Mobile Edge Computing Server Cooperative Caching Method Based on Spatio-Temporal Graph Convolution Model

Abstract

The present invention discloses a collaborative caching method for a Mobile Edge Computing (MEC) server based on a spatio-temporal graph convolutional model. The method includes: integrating a graph convolutional neural network and a gated recurrent unit to construct a spatio-temporal graph convolutional model for predicting content popularity, dividing a collaborative domain, and designing a heuristic collaborative caching method to minimize the average access delay. The present invention constructs a topological graph of MEC servers based on proximity relationships and semantic relationships, constructs a feature matrix with the content popularity information of MEC servers, and simultaneously integrates a graph convolutional neural network and a gated recurrent unit to construct a spatio-temporal graph convolutional model, so as to mine the spatio-temporal features of content popularity and make effective predictions; on the basis of known predicted content popularity, the hierarchical clustering method is used to divide the collaborative domain of MEC servers and design a heuristic collaborative caching method, thereby minimizing the average access delay.

Description

Technical Field

[0001] The present invention belongs to the field of computer technology, and more specifically, relates to a collaborative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model. Background Art

[0002] In the industrial Internet of things, industrial devices upload the massive data collected to the cloud data center for data analysis and then provide user access. Different users may request the same content from the cloud data center in the same time period, resulting in frequent repeated requests for the content, imposing a heavy burden on the backhaul link of the core network.

[0003] To solve the above problems, mobile edge caching technology has received extensive attention. The operator caches content in advance at the edge node to relieve the pressure on the backhaul link and reduce the access delay. In the caching scenario of mobile edge computing (MEC) servers, most of the existing caching policies reduce the access delay by predicting the content popularity and caching popular content in advance during off-peak traffic periods. However, these policies only focus on the temporal characteristics of content popularity, do not fully consider the geographical topology of MEC servers, and ignore the spatial correlation of content popularity. Due to the limited storage capacity of edge nodes and the dynamic and changeable user requests, there are still problems in choosing what content to cache and how to place it in the MEC architecture. Summary of the Invention

[0004] Aiming at the above defects or improvement requirements of the prior art, the present invention provides a collaborative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model, integrating a graph convolutional neural network and a gated recurrent unit to construct a spatio-temporal graph convolutional model, aiming to predict content popularity, and by dividing the collaboration domain and designing a heuristic collaborative caching method, aiming to minimize the average access delay. The present invention constructs a topology graph based on the proximity relationship and semantic relationship of mobile edge servers, and at the same time integrates a graph convolutional neural network and a gated recurrent unit to construct a spatio-temporal graph convolutional model to mine the spatio-temporal characteristics of content popularity and make an effective prediction; on the basis of the known predicted content popularity, the hierarchical clustering method is used to divide the collaboration domain of MEC servers and design a heuristic collaborative caching method to reduce the average access delay.

[0005] To achieve the above object, the present invention provides a collaborative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model, including the following steps:

[0006] (1) Construct a topology graph of MEC servers based on the proximity relationship and semantic relationship, construct a feature matrix with the content popularity information of mobile edge computing MEC servers, and at the same time integrate a graph convolutional neural network and a gated recurrent unit to form a spatio-temporal graph convolutional model;

[0007] (2) Use the time series in the feature matrix as the graphical signal of the MEC server topology graph and input it into the graph convolutional neural network, and use the graph convolutional method based on the spectral domain to extract the spatial features of content popularity among different MEC servers;

[0008] (3) Use the time series of the obtained spatial features of content popularity as the input of the gated recurrent unit. The gated recurrent unit dynamically captures the time features through the forgetting factor and the update state unit, and predicts the content popularity of all MEC servers in the region at any moment;

[0009] (4) Based on the popularity of each content among all MEC servers, considering the cooperative caching of MEC servers, use the hierarchical clustering method to divide the cooperative domains of MEC servers, and minimize the average access latency of content in all cooperative domains through a heuristic cooperative caching method.

[0010] Compared with the existing MEC server caching strategy, the present invention provides a cooperative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model, integrating a graph convolutional neural network and a gated recurrent unit to construct a spatio-temporal graph convolutional model, aiming to predict content popularity. By dividing cooperative domains and designing a heuristic cooperative caching method, the aim is to minimize the average access latency. The present invention constructs a topology graph based on the proximity relationship and semantic relationship of mobile edge servers, and at the same time integrates a graph convolutional neural network and a gated recurrent unit to construct a spatio-temporal graph convolutional model to mine the spatio-temporal features of content popularity and make effective predictions; based on the known predicted content popularity, use the hierarchical clustering method to divide the cooperative domains of MEC servers and design a heuristic cooperative caching method to minimize the average access latency. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a schematic diagram of the spatio-temporal graph convolutional model of a cooperative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model in an embodiment of the present invention;

[0012] Figure 2 It is a schematic diagram of spatial feature mining of a cooperative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model in an embodiment of the present invention;

[0013] Figure 3 It is a schematic diagram of time feature mining of a cooperative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model in an embodiment of the present invention;

[0014] Figure 4 It is a schematic diagram of the cooperative domain division process of a cooperative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0015] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0016] Mobile edge caching technology is a relatively key technology in the field of industrial Internet of Things. Due to the massive increase in the data collected by the industrial Internet of Things, the content requested by users from the cloud data center is also increasing. The traditional remote network communication mode between users and the cloud data center can no longer meet the low-latency access requirements of the industrial Internet of Things. Mobile edge caching technology has received extensive attention in recent years. Its goal is to cache the frequently requested content in the MEC server closer to the user in advance to meet the repeated requests of users, reduce the redundant content transmission on the backhaul link, save network resources, shorten the latency generated by the content transmission distance, and improve the user experience.

[0017] To achieve entity-level MEC server collaborative caching, the present invention provides a mobile edge computing server collaborative caching method based on a spatio-temporal graph convolutional model, which specifically includes:

[0018] (1) Construct an MEC server topology graph based on the proximity relationship and semantic relationship, construct a feature matrix with the content popularity information of the MEC server, and integrate a graph convolutional neural network and a gated recurrent unit to form a spatio-temporal graph convolutional model;

[0019] (2) Take the time series in the feature matrix as the graph signal of the MEC server topology graph and input it into the graph convolutional neural network, and use the graph convolutional method based on the spectral domain to extract the spatial features of the content popularity in different MEC servers;

[0020] (3) Take the time series of the content popularity spatial features obtained as the input of the gated recurrent unit. The gated recurrent unit dynamically captures the time features through the forgetting factor and the update state unit, and predicts the content popularity of all MEC servers in the region at any moment;

[0021] (4) On the basis of obtaining the popularity of each content in all MEC servers, considering the collaborative caching of MEC servers, use the hierarchical clustering method to divide the collaborative domain of MEC servers, and minimize the average access latency of the content in all collaborative domains through a heuristic collaborative caching method.

[0022] Figure 1It is a schematic diagram of the spatio-temporal graph convolutional model of a mobile edge computing server collaborative caching method in an embodiment of the present invention; specifically, the construction of the spatio-temporal graph convolutional model in step (1) includes:

[0023] Construct the MEC server topology graph G: Use the weighted undirected graph G = (V, E) to represent the topology graph structure of M MEC servers in the urban area. Where V = {v1, v2,..., v M} is the set of all MEC servers, E = {e 1，2 , …, e m，n} is the set of edges between MEC servers with connection relationships, e m，n = 1 indicates that MEC servers s m and s n are connected, e m，n = 0 indicates that MEC servers s m and s n are not connected, W = {w 1，2 ,..., w m，n} represents the set of edge weights, and the larger the value of w m，n , the stronger the correlation between MEC servers s m and s n .

[0024] Use the Gaussian similarity in the form of Equation (1) to characterize the proximity relationship of MEC servers

[0025]

[0026] Use the cosine similarity in the form of Equation (2) to characterize the semantic relationship of MEC servers with similar access requirements

[0027]

[0028] Among them, Dis m，n represents the Gaussian similarity between MEC servers s m and s n , exp is the exponential with the natural constant e as the base, L m and L n respectively represent the two-dimensional spatial coordinates of servers s m and s n , ||.|| represents the modulus of the vector, θ is a fixed coefficient, R represents the maximum distance for two MEC servers to become neighbors, Fuc m，n represents the semantic relationship between MEC servers s m and s n , p m，i is the popularity of content f i on MEC server s m , pn，i For content f i Popularity on MEC server s n

[0029] If s m and s n Have a proximity relationship (Dis m，n ≠0), then construct an edge on the graph and set e m，n = 1; Otherwise, check s m and s n Semantic relationship Fuc m，n When Fuc m，n Is greater than the set semantic threshold β, construct an edge on the graph and set e m，n = 1. The edge weight calculation formula of G is shown in Equation (3):

[0030]

[0031] Secondly, construct the feature matrix Q, and use the popularity of content f i As the node information feature in the MEC server topology graph G, Q = [Q t-N+1 ,..., Q t T ∈R M×N . Where M is the total number of MEC servers, and N is the length of the historical time series. Q t ∈R M×t Represents the content popularity of f i At all mobile edge computing servers at time t. At the current time t, the popularity p i Of content f m On MEC server s m，i Is defined as formula (4). Where, num m，i (t) is the number of times content f i Is requested by users in the time period [t - 1, t], Is the total number of all content requests in the time period s m , and L is the number of different contents f i .

[0032]

[0033] Construct a spatio-temporal graph convolutional model. Assume that the time step of the feature matrix Q is n. The model first sequentially inputs the time series in Q as the graph signal of the MEC server topology graph G into the graph convolutional neural network, and uses the graph convolutional method based on the spectral domain to extract the spatial features of the popularity of content f i Among different MEC servers; Secondly, the time series Q' t ​​As the input of the gated recurrent unit, the gated recurrent unit dynamically captures the temporal features of Q′ through the forgetting factor and the update state unit. t Finally, the output layer uses a fully connected layer to generate the popularity of all MEC servers in the region at time t+1. i Popularity of all MEC servers in the region

[0034] Figure 2 FIG. is a schematic diagram of spatial feature mining of a mobile edge computing server cooperative caching method based on a spatio-temporal graph convolutional model in an embodiment of the present invention; specifically, the extraction of the spatial features of the content popularity in the topological graph in step (2) includes:

[0035] Adopt a graph convolution method based on the spectral domain to extract the spatial features of the content popularity in the topological graph, and use the content popularity sequence Q in the feature matrix Q t As the signal input of the MEC server topological graph G, use the diagonalized linear operator defined in the Fourier domain to convolve the signal Q t to obtain Equation (5):

[0036] g θ * G Q t =Ug θ U T Q t (5)

[0037] Adopt the first-order Chebyshev graph convolution to approximately solve Equation (5) to obtain the final propagation formula (6) of the graph convolution:

[0038]

[0039] Stack the multi-level neighborhood information transmission model as shown in Equation (7):

[0040]

[0041] where g θ is the convolution filter, * G represents the convolution operation operator, U is the matrix composed of the eigenvectors of the Laplacian matrix of the MEC server topological graph G, U T Q t represents the Fourier transform on the topological graph G, H (1) represents the output of the first-layer graph signal, H (0) =Q t is the initial feature state, W (1) and W (2) represent the learned parameter matrices. An adjacency matrix that represents the addition of the degree of the node itself is used to prevent the node from losing its own feature information when propagating information. Here, A is the adjacency matrix of G, and I is the identity matrix. In the adjacency matrix, 0 is usually used to represent that the nodes are not connected, and 1 is used to represent that they are connected, without considering the relationship of the connection strength between the graph nodes. Using the weight of the edge as the value of the adjacency matrix, let A i，j = w i，j . The greater the weight, the higher the degree of association. is the degree matrix of . σ is the activation function of ReLU.

[0042] Figure 3 is a schematic diagram of time feature mining of a mobile edge computing server collaborative caching method based on a spatio-temporal graph convolutional model in an embodiment of the present invention; specifically, the extraction of the time feature of the content popularity in the topological graph in step (3) includes:

[0043] Using a gated recurrent unit to extract time features, and taking the time series Q′ t of the content popularity spatial features that have been obtained and h t-1 as the input of the gated recurrent unit. The output of the historical memory information and the new input information of the content popularity is determined by the reset gate and the update gate. The specific formulas are shown in formulas (8) and (9):

[0044] r t = σ(W r [Q′ t , h t-1 + b r ) (8)

[0045] u t = σ(W u [Q′ t , h t-1 + b u ) (9)

[0046] After the gated signal is known, the local information is extracted from the long-term information through the reset gate r t and concatenated with the content popularity sequence Q′ t with spatial features to obtain the current node state z t , as shown in formula (10):

[0047] z t = tanh(W z [Q′ t , (r t * h t-1 )]+ b z ) (10)

[0048] The same update gate signal u is used in the final updated memory stage t to retain the hidden state h of the previous node t-1 and the information of the current node state z t to obtain the update expression and the formula for the final prediction result, as shown in Equations (11) and (12):

[0049] h t = u t * h t-1 + (1 - u t ) * z t (11)

[0050]

[0051] where h t-1 represents the hidden state at time t - 1, W u and W r are weight matrices, b u and b r are bias values, r t represents the reset gate, u t represents the gate signal, z t represents the current node state, b z is the bias term, and tan h is the non - linear activation function, represents the predicted content popularity

[0052] Figure 4 is the intention of the collaboration domain division process in a mobile edge computing server collaborative caching method based on a spatio - temporal graph convolution model in an embodiment of the present invention; specifically, the collaboration domain division process in step (4) includes:

[0053] (1.1) Initialize the collaboration domain: Use the hierarchical clustering method to divide the MEC servers into collaboration domains, with each MEC server as a separate collaboration domain. The Gaussian similarity Dis of the MEC servers characterized by formula (1) i，j is used as the distance consideration criterion. Assuming that the number of MEC servers in two collaboration domains is represented by N a and N b respectively, the distance calculation formula between collaboration domains is as shown in (13):

[0054]

[0055] (1.2) According to the obtained collaboration domain distances, find the two collaboration domains with the shortest distance. If the distance between them is less than the threshold θ, then merge these two collaboration domains. After obtaining the new collaboration domain, delete the above two old collaboration domains, and then recalculate the distances between the new collaboration domain and other collaboration domains using formula (13);

[0056] (1.3) Repeat step (1.2) to merge the collaboration domains. The termination condition is that the distance between the two closest collaboration domains is greater than the threshold θ.

[0057] The collaborative caching method in step (4) specifically includes:

[0058] (2.1) Design a heuristic collaborative caching method to obtain the cache content placement scheme in each collaborative area to optimize the average content access delay. Assume that based on different content f i The cache information on the MEC server constructs a cache matrix X, and the content cache matrix X = {x m，i |f i ∈F,s m ∈S}, x m，i =1 indicates MEC server s m Cache content i ;x m，i =0 indicates MEC server s m No cached content i . Let the average access delay reduction of the content be the cache benefit, and the content f i Cache on MEC servers m The cache benefit is Δα m，i First, initialize the cache matrix X, cache benefit matrix Δα to zero and MEC server cache capacity. If s m All MEC servers in the collaborative domain do not cache content f i , select formula (14) to calculate the cache benefits of all uncached content. If in the current iteration, s m There is already a MEC server caching content f in the collaborative domain i , select formula (15) to calculate the cache benefits of all uncached content:

[0059]

[0060]

[0061] Among them, p k，i Represented as content f i On MEC servers k Popularity on Indicates s m The collaborative domain, Indicates s m All uncached content f in the collaborative domain i The MEC server set, γ is the unit transmission delay of content generated by routing between collaborative servers, γ0 represents the delay of content transmission from the cloud data center to s m Transmission through the route generates unit transmission delay, d0，k Denote s k the distance to the cloud data center, d k，m Denote the s i of the uncached content f k to s m distance, d k，n Denote s k the shortest distance to the MEC server that has cached the content f i in the cooperation domain, d′ k，n = min{d k，n , d k，m}.

[0062] (2.2) Select the maximum caching gain Δα from the caching gain matrix Δα m，i , and cache the content f i into sm, set the caching gain Δα m，i = 0. Then update the set of MEC servers of the uncached content f i , the caching gain of the uncached content f i in the MEC server, and the remaining storage space of s m ;

[0063] (2.3) Obtain a locally optimal placement result for each iteration. If the cache in the MEC server is full, set the caching gain of all cached content in this server to zero. Repeat the above steps (2.1) and (2.2) until the remaining storage space of the MEC servers in each cooperation domain is unavailable, and return the cache matrix X.

Claims

1. A collaborative caching method for mobile edge computing servers based on a spatio-temporal graph convolutional model, characterized in that, It includes the following steps: (1) Construct a topology graph of MEC servers based on proximity relationship and semantic relationship, construct a feature matrix with the content popularity information of mobile edge computing (MEC) servers, and integrate a graph convolutional neural network and a gated recurrent unit to form a spatio-temporal graph convolutional model; (2) Take the time series in the feature matrix as the graph signal of the MEC server topology graph and input it into the graph convolutional neural network, and use the graph convolutional method based on the spectral domain to extract the spatial features of content popularity in different MEC servers; (3) Take the time series of the obtained spatial features of content popularity as the input of the gated recurrent unit. The gated recurrent unit dynamically captures the time features through the forgetting factor and the update state unit, and predicts the content popularity of all MEC servers in the region at any moment; (4) On the basis of obtaining the popularity of each content in all MEC servers, considering the collaborative caching of MEC servers, use the hierarchical clustering method to divide the collaborative domains of MEC servers, and minimize the average access delay of content in all collaborative domains through a heuristic collaborative caching method; The collaborative caching method in step (4) specifically includes: (2.1) Design a heuristic collaborative caching method to obtain the cache content placement scheme in each collaborative area to optimize the average content access delay; Build a cache matrix based on cache information on MEC servers , content cache matrix , Indicates the MEC server Cache content ; Indicates the MEC server No cached content ; Let the average access delay reduction of the content be the cache benefit, content Cache on MEC server The cache benefit is ;First initialize the cache matrix , cache benefit matrix is zero and the MEC server cache capacity, if All MEC servers in the collaborative domain do not cache content , choose formula (14) to calculate the cache benefits of all uncached content, if in the current iteration, There is already a MEC server cache content in the collaborative domain , choose formula (15) to calculate the caching benefits of all uncached content: Among them, denotes the popularity on the MEC server ; denotes the collaboration domain ; denotes the set of MEC servers for all uncached content in the collaboration domain ; is the unit transmission delay generated by routing the content among collaboration servers, ; denotes the unit transmission delay generated by routing the content from the cloud data center to ; denotes the distance from to ; denotes the shortest distance from to the MEC server that has cached the content in the collaboration domain, ; (2.2) Select the maximum caching benefit from the caching benefit matrix and cache the content to and set the caching benefit ; then update the MEC server set of the uncached content , the caching benefit of the uncached content in the MEC server, and the remaining storage space of ; (2.3) The local optimal placement result is obtained in each iteration. If the cache content in the MEC server is full, the cache revenue of all cache content in this server is set to zero; repeat the above steps (2.1) and (2.2) until the remaining storage space of the MEC servers in each cooperation domain is unavailable, and return the cache matrix .

2. The mobile edge computing server collaborative caching method based on the spatio-temporal graph convolutional model according to claim 1, characterized in that, In step (1), constructing the topology graph of MEC servers based on proximity relationship and semantic relationship specifically includes: Construct the MEC server topology graph G: Use a weighted undirected graph to represent the topology graph structure of MEC servers within the urban area, where is the set of all MEC servers, is the set of edges between MEC servers with connection relationships, represents that MEC server and are connected, represents that MEC server and are not connected, represents the set of edge weights, the larger the value, the stronger the correlation between MEC servers and ; Use the Gaussian similarity shown in formula (1) to represent the proximity relationship of MEC servers (1) Use the cosine similarity shown in formula (2) to represent the semantic relationship of MEC servers with similar access requirements (2) Among them, represents the MEC server and the Gaussian similarity of is the exponential with the natural constant as the base, and respectively represent the two-dimensional spatial coordinates of the servers and ; represents the modulus of the vector, is a fixed coefficient, represents the maximum distance for two MEC servers to become neighbors, represents the semantic relationship between the MEC servers and ; is the popularity of the content on the MEC server ; is the popularity of the content on the MEC server ; if and Has a neighboring relationship ( ), then construct edges on the graph and let Otherwise, check and Semantic relationship ,when Greater than the set semantic threshold , construct edges on the graph and let The edge weight calculation formula is shown in formula (3):

3. The method for collaborative caching of mobile edge computing servers based on a spatio-temporal graph convolutional model according to claim 2, wherein In step (1), constructing the feature matrix with the content popularity information of MEC servers specifically includes: Construct a feature matrix , take the popularity of the content as the node information feature in the MEC server topology graph ; where is the total number of MEC servers, and is the length of the historical time series; represents the content popularity at time on all mobile edge computing servers; at the current time, the popularity of the content on the MEC server is defined as in Equation (4); where is the number of times the content is requested by users in the time period , is the total number of all content requests in this time period , and is the number of different contents .

4. The method for collaborative caching of mobile edge computing servers based on a spatio-temporal graph convolutional model according to claim 3, wherein In step (1), integrating the graph convolutional neural network and the gated recurrent unit to form a spatio-temporal graph convolutional model specifically includes: Build a spatio-temporal graph convolutional model, assuming the feature matrix has a time step of . First, the model sequentially takes the time series in as the graph signal of the MEC server topology graph and inputs it into the graph convolutional neural network, using the spectral-domain-based graph convolution method to extract the spatial features of the popularity of content in different MEC servers. Second, the time series of the spatial features of the content popularity that have been obtained is used as the input of the gated recurrent unit, and the gated recurrent unit dynamically captures time features through the forgetting factor and the update state unit. Finally, the output layer uses a fully connected layer to generate the popularity of all MEC servers in the region at time . .​ 5. The collaborative caching method for mobile edge computing servers based on the spatio-temporal graph convolutional model according to claim 1 or 2, characterized in that, Step (2) specifically includes: Adopt a graph convolution method based on the spectral domain to extract the spatial features of content popularity in the topological graph, and use the content popularity sequence in the feature matrix as the signal input of the MEC server topological graph , and use the diagonalized linear operator defined in the Fourier domain to convolve the signal , obtaining Equation (5): ​ （5） Use the first-order Chebyshev graph convolution to approximately solve formula (5) to obtain the final propagation formula (6) of graph convolution: （6） Stack the multi-level neighborhood information transmission model as shown in formula (7): （7） Among them, is a convolutional filter, represents the convolutional operation operator, is the matrix composed of the eigenvectors of the Laplacian matrix of the MEC server topology graph , represents the Fourier transform on the topology graph , represents the output of the -th layer graph signal, is the initial feature state, and represent the learned parameter matrix; represents the adjacency matrix with the degree of the node itself added to avoid the node losing its own feature information when propagating information; among them is the adjacency matrix, is the identity matrix; in the adjacency matrix, 0 is usually used to represent that the nodes are not connected, and 1 is used to represent that they are connected to each other, without considering the relationship of the association strength between the graph nodes; the weight of the edge is used as the value of the adjacency matrix, let , the greater the weight, the higher the degree of association; is the degree matrix, , is the activation function of ReLU.

6. The collaborative caching method for mobile edge computing servers based on the spatio-temporal graph convolutional model according to claim 1 or 2, characterized in that, Step (3) specifically includes: The gated recurrent unit is used to extract temporal features from the time series of the content popularity spatial features that have been obtained. and are used as the inputs of the gated recurrent unit. The reset gate and update gate are used to determine the output of the content popularity historical memory information and new input information. The specific formulas are shown in Equations (8) and (9) as follows: （8） （9） After the known gating signal, reset the gate Extract local information from the long-term information and splice it with the content popularity sequence with spatial characteristics to obtain the current node state , as shown in Equation (10): （10） The last update memory stage uses the same update gating signal to retain the hidden state of the previous node and the information of the current node to obtain the update expression and the formula for the final prediction result, as shown in Equations (11) and (12): （11） （12） Among them, represents the hidden state at a moment, and is the weight matrix, and is the bias value, represents the reset gate, represents the gating signal, represents the current node state, is the bias term, is the non-linear activation function, represents the predicted content popularity.

7. The mobile edge computing server collaborative caching method based on the spatio-temporal graph convolution model according to claim 1 or 2, characterized in that, The process of collaborative domain division in step (4) specifically includes: (1.1)Initialize the cooperation domain: Use the hierarchical clustering method to divide the cooperation domain of MEC servers. Each MEC server is regarded as an individual cooperation domain. The Gaussian similarity of MEC servers characterized by formula (1) is used as the distance consideration criterion. Assume that the number of MEC servers in two cooperation domains is represented by and respectively. Then the distance calculation formula between cooperation domains is shown in (13): （13） (1.2) According to the obtained collaboration domain distances, find the two collaboration domains with the shortest distance. If the distance between them is less than the threshold , then merge these two collaboration domains; after obtaining the new collaboration domain, delete the above two old collaboration domains, and then use formula (13) to recalculate the distances between the new collaboration domain and other collaboration domains; (1.3) Repeat step (1.2) to merge the collaboration domains, and the termination condition is that the distance between the two closest collaboration domains is greater than the threshold value .

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