An improved parallel coordinate-based multi-dimensional spectrum situation visual analysis method

Abstract

The application provides a kind of multi-dimensional spectrum situation visual analysis method based on improved parallel coordinates, which includes the following steps: step 1: taking the radiation source of spectrum data as the core, based on the information of five dimensions of radiation source space position, signal type, field strength, time and frequency, a parallel coordinate system is constructed, and the spectrum data is represented as E=(Location, Type, Energy, Time, Frequency) in the parallel coordinate system;Step 2: based on the parallel coordinate system, a double distance space clustering method is used to establish a parallel coordinate, and all points in the spectrum data are marked based on the parallel coordinate;Step 3: the similarity measure is used to determine the cluster of edge binding in the spectrum data;Step 4: the force-directed layout binding algorithm is used to bind the edges of the same cluster.

Description

Technical Field

[0001] This invention relates to the field of spectrum situation visualization and analysis technology, and in particular to a multidimensional spectrum situation visualization and analysis method based on improved parallel coordinates. Background Technology

[0002] Battlefield electromagnetic spectrum data is characterized by its large volume and multiple dimensions, and the interrelationship between its temporal and spatial attributes. Therefore, analysis across different dimensions is necessary to draw conclusions. Visualization analysis, as a method that transforms abstract data into intuitive visuals and provides a means of human-computer interaction, is increasingly becoming a hot research topic in related fields.

[0003] Current visualization analysis of spectral situation primarily focuses on one or two dimensions, such as spatiotemporal characteristics or spectral properties. While this can reveal patterns in the dimension of interest, it neglects features in other dimensions and severs the correlations between different dimensions. Therefore, current visualization analysis methods have poor visualization effects on spectral situation distribution.

[0004] To fully demonstrate the changing characteristics of the spectral situation, relying on only one or a few dimensions is insufficient to visualize the patterns of change. Furthermore, the large volume, complexity, and obscure formulas of the data hinder its visualization. Current spectral data visualization systems offer limited research on the multidimensional characteristics of the spectrum, or are relatively technical and ill-suited to the visualization needs of rapidly changing spectral mapping data. Therefore, there is an urgent need to develop a visualization analysis method that, while fulfilling the requirement of visually representing the battlefield spectral situation, allows personnel to explore the changing patterns of the spectral situation through interactive means.

[0005] Parallel coordinates are widely used in high-dimensional data visualization in disciplines such as mathematics, statistics, biomedicine, and meteorology, and have shown good performance. However, there are still some problems with directly applying parallel coordinates to the visualization of spectrum mapping data: First, there is the issue of spatial dimension projection. Spatial domain, as one of the important dimensions of spectrum data, represents the geographical attributes of radiation sources. Spatial domain itself has three dimensions: latitude, longitude, and altitude. During parallel coordinate mapping, since these dimensions are mapped as one-dimensional axes, directly projecting latitude, longitude, and altitude as three dimensions increases the dimensionality of the data and complicates the spectrum data analysis process. If a one-dimensional projection is used, the dimensionality reduction effect may cause spatially proximate radiation sources to appear relatively far apart on the one-dimensional coordinate axis, affecting the visual analysis effect. Second, there is the visual aliasing caused by large-scale spectrum mapping data. Because parallel coordinates directly plot the data on each coordinate axis, large data volumes can cause lines to overlap, severely impacting data analysis. Thirdly, there is the issue of coordinate axis sorting. Parallel coordinates can intuitively reveal the data distribution patterns of two adjacent coordinate axes. For high-dimensional spectrum mapping data, the distribution of characteristics such as space-frequency, space-time, time-frequency, and frequency-energy are key concerns for battlefield commanders. One of the research topics is how to visualize these multidimensional related characteristics.

[0006] To clearly demonstrate the changing characteristics of battlefield area spectral mapping data, this invention mainly focuses on the following three aspects:

[0007] First, to address the problem that parallel coordinates are difficult to represent the geographic spatial dimension, a region-embedded parallel coordinate is proposed for the visualization of spectrum mapping data. By linking the map with the parallel coordinate, the shortcomings of parallel coordinates in representing the geographic spatial dimension are overcome, and its ability to represent the airspace is enhanced.

[0008] Secondly, in response to the visual aliasing problem caused by the large scale of spectrum mapping data, a force-guided layout control edge binding operation under the parallel coordinate system was designed, and an iterative update process was designed to bind and aggregate curves, which effectively reduced the visual aliasing effect caused by large-scale data.

[0009] Third, interactive operations such as axis swapping and selecting coordinate subsets are designed to enhance the user experience and allow users to select appropriate coordinate axes and data subsets for analysis by clicking with the mouse. Summary of the Invention

[0010] To address the aforementioned issues, this invention provides a multi-dimensional spectrum situation visualization analysis method based on an improved parallel coordinate system, specifically for the visualization analysis of battlefield spectrum mapping data. It combines spatial information with time, frequency, and energy domains according to the different spatiotemporal attributes of the battlefield spectrum mapping data, analyzing the spatial characteristics of frequency-using equipment, the temporal sequence characteristics of electromagnetic events, and the distribution of attribute characteristics. This is combined with traditional parallel coordinate interaction methods such as axis swapping and brushing techniques to explore the spectrum situation distribution across different dimensions and in key regions. Furthermore, a force-guided layout edge-binding algorithm is introduced to reduce visual overlap and clutter in large-scale data.

[0011] This invention is achieved through the following technical means:

[0012] A multidimensional spectral situation visualization analysis method based on improved parallel coordinates, characterized by the following steps:

[0013] Step 1: Taking the radiation source of the spectrum data as the core, construct a parallel coordinate system based on the spatial location of the radiation source, signal type, field strength, time, and frequency. In this parallel coordinate system, the spectrum data is represented as E = (Location, Type, Energy, Time, Frequency).

[0014] Step 2: Based on the established parallel coordinate system, the dual distance space clustering method is used to determine the parallel coordinate clusters;

[0015] Step 3: Use the force-guided layout binding algorithm to bind edges of the same cluster to realize the drawing of parallel coordinates;

[0016] Step 4: Visualize the multidimensional spectrum mapping data based on the obtained parallel coordinates.

[0017] Furthermore, the specific operational steps of step 2 include:

[0018] Step 21: For the two sets of spectrum mapping data E i and E j Their spatial coordinates are L i =(x i y i h i ) and L j =(x j y j h j The attribute information is Attr. i and Attr j ,but:

[0019] E i and E j Spatial distance is expressed in Euclidean distance as:

[0020]

[0021] E i and E j The attribute distance is expressed using Minkowski distance as follows:

[0022]

[0023] Among them, Attr ik It is Attr i The k-th dimension attribute data; D kmax D represents the difference between the maximum and minimum values ​​of the k-th dimension attribute data. kmax =Attr kmax -Attr kmin ; m represents the dimension of the attribute;

[0024] Step 22: Set the minimum spatial threshold ε geo and minimum attribute threshold ε Attr ;

[0025] Step 23: Select unlabeled sample data E from the spectrum mapping data sample space where clustering is required. i Calculate the spatial distance between this sample data and other sample data, and compare it with the minimum spatial threshold ε. geo Comparison, denoted as set E geo ={D k |D geo (f i f j )},(k≤n);

[0026] Step 24: Calculate set E geo All samples and sample data E i The attribute distance between them, and the minimum attribute threshold ε Attr Comparison, denoted as set E Attr ={D l |D Attr (f i f j )},(l≤k);

[0027] Step 25: Recursively search E geo Samples in Attr that have not yet completed clustering will simultaneously satisfy D geo ≤ε geo And D Attr ≤ε geo The samples are labeled as one class;

[0028] Step 26: Check all samples in the sample space, randomly select a sample data Ei from the unlabeled samples, and repeat steps 23-25 ​​until all samples are labeled to complete the classification of the spectral mapping data and obtain multiple clusters.

[0029] Furthermore, step 3 includes the following specific steps:

[0030] Step 31: Calculate the correlation between different edges in the cluster and group those with similar correlation into one cluster;

[0031] Step 32: In the obtained clusters, the force-guided layout edge binding algorithm is used to bind the edges of the same cluster again.

[0032] Furthermore, the specific steps of step 31 include:

[0033] Step 311: Use E′ i ={X i Y i} represents X i and Y i An edge with endpoint C = {E′} i} 1≤i≤N Let C, G(Y) be a cluster consisting of N edges. i Y f ) represents an edge in cluster C;

[0034] Step 312: Determine the dimension div f upper distance from endpoint X f Let the p nearest endpoints be denoted as the set R of associated points. x ={X f |1≤f≤p}, and calculate X. f With set R x The distance to all points is calculated, and the maximum value is denoted as .

[0035] Step 313: Determine the dimensionality div f+1 upper distance from endpoint Y f Let the p nearest endpoints be denoted as the set R of associated points. Y ={Y f |1≤f≤p}, and calculate Y f With set R Y The distance to all points is calculated, and the maximum value is denoted as .

[0036] Step 314: Via E f The two endpoints X f and Y f We obtain edge E f The set of associated edges is:

[0037]

[0038] Step 315: Calculate the correlation between the two endpoints using the Gaussian kernel function:

[0039]

[0040] The Euclidean distance between the two points is d(X). i X j );

[0041] Step 316: Calculate edge E based on the degree of association between the two endpoints. f Relevance:

[0042] GE i E f )=G(X i X f )G(Y i Y f (6);

[0043] Among them, G(X) i X f ) represents endpoint X f The degree of correlation; G(Y) i Y f ) represents endpoint Y f The degree of correlation.

[0044] Furthermore, the specific steps of step 32 include:

[0045] Step 321: Set the number of control points P, the total number of iterations M, the displacement S, and the number of calculation rounds I in each iteration, and initialize P = 1;

[0046] Step 322: Decompose an edge into P+1 identical line segments according to the number of control points P;

[0047] Step 323: Define a global elasticity coefficient K to control the degree of edge deformation, and calculate the local elasticity coefficient K for each line segment. l :

[0048]

[0049] Where N represents the number of division points;

[0050] Step 324: Calculate the force F at each control point and bind the edges:

[0051] F = Fe + Fs (8)

[0052] S n+1 =S n×F / |F| (9)

[0053] Where Fe is the charge attraction force on the control point; Fs is the elastic tension on the control point; S gradually decreases during the iterative update process, and the initial value is S0 = 1;

[0054] Step 325: Increment the number of control points P by 1, return to step 322 for iterative updates, until the total number of iterations M is reached.

[0055] Compared with the prior art, the present invention has the following advantages:

[0056] 1. This invention combines spatial information with time, frequency, and energy domains according to the different spatiotemporal attribute information of battlefield spectrum mapping data. By combining the spatial characteristics of frequency equipment, the time sequence characteristics of electromagnetic events, and the distribution of attribute characteristics with traditional coordinate axis exchange and brushing techniques in parallel coordinate systems, the spectrum situation distribution between different dimensions and key intervals can be obtained.

[0057] 2. In view of the characteristics of large scale, complexity and variability of spectrum data, this invention introduces a force-guided layout edge binding algorithm, which reduces the visual overlap and confusion of large-scale data and effectively improves the visualization effect. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of edges and edge clusters.

[0059] Figure 2 Example of a force-guided model.

[0060] Figure 3 A visualization of the results of implementing the visualization analysis method. Detailed Implementation

[0061] The present invention will be further described below with reference to specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0062] Battlefield spectrum mapping data generally includes information in four dimensions: frequency, field strength, space, and time. In addition, electromagnetic signals also include parameters such as pulse width, polarization, phase, and signal type. This invention takes the radiation source as the core and selects information in five dimensions—the spatial location of the radiation source, signal type, field strength, time, and frequency—to construct a parallel coordinate system.

[0063] E=(Location, Type, Energy, Time, Frequency) (1)

[0064] Where E refers to spectrum mapping data, Location is the spatial location of the radiation source, Type represents the signal type, Energy represents the field strength, Time represents the time, and Frequency represents the frequency; the signal type is classified into communication signals, electromagnetic interference signals, and reconnaissance signals according to the various signal types that appear on the battlefield.

[0065] To effectively extract the location and spectral distribution characteristics of radiation sources in the battlefield area, spatial clustering is employed to cluster radiation sources with different spatial coordinates and attributes (spatial location, frequency). During clustering, to ensure geographical proximity and similar attribute information, a clustering algorithm that balances spatial characteristics and attribute information must be selected. Therefore, this invention employs a dual-distance spatial clustering method, and further incorporates a parallel coordinate design.

[0066] For spectrum mapping data, assuming the two sets of data are E i and E j Its spatial location coordinates are L i =(x i y i h i ) and L j =(x j y j h j ), the attribute information is Attr i and Attr j .

[0067] The spatial distance between the two sets of data is represented by Euclidean distance:

[0068]

[0069] Attribute distance is represented using Minkowski distance:

[0070]

[0071] Among them, Atti ik It is Attr i The k-th dimension attribute data; D kmax D represents the difference between the maximum and minimum values ​​of the k-th dimension attribute data. kmax =Attr kmax -Attr kmin ; m represents the dimension of the attribute (i.e., how many attributes are used in the calculation);

[0072] Introducing a minimum spatial threshold ε geo and minimum attribute threshold ε Attr As a standard for clustering based on spatial distance and attribute distance.

[0073] Based on this, the steps of spatial clustering include:

[0074] S1: Select unlabeled sample data E from the spectral mapping data that needs to be clustered. i Calculate the spatial distance between this sample data and other sample data, and compare it with the minimum spatial threshold ε. geo Comparison, denoted as set E geo ={D k |D geo (f i f j )},(k≤n);

[0075] S2: Calculate set E geo The attribute distances between all samples and sample data Ei, and the minimum attribute threshold ε. Attr Comparison, denoted as set E Attr ={D l |D Attr (f i f j )},(l≤k);

[0076] S3: Circular recursive search E geo and E Attr All samples that have not yet completed clustering will simultaneously satisfy D geo ≤ε geo And D Attr ≤ε geo The samples are labeled as one class;

[0077] S4: Check all samples in the sample space, randomly select a sample data Ei from the unlabeled samples, and repeat the above steps until all samples are labeled, that is, all data has been classified, then the algorithm ends.

[0078] To enhance the visualization of large-scale spectral mapping data using parallel coordinates and maintain visual continuity of connections, edge binding is employed. This allows for the transmission of more dataset information within a smaller screen area, focusing visual attention on the distribution and variation patterns of the data itself. Therefore, a similarity metric is first introduced to determine the clusters of edge bindings. Then, a force-guided layout edge binding algorithm is used to further bind edges within the same cluster, thereby reducing the visual clutter caused by multiple edges and improving the data's visual expressiveness.

[0079] (1) Similarity measurement

[0080] To discover the distribution trends of spectral data across different dimensions, data with similar distributions, trends, and close distances are sorted for easy visualization, allowing for clear analysis of the trend relationships between the data in two dimensions. To this end, this invention introduces a similarity measurement method, which describes the similarity between different edges by calculating the distance between the endpoints of two edges and their directional trends, and groups edges with similar similarities together.

[0081] For clarity, the following definitions are provided:

[0082] E′ i ={X i Y i} represents X i and Y i An edge E′ with endpoint i C = {E′ i} 1≤i≤N Let C be a cluster of N edges. Given a positive integer p, find one edge E. f The method for calculating associated edges is as follows:

[0083] Find the dimension div f upper distance from endpoint X f Let the p nearest endpoints be denoted as the set R of associated points. x ={X f |1≤f≤p}, and calculate X. f With set R x The distance to all points is calculated, and the maximum value is denoted as . Similarly, we can obtain the dimension div f+1 upper distance from endpoint Y f The set R of the p nearest endpoints Y =(Y f |1≤f≤p} and the maximum distance

[0084] Then edge E f The set C containing the associated edges Ef Both endpoints are endpoint X. f and endpoint Y f The set of associated points of the edge:

[0085]

[0086] like Figure 1 As shown, when p=5, edge E i There are 3 associated edges, with endpoint X i There are 5 associated points, endpoint Y i There are 5 associated points, and one endpoint of E1 is not at endpoint Y. i Since E1 is not an edge E, it is not part of the set of associated points.i Similarly, E2 is also an edge E. i The associated edges.

[0087] By following the steps above, we obtain edge E. f The set of associated edges based on In the edge binding algorithm for force-guided layout, edges E f The distance of the associated edge to edge E f The closer the edges are, the greater their influence; the farther apart they are, the smaller their influence. This influence is defined as similarity, and it is used to measure the influence of different edges within the same edge cluster on edge E. f The magnitude of the influence determines the curvature of the edge binding.

[0088] The similarity of an edge is composed of the similarity of its two endpoints. The Gaussian kernel function is used to calculate the similarity between the two endpoints. Let's assume an edge E... f The two sets of associated endpoints are R X and R Y The Euclidean distance between two points is represented by d(X). i X j If ), then the degree of association between the two endpoints is expressed as:

[0089]

[0090] After calculating the affinity of the endpoints, the affinity of the edges is calculated based on the affinity of the two endpoints. The calculation formula is as follows:

[0091] G(E i E f )=G(X i Y f )G(Y i Y f )

[0092] (2) Force-guided layout edge binding algorithm

[0093] The force-guided model divides edges into multiple segments and then controls deformation according to the segment nodes. It treats edges as springs and nodes as charged particles, controlling the shape, size, and direction of the edges through the magnitude and direction of the interaction forces. This allows edges of the same cluster to group together. The force-guided model effectively reduces data clutter, thus improving data visualization. It has proven effective in large-scale network layout optimization, treating complex networks as physical structures and constructing force-guided models based on nodes. This allows for the intuitive display of chaotic network models. This invention, considering the large scale and difficulty in discovering patterns in electromagnetic spectrum data, introduces force-guided layout into the parallel coordinate visualization analysis process. By bundling similar data, it enables the discovery of data patterns.

[0094] To allow the edges to change shape during binding and to minimize visual impacts such as edge intersections and overlaps, the edges are subdivided into multiple segments, such as... Figure 2 As shown, the edge is divided into 5 identical line segments by four equal division points, and edge E is controlled by nodes p0, p1, p2, and p3. i The shape, endpoint X p and Y p and X q and Y q remain unchanged. Figure 2 A schematic diagram of the force-guided model is given.

[0095] Figure 2 The two interacting edges X are shown. p Y p X q Y q The force-guided model posits that the deformation of each line segment is jointly controlled by the elastic tension of adjacent nodes and the charge attraction of adjacent edge nodes. A global elastic coefficient K is defined to control the degree of edge deformation, where a larger K results in greater edge deformation, and vice versa. Since each edge has a different length and is subdivided into different segments, the number of control points (i.e., the aforementioned division points) affects the number and length of segments, and thus also the degree of edge deformation. Therefore, the local elastic coefficient K for each segment is calculated separately. l Based on this, the deformation of the nodes is calculated.

[0096]

[0097] Where N represents the number of nodes, and so on. Figure 2 Taking point p2 as an example, the elastic tensions it experiences from p1 and p3 are as follows:

[0098] F S1 =K l *d(p1, p2)

[0099] F S2 =K l *d(p2, p3)

[0100] Because of edge X p Y p Since the edges are divided equally, d(p1, p2) = d(p2, p3). Therefore, each node on an edge receives the same elastic gravitational force from its neighboring nodes.

[0101] Node p2 is also subject to the electric charge attraction from its adjacent node q2. This electric charge attraction is directly proportional to the similarity between the two edges and inversely proportional to the square of the distance between the nodes. The calculation formula is as follows:

[0102]

[0103] Therefore, the force acting on node p2, which is the resultant force of elastic tension and charge attraction, is:

[0104] F = F S1 +F S2 +F e

[0105] To achieve the desired data clustering effect from the force-guided layout, multiple iterative updates of control points are needed to gradually improve the clustering effect and complete the clustering of large-scale data. Three sets of parameters are designed to control the iterative update process of the force-guided layout: the number of control points P, the number of iterations M, the displacement S, and the number of rounds I in each iteration. Initialization is P=1, and the midpoint of the line is used as the initial update control point. Each iteration updates the control points according to the length of the line, and so on.

[0106] The specific iterative update steps are as follows:

[0107]

[0108]

[0109] Example

[0110] To verify the practical effect of the proposed method, a system based on an improved parallel coordinate multidimensional spectral situation visualization analysis method was constructed (the system construction process adopts the implementation method in the prior art, which is not modified in this application and will not be described in detail here), and the above method was implemented. The system software platform is VS2015, the graphics engine is OSG, and the development language is C++. Open Scene Graph (OSG) is an open-source 3D graphics engine widely used in virtual simulation, virtual reality, and visualization analysis. It uses OpenGL as its underlying platform, is written in C++, and can run on multiple operating systems such as Windows, UNIX / Linux, and Mac OS X. It features rapid development, rich functionality, free and open source, strong scalability and portability, and is suitable for rendering large-scale scenes. The visualization analysis method demonstrated by the system developed based on the method proposed in this invention is as follows: Figure 3 As shown.

[0111] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multidimensional spectral situation visualization analysis method based on improved parallel coordinates, characterized in that, Includes the following steps: Step 1: Using the radiation source of the spectrum data as the core, construct a parallel coordinate system based on the spatial location of the radiation source, signal type, field strength, time, and frequency. In this parallel coordinate system, the spectrum data is represented as follows: ； Step 2: Based on the established parallel coordinate system, the dual distance space clustering method is used to determine the parallel coordinate clusters; Step 3: Use the force-guided layout binding algorithm to bind edges of the same cluster to realize the drawing of parallel coordinates; Step 4: Visualize the multidimensional spectrum mapping data based on the obtained parallel coordinates; Step 3 includes the following specific steps: Step 31: Calculate the correlation between different edges in the cluster and group those with similar correlation into one cluster; Step 32: In the obtained clusters, the force-guided layout edge binding algorithm is used to bind the edges of the same cluster again; Step 31 includes the following specific steps: Step 311: Use express and An edge with endpoint 1. Let C represent a cluster consisting of N edges. This represents an edge in cluster C; Step 312: Determine the dimensions upper distance to endpoint The p nearest endpoints are denoted as the set of associated points. and calculate With sets The distance to all points is calculated, and the maximum value is denoted as . ; Step 313: Determine the dimensionality upper distance to endpoint The closest Let the set of endpoints be denoted as the set of associated points. and calculate With sets The distance to all points is calculated, and the maximum value is denoted as . ; Step 314: Through The two endpoints as well as , get the edge The set of associated edges is: ； Step 315: Calculate the correlation between the two endpoints using the Gaussian kernel function: ； The Euclidean distance between the two points is ; Step 316: Calculate the edge based on the degree of association between the two endpoints. Relevance: ； in, Endpoints The degree of correlation; Endpoints The degree of correlation; Step 32 includes the following specific steps: Step 321: Set the number of control points P, the total number of iterations M, the displacement S, and the number of calculation rounds I in each iteration, and initialize P=1; Step 322: Decompose an edge into P+1 identical line segments according to the number of control points P; Step 323: Define a global elasticity coefficient K to control the degree of edge deformation, and calculate the local elasticity coefficient for each line segment. : ； Where N represents the number of division points; Step 324: Calculate the force F at each control point and bind the edges: ； ； Where Fe is the charge attraction force on the control point; Fs is the elastic tension on the control point; S gradually decreases during the iterative update process, and the initial value is S0=1; Step 325: Increment the number of control points P by 1, return to step 322 for iterative updates, until the total number of iterations M is reached.

2. The method for multidimensional spectral situation visualization analysis based on improved parallel coordinates according to claim 1, characterized in that, Step 2 includes the following specific steps: Step 21: For the two sets of spectrum mapping data and Their spatial coordinates are respectively and The attribute information is as follows: and ,but: and Spatial distance is expressed in Euclidean distance as: ； and The attribute distance is expressed using Minkowski distance as follows: ； in, yes The Dimensional attribute data; This represents the difference between the maximum and minimum values ​​of the k-th dimension attribute data. ; m represents the dimension of the attribute; Step 22: Set the minimum space threshold and minimum attribute threshold ; Step 23: Select unlabeled sample data from the spectrum mapping data sample space where clustering is required. Calculate the spatial distance between this sample data and other sample data, and compare it with the minimum spatial threshold. Comparison, denoted as a set ; Step 24: Calculate the set All samples and sample data The attribute distance between them, and the minimum attribute threshold. Comparison, denoted as a set ; Step 25: Recursive Search and Samples that have not yet completed clustering will simultaneously satisfy... and The samples are labeled as one class; Step 26: Examine all samples in the sample space and randomly select one sample from the unlabeled samples. Repeat steps 23-25 ​​until all samples are labeled, completing the spectral mapping data classification and obtaining multiple clusters.

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