CN114722926A - Convolution clustering method for scale vortex time sequence diagram in towed sensor array - Google Patents

Abstract

The invention discloses a convolution clustering method for a scale vortex time sequence diagram in a towed sensor array. The method comprises the following steps: building an integral link of a towing system; laying and recovering a towed sensor array to obtain time sequence data; calculating the similarity of time sequence segmented characteristic vectors by using a continuous bag-of-words model in the word vectors, carrying out hierarchical clustering, uniformly representing the characteristic vectors in the category by using a clustering center, dividing the segmented time sequence characteristic vector value represented by the similarity into a training sample and a sample to be tested, and selecting the key characteristic vector category with stage representativeness of the mesoscale vortex as a label; establishing and training a graph convolution network model, establishing an affinity graph, inputting a sample to be tested into the trained GCN, and obtaining representative clustering output of a mesoscale vortex stage; and (4) carrying out secondary clustering based on the graph convolution network to finally obtain a clustering result of the time sequence. According to the invention, a high-accuracy time sequence classification result is finally obtained through twice clustering.

Description

Convolution clustering method for scale vortex time sequence diagram in towed sensor array

Technical Field

The invention relates to the technical field of marine observation and deep learning, in particular to a convolution clustering method for a scale vortex time sequence diagram in a towed sensor array, and belongs to the technical field of time sequence classification.

Background

The ocean is the largest resource in the world, and abundant mineral resources and oil gas resources are stored. In the exploration activities of various marine resources, the marine towing system plays an important role and role, not only relates to the exploration and exploration of the marine resources, but also is very important in the fields of civilian use, fishery, military use and the like. The ocean science is used for researching the natural phenomena, properties and change rules of the ocean and developing and utilizing a knowledge system related to the ocean; the research objects are the oceans occupying 71 percent of the surface of the ball, including seawater, substances dissolved and suspended in seawater, organisms living in the oceans, seabed sediments and seabed rocky circles, and atmospheric boundary layers and estuary coastal zones on the sea surface. Thus, marine science is an important component of the earth science. The research field of marine science is very wide, and the main contents of the research field comprise basic research on physical, chemical, biological and geological processes in the sea and application research for marine resource development and utilization, marine military activities and the like. Towing systems are currently a powerful tool that can meet the above requirements. The towing system integrates multidisciplinary sensors, and the observation elements comprise temperature, salinity, pressure and conductivity. In order to guarantee the observation precision and the observation depth, the dragging system is required to have good hydrodynamic performance, the water exchange channel is smooth, and the sensor has quick response capability and high-precision measurement performance.

The Graph Convolutional neural Network (GCN) is a method for processing Graph domain information based on deep learning, combines Graph broadcasting operation and deep learning algorithm, can enable the structure information and vertex attribute information of a Graph to participate in learning, shows good effect and interpretability in the applications of vertex classification, Graph classification, link prediction and the like, and becomes a widely applied Graph analysis method.

But the GCN semi-supervised learning also has certain defects: (1) if the number of nodes with label is too small during semi-supervision, the performance of the GCN is seriously reduced. (2) The shallow GCN network cannot spread label information over a large area (the deeper the hierarchy, the larger the receptive field of the nodes) (3) the deep GCN network causes the problem of excessive smoothing.

Disclosure of Invention

The invention aims to provide a convolution clustering method for a scale vortex time sequence diagram in a towed sensor array, which is used for solving the problems.

In order to achieve the purpose, the invention provides a specific technical scheme that:

a convolution clustering method for a scale vortex time series diagram in a towed sensor array comprises the following steps:

s1: building an integral link of a towing system;

s2, laying and recycling the towed sensor array to acquire three-dimensional section observation data of the towed sensor array to obtain time sequence data;

s3: calculating the similarity of time sequence segmented feature vectors by using a Continuous Bag-of-Words (CBOW) model in the word vectors, carrying out hierarchical clustering, uniformly representing the feature vectors in the category by using a clustering center, dividing the segmented time sequence feature vector value represented by the feature vectors into a training sample and a sample to be tested, and selecting the category of key feature vectors with stage representativeness of the mesoscale vortex as a label;

s4: establishing and training a Graph Convolutional Network (GCN) model, inputting the characteristic vector representation of the original time sequence segmentation, ideally outputting the stage representative time sequence characteristic vector category of the life cycle of the mesoscale vortex, establishing an affinity Graph, inputting a sample to be tested to the trained GCN, and obtaining possible mesoscale vortex stage representative clustering output.

Further, in S1, the building of the overall link of the towing system includes the following steps:

the towing system consists of a deck unit, a towing chain, a fixed-depth submersible vehicle, an electrode and the like. The total length of the towing cable is L and totally comprises N_sA sensor integration module, wherein the distance from the ith node to the previous node is set as L_i。

In S2, the deployment and recovery of the towed sensor (towed optical, temperature, salinity, pressure sensor) array includes the following steps:

1) the towing chain laying and recovering process is implemented by a deck unit winch, an A frame and a module assembling and disassembling device. Let the navigational speed be v, the towing time be T, and the length of the cable corresponding to the ith node from the water surface be l_iThe fixed-depth submersible vehicle ensures that the bottom end of the towing chain is observed in a three-dimensional section within a certain depth, and the tension F (t) is tested in real time to ensure that the bottom end of the towing chain is at the bearing capacity limit F of the winch_maxWithin.

2) Based on the electromagnetic coupling principle, the towing system realizes non-contact power supply and data transmission in the same transmission link, and the overwater electric control system converts direct current into high-frequency alternating current signals, supplies power to the underwater sensor integration module and carries out data communication. Setting the time sequence of the absorbance, the fluorescence, the temperature, the conductivity and the pressure collected by the ith sensor integration module at the jth time as A_i,j(t)，F_i,j(t)，T_i,j(t)，C_i,j(t)，D_i,j(t)，t∈(0,T)，i＝1，2，…，N_s，j＝1，2，…，N_sThe set of multi-dimensional stereo observation time series is S_i,j(t)。

Further, the S3 is specifically as follows:

1) time series data S_i,j(t) dividing into m subsequences, and setting the subsequence S of the f-th section_i,j,f(T) has a length of T ', T ∈ [0, T']The subsequence is also divided into a training subsequence and a subsequence to be detected;

2) establishing a continuous bag-of-words model CBOW in word vectors, calculating the similarity of the segmented feature vectors of the training time sequences, carrying out hierarchical clustering, uniformly representing the feature vectors in the category by a clustering center, carrying out classifier training, inputting the subsequence to be tested into the trained classifier for classification, and classifying the subsequence by adopting An hierarchical clustering algorithm (An iterative clustering algorithm).

Further, the classifying specifically includes: firstly, the time series data S_i,j(t) m subsequences, the f-th subsequence S_i,j,f(t) input into the continuous bag of words model CBOW, for S_i,j,f(t) extracting the features to obtain a feature vector C₁,C₂............C_mAssuming that each eigenvector is a cluster class, performing similarity calculation by using a discrete Fourier distance (Frechettstance), merging two cluster classes with the highest similarity, and updating a similarity matrix; dividing the track set into a certain number of clusters by using a hierarchical clustering algorithm, and finally obtaining new characteristic vectors K after clustering₁,K₂,............,K_nWherein (m.gtoreq.n). The discrete Fourier distance is used for evaluating nearest neighbor connection, and the method has the advantages of high diagnosis accuracy, high speed and strong adaptability because the method simultaneously considers the sequencing of positions and time and the factor of spatial distance.

Wherein the discrete Fourier distance evaluation nearest neighbor connections are as follows:

let feature vector C_iIs composed of p feature points, feature vector C_jThe device consists of q track points; using σ (C)_i) And σ (C)_j) Representing the sequential sets of two feature points, respectively, then has σ (C)_i)＝(u₁,…,u_p) And σ (C)_j)＝(u₁,…,u_q) The following sequence point pairs L can be obtained as shown in the formula:

L＝(u_a1,v_b1),(u_a2,v_b2),...,(u_am,v_bm) (1)

wherein, a₁＝1,b₁＝1,a_m＝p,b_mQ; for any i 1,2,3, a_i+1＝a_iOr a_i+1＝a_i+1And b_i+1＝b_i；

C_jThe length L between sequences between feature points is expressed as follows:

then its discrete frochet distance is defined as follows:

δ_F(C_i,C_j)＝min||L|| (3)

the quality of the clustering task is evaluated using the silhouette distance, which is given by the following formula for the ith (i vector distance to other points in the cluster) data point:

and a (i) is the average dissimilarity between the ith data point and all other points in the cluster to which the ith data point belongs.

Further, the S4 includes the following:

establishing an affinity graph, and calculating a corresponding sparse symmetric adjacency matrix as

N is the total number of nodes of the low-dimensional mapping of the scale vortex data in the historical observation, and D is the characteristic dimension of the data obtained by detection in the given translation window;

the GCN is used as a backbone network to further extract the obvious connection relation, and the L-th layer calculation process is as follows:

adding self-loop edges (self-loops) to the adjacency matrix A, i.e.

I is an identity matrix, wherein

Angle matrix

Is composed of

F_lDenotes the l-th layer embedding characteristics, F₀As input feature vector K₁,K₂,............,K_n；

Is a learnable matrix, maps the embedded features to a new space, and σ is a nonlinear activation function ReLU; f_LAn output feature map representing the L layer; f_LThe predicted affinity graph aggregates information from the neighborhood and encodes the graph structure, which is trained with a pair of features connected by the affinity graph edges as input to the classifier. The use minimizes the supervised contrast Loss (Supervised diagnostic Loss) between the predicted edge confidence and the true edge label.

The edges in the affinity graph are composed of dense connections within each mesoscale vortex propagation process cluster and sparse connections between approximate clusters. The structure retention sampling is to recombine training nodes in a cluster, the target is a subgraph formed by data characteristic vectors obtained by sampling mesoscale vortex detection, and a representative retention sample has the capability of representing the self structural characteristics of the mesoscale vortex, namely the edge connection in the cluster and the connection between near clusters. At the same time, the approximate clusters of the subgraph will also be sampled and the edges between the approximate clusters will be used as negative samples according to probability to improve performance gain. Firstly, randomly selecting M clusters as samples, and expanding the M clusters to N neighbor clusters to obtain a subgraph Q consisting of M multiplied by N clusters_n(ii) a Introducing a cluster randomness strategy from Q_nIn random selection of K_nIndividual clustering, and sample randomness strategy, from Q_nIn selecting K at random_mEach node is used for reconstructing an affinity graph Q based on the sampling nodes;

when clustering is carried out, the method willThe attributes of the mesoscale vortex samples to be classified are represented in the same mode and are sent to the GCN to predict edge scores, graph analysis is directly trimmed according to the predicted edge scores, graph refinement is carried out to calculate node intimacy, further unrelated edges are deleted, and then a clustering reasoning result is obtained. Suppose two nodes N_iAnd N_jAre each connected to n_iAnd n_jAnd the edge is provided with k common neighbor nodes, wherein C represents a clustering function, and the node affinity I can be represented as an aggregation operation:

I＝C(k/n_i,k/n_j) (6)

setting given adjacency matrix

The mutual adjacency number of the node pair is

Each element in (1)

Represents N_iAnd N_jP represents a maximum function, v represents a vector (vector) function, and then the node affinity I is expressed as:

through the steps, the nodes can be classified, and then the representative time sequence of the mesoscale vortex stage is classified.

The invention has the advantages and technical effects that:

the invention uses a word vector model to carry out similarity calculation on time sequence data, carries out hierarchical clustering, forms a new characteristic vector, constructs an affinity graph, and carries out secondary clustering based on a Graph Convolution Network (GCN) to finally obtain a clustering result of a time sequence. According to the invention, a high-accuracy time sequence classification result is finally obtained through twice clustering.

Drawings

FIG. 1 is a schematic overall flow chart of the present invention.

FIG. 2 is a block diagram illustrating a specific process of the present invention.

Detailed Description

In order to make the objects, embodiments and advantages of the present invention clearer, the present invention is further described in detail below by way of specific examples with reference to the accompanying drawings.

Example (b):

a convolution clustering method for a scale vortex time series diagram in a towed sensor array comprises the following steps (the specific flow is shown in figure 2):

firstly, collecting multi-dimensional stereo observation time sequence data of a towed sensor array through the arrangement and recovery of a marine test towed optical sensor array, a temperature sensor array, a salinity sensor array and a pressure sensor array, as shown in figure 1.

1. The towing system consists of a deck unit, a towing chain, a fixed-depth submersible vehicle, an electrode and the like. The total length of the towing cable is L and totally comprises N_sA sensor integration module, wherein the distance from the ith node to the previous node is set as L_i. The towing chain laying and recovering process is implemented by a deck unit winch, an A frame and a module assembling and disassembling device. Let the navigational speed be v, the towing time be T, and the length of the cable corresponding to the ith node from the water surface be l_iThe fixed-depth underwater vehicle ensures that the bottom end of the towing chain is observed in a three-dimensional section in a certain depth, and the tension F (t) is tested in real time to ensure that the bottom end of the towing chain is positioned at the bearing capacity limit F of the winch_maxWithin.

2. Setting the time sequence of the absorbance, the fluorescence, the temperature, the conductivity and the pressure collected by the ith sensor integration module at the jth time as A_i,j(t)，F_i,j(t)，T_i,j(t)，C_i,j(t)，D_i,j(t)，t∈(0,T)，i＝1，2，…，N_s，j＝1，2，…，N_sThe set of multi-dimensional stereo observation time series is S_i,j(t)。

Secondly, calculating the similarity of the time sequence segmented characteristic vectors by using a Continuous Bag-of-Words (CBOW) model in the word vectors, carrying out hierarchical clustering, uniformly representing the characteristic vectors in the class by using a clustering center, dividing the segmented time sequence characteristic vector value represented by the similarity into a training sample and a sample to be tested, and selecting the class of the key characteristic vectors of which the mesoscale vortexes have stage representativeness as a label;

1. multidimensional stereo observation time sequence S for sensor integrated module_i,j(t) dividing the sequence into m subsequences, and setting the subsequence S of the f-th segment_i,j,f(T) has a length of T ', T ∈ [0, T']。

2. Establishing a continuous bag-of-words model CBOW in word vectors, calculating the similarity of the segmented feature vectors of the training time sequences, carrying out hierarchical clustering, uniformly representing the feature vectors in the category by a clustering center, carrying out classifier training, inputting the subsequence to be tested into the trained classifier for classification, and classifying the subsequence by adopting An hierarchical clustering algorithm (An iterative clustering algorithm). Firstly, the time series data S_i,j(t) m subsequences, the f-th subsequence S_i,j,f(t) input into the continuous bag of words model CBOW, for S_i,j,f(t) extracting the features to obtain a feature vector C₁,C₂............C_mAssuming that each eigenvector is a cluster class, performing similarity calculation by using a discrete Fourier distance (Frechet distance), merging two cluster classes with the highest similarity, and updating a similarity matrix; dividing the track set into a certain number of clusters by using a hierarchical clustering algorithm, and finally obtaining new characteristic vectors K after clustering₁,K₂,............,K_nWherein (m.gtoreq.n). The discrete Fourier distance is used for evaluating nearest neighbor connection, and the method has the advantages of high diagnosis accuracy, high speed and strong adaptability because the method simultaneously considers the sequencing of positions and time and the factor of spatial distance. Let feature vector C_iIs composed of p feature points, feature vector C_jThe device consists of q track points; using σ (C)_i) And σ (C)_j) Representing the sequential sets of two feature points, respectively, then has σ (C)_i)＝(u₁,…,u_p) And σ (C)_j)＝(u₁,...,u_q) Can be obtained asThe following sequence point pairs L are shown as the formula:

L＝(u_a1,v_b1),(u_a2,v_b2),...,(u_am,v_bm) (1)

wherein, a₁＝1,b₁＝1,a_m＝p,b_mQ. For any i 1,2,3, a_i+1＝a_iOr a_i+1＝a_i+1And b_i+1＝b_i。

C_jThe length L between sequences between feature points is expressed as follows:

then its discrete frochet distance is defined as follows:

δ_F(C_i,C_j)＝min||L|| (3)

the quality of the clustering task was evaluated using the silhouette distance, which is given by the following equation for the ith (i vector distance to other points in the cluster) data point

and a (i) is the average dissimilarity between the ith data point and all other points in the cluster to which the ith data point belongs.

And step three, establishing and training a Graph Convolutional Network (GCN) model, inputting the feature vector representation of the original time sequence segment, ideally outputting the class of the phase representative time sequence feature vector of the life cycle of the mesoscale vortex, establishing an affinity Graph, inputting the sample to be detected to the trained GCN, and obtaining possible mesoscale vortex phase representative clustering output.

Computing a corresponding sparse symmetric adjacency matrix as

N isAnd D is the characteristic dimension of the data obtained by detection in the given translation window.

The GCN is used as a backbone network to further extract the obvious connection relation, and the L-th layer calculation process is as follows:

adding self-loop edges (self-loops) to the adjacency matrix A, i.e.

I is an identity matrix, wherein

Angle matrix

Is composed of

F_lDenotes the l-th layer embedding characteristics, F₀As input feature vector K₁,K₂,............,K_n；

Is a learnable matrix, maps the embedded features to a new space, and σ is a nonlinear activation function ReLU; f_LAn output feature map representing the L layers; f_LThe predicted affinity graph aggregates information from the neighborhood and encodes the graph structure, which is trained with a pair of features connected by the affinity graph edges as input to the classifier. The use minimizes the supervised contrast Loss (Supervised diagnostic Loss) between the predicted edge confidence and the true edge label.

The edges in the affinity graph are composed of dense connections within each mesoscale vortex propagation process cluster and sparse connections between approximate clusters. The structure-preserving sampling recombines training nodes in a cluster, and the target is sampling mesoscale vortex detectionAnd (3) forming a subgraph by the obtained data feature vector, wherein the representative retained sample has the capability of representing the self structural characteristics of the mesoscale vortex, namely the edge connection in the cluster and the connection between the near clusters. At the same time, the approximate clusters of the subgraph will also be sampled and the edges between the approximate clusters will be used as negative samples according to probability to improve performance gain. Firstly, randomly selecting M clusters as samples, and expanding the M clusters to N neighbor clusters to obtain a subgraph Q consisting of M multiplied by N clusters_n(ii) a Introducing a cluster randomness strategy from Q_nIn random selection of K_nIndividual clustering, and sample randomness strategy, from Q_nIn random selection of K_mEach node is used for reconstructing an affinity graph Q based on the sampling nodes;

during clustering reasoning, the attributes of the mesoscale vortex samples to be classified are represented in the same mode and are sent to a GCN to predict edge scores, graph analysis is directly pruned according to the predicted edge scores, and graph refinement is carried out to calculate the node intimacy and further delete unrelated edges, so that a clustering reasoning result is obtained. Suppose two nodes N_iAnd N_jAre each connected to n_iAnd n_jAnd the edge is provided with k common neighbor nodes, wherein C represents a clustering function, and the node affinity I can be represented as an aggregation operation:

I＝C(k/n_i,k/n_j) (6)

setting given adjacency matrix

The mutual adjacency number of the node pair is

Each element in (1)

Represents N_iAnd N_jP represents a maximum function, v represents a vector (vector) function, and then the node affinity I is expressed as:

on the basis of the above embodiments, the present invention continues to describe the technical features and functions of the technical features in the present invention in detail to help those skilled in the art fully understand the technical solutions of the present invention and reproduce them.

Claims (5)

1. A convolution clustering method for a scale vortex time series diagram in a towed sensor array is characterized by comprising the following steps:

s1: building an integral link of a towing system;

s2, laying and recycling the towed sensor array to acquire three-dimensional section observation data of the towed sensor array to obtain time sequence data;

s3: calculating the similarity of time sequence segmented characteristic vectors by using a continuous bag-of-words model in the word vectors, carrying out hierarchical clustering, uniformly representing the characteristic vectors in the category by using a clustering center, dividing the segmented time sequence characteristic vector value represented by the similarity into a training sample and a sample to be tested, and selecting a key characteristic vector category with stage representativeness of the mesoscale vortex as a label;

s4: establishing and training a graph convolution network model, inputting the segmented characteristic vector representation of an original time sequence, ideally outputting the class of the phase representative time sequence characteristic vector of the life cycle of the mesoscale vortex, establishing an affinity graph, inputting a sample to be tested to the trained GCN, and obtaining possible mesoscale vortex phase representative clustering output.

2. The clustering method according to claim 1, wherein the S3 is specifically as follows:

1) time series dataS_i,j(t) dividing the sequence into m subsequences, and setting the subsequence S of the f-th segment_i,j,f(T) has a length of T ', T ∈ [0, T']The subsequence is also divided into a training subsequence and a subsequence to be detected;

2) establishing a continuous bag-of-words model CBOW in word vectors, calculating the similarity of the segmented feature vectors of the training time sequence, carrying out hierarchical clustering, uniformly representing the feature vectors in the category by a clustering center, carrying out classifier training, inputting the subsequence to be tested into the trained classifier for classification, and classifying the subsequence by adopting a hierarchical clustering algorithm.

3. The clustering method according to claim 2, wherein the classifying specifically comprises: firstly, the time series data S_i,j(t) m subsequences, the f-th subsequence S_i,j,f(t) input into the continuous bag of words model CBOW, for S_i,j,f(t) extracting the features to obtain a feature vector C₁,C₂............C_mAssuming that each eigenvector is a cluster class, performing similarity calculation by using a discrete Fourier distance (Frechet distance), merging two cluster classes with the highest similarity, and updating a similarity matrix; dividing the track set into a certain number of clusters by using a hierarchical clustering algorithm, and finally obtaining new characteristic vectors K after clustering₁,K₂,............,K_nWherein m is more than or equal to n.

4. The clustering method according to claim 3, wherein the discrete Fourier distance evaluation nearest neighbor connections are as follows:

let feature vector C_iIs composed of p feature points, feature vector C_jThe device consists of q track points; using σ (C)_i) And σ (C)_j) Representing the sequential sets of two feature points, respectively, then has σ (C)_i)＝(u₁,...,u_p) And σ (C)_j)＝(u₁,…,u_q) The following sequence point pairs L can be obtained as shown in the formula:

L＝(u_a1,v_b1),(u_a2,v_b2),...,(u_am,v_bm) (1)

wherein, a₁＝1,b₁＝1,a_m＝p,b_mQ; for any i 1,2,3, a_i+1＝a_iOr a_i+1＝a_i+1And b_i+1＝b_i；

C_jThe length L between sequences between feature points is expressed as follows:

then its discrete frochet distance is defined as follows:

δ_F(C_i,C_j)＝min||L|| (3)

using silhouette distance to assess the quality of the clustering task, for the ith data point: distance data points of the i vector to other points in the cluster, the silhouette distance is given by the following equation

and a (i) is the average dissimilarity between the ith data point and all other points in the cluster to which the ith data point belongs.

5. The clustering method according to claim 1, wherein the S4 comprises the following:

1) establishing an affinity graph, and calculating a corresponding sparse symmetric adjacency matrix as

N is the total number of nodes of the low-dimensional mapping of the scale vortex data in the historical observation, and D is the characteristic dimension of the data obtained by detection in the given translation window;

the GCN is used as a backbone network to further extract the obvious connection relation, and the L-th layer calculation process is as follows:

adding self-loop edges (self-loops) to the adjacency matrix A, i.e.

I is an identity matrix, wherein

Angle matrix

Is composed of

F_lDenotes the l-th layer embedding characteristics, F₀As input feature vector K₁,K₂,............,K_n；

Is a learnable matrix, maps the embedded features to a new space, and σ is a nonlinear activation function ReLU; f_LAn output feature map representing the L layers; f_LThe predicted affinity graph gathers information from the neighborhood and encodes the graph structure, and a pair of features connected by the edges of the affinity graph are used as classifier input during training; the use minimizes the Supervised contrast Loss (Supervised contrast Loss) between the predicted edge confidence and the true edge label.

2) Firstly, randomly selecting M clusters as samples, and expanding the M clusters to N neighbor clusters to obtain a subgraph Q consisting of M multiplied by N clusters_n(ii) a Introducing a cluster randomness strategy from Q_nIn random selection of K_nIndividual clustering, and sample randomness strategy, from Q_nIn selecting K at random_mEach node is used for reconstructing an affinity graph Q based on the sampling nodes;

3) when clustering is carried out, the method willThe attributes of the mesoscale vortex samples to be classified are represented in the same mode and are sent to a GCN to predict edge scores, graph analysis is directly pruned according to the predicted edge scores, and graph refinement is carried out to calculate the node intimacy and further delete unrelated edges so as to obtain a clustering reasoning result; suppose two nodes N_iAnd N_jAre each connected to n_iAnd n_jAnd the edge is provided with k common neighbor nodes, wherein C represents a clustering function, and the node affinity I can be represented as an aggregation operation:

I＝C(k/n_i,k/n_j) (6)

setting given adjacency matrix

The mutual adjacency number of the node pair is

Each element in (1)

Represents N_iAnd N_jP represents a maximum function, v represents a vector (vector) function, and then the node affinity I is expressed as:

through the steps, the nodes can be classified, and then the representative time sequence of the mesoscale vortex stage is classified.

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