Online network measurement traffic recovery method, terminal device and storage medium

Abstract

The application discloses an online network measurement flow recovery method, a terminal device and a storage medium. Network flow data at each moment is modeled according to a two-dimensional matrix model; a basic subspace column is trained according to flow data at historical moments, and indexes of the columns are marked, and a leverage score is obtained by calculation; according to the indexes of the subspace columns, a subspace column that needs full sampling at the current moment is selected, and only part of elements in the remaining columns are sampled; whether sampling needs to be continued is judged according to a sampling matrix at the current moment; when a maximum residual value is less than a certain threshold, unsampled data is recovered by using subspace matrix filling; when the maximum residual value is greater than a certain threshold, columns that need to be continuously measured are selected according to residual sizes, a column space is updated, and then the unsampled data is recovered. The application solves the problems of low recovery precision and inability to recover online in the prior art, and realizes online network measurement with low overhead.

Description

Technical Field

[0001] This invention relates to the field of network measurement technology, and in particular to an online network measurement traffic recovery method, terminal device, and storage medium. Background Technology

[0002] A traffic matrix records the traffic (number of packets, transmission latency, etc.) exchanged between nodes across a network. Each row in the traffic matrix represents an origin node, and each column represents a destination node. The elements in the matrix represent the traffic volume from the origin node in that row to the destination node in that column within a certain time period. Obtaining complete traffic matrix information helps network administrators better perform subsequent tasks such as network optimization, traffic scheduling, and anomaly detection. However, as network scale continues to increase, obtaining complete network traffic matrix information becomes increasingly difficult. How to efficiently measure and reconstruct the traffic matrix has become a research hotspot in recent years.

[0003] Currently, there are many studies both domestically and internationally on flow matrix filling techniques, which can be broadly divided into the following two categories:

[0004] The first category is based on passive measurement (sampling) methods. Some literature utilizes existing measurement data and analyzes the temporal and spatial correlations of network data to impute missing data. Specifically, this involves analyzing both temporal and spatial correlations within the network data. Furthermore, some studies have proposed methods that simultaneously utilize the temporal and spatial correlations of network data for missing data imputation. This approach can predict the values ​​of missing data more accurately than methods using only temporal or spatial correlations.

[0005] The second category is based on active measurement (sampling) methods. Since not every element in the flow matrix leaks the same information, the measurement location has a certain impact on the recovery accuracy. Some studies have tried to study methods for actively selecting measurement locations. Xie et al. proposed MC-E2E to actively select measurement locations. This method first obtains some initial measurement samples through random measurement, and then applies an iterative approach to continue selecting subsequent measurement samples. The iterative process for each round is as follows: the existing samples are used to recover the flow matrix, and then the measurement locations with larger recovery errors are adaptively selected for further measurement. MC-E2E provides a stopping condition to terminate the iteration, that is, when the recovery error is less than a certain preset threshold, the active measurement process terminates. Liu et al. proposed a dynamic sampling method for active measurement. This method uses the Local Coherence algorithm [8] to select measurement locations. First, some samples are randomly measured, and these samples are decomposed by SVD to obtain an estimated leverage score. Then, the leverage score is used as a probability to determine the location for further sampling. This method also uses the stopping condition in MC-E2E to determine whether the sampling is sufficient.

[0006] Existing low-overhead network measurement techniques based on matrix filling cannot achieve the required accuracy and efficiency in real-world network environments. For passive measurement methods, schemes that simply use temporal or spatial correlation suffer from low accuracy because they rely on only one dimension of information to reconstruct the matrix. Methods using both temporal and spatial correlation cannot determine whether the current measurement data is sufficient to reconstruct the traffic matrix; therefore, when the measurement data lacks sufficient information, the accuracy of traffic matrix reconstruction is low. Active measurement schemes achieve higher accuracy by proactively selecting high-information measurement locations; however, active measurement involves multiple iterations to select optimal locations, making the algorithms too time-consuming and unsuitable for subsequent network tasks. Furthermore, most existing low-overhead measurement methods are only applicable to offline recovery and cannot support real-time online data recovery in network operations and maintenance. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide an online network measurement traffic recovery method, terminal equipment and storage medium to overcome the shortcomings of the prior art, such as high measurement cost, low recovery accuracy and inability to support online recovery, so as to realize real-time data measurement and recovery in network operation and maintenance.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an online network measurement traffic recovery method, comprising the following steps:

[0009] S1. Model the raw network traffic data collected at each moment into matrix data;

[0010] S2. Obtain the basic subspace columns using the matrix data corresponding to the first time step, mark the index of the subspace columns, obtain the leverage score of each column of the matrix data corresponding to the first time step, and determine the sampling weight of each element in each column based on the leverage score.

[0011] S3. Based on the index of the subspace column, select the subspace column that needs to be fully sampled at the current time. For the remaining columns of the matrix data at the current time, sample some elements according to the sampling weight.

[0012] S4. Calculate the maximum value of the residual between the partially sampled column and the subspace column at the current time. If the maximum value is less than the preset parameter value, directly restore each partially sampled column; otherwise, add the partially sampled column corresponding to the maximum value to the current subspace column set, add the index of the partially sampled column corresponding to the maximum value to the index set, update the subspace, and proceed to step S5.

[0013] S5. For the matrix data at the next time step, use the updated subspace, return to step S3, and restore the partial measurement matrix at the current time step.

[0014] In network operations and maintenance, this invention obtains the measurement matrix at each new time step (T) based on the subspace column index of the previous time step (T-1) and the sampling probability of each element in the partial sampling columns trained at the first time step. The column space of the current time step (T) is then obtained based on the subspace columns. The residual between the remaining sampled columns and the column space determines whether adaptive sampling needs to continue. After sampling, a subspace-based matrix filling method is used to recover the partially measured matrix. After recovery, a projection method is used to calculate whether there is redundant sampling in the current subspace. If so, its index is removed from the subspace index set; this index is used to determine the sampling for the next time step. This invention supports online measurement and recovery when facing continuously arriving traffic matrices; secondly, the continuously updated column space effectively improves recovery accuracy.

[0015] In step S2 of this invention, the specific implementation process of obtaining the basic subspace columns using the matrix data corresponding to the first time step and marking the index of the subspace columns includes:

[0016] 1) Measure the flow matrix M at the first moment completely as historical data, and calculate the rank r of the historical data matrix M;

[0017] 2) Randomly sample a column from M, add the data of this column to the subspace column set, and add the index of this column to the index set; perform matrix decomposition on the subspace column set, i.e., S = UΣV TWhere S is the subspace column set, I is the index set, U and V are orthogonal matrices, Σ is a diagonal matrix, and U is the current subspace;

[0018] 3) Find the column with the largest distance from the current subspace U, i.e., the t-th column. Among them, M t This represents the t-th column of the flow matrix M.

[0019] 4) Add the data in column t to the current subspace set, add index t to the index set, perform matrix decomposition on the updated current subspace set, and update the current subspace;

[0020] 5) Repeat steps 3) and 4) to find column r-1 of the data. This column r-1, together with the column sampled in step 2), constitutes a subspace of the historical data. Return the final subspace index I. * .

[0021] In step S2, the sampling weight W of the i-th element in each column i The specific implementation process includes:

[0022]

[0023] in, n is the dimension of the flow matrix M, μ i (M) corresponds to the leverage score in the i-th row, ν j (M) corresponds to the leverage score in column j, e i and e j These are the i-th and j-th standard basis vectors, respectively.

[0024] In step S4, the maximum value of the residual between the partially sampled column and the subspace column at the current time is calculated. If this maximum value is less than a preset parameter value, the specific implementation process of directly restoring each partially sampled column includes:

[0025] A) Based on the subspace column index obtained in the previous time step, select the current time step flow matrix M. 1 The columns that need to be fully sampled are used to obtain the set S of the subspace columns at the current time. 1 The set S of the subspace columns at the current moment 1 Perform matrix decomposition to obtain the estimated subspace U at the current time step. 1 ;

[0026] B) Calculate the maximum value of the residual between the partially sampled columns of the current flow matrix and the estimated subspace at the current time, where the formula for calculating this maximum value res1 is:

[0027]

[0028] in, In the flow matrix M 1 The middle part of the sampling column, where t is the column index and Ω is the sampling position in the t-th column.

[0029] C) If res1 is less than the preset parameter value, then use the following formula to recover the column of each partial sample. in, This is the t-th column after restoration.

[0030] In step S4, the specific implementation process of updating the subspace includes:

[0031] The set of subspace columns generated r submatrices Each submatrix represents a matrix consisting of the remaining columns excluding the column corresponding to that submatrix;

[0032] For r submatrices Perform matrix decomposition to obtain r secondary subspaces. The minimum residual value is obtained by the following formula:

[0033]

[0034] in,

[0035] If res2 is less than the preset value, then the index of the column corresponding to the smallest residual value is deleted from the index set to obtain the updated subspace.

[0036] As an inventive concept, the present invention also provides a terminal device, which includes:

[0037] One or more processors;

[0038] A memory having stored one or more programs that, when executed by one or more processors, cause the one or more processors to implement the steps of the method described above.

[0039] As an inventive concept, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described above.

[0040] Compared with existing technologies, the beneficial effects of this invention are as follows: The low-overhead online network measurement recovery method based on changing subspace matrix filling provided by this invention, when a new time (T) arrives in network operation and maintenance, obtains the measurement matrix based on the subspace column index of the previous time (T-1) and the sampling probability of each element in the partial sampling column trained by the first time. The column space of the current time (T) is obtained based on the subspace columns. The residual between the remaining sampled columns and the column space determines whether adaptive sampling needs to continue. After sampling, the matrix of partial measurement is recovered using a subspace-based matrix filling method. After recovery, the presence of redundant sampling in the current subspace is calculated using a projection method. If redundant sampling is found, its index is removed from the subspace index set, and this index is used to determine the sampling for the next time. Compared with other inventions mentioned above, firstly, it supports online measurement and recovery when facing continuously arriving traffic matrices; secondly, the recovery accuracy is effectively improved through continuously updated column spaces. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the method according to an embodiment of the present invention;

[0042] Figure 2 (a) and Figure 2 (b) in the figure is a network traffic data modeling diagram according to an embodiment of the present invention; Figure 2 (a) in the diagram represents a network with five nodes. Figure 2 (b) in the figure represents the result after matrix modeling;

[0043] Figure 3 In this embodiment of the invention, the sampling at the current time is guided by the subspace column index I of the historical time.

[0044] Figure 4 In this embodiment of the invention, the residual res1 is used to determine whether sampling needs to continue at the current time.

[0045] Figure 5 This is a schematic diagram showing the mapping of samples in a sampling column to subspaces in an embodiment of the present invention;

[0046] Figure 6 This is a schematic diagram illustrating how the residual res2 is used to determine whether the current subspace column index needs to be updated, according to an embodiment of the present invention.

[0047] Figures 7(a) to 7(f)Figure 7(a) shows the value settings of parameters η and δ in different datasets in the embodiments of the present invention; Figure 7(b) shows the correspondence between parameter η and the number of subspace columns in the Abilene dataset; Figure 7(c) shows the correspondence between the number of subspace columns and the error rate of the recovered data in the Abilene dataset; Figure 7(d) shows the correspondence between parameter η and the number of subspace columns in the PlanetLab dataset; Figure 7(e) shows the correspondence between parameter δ and the number of subspace columns in the PlanetLab dataset; Figure 7(f) shows the correspondence between the number of subspace columns and the error rate of the recovered data in the PlanetLab dataset. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Example 1

[0050] Embodiment 1 of this invention provides a low-overhead online network measurement data recovery method based on changing subspace matrix filling. The principle of the method is as follows: Figure 1 As shown, the steps include:

[0051] Step S1: Model the raw network traffic data collected at each time moment into matrix data based on the two-dimensional matrix model;

[0052] See Figure 2 In (a) and 2(b) of the figure, the embodiments of the present invention model the data at each time step into a two-dimensional matrix model (e.g., Figure 2 (a) and Figure 2 In (b) of the diagram, Origin represents the source node and Destination represents the destination node. In network operations and maintenance, at each new moment, this invention can determine how to perform measurements in the new moment's data and infer unmeasured data from the measured data. Figure 2 In (a) of the diagram, the number of network nodes is n = 5.

[0053] Step S2: In the first time step, the entire flow matrix is ​​fully measured to form a historical data matrix. A basic subspace column is trained based on the historical data, and the indices of these columns are labeled. A leverage score is calculated, which determines which elements to sample in the partially sampled columns. Specifically, the subspace column indices determine which columns are fully sampled in the next time step, and the leverage score determines which positions are sampled in all partially sampled columns in subsequent time steps.

[0054] Step S3: Select the subspace column that needs to be fully sampled at the current time based on the subspace column index. For the remaining columns, only a portion of the elements are sampled, and the sampling position is determined by the leverage score.

[0055] Step S4: Calculate the residual between the sampled columns and the current column space based on the data matrix collected at the current time. If the maximum residual is less than a certain threshold, stop sampling and use a matrix filling scheme based on subspace to restore the matrix. Otherwise, sample the columns with the maximum residual and update the column space. After updating the column space, use the new column space to restore the matrix.

[0056] Step S5: Update the index of the subspace column at the current time step to guide the sampling at the next time step.

[0057] Step S6: For each moment of data, repeat steps 3-5 to measure and recover the data.

[0058] This invention utilizes subspace-based matrix filling for low-overhead network traffic measurement. Leveraging the spatiotemporal coherence of network traffic data, it determines the columns constituting the subspace at the current time step based on the subspace column index from the previous time step. Simultaneously, it calculates residuals to determine if the current subspace columns are insufficient to recover the matrix. Furthermore, sampling based on leverage scores in some sampled columns also improves residual calculation and the recovery process, making it more accurate.

[0059] Step S2 trains an index I for a subspace column based on historical data. * ,include:

[0060] Step S21: Completely measure the flow matrix M at the first moment as historical data, and calculate the rank (denoted as r) of the historical data matrix M;

[0061] Step S22: Randomly sample a column from M and add it to the subspace column set S. Add its index to the index set I to obtain the current subspace U. The method for obtaining the current subspace is to perform skinny SVD (thin SVD decomposition, which only retains the part containing the non-zero elements of the singular value matrix Σ) on the subspace column set. In this step, the subspace column set is S, so performing skinny SVD decomposition on S yields S = UΣV TΣ, where U and V are orthogonal matrices, and Σ is a diagonal matrix. U is the left singular matrix, usually referred to as the column space, and V is the right singular matrix, usually referred to as the row space.

[0062] Step S23: Construct the following objective function to find the column (column t) that has the largest distance to the current subspace U among the remaining columns:

[0063]

[0064] Among them, M t This represents the t-th column in matrix M. This is the projection matrix.

[0065] Step S24: Add the t-th column obtained in step 23 to the current subspace set, add its index t to the subspace index set, and use Skinny SVD to update the current subspace.

[0066] Step S25: Repeat steps 23-24 to find the subspace of historical data that is formed by column r-1 and the column sampled in step S22, and return the final subspace index I. * .

[0067] In step S2, a sampling weight W is calculated. i The process is as follows:

[0068] Step S26: Perform skinny SVD decomposition on the flow matrix M at the first time step, and calculate the leverage score of the flow matrix at the first time step. The leverage score is defined as follows:

[0069] Definition 1: (Leverage Score) For a matrix M of size n×n and rank r, its lean SVD decomposition is M=UΣV T Where U and V are both orthogonal matrices, the leverage score of matrix M is defined as:

[0070]

[0071] μ i (M) corresponds to the leverage score in the i-th row, ν j (M) corresponds to the leverage score in column j. i and e j These are the i-th and j-th standard basis vectors. Leverage scores typically describe the amount of information carried by an element; the higher the score, the more information the element carries. For a given column, when selecting bit samples in that column, the corresponding row's leverage score should be chosen whenever possible, i.e., for μ... i(M) Elements with high values ​​are sampled (see 1. Y. Chen, S. Bhojanapalli, S. Sanghavi, and R. Ward, “Coherent matrix completion,” in Proc. Int. Conf. Mach. Learn., 2014, pp. 674–682.).

[0072] Step S27: Calculate the sampling weight W of the i-th element in any column based on the leverage score. i for

[0073]

[0074] like Figure 3 As shown, step S3 samples the traffic data at the current moment, specifically including:

[0075] Step S31, based on the subspace column index I obtained in the previous time step * To select the current flow matrix M 1 Columns requiring full sampling;

[0076] Step S32: For the remaining columns, according to the sampling weights W obtained in steps S26-S27... i To sample a subset of elements, the total number of samples ranges from [1, n].

[0077] like Figure 4 The adaptive sampling and recovery step S4 shown includes:

[0078] Step S41: Obtain the set S of subspace columns at the current time based on the columns sampled in step S31. 1 , for S 1 Perform skinny SVD decomposition, S 1 =U 1 Σ 1 (V 1 ) T Obtain the estimated subspace U at the current time. 1 ;

[0079] Step S42, calculate the column of each partial sample and the current estimated subspace U. 1 The maximum value of the residual (denoted as res1), where the maximum value of the residual res1 is calculated as follows:

[0080]

[0081] in In matrix M 1 The middle part of the sampling column, where t is the column index and Ω is the sampling position in that column. like Figure 5 As shown, this indicates that in subspace U 1 The corresponding Ω row.

[0082] Step S43: If res1 is less than a preset parameter η, it means that the current sampling can recover the matrix. The following formula (recovering columns of partial samples based on existing subspaces is a well-known technique; see (Balcan MFF, Zhang H. Noise-tolerant life-long matrix completion via adaptive sampling[J]. Advances in Neural Information Processing Systems, 2016, 29.) is used to recover the columns of each partial sample.

[0083]

[0084] Step S44: If res1 is greater than a preset parameter η, then adaptively, the column with the largest current residual is added to the current subspace column set, its index is added to the index set, the subspace is updated, and the updated subspace and formula (5) are used to recover the partial measurement matrix at the current time. The parameter η needs to be set to different values ​​depending on the dataset. When η is set too small, more columns will be selected as subspace columns, the sampling rate will increase accordingly, and the recovery accuracy will also improve. Conversely, when η is set larger, fewer columns will be considered as subspace columns, the sampling rate will decrease accordingly, and the recovery accuracy will also decrease. The correspondence between the parameter η and the number of subspace columns under different datasets is as follows: Figures 7(a) to 7(f) As shown, the value of parameter η has been varied in different datasets. Figures 7(a) to 7(f) The information is provided in the text.

[0085] like Figure 6 As shown, step 5 includes:

[0086] Step S51: Generate a subspace column set r submatrices Each submatrix represents a matrix consisting of the remaining columns excluding a certain column. This represents the matrix consisting of the remaining columns excluding the first column.

[0087] Step S52, for r submatrices Perform Skinny SVD decomposition on each subspace to obtain r secondary subspaces. S 1Each column in the matrix has its residual (denoted as res2) calculated with its corresponding subspace in the following way, and the minimum residual value is obtained:

[0088]

[0089] in,

[0090] Step S53: If res2 is less than a preset parameter δ, then delete the index of the column corresponding to the smallest residual value from the index set. Parameter δ is also used to determine the number of subspace columns. The correspondence between parameter δ and the number of subspace columns varies across different datasets as follows: Figures 7(a) to 7(f) As shown, the value of parameter δ has been varied in different datasets. Figures 7(a) to 7(f) The information is provided in the text.

[0091] The present invention provides a low-overhead online network measurement method based on variable subspace matrix filling. This method models network traffic data at each time step as a matrix. Using a subspace matrix filling method, it completely measures some columns and then measures some elements in the remaining columns to recover the matrix information. A variable subspace method is designed, leveraging the spatiotemporal correlation of network traffic data and the characteristic that subspace columns do not change significantly between adjacent time steps. The subspace column indices of the traffic matrix at the previous time step are used to determine the subspace columns of the traffic matrix at the current time step. When a subspace column of the traffic matrix changes, this method can capture the change in real time and add new samples to ensure recovery quality. After recovering the traffic matrix at the current time step, a corresponding subspace update algorithm is designed to determine whether there is redundancy in the subspace columns at the current time step and update the index. The updated index reduces the sampling overhead of subsequent time steps. Compared to traditional matrix filling methods, this method firstly supports online measurement and recovery when facing traffic matrices at continuously arriving time steps; secondly, it effectively improves recovery accuracy through continuously updated column spaces.

[0092] Example 2

[0093] Embodiment 2 of the present invention provides a terminal device corresponding to Embodiment 1 above. The terminal device can be a processing device for a client, such as a mobile phone, a laptop, a tablet computer, a desktop computer, etc., to execute the method of the above embodiments.

[0094] The terminal device in this embodiment includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in Embodiment 1 described above.

[0095] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0096] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0097] Example 3

[0098] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to Embodiment 1 above, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, they implement the steps of the method of Embodiment 1 above.

[0099] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0100] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0101] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0102] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0103] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0104] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for recovering online network traffic measurement, characterized in that, Includes the following steps: S1. Model the raw network traffic data collected at each moment into matrix data; S2. Obtain the basic subspace columns using the matrix data corresponding to the first time step, mark the index of the subspace columns, obtain the leverage score of each column of the matrix data corresponding to the first time step, and determine the sampling weight of each element in each column based on the leverage score. S3. Based on the index of the subspace column, select the subspace column that needs to be fully sampled at the current time. For the remaining columns of the matrix data at the current time, sample some elements according to the sampling weight. S4. Calculate the maximum value of the residual between the partially sampled column and the subspace column at the current time. If the maximum value is less than the preset parameter value, directly restore each partially sampled column; otherwise, add the partially sampled column corresponding to the maximum value to the current subspace column set, add the index of the partially sampled column corresponding to the maximum value to the index set, update the subspace, and proceed to step S5. S5. For the matrix data at the next time step, use the updated subspace, return to step S3, and restore the partial measurement matrix at the current time step; In step S2, the basic subspace columns are obtained using the matrix data corresponding to the first time step. The specific implementation process of marking the index of the subspace columns includes: 1) Measure the flow matrix M at the first moment completely as historical data, and calculate the rank r of the historical data matrix M; 2) Randomly sample a column from M, add the data of that column to the subspace column set, and add the index of that column to the index set; perform matrix decomposition on the subspace column set, i.e. Where S is the subspace column set, I is the index set, and U and V are orthogonal matrices. Let U be a diagonal matrix, and U be the current subspace. 3) Find the column with the largest distance from the current subspace U, i.e., the t-th column. ;in, This represents the t-th column of the flow matrix M. ; 4) Add the data in column t to the current subspace set, add index t to the index set, perform matrix decomposition on the updated current subspace set, and update the current subspace; 5) Repeat steps 3) and 4) to find column r-1 of the data. This column r-1, together with the column sampled in step 2), constitutes a subspace of the historical data. Return the final subspace index I. * ; In step S2, the sampling weight of the i-th element in each column The specific implementation process includes: ； in, , where n is the dimension of the flow matrix M. This corresponds to the leverage score in the i-th row. This corresponds to the leverage score in column j. and These are the i-th and j-th standard basis vectors, respectively.

2. The online network measurement traffic recovery method according to claim 1, characterized in that, In step S4, the maximum value of the residual between the partially sampled column and the subspace column at the current time is calculated. If this maximum value is less than a preset parameter value, the specific implementation process of directly restoring each partially sampled column includes: A) Based on the subspace column index obtained in the previous time step, select the current time step flow matrix M. 1 The columns that need to be fully sampled are used to obtain the set S of the subspace columns at the current time step. 1 The set S of the subspace columns at the current moment 1 Perform SVD matrix decomposition to obtain the estimated subspace U at the current time step. 1 ; B) Calculate the maximum value of the residual between the partially sampled columns of the current flow matrix and the estimated subspace at the current time, where the formula for calculating this maximum value res1 is: ； in, In the flow matrix M 1 The middle part of the sampling column, where t is the column index and Ω is the sampling position in the t-th column. , In subspace U 1 The corresponding Ω row; C) If res1 is less than the preset parameter value, then use the following formula to recover the column of each partial sample. : ;in, For the restored t-th column, This is the estimated subspace at the current time.

3. The online network measurement traffic recovery method according to claim 2, characterized in that, In step S4, the specific implementation process of updating the subspace includes: The set of subspace columns generated r submatrices Each submatrix represents a matrix consisting of the remaining columns excluding the column corresponding to that submatrix; For r submatrices Perform matrix decomposition to obtain r secondary subspaces. The minimum residual value can be obtained using the following formula: ； in, ; If res2 is less than the preset value, then the index of the column corresponding to the smallest residual value is deleted from the index set to obtain the updated subspace.

4. A terminal device, characterized in that, include: One or more processors; A memory having stored one or more programs thereon, which, when executed by one or more processors, cause the one or more processors to perform the steps of the method according to any one of claims 1 to 3.

5. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 3.

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