Hierarchical network topology estimation method based on information bottleneck theory

Abstract

The invention discloses a hierarchical network topology estimation method based on an information bottleneck theory, and the method comprises the steps: carrying out the merging of end-to-end traffic time sequences, introducing comparative learning, generating random perturbation for the merged end-to-end traffic time sequences in a time domain and a frequency domain, and carrying out the estimation of the hierarchical network topology. The end-to-end traffic time sequence is comprehensively represented from the perspective of time-frequency consistency analysis through comparative learning, end-to-end traffic time sequence embedding is obtained, and finally, the length of a shared path is measured by adopting the Euclidean distance embedded by the end-to-end traffic time sequence, and the network topology is recovered from bottom to top. According to the method, an information bottleneck theory is adopted, information related to topology estimation is reserved, noise is compressed, end-to-end flow time sequences are combined based on confidence, time sequence data are effectively represented from a time domain and a frequency domain at the same time by adopting comparative learning, features capable of reflecting variation difference and consistency between different time sequence data are extracted, and the time sequence data are effectively represented. And the length of the shared path is better measured, so that the network topology structure is more accurately recovered.

Description

Technical Field

[0001] The present invention belongs to the technical field of Internet network topology, and particularly relates to a hierarchical network topology estimation method based on the information bottleneck theory. Background Art

[0002] The Internet router-level network topology structure refers to the Internet router network device nodes and the connection relationships between the nodes. Mastering the accurate network topology through measurement helps to more effectively supervise the network. There are currently two mainstream Internet router-level network topology measurement methods, the method based on internal node cooperation and the method based on network tomography. The method based on internal node cooperation identifies the topology by the mutual cooperation of internal nodes in the network to feedback routing information. However, as more and more routers in the network no longer cooperate with each other, this method will generate a large number of unidentifiable anonymous routers and cannot accurately identify the topology structure. The topology identification method based on network tomography (also known as topology estimation) estimates the topology by end-to-end measurement to obtain the performance parameters of the network. Compared with the method based on internal node cooperation, this method does not require the mutual cooperation of internal nodes and is more suitable for the current complex network environment.

[0003] The Internet router-level hierarchical network topology estimation technology based on network tomography is a typical inverse problem: inferring the network topology based on the traffic time series sampled by end-to-end measurement. The network tomography hierarchical topology estimation technology performs end-to-end measurement, that is, at the source node, probe packets are sent to the destination node and the end-to-end traffic time series such as the delay and packet loss rate of the probe packets are collected. Then, the correlation of the end-to-end traffic time series is calculated to measure the shared path length, and finally the topology structure is identified based on the shared path length. The network tomography topology measurement uses the correlation of the end-to-end traffic time series to inversely deduce the hierarchical topology structure. This is because the network topology affects the traffic performance parameters (including packet loss rate, delay, flow behavior, etc.). Therefore, the correlation of the end-to-end traffic time series of different paths can reflect the length of the shared path. In addition, the hierarchical network topology structure can be easily inferred from the length of the shared path. Therefore, the key to hierarchical network topology estimation lies in accurately measuring the shared path length of different terminal node pairs.

[0004] Most methods use the time-domain features of end-to-end time series for inference. For example, the packet loss rate feature adopted in the literature "Y. Li, and Deng. K. Simultaneous topology and loss tomography via a modified themedictionary model, IEEE Transactions on Signal Processing, 2022, 70, 4239-4251", and the higher-order cumulants of delay adopted in the literature "K. D. Smith, S. Jafarpour, A. Swami, and F. Bullo. Topologyinference with multivariate cumulants: the mobius inference algorithm, IEEETransactions on Networking, 2022, 30(5)2102-2116"; there are also some methods that utilize frequency-domain features, such as the wavelet packet decomposition adopted in the literature "J. Ye, G. Fei, W, Qi, Y. Zhou, and G. Hu. Network topologyinference by exploring underlying traffic behaviors, in GLOBECOM 2023-2023IEEEGlobal Communications Conference, 2023, 1705-1710".

[0005] The key to hierarchical topology estimation in network tomography lies in how to calculate the length of the shared path through the correlation metric of the end-to-end traffic time series. If the behavior of the probe packets on the shared path is exactly the same, and the random variables of the traffic time series sampled by the probe packets on the non-shared path are completely independent, then the topology can be recovered completely accurately. However, due to the time-varying and non-stationary background traffic in the Internet network, end-to-end measurement cannot guarantee that the behavior of the probe packets on the shared path is exactly the same. And due to the limitation of the number of probe packets, the end-to-end traffic time series on the non-shared path cannot be completely independent either. Thus, the biased end-to-end traffic time series obtained by sampling is difficult to accurately measure the length of the shared path. Therefore, when the shared path is shorter and the non-shared path is longer, the noise of the end-to-end traffic time series is greater, resulting in lower correlation, making it difficult to accurately measure the length of the shared path, and further leading to poor estimation effect of the network topology structure. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a hierarchical network topology estimation method based on the information bottleneck theory, which merges end-to-end traffic time series according to confidence levels, introduces contrastive learning based on time-frequency consistency for pre-training to represent the end-to-end traffic time series, and uses the Euclidean distance to measure the length of the shared path to achieve top-down restoration of the hierarchical network topology.

[0007] The technical solution adopted by the present invention is as follows: A hierarchical network topology estimation method based on the information bottleneck theory, and the specific steps are as follows:

[0008] S1. Merging of end-to-end traffic time series based on the information bottleneck theory;

[0009] Establish an information bottleneck optimization problem, use an existing network topology estimation algorithm to initially restore the network topology, set corresponding thresholds to distinguish between parts with higher and lower confidence levels, and merge the end-to-end traffic time series corresponding to the parts with higher confidence levels.

[0010] S2. Representation of end-to-end traffic time series;

[0011] Based on step S1, introduce self-supervised contrastive learning of time-frequency consistency, perform random perturbations on the merged end-to-end traffic time series in both the time domain and the frequency domain to generate an enhanced data sample library, then encode the data samples in both the time domain and the frequency domain respectively, project them onto the same time-frequency space, and finally comprehensively represent the end-to-end traffic time series from the perspective of time-frequency consistency analysis through contrastive learning to obtain the end-to-end traffic time series embedding.

[0012] S3. Restoration of hierarchical network topology;

[0013] Based on step S2, preprocess the end-to-end traffic time series through the self-supervised contrastive learning method of time-frequency consistency to obtain the feature vector matrix of the end-to-end traffic time series, then use the Euclidean distance of the features of the end-to-end traffic time series of the destination node pairs to measure the length of the shared path to obtain the distance set between the destination node pairs. Finally, use a bottom-up approach to continuously fuse the destination node pairs with the longest shared paths to restore the network topology.

[0014] Further, the specific steps of step S1 are as follows:

[0015] Perform the merging of end-to-end traffic time series based on the information bottleneck theory, construct an information bottleneck optimization problem, that is, extract a compressed representation Z from the input end-to-end traffic time series variable X, so that it can retain the key information of the shared path length target variable Y and remove irrelevant information to the greatest extent. Then the expression of the information bottleneck optimization problem is as follows:

[0016]

[0017] Among them, β represents the trade-off parameter. The input information quantity I(X; Z) represents the information quantity inherited by Z from X, and the specific expression is as follows:

[0018]

[0019] Among them, p(·) represents the probability of ·. The target information quantity I(Z; Y) represents the useful information quantity that Z has for predicting Y.

[0020] Use the existing network topology estimation algorithm to initially restore the network topology. Set the input as the source node s, n destination nodes {d1, d2, …, d i , …, d n}}, and the set of end-to-end traffic time series random variables from the source node s to the destination nodes {x1, x2, …, x n}}. The output is the network topology T = (N, E).

[0021] Among them, N represents the set of nodes in the network topology, and E represents the set of edges.

[0022] Then establish a shared path length model. Set that there are w intermediate nodes f1, f2, …, f w in the model, and each intermediate node f g has a set N g of h G destination child nodes. path(s, f g ) is the path from s to f g , that is, the shared path from s to the destination child node pair. For any two different destination nodes d G and d i in N j , and any destination node d G that does not belong to N k , f r is the parent node of f g and d k . path(s, f r ) is the path from s to f r , that is, the shared path from s to the node pair {d i , d k} or the node pair {d j , d k}. Then the expressions of the end-to-end traffic time series random variables corresponding to the destination nodes d i , d j and d k are as follows:

[0023]

[0024] Among them, and respectively represent path(s,f r ), path(f r ,f g ), path(f g ,d i ), path(f g ,d j ), and path(f r ,d k ), which correspond to the flow time series random variables. The flow time series random variable corresponding to the shared path of the node pair {d i ,d j} is The flow time series random variables corresponding to the non - shared paths are and The flow time series random variable corresponding to the shared path of the node pair {d i ,d k} is The flow time series random variables corresponding to the non - shared paths are and

[0025] Then set the corresponding thresholds to distinguish the parts with higher and lower confidence levels in topology recovery. And for any two different destination nodes d G and d i in N j , as well as any destination node d G that does not belong to N k , if the lengths of the shared paths of {d i ,d k} and {d j ,d k} are the same and the length values are different, then set γ% of the average length value of the shared paths as the threshold, and judge all the shared paths from bottom to top, and merge the end - to - end flow time series corresponding to the parts with higher confidence levels.

[0026] Among them, the value of γ is set according to the actual situation. Judge whether the absolute value of the difference between the node pair corresponding to the shared path of each intermediate node f r and the average length value is greater than the pre - set threshold. If so, it is considered that the confidence level of the topology recovery part corresponding to this shared path is low; if not, it is considered that the confidence level of the corresponding topology recovery part is high. Retain the topology recovery part corresponding to the shared path and merge the end - to - end flow time series random variables x l of all the destination nodes corresponding to the shared path. After merging, the random variable The expression is as follows:

[0027]

[0028] Further, the specific steps of step S2 are as follows:

[0029] Based on step S1, after the end-to-end traffic time series is merged by confidence-driven, an end-to-end traffic time series characterization model is constructed to perform contrastive learning on the end-to-end traffic time series.

[0030] Among them, the characterization model includes: a time-domain encoder G T , a frequency-domain encoder G F , and two spatial projection modules R T and R F . The input of the model is end-to-end traffic time series of different categories, including: delay, packet loss rate, and traffic behavior.

[0031] In the time-domain encoder G T and the frequency-domain encoder G F , the model first generates an enhanced data sample library in the time domain and the frequency domain respectively through a series of random perturbations, and then encodes the original data samples and the enhanced data samples in the time domain and the frequency domain respectively. In the two spatial projection modules R T and R F , the model maps the encodings in the time domain and the frequency domain to the same time-frequency space respectively. Finally, the model sets the loss functions in the time domain, the frequency domain, and the time-frequency domain, and adopts contrastive learning pre-training, and adopts the strategy of pulling positive samples closer and negative samples farther in the time domain, the frequency domain, and the time-frequency space to learn the time-frequency consistency features of the data, and finally outputs the embedding V of the end-to-end traffic time series.

[0032] Further, in step S2, the end-to-end traffic time series characterization model is specifically as follows:

[0033] (1) End-to-end traffic time series time-domain encoder G T ;

[0034] For the i-th end-to-end time series x i , its time domain representation is Enhance it in the time domain. By randomly combining a series of enhancement operations, generate an enhancement library for each x i in the time domain, and obtain the samples

[0035] Among them, the enhancement operations include: randomly combining jitter, scaling, or time shift for .

[0036] After enhancing all end-to-end time series, the time series and the enhancement library are input into the Transformer encoder. The Transformer encoder takes the end-to-end time series as input, converts it into a high-dimensional representation, and uses contrastive learning to extract the features of the time series in the time domain while using the Transformer encoder.

[0037] For an end-to-end time series Randomly select an enhanced sample Input it into a contrastive time encoder to obtain the embeddings before and after data enhancement and For the j-th end-to-end time series Take as a positive sample pair, and as a negative sample pair.

[0038] Then set the loss function in the time domain space to maximize the similarity between positive sample pairs and minimize the similarity between negative sample pairs. Use NT-Xent as the distance function in contrastive learning to define the encoder loss function in the time domain, and the expression is as follows:

[0039]

[0040] where sim(u, v) = u T v / ||u||||v|| represents the cosine similarity between u and v, τ represents the time scale adjustment parameter, u T represents the transpose of u, and X represents all input end-to-end traffic time series.

[0041] (2) End-to-end traffic time series frequency domain encoder G F ;

[0042] In the frequency domain encoder, similar to the time domain encoder, by randomly combining a series of enhancement operations, generate an enhancement library for each x in the frequency domain i First, generate frequency domain data by performing Fourier transform on Then perturb the spectrum by adding or removing frequency components to obtain the enhanced samples and and Respectively pass through the frequency domain encoder G composed of Transformers F to obtain the representations before and after frequency domain data enhancement and

[0043] Then, define the representations before and after the same sample data augmentation as positive sample pairs, and the embeddings between different samples as negative sample pairs. And use NT-Xent as the distance function to define the encoder loss function in the specific frequency domain. The expression is as follows:

[0044]

[0045] (3) Time-frequency consistency embedding;

[0046] Respectively project the time-domain embedding T and the frequency-domain-based embedding F into the same time-frequency space through two projection modules R and to obtain a positive sample pair Similarly, three negative sample pairs and

[0047] can be obtained. Among them, the time-domain embedding and the frequency-domain embedding

[0048] In the same time-frequency space, the Euclidean distance is used to represent the distance between two embedding vectors, that is represents and The distance between them. Similarly, the distances between the embedding vectors of three negative sample pairs and are obtained respectively and

[0049] Set a new loss function L C,i in the time-frequency space. The expression is as follows:

[0050]

[0051] Among them, S pair represents the distances of the embeddings of three negative sample pairs based on the time-frequency domain. represents one of S pair Each pair of them has at least one embedding obtained from the data-augmented sample. δ represents a predefined constant used to keep the negative samples away from each other.

[0052] The characterization model includes three loss functions: time-domain-based, frequency-domain-based, and time-frequency consistency loss. When the entire model is trained, the pre-training loss L TF-C,i of the entire model is defined as follows:

[0053] L TF-C,i = λ(L T,i + L F,i)+(1-λ)L C,i

[0054] Among them, λ controls the relative importance of the contrast and consistency losses, and the sum of the losses of all pre-training samples is the total loss.

[0055] After the training of the entire model is completed, the final embedded feature vector matrix of all end-to-end traffic time series is obtained

[0056] Among them, represents the real number field, m represents the dimension of the embedding vector of each end-to-end traffic time series, and n represents the number of destination nodes, that is, the number of corresponding end-to-end traffic time series.

[0057] Furthermore, the specific steps of step S3 are as follows:

[0058] S31. Input data;

[0059] The input data includes: source node s, destination node set D (|D|≥2), embedded feature vector matrix V, and merging threshold parameter Δ>0.

[0060] S32. Initialize the estimated hierarchical network topology;

[0061] The initialization includes: the edge set in the topology The node set N of the topology = {s}, calculate the Euclidean distance between pairwise vectors in the feature vector matrix, and obtain the set dis(D 2 ) of the length metrics of the shared paths of the destination node pairs.

[0062] S33. Fuse node pairs;

[0063] Traverse the destination point set D, select the destination node pair {d i , d j} with the smallest similarity metric distance dis(d i , d j ), and at the same time construct the parent node f(d i , d j ). i , d j ) of the node pair {d

[0064] S34. Update the set;

[0065] Update the remaining destination node set, the edge set and the node set of the estimated topology respectively, delete the node pair {d i , d j}, D = D / {d i , d j}; add the node pair {d i , d j} Add the estimated topological node set, N = N ∪ {d i , d j}; Finally, add two edges between the parent node and the node pair to the estimated topological edge set, E = E ∪ {(f(d i , d j ), d i ), (f(d i , d j ), d j )}.

[0066] S35. Merge neighbor nodes;

[0067] Based on step S34, continue to search for eligible nodes in the remaining destination point set D as neighbor nodes of the node pair {d i , d j}. By traversing the set D, determine whether there exists d k ∈ D, and the similarity metric distance between it and the two nodes in the node pair is less than the threshold parameter Δ, that is, determine whether it satisfies:

[0068] If it exists, add it as a neighbor node of the node pair {d i , d j} to the topological set, and update the output data: D = D / {d k}, N = N ∪ {d k}, E = E ∪ {(f(d i , d j ), d k ); if not, directly proceed to step S36.

[0069] S36. Update the distance;

[0070] Update the distance ρ between the parent node f(d i , d j ) of the constructed node pair {d i , d j} and the remaining nodes in D. Traverse all the nodes in D. For Calculate the distance ρ, and the expression is as follows:

[0071]

[0072] Among them, c(f(d i , d j )) represents all the leaf nodes of the topology with the constructed node f(d i , d j ) as the root node. Finally, update D = D ∪ {f(d i , d j )}.

[0073] S37. Determine whether the aggregation is completed;

[0074] If there is only one node d left in D k , then N = N ∪ {d k}, E = E ∪ {(s, d k )}; otherwise, repeat steps S33 to S36.

[0075] S38. Output the estimated hierarchical topology;

[0076] The estimated hierarchical topology T = (N, E), which is the restored network topology. And use the parameter Δ to determine whether there are other nodes in the set D that belong to the same class as the aggregation node. The expression is as follows:

[0077]

[0078] where α ∈ (0, 1].

[0079] Advantages of the present invention: The present invention discloses a method for estimating a hierarchical network topology based on the information bottleneck theory. First, end-to-end traffic time series are merged based on the information bottleneck theory, and then contrastive learning is introduced to generate random perturbations for the merged end-to-end traffic time series in both the time domain and the frequency domain to enhance the data. Through contrastive learning, the end-to-end traffic time series are more comprehensively characterized from the perspective of time-frequency consistency analysis to obtain the embedding of the end-to-end traffic time series. Finally, the Euclidean distance of the embedding of the end-to-end traffic time series is used to measure the length of the shared path and the network topology is restored from bottom to top. The method of the present invention overcomes the problems of the existing hierarchical network topology estimation methods being limited by the bias caused by end-to-end measurements in non-stationary networks, and it is difficult to accurately measure the length of the shared path separately from the time domain or the frequency domain, resulting in inaccurate topology estimation, especially the topology structure closer to the source node is more inaccurate. The method of the present invention adopts the information bottleneck theory, tries to retain the information related to topology estimation, compress the noise, merge the end-to-end traffic time series based on confidence, and uses contrastive learning to effectively characterize the time series data in both the time domain and the frequency domain, effectively extracting the features that can reflect the differences and consistencies in the changes between different time series data, better measuring the length of the shared path, and thus more accurately restoring the network topology structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a flowchart of a method for estimating a hierarchical network topology based on the information bottleneck theory of the present invention.

[0081] Figure 2 It is a schematic diagram of the shared path length model in an embodiment of the present invention.

[0082] Figure 3 It is a schematic diagram of the end-to-end traffic time series characterization model in an embodiment of the present invention. Detailed implementation manners

[0083] The method of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0084] As Figure 1 shown, the flowchart of a hierarchical network topology estimation method based on the information bottleneck theory of the present invention is as follows:

[0085] S1. Merging of end-to-end traffic time series based on the information bottleneck theory;

[0086] Establish an information bottleneck optimization problem, initially restore the network topology using an existing network topology estimation algorithm, set corresponding thresholds to distinguish between parts with higher and lower confidence levels, and merge the end-to-end traffic time series corresponding to the parts with higher confidence levels.

[0087] S2. Characterization of end-to-end traffic time series;

[0088] Based on step S1, introduce self-supervised contrastive learning of time-frequency consistency, perform random perturbations on the merged end-to-end traffic time series in both the time domain and the frequency domain to generate an enhanced data sample library, then encode the data samples in both the time domain and the frequency domain respectively, project them onto the same time-frequency space, and finally comprehensively characterize the end-to-end traffic time series from the perspective of time-frequency consistency analysis through contrastive learning to obtain the end-to-end traffic time series embedding.

[0089] S3. Restoration of hierarchical network topology;

[0090] Based on step S2, preprocess the end-to-end traffic time series through the self-supervised contrastive learning method of time-frequency consistency to obtain the feature vector matrix of the end-to-end traffic time series, then use the Euclidean distance of the features of the end-to-end traffic time series of the destination node pairs to measure the shared path length to obtain the distance set between the destination node pairs. Finally, use a bottom-up approach to continuously fuse the destination node pairs with the longest shared paths to restore the network topology.

[0091] In this embodiment, the specific steps of step S1 are as follows:

[0092] The merging of end-to-end traffic time series is a method based on the information bottleneck theory. By merging the end-to-end traffic time series with high confidence, redundant information is reduced, the information utilization rate is improved, more robust structural information is retained, and the discrimination ability is enhanced. The information bottleneck principle is a theoretical framework for information compression and representation learning, which describes an optimal representation learning method, that is, while retaining the necessary information of the target variable, as much irrelevant information as possible is discarded.

[0093] Based on the information bottleneck theory, perform end-to-end traffic time series merging, and construct an information bottleneck optimization problem, that is, extract a compressed representation Z from the input end-to-end traffic time series variable X, so that it can not only retain the key information of the shared path length target variable Y, but also remove irrelevant information to the greatest extent. Then the expression of the information bottleneck optimization problem is as follows:

[0094]

[0095] Among them, β represents the trade-off parameter, which is used to adjust the balance between retaining information related to the target variable and compressing information. And the input information amount I(X;Z) represents the information amount that Z inherits from X, and it is expected to be as small as possible in order to remove redundant information. The specific expression is as follows:

[0096]

[0097] Among them, p(·) represents the probability of ·. The target information amount I(Z;Y) represents the useful information amount that Z has for predicting Y, and it is expected to be as large as possible to ensure that Z can effectively predict Y.

[0098] Use the existing network topology estimation algorithm to initially restore the network topology. Set the input as the source node s, n destination nodes {d1, d2, …, d i , …, d n}, and the set of end-to-end traffic time series random variables {x1, x2, …, x n} from the source node s to the destination nodes. The output is the network topology T = (N, E).

[0099] Among them, N represents the set of nodes in the network topology, and E represents the set of edges.

[0100] Then establish a shared path length model. Set that there are w intermediate nodes f1, f2, …, f w in the model. Each intermediate node f g has a set N g of h G destination child nodes. path(s, f g ) is the path from s to f g , that is, the shared path from s to the destination child node pair. For any two different destination nodes d G and d i in N j , and any destination node d G that does not belong to N k , f r is the parent node of f g and d k . path(s, f r ) is the path from s to f rThe path, i.e., from s to the node pair {d i , d k} or the node pair {d j , d k}. Then the end-to-end traffic time series random variable expressions corresponding to the destination nodes d i , d j and d k are as follows:

[0101]

[0102] Among them, and respectively represent the traffic time series random variables corresponding to path(s, f r ), path(f r , f g ), path(f g , d i ), path(f g , d j ) and path(f r , d k ). The traffic time series random variable corresponding to the shared path of the node pair {d i , d j} is The traffic time series random variable corresponding to the non-shared path is and The traffic time series random variable corresponding to the shared path of the node pair {d i , d k} is The traffic time series random variable corresponding to the non-shared path is and

[0103] The shared path length model established in this embodiment is as Figure 2 shown. In the figure, s is the source node, d i , d j and d k are the destination nodes, f1 is the parent node of d i and d j , and f2 is the parent node of f1 and d k . path(s, f1) represents the path from s to f1, i.e., the shared path from s to the node pair {d i , d j}, and path(s, f2) represents the path from s to f2, i.e., the path from s to the node pair {d i , d k} or the node pair {d j , d k} of the shared path, then Figure 2 in the destination node d i , d j and d k The corresponding end-to-end traffic time series random variable expressions are as follows:

[0104] x i = y1 + y2 + y3

[0105] x j = y1 + y2 + y4

[0106] x k = y1 + y5

[0107] Among them, y1, y2, y3, y4, and y5 respectively represent the traffic time series random variables corresponding to path(s,f1), path(f1,f2), path(f2,d i ), path(f2,d j ), and path(f1,d k ). The traffic time series random variable corresponding to the shared path of the node pair {d i , d j} is y1 + y2, and the traffic time series random variables corresponding to the non-shared paths are y3 and y4. The traffic time series random variable corresponding to the shared path of the node pair {d i , d k} is y1, and the traffic time series random variables corresponding to the non-shared paths are y2 + y3 and y5.

[0108] Then set corresponding thresholds to distinguish the parts with higher and lower confidence levels in topology recovery, and for any two different destination nodes d G in N i and d j , as well as any destination node d G that does not belong to N k , {d i , d k} and {d j , d k} have the same shared path length, but due to the influence of noise, these two length values are often different. Then set γ% of the average length value of the shared path as the threshold, and judge all shared paths from bottom to top, and merge the end-to-end traffic time series corresponding to the parts with higher confidence levels.

[0109] Among them, the value of γ is set according to the actual situation. Judge each intermediate node f rWhether the absolute value of the difference between the node pair corresponding to the shared path and the average length value is greater than a preset threshold. If so, it is considered that the confidence of the topology recovery part corresponding to the shared path is low; otherwise, it is considered that the confidence of the corresponding topology recovery part is high. Retain the topology recovery part corresponding to the shared path and merge the end-to-end traffic time series random variables x of all the destination nodes corresponding to the shared path l , the merged random variable The expression is as follows:

[0110]

[0111] In this embodiment, the traffic time series random variable corresponding to the shared path of the node pair {d i , d j} is y1 + y2, and the traffic time series random variables corresponding to the non-shared paths are y3 and y4. The traffic time series random variable corresponding to the shared path of the node pair {d i , d k} is y1, and the traffic time series random variables corresponding to the non-shared paths are y2 + y3 and y5. Compared with the node pair {d i , d j}, the node pair {d i , d k} has a longer shared path, and the correlation of the traffic time series random variable corresponding to the shared path is stronger. At the same time, the non-shared path is shorter, and the noise of the traffic time series random variable corresponding to the non-shared path is smaller. Therefore, theoretically, the shared path length metric of the node pair {d i , d j} should be more accurate than the shared path length metric of the node pair {d i , d k}. Therefore, from bottom to top, the longer the shared path, the more accurate its shared path length metric.

[0112] Then Figure 2 in the topology shown, for the destination node pair {d i , d j} corresponding to path(s, f2), the shared path is not processed. Then, from bottom to top, for path(s, f1), if the absolute value of the difference between the node pair {d i , d k} or {d j , d k} corresponding to path(s, f1) and the average length value is greater than the set threshold, it is considered that the confidence of the topology recovery part corresponding to path(s, f1) is low. If the node pair {d i , d k} and {d j , dk If the absolute value of the difference between the shared path length of {} and the average length value is less than the threshold, it is considered that the confidence of the topology recovery part corresponding to path(s,f1) is relatively high, and the topology recovery part corresponding to path(s,f1) is retained and the destination node d corresponding to path(s,f1) is merged i 、d j and d k of the end-to-end traffic time series random variable x i 、x j and x k ,After merging, the random variable z f1 The expression is as follows:

[0113] z f1 =x i +x j +x k

[0114] =3y1+2y2+y3+y4+y5

[0115] After merging the end-to-end traffic time series random variables, the noise contribution of a single variable is reduced, the overall variance becomes smaller, and finally the features become more robust and are not interfered by the random fluctuations of individual time series. By removing some local noise, only the more important global similarity information is retained for more accurate contrast learning embedding representation in the future.

[0116] In this embodiment, the specific steps of step S2 are as follows:

[0117] Based on step S1, after merging the end-to-end traffic time series driven by confidence, a end-to-end traffic time series representation model is constructed to perform contrast learning on the end-to-end traffic time series.

[0118] Among them, the representation model includes: a time-domain encoder G T ,a frequency-domain encoder G F ,and two spatial projection modules R T and R F 。The input of the model is end-to-end traffic time series of different categories, including: delay, packet loss rate, traffic behavior.

[0119] The end-to-end traffic time series is a typical non-stationary time series, and its distribution parameters and patterns change over time. A self-supervised pre-training method based on time-frequency consistency is introduced to perform data augmentation on the end-to-end traffic time series and extract complex features. The objectives of contrastive learning and information bottleneck are similar, learning a representation Z from the input data X such that Z only retains useful information while removing noise and irrelevant factors. Z can effectively distinguish different topological structures. Contrastive learning will naturally compress the input information by the model. Due to data augmentation, the model learns that details unimportant for the target task can be ignored, thus reducing I(X; Z). Contrastive learning also enhances the mutual information to retain useful information. By positive sample contrast (different perspectives of the same sample should be close), maximizing I(Z; Y) can still distinguish meaningful patterns. In the network topology recovery task, this means that the model can more robustly capture the shared features on the end-to-end path while ignoring individual measurement noises.

[0120] In the time-domain encoder G T and the frequency-domain encoder G F , the model first generates an augmented data sample library in the time domain and frequency domain respectively through a series of random perturbations, and then encodes the original data samples and augmented data samples in the time domain and frequency domain respectively. In the two spatial projection modules R T and R F , the model maps the encodings in the time domain and frequency domain to the same time-frequency space simultaneously and optimizes to reduce the Euclidean distance between the embeddings in the time domain and frequency domain of the same sample. Finally, the model adopts contrastive learning pre-training by setting the loss functions in the time domain, frequency domain, and time-frequency domain, and takes the strategy of pulling positive samples closer and negative samples farther in the time domain, frequency domain, and time-frequency space to learn the time-frequency consistency features of the data, learning a low-dimensional and compact feature representation Z, and finally outputting the embedding of the end-to-end traffic time series, which can effectively extract the features reflecting the differences and consistencies of different time series changes, so as to more accurately measure the length of the shared path.

[0121] As Figure 3 shown, in this embodiment, in step S2, the end-to-end traffic time series characterization model is specifically as follows:

[0122] (1) The end-to-end traffic time series time-domain encoder G T ;

[0123] For the i-th end-to-end time series x i , its time-domain representation is Augment it in the time domain. To more robustly generate the embeddings in the time domain and frequency domain, by randomly combining a series of augmentation operations, generate an augmentation library for each x i in the time domain to expose the model to complex time dynamics and obtain samples

[0124] Among them, the enhancement operations include: Randomly combining jitter, scaling, or time shift.

[0125] After enhancing all end-to-end time series, the time series and the enhancement library are input into the Transformer encoder. The Transformer encoder was originally designed to process natural language, and its attention mechanism and multi-layer architecture make it very suitable for processing time series. The Transformer encoder inputs the end-to-end time series and then transforms it into high-dimensional representations that can capture the dependencies and patterns between different time points of the time series, thereby extracting the features in the sequence. Then, the Transformer encoder uses contrastive learning to simultaneously mine the features in the time domain of the time series.

[0126] For an end-to-end time series Randomly select an enhanced sample Input it into a contrastive time encoder to obtain the embeddings before and after data enhancement And Since the embeddings of the same sample before and after data enhancement should be closer, while the embeddings between different samples are more distant, for the j-th end-to-end time series Regard As a positive sample pair, And As a negative sample pair.

[0127] Then set the loss function in the time domain space to maximize the similarity between positive sample pairs and minimize the similarity between negative sample pairs. The NT-Xent is used as the distance function in contrastive learning to define the encoder loss function in the time domain, and the expression is as follows:

[0128]

[0129] Among them, sim(u, v) = u T v / ||u||||v|| represents the cosine similarity between u and v, τ represents the time scale adjustment parameter, u T Represents the transpose of u, and X represents all input end-to-end traffic time series.

[0130] (2) End-to-end traffic time series frequency domain encoder G F ;

[0131] In the frequency domain encoder, similar to the time domain encoder, by randomly combining a series of enhancement operations, an enhancement library is generated for each x in the frequency domain, in order to expose the model to complex frequency dynamics. First, it is transformed by Fourier transform i to generate an enhancement library, in order to expose the model to complex frequency dynamics. First, it is transformed by Fourier transform Generate frequency-domain data Then, perturb the spectrum by adding or deleting frequency components to obtain an enhanced sample and respectively pass through the frequency-domain encoder G composed of transformers F to obtain the representations before and after frequency-domain data augmentation and

[0132] Then, define the representations before and after data augmentation of the same sample as a positive sample pair, and the embeddings between different samples as negative sample pairs. And use NT-Xent as the distance function to define the encoder loss function for the specific frequency domain, and the expression is as follows:

[0133]

[0134] (3) Time-frequency consistency embedding;

[0135] To make the embedding based on the time domain as close as possible to the embedding based on the frequency domain respectively pass through two projection modules R T and R F to project the time-domain embedding and the frequency-domain embedding into the same time-frequency space, and then obtain a positive sample pair Similarly, three negative sample pairs can be obtained and

[0136] Among them, the time-domain embedding the frequency-domain embedding

[0137] In the same time-frequency space, use the Euclidean distance to represent the distance between two embedding vectors, that is represents and the distance between them. Similarly, the distances between the embedding vectors of the three negative sample pairs and are obtained respectively and

[0138] To try to shorten the distance between the time-domain and frequency-domain embeddings of the same transformed samples as much as possible, while pushing away the distances between different transformations, a new loss function L C,i is set in the time-frequency space, and the expression is as follows:

[0139]

[0140] Among them, S pairDenotes the distances of the embeddings in the time-frequency domain for three negative sample pairs. Denotes S pair One of them, and for each pair, at least one of the embeddings is obtained from the data-augmented samples. δ represents a predefined constant used to keep the negative samples apart.

[0141] The characterization model includes three loss functions: time-domain based, frequency-domain based, and time-frequency consistency loss. When the entire model is being trained, the pre-training loss L of the entire model is defined. TF-C,i The expression is as follows:

[0142] L TF-C,i = λ(L T,i + L F,i ) + (1 - λ)L C,i

[0143] Where λ controls the relative importance of the contrast and consistency losses, and the sum of the losses of all pre-training samples is the total loss.

[0144] When the training of the entire model is completed, the final embedding feature vector matrix of all end-to-end traffic time series is obtained.

[0145] Where, Denotes the real number field, m represents the dimension of the embedding vector of each end-to-end traffic time series, and n represents the number of destination nodes, that is, the number of corresponding end-to-end traffic time series.

[0146] In this embodiment, step S3 is specifically as follows:

[0147] S31. Input data;

[0148] The input data includes: source node s, destination node set D (|D| ≥ 2), embedding feature vector matrix V, and merging threshold parameter Δ > 0.

[0149] S32. Initialize the estimated hierarchical network topology;

[0150] The initialization includes: the edge set in the topology The node set N of the topology = {s}, calculate the Euclidean distances between pairwise vectors in the feature vector matrix, and obtain the set dis(D 2 ) of the length metrics of the shared paths for destination node pairs.

[0151] S33. Fuse node pairs;

[0152] Traverse the destination point set D, and select the destination node pair {d i , d j} with the smallest similarity metric distance dis(d i , dj}, and construct the node pair {d i , d j} with its parent node f(d i , d j ).

[0153] S34. Update the sets;

[0154] Respectively update the remaining destination node set, the edge set and the node set of the estimated topology, and delete the node pair {d i , d j}, D = D / {d i , d j}; Add the node pair {d i , d j} to the estimated topology node set, N = N ∪ {d i , d j}; Finally, add two edges between the parent node and the node pair to the estimated topology edge set, E = E ∪ {(f(d i , d j ), d i ), (f(d i , d j ), d j )}.

[0155] S35. Fuse neighbor nodes;

[0156] Based on step S34, continue to search for eligible nodes in the remaining destination point set D as the neighbor nodes of the node pair {d i , d j}. Determine whether there is a d k ∈ D by traversing the set D, and the similarity metric distance between it and the two nodes in the node pair is less than the threshold parameter Δ, that is, determine whether it satisfies:

[0157] If it exists, use it as the neighbor node of the node pair {d i , d j} and add it to the topology set, and update the output data: D = D / {d k}, N = N ∪ {d k}, E = E ∪ {(f(d i , d j ), d k )}; if not, directly proceed to step S36.

[0158] S36. Update the distance;

[0159] Update the parent node f(d i , d j} that constructs the node pair {d i , dj ) The distance ρ from the remaining nodes in D. Traverse all the nodes in D. For Calculate the distance ρ. The expression is as follows:

[0160]

[0161] Among them, c(f(d i , d j )) represents all the leaf nodes of the topology of the constructed node f(d i , d j ). Finally, update D = D ∪ {f(d i , d j )}.

[0162] S37. Determine whether the aggregation ends;

[0163] If there is only one remaining node d in D k , then N = N ∪ {d k}, E = E ∪ {(s, d k )}; otherwise, repeat steps S33 to S36.

[0164] S38. Output the estimated hierarchical topology;

[0165] The estimated hierarchical topology T = (N, E), that is, the restored network topology. And use the parameter Δ to determine whether there are other nodes in the set D that belong to the same class as the aggregated node. Adjusting the value of Δ can estimate the general hierarchical topology structure. The expression is as follows:

[0166]

[0167] Among them, α ∈ (0, 1], and the value is taken according to the actual situation, which is used to adjust the value of the threshold Δ.

[0168] In summary, compared with the existing methods, the method of the present invention is based on the information bottleneck theory, combines the end-to-end traffic time series of the parts with higher confidence in the existing topology estimation, thereby removing part of the local noise and improving the stability of feature extraction. And the method of the present invention introduces a self-supervised pre-training method based on time-frequency consistency, performs data augmentation on the end-to-end traffic time series and extracts complex time-frequency domain features, enabling the model to more robustly capture the shared features on the end-to-end path, while ignoring the individual measurement noises on the shared path or non-shared path, effectively characterizing the length of the shared path and reducing the error brought by end-to-end measurement.

[0169] Those of ordinary skill in the art will realize that the embodiments described herein are to assist the reader in understanding the principles of the present invention and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, various modifications and variations can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A hierarchical network topology estimation method based on information bottleneck theory, the specific steps are as follows: S1, end-to-end traffic time series merging based on information bottleneck theory; Establish an information bottleneck optimization problem, use the existing network topology estimation algorithm to preliminarily restore the network topology, set corresponding thresholds to distinguish between parts with higher and lower confidence, and merge the end-to-end traffic time series corresponding to the parts with higher confidence; S2, end-to-end traffic time series characterization; Based on step S1, self-supervised contrastive learning of time-frequency consistency is introduced to perform random perturbations on the merged end-to-end traffic time series in the time domain and frequency domain respectively to generate an enhanced data sample library. The data samples are then encoded in the time domain and frequency domain respectively and then projected into the same time-frequency space. Finally, contrastive learning is used to comprehensively characterize the end-to-end traffic time series from the perspective of time-frequency consistency analysis to obtain the end-to-end traffic time series embedding. S3, hierarchical network topology recovery; Based on step S2, the end-to-end traffic time series is preprocessed by a time-frequency consistent self-supervised contrastive learning method to obtain a feature vector matrix of the end-to-end traffic time series. Then, the Euclidean distance of the characteristics of the end-to-end traffic time series of the destination node pairs is used to measure the shared path length to obtain the distance set between the destination node pairs. Finally, the network topology is restored by continuously fusing the destination node pairs with the longest shared path from the bottom up.

2. A hierarchical network topology estimation method based on information bottleneck theory according to claim 1, characterized in that: The step S1 is specifically as follows: Based on the information bottleneck theory, the end-to-end traffic time series are merged and the information bottleneck optimization problem is constructed, that is, a compressed representation Z is extracted from the input end-to-end traffic time series variable X, so that it can retain the key information of the shared path length target variable Y and remove irrelevant information to the greatest extent. The expression of the information bottleneck optimization problem is as follows: Among them, β represents the trade-off parameter; and the input information I(X; Z) represents the amount of information inherited by Z from X. The specific expression is as follows: Among them, p(·) represents the probability; the target information I(Z;Y) represents the useful information of Z for predicting Y; The existing network topology estimation algorithm is used to preliminarily restore the network topology, setting the input as the source node s, n destination nodes {d1, d2, …, d i ,…,d n }, the set of random variables {x1,x2,…,x n }, the output is the network topology T = (N, E); Among them, N represents the node set of the network topology, and E represents the edge set; Then establish a shared path length model, assuming that there are w intermediate nodes f1, f2, ..., f w , each intermediate node f g There is h g The set of N destination child nodes G ,path(s,f g ) is s to f g , that is, the shared path from s to the destination child node pair; for N G Any two different destination nodes d i and d j , and any one that does not belong to N G The destination node d k , f r f g and d k The parent node of path(s,f r ) is s to f r The path from s to the node pair {d i ,d k } or node pair {d j ,d k } shared path; then the destination node d i d j and d k The corresponding end-to-end traffic time series random variable expressions are as follows: in, and Respectively represent path(s,f r )、path(f r ,f g )、path(f g ,d i )、path(f g ,d j ) and path(f r ,d k ) corresponds to the random variable of the traffic time series; the node pair {d i ,d j The traffic time series random variable corresponding to the shared path of} is The traffic time series random variable corresponding to the non-shared path is and Node pair {d i ,d k The traffic time series random variable corresponding to the shared path of} is The traffic time series random variable corresponding to the non-shared path is and Then set the corresponding threshold to distinguish the parts with higher and lower confidence in the topology recovery, and for N G Any two different destination nodes d i and d j , and does not belong to N G Any destination node d k , {d i ,d k } and {d j ,d k }, if the lengths of the shared paths are consistent but different, then γ% of the average length of the shared paths is set as the threshold, all shared paths are judged from the bottom up, and the end-to-end traffic time series corresponding to the parts with higher confidence are merged; The value of γ is set according to the actual situation; determine each intermediate node f r Whether the absolute value of the difference between the node pair corresponding to the shared path and the average length value is greater than the preset threshold, if so, it is considered that the confidence of the topology recovery part corresponding to the shared path is low, otherwise it is considered that the corresponding topology recovery part has a high confidence; retain the topology recovery part corresponding to the shared path and merge the end-to-end traffic time series random variables x of all destination nodes corresponding to the shared path l , the combined random variable The expression is as follows:

3. The hierarchical network topology estimation method based on information bottleneck theory according to claim 1 is characterized in that: The step S2 is specifically as follows: Based on step S1, after the confidence-driven end-to-end traffic time series are merged, an end-to-end traffic time series representation model is constructed to perform comparative learning on the end-to-end traffic time series; The representation model includes: a time domain encoder G T , a frequency domain encoder G F , and two spatial projection modules R T and R F ;The input of the model is different categories of end-to-end traffic time series, including: delay, packet loss rate, and traffic behavior; In the time domain encoder G T and frequency domain encoder G F In the model, the model first generates an enhanced data sample library in the time domain and frequency domain through a series of random perturbations, and then encodes the original data samples and the enhanced data samples in the time domain and frequency domain respectively; T and R F In the model, the encoding of time domain and frequency domain are mapped to the same time-frequency space respectively; finally, the model sets the loss functions in time domain, frequency domain and time-frequency domain, adopts contrastive learning pre-training, and adopts the strategy of pulling positive samples closer and negative samples farther away in time domain, frequency domain and time-frequency space to learn the characteristics of time-frequency consistency of data, and finally outputs the embedding V of end-to-end traffic time series.

4. The hierarchical network topology estimation method based on information bottleneck theory according to claim 1 is characterized in that: The step S3 is specifically as follows: S31, input data; The input data includes: source node s, destination node set D (|D|≥2), embedded feature vector matrix V, and merge threshold parameter Δ>0; S32, initializing the estimated hierarchical network topology; Initialization includes: edge set in topology The node set N = {s} of the topology is used to calculate the Euclidean distance between two vectors in the eigenvector matrix, and obtain the length measurement set dis(D 2 ); S33, fusion node pair; Traverse the destination point set D and select the similarity metric distance dis(d i ,d j )The smallest destination node pair {d i ,d j }, and construct node pair {d i ,d j }'s parent node f(d i ,d j ); S34, update the set; Update the remaining destination node set, the edge set and node set of the estimated topology respectively, and delete the node pair {d i ,d j }, D=D / {d i ,d j }; Set the node pair {d i ,d j }Add the estimated topological node set, N=N∪{d i ,d j }; Finally, add the two edges of the parent node and the node pair to the estimated topological edge set, E = E∪{(f(d i ,d j ),d i ),(f(d i ,d j ),d j )}; S35, merge neighbor nodes; Based on step S34, continue to search for nodes that meet the conditions in the remaining destination point set D as node pairs {d i ,d j }'s neighbor node; by traversing the set D, determine whether there is d k ∈D, its similarity measurement distance with the two nodes in the node pair is less than the threshold parameter Δ, that is, whether it satisfies: If it exists, it is used as a node pair {d i ,d j }’s neighbor nodes are added to the topology set and the output data is updated: D = D / {d k }, N=N∪{d k }, E=E∪{(f(d i ,d j ),d k )}, if not, proceed directly to step S36; S36, updating the distance; Update the construction node pair {d i ,d j }'s parent node f(d i ,d j ) and the distance ρ between the remaining nodes in D, traverse all the nodes in D, for Calculate the distance ρ, the expression is as follows: Among them, c(f(d i ,d j )) represents the node f(d i ,d j ) represents all the leaf nodes of the topology of the root node, and finally updates D=D∪{f(d i ,d j )}; S37, judging whether the polymerization is completed; If there is only one node d left in D k , then N=N∪{d k }, E=E∪{(s,d k )}; otherwise, repeat steps S33 to S36; S38, outputting the estimated hierarchical topology; The estimated hierarchical topology T = (N, E) is the restored network topology. The parameter Δ is used to determine whether there are other nodes in the set D that belong to the same class as the aggregated node. The expression is as follows: Among them, α∈(0,1].

5. The hierarchical network topology estimation method based on information bottleneck theory according to claim 3 is characterized in that: In step S2, the end-to-end traffic time series characterization model is specifically as follows: (1) End-to-end traffic time series time domain encoder G T ; For the i-th end-to-end time series x i , which is expressed in time domain as Enhance it in the time domain by randomly combining a series of enhancement operations, i Generate an enhanced library and obtain samples The enhancement operation includes: Random combination of jitter, scaling, or time-shifting; After all end-to-end time series are enhanced, the time series and the enhanced library are input into the transformer encoder; the transformer encoder inputs the end-to-end time series and then converts it into a high-dimensional representation, and the transformer encoder is used to simultaneously use contrastive learning to mine the time domain features of the time series; For an end-to-end time series Randomly select an augmented sample Input it into a contrastive temporal encoder to get the embedding before and after data augmentation and For the jth end-to-end time series Will is regarded as a positive sample pair, and It is a negative sample pair; Then set the loss function of the time domain space to maximize the similarity between positive sample pairs and minimize the similarity between negative sample pairs; use NT-Xent as the distance function in contrastive learning and define the encoder loss function in the time domain. The expression is as follows: Where sim(u,v)=u T v / ||u||||v|| represents the cosine similarity of u and v, τ represents the time scale adjustment parameter, u T represents the transpose of u, X represents the end-to-end traffic time series of all inputs; (2) End-to-end traffic time series frequency domain encoder G F ; In the frequency domain encoder, consistent with the time domain encoder, a series of enhancement operations are randomly combined to generate a i To generate an enhanced library, first Fourier transform Generating frequency domain data The spectrum is then perturbed by adding or removing frequency components to obtain enhanced samples and The frequency domain encoder G composed of transformers is F , get the representation before and after frequency domain data enhancement and Then, the representation of the same sample data before and after enhancement is defined as a positive sample pair, the embedding between different samples is a negative sample pair, and NT-Xent is used as the distance function to define the encoder loss function in the specific frequency domain. The expression is as follows: (3) Time-frequency consistent embedding; Through two projection modules R T and R F Embedding the time domain Frequency-domain based embedding Projected into the same time-frequency space, and then get a positive sample pair Similarly, we can get three negative sample pairs and Among them, time domain embedding Frequency Domain Embedding In the same time-frequency space, the Euclidean distance is used to represent the distance between two embedding vectors, that is, express and The distance between them, similarly, we get three negative sample pairs respectively. and The distance between the embedding vectors and Set a new loss function L in the time-frequency space C,i , the expression is as follows: Among them, S pair represents the distance of the embedding based on the time-frequency domain of the three negative sample pairs, Indicates S pair One of them, for each pair, at least one embedding is obtained from the data augmented sample; δ represents a predefined constant used to make negative samples far away from each other; The representation model includes three loss functions: time domain-based, frequency domain-based and time-frequency consistency loss; when the entire model is trained, the pre-training loss L of the entire model is defined TF-C,i The expression is as follows: L TF-C,i =λ(L T,i +L F,i )+(1-λ)L C,i Among them, λ controls the relative importance of contrast and consistency loss, and the sum of the losses of all pre-training samples is the total loss; After the entire model training is completed, the final embedding feature vector matrix of all end-to-end traffic time series is obtained in, represents the real number domain, m represents the dimension of the embedding vector of each end-to-end traffic time series, and n represents the number of destination nodes, that is, the number of corresponding end-to-end traffic time series.

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