the weight matrix of the hidden layer of the SkiGram expansion model as potential vector representation of the node.
7. The method of claim 6, wherein the network node in step S2 comprises a discrete attribute feature vector and a continuous attribute feature vector, wherein the discrete attribute feature vector and the continuous attribute feature vector
Obtaining the discrete attribute feature vector: performing one-hot coding on all discrete node attributes in a network, and splicing the coding sequence of each type of attribute to obtain a final discrete attribute feature vector;
obtaining the continuity attribute feature vector: the method comprises the following steps of (1) calculating word frequency, and normalizing the word frequency; (2) calculating the frequency of the inverse document; (3) calculating a TF-IDF value, and using the product of the word frequency and the inverse document frequency as the TF-IDF value; (4) splicing TF-IDF values of each word in the document to form a feature vector of a text attribute;
and splicing the attribute coding feature vectors of the nodes end to obtain the node attribute feature vector in the network.
8. The graph embedding link prediction method fusing the topology and the node attributes according to claim 7, wherein the attribute information of each node is processed into equal-dimension feature vectors, and the nodes missing some kind of attributes are filled with 0 at the corresponding attribute feature positions, thereby obtaining the attribute features of the nodes with the same dimension.
9. The graph embedding link prediction method fusing topology and node attributes according to any one of claims 2 to 8, wherein a link prediction task is used as a target guide, a neural network is established to deeply fuse network structure features and node attribute features, and f is defined as two nodes vi,vjSimilarity function, using Softmax function to define node viFor vjConditional probability of (2):
wherein, p (v)j|vi) Measure vjAnd viThe possibility of connection;
the structural similarity between nodes needs to be extracted from the neighbor nodes of the nodes and is independent based on conditionsAssuming sexuality, define node viNode set N adjacent theretoiThe conditional probability between is:
wherein N isiRepresentative node viThe likelihood function L of the whole model is:
the likelihood function L is taken as a learning target of the model, and the structure of the characteristic depth fusion model comprises an input layer, a hidden layer and an output layer, specifically,
the input layer: the node structure vector representation is marked as u and contains the node structure information, and the node attribute coding vector representation is marked as u' and contains the node attribute information;
the hidden layer: weighting the structure characteristic vector u and the attribute characteristic vector u 'and inputting the weighted structure characteristic vector u and the weighted attribute characteristic vector u' into a multi-layer perceptron, wherein the hidden representation of each layer is marked as h0，h1，...hnThe hidden layer is defined as follows:
hk＝k(Wkhk-1+bk)，k＝1，2，...，n
wherein gamma represents the weight of the attribute feature,krepresenting the activation function, n representing the number of layers of the hidden layer; a tower structure with the number of neurons of the current layer reduced by half compared with that of the previous layer is adopted in the hidden layer;
the output layer; converting the output h of the last layer of the hidden layer into a probability vector o comprising the input node viLink prediction for other nodes:
o＝[p(v1|vi)，p(v2|vi)，...，p(v|V||vi)]
taking the corresponding row in the weight matrix of the hidden layer and the output layer as a node vjIs an abstract representation of (1), denoted as ujNode vi，vjThe similarity function of (a) is defined as:
further, a formula for calculating the connection probability in the vector o is obtained:
the optimization objective function of the entire model is then denoted as Θ
From the formula for calculating the connection probability, one can obtain:
10. the graph embedding link prediction method fusing the topological structure and the node attribute as claimed in claim 9, wherein in a network training process of the constructed depth model, an Adam optimization framework model is used, an Adam optimizer designs independent adaptive learning rates for different parameters by calculating first moment estimation and second moment estimation of a gradient, uses a higher learning rate for parameters which are not frequently updated and a lower learning rate for parameters which are frequently updated, and finally, a probability value of connection between an output node of the neural network and other nodes in the network is established at an output layer of the neural network.
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