Scatter plot similarity measurement method, terminal device, and storage medium

By combining PointNet network with contrastive learning and data augmentation, the problems of high label cost and subjective judgment bias in scatter plot similarity measurement are solved, and an efficient and accurate unsupervised scatter plot similarity measurement is achieved.

CN115564974BActive Publication Date: 2025-11-18CENT SOUTH UNIV
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Patent Information

Application Number
CN202211362223.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-11-02
Publication Date
2025-11-18
Estimated Expiration
2042-11-02

AI Technical Summary

Technical Problem

Existing technologies suffer from high labeling costs and subjective judgment differences leading to biased results in scatter plot similarity measurement, and also have poor scalability.

Method used

By employing the PointNet network combined with contrastive learning, scatter plot features are extracted through sampling and data augmentation methods, and similarity is calculated using unsupervised learning, thereby reducing network complexity and improving the accuracy of the results.

Benefits of technology

It achieves label-free scatter plot similarity measurement, reduces costs, improves the objectivity and scalability of results, and can measure similarity in dimensions that are difficult to calculate using traditional methods.

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Abstract

The application discloses a scatter plot similarity measurement method, a terminal device and a storage medium, uses PointNet as a feature extractor, and integrates a sampling operation into the similarity measurement method, performs comparative learning training on a two-dimensional point cloud with the aid of PointNet, uses point cloud data as input to enable the measurement result to be independent of the visual representation of the scatter plot, enables the network to learn the features of the scatter data itself, and the sampling operation enables irregular point cloud data to better cooperate with the PointNet, different data enhancement operations guide the learning direction of the network, and the similarity in different dimensions of the scatter plot is measured. The application does not require labeled data, and solves the problems of high cost of manually obtaining labels and deviation of results caused by subjective judgments of different people.
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Description

Technical Field

[0001] This invention relates to a scatter plot similarity measurement technique, and more particularly to a scatter plot similarity measurement method, terminal device, and storage medium. Background Technology

[0002] The basic idea of ​​scatter plot similarity measurement is to perform feature calculation on the input scatter plot data and measure the similarity of the scatter plots by the distance between the features. According to the type of input data and the principle of feature calculation, the existing measurement methods can be divided into the following four categories: (1) traditional calculation methods based on scatter plot images; (2) traditional calculation methods based on scatter plot point cloud data; (3) deep learning methods based on scatter plot images; and (4) deep learning methods based on scatter plot point cloud data.

[0003] Methods based on scatter plot image data use rendered scatter plot images as input, but the measurement results of these image-based methods are affected by the visualization (such as the size, shape, color, and axis selection of points), which can cause some characteristics of the scatter plot data itself to be ignored. Methods based on scatter plot point cloud data use raw scatter data as input, meaning the data only contains the coordinate information of each point, so the final measurement results can be independent of the visualization. Methods based on traditional computation use manually designed feature descriptors to calculate features of the input data, but can only measure similarity in dimensions that can be calculated manually. Methods based on deep learning use deep neural networks to automatically extract features from the input data, so similarity can also be measured in dimensions that are difficult to calculate manually.

[0004] Traditional computational methods based on scatter plot images: Tatu et al. [1] developed many image processing methods to quantify correlation and class separation, i.e. the degree of separation of (colored) classes in a scatter plot. Lehmann et al. [2] used a greedy method to allow users to interactively find a large number of related plots in a large space. Shao et al. [3] proposed a basalt-based matching and sorting scheme to facilitate querying specific patterns using a set of basic image patches extracted from existing scatter plots.

[0005] Traditional computational methods based on scatter plot point cloud data: Scagnostics describes a series of measures of certain attributes in scatter plot point clouds. This term and idea were coined by John Tukey and Paul Tukey, although they did not publish it. Later, Wilkinson et al. [4] elaborated on Scagnostics based on the latest advances in graph theory for high-dimensional scatter plot data and gave specific computational methods, defining nine artificial features (such as data distribution, density, shape, monotonicity, etc.) to describe scatter plots. Sips et al. [5] proposed two quality measurement methods to quantify class consistency through centroid and spatial distribution entropy. Reshef et al. [6] developed the Maximum Information Coefficient (MIC) score to detect linear and nonlinear associations between pairs of variables.

[0006] Deep learning methods based on scatter plot images: Ma et al. [7] used human visual perception information to simulate subjective similarity. The core idea is to use human judgment of scatter plot similarity as training data and use state-of-the-art deep neural networks to automatically construct features from scatter plot images. Convolutional neural networks can learn rich semantic features from large-scale data by adjusting their internal parameters.

[0007] Deep learning methods based on scatter plot point cloud data: [8] et al. proposed a new visual quality metric based on human perception using CNN to evaluate the relevance in scatter plots and rated the relevance of the visualization dimensions of scatter plots.

[0008] The above deep learning methods also have some problems: (1) A huge labeled dataset is needed to guide the learning direction of the network, and the cost of manually generating these labels is very high; (2) Differences in subjective judgment by each person will cause deviations in the results; (3) Poor scalability, only features of specific dimensions can be extracted based on label information, and when other dimensions are to be measured, relabeling is required. Summary of the Invention

[0009] The technical problem to be solved by this invention is to provide a scatter plot similarity measurement method, terminal device and storage medium to address the shortcomings of existing technologies, thereby effectively solving the problem of high cost of obtaining labels in supervised learning.

[0010] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a scatter plot similarity measurement method, comprising the following steps:

[0011] S1. Obtain the original point cloud dataset S of multiple scatter plots;

[0012] S2. Sample each scatter plot in the original point cloud dataset S to obtain the sampled dataset P;

[0013] S3. Perform data augmentation on each scatter plot in the dataset P to obtain the augmented dataset P';

[0014] S4. Using the dataset P and the augmented dataset P' as inputs to the PointNet network, extract the features of the dataset P and the augmented dataset P' to obtain the first feature set H and the second feature set H'.

[0015] S5. Calculate the similarity between the first feature set H and the second feature set H' to obtain the similarity matrix V;

[0016] S6. Calculate the contrast loss function L of the PointNet network using the similarity matrix V;

[0017] S7. Minimize the contrast loss function L to optimize the parameters of the PointNet network.

[0018] This invention proposes a scatter plot similarity measurement model based on PointNet and contrastive learning. It utilizes a PointNet network with optimized parameters to extract features from scatter plots and then calculates the similarity between these features. PointNet allows the network to use scatter plot point cloud data as input. The unsupervised contrastive learning approach of this invention effectively addresses the high cost of obtaining labels in existing supervised learning methods. The determined data augmentation method ensures the objectivity of the final result, and the selection of different data augmentation methods can extract features from various dimensions. This invention introduces sampling techniques into the similarity measurement method, effectively reducing the network complexity while ensuring the accuracy and stability of the similarity measurement results.

[0019] To further optimize the PointNet network and improve the accuracy of similarity measurement results, the method of this invention also includes:

[0020] S8. Repeat steps S4 to S7. When the preset number of iterations is reached or the contrast loss function L converges, the feature extraction network of the scatter plot is obtained.

[0021] In this invention, the feature extraction network of the scatter plot is used to extract the features of the scatter plot, and the distance between the features is calculated to obtain the similarity between the scatter plots.

[0022] In step S1 of the present invention, the original point cloud dataset S is in the format [n, m, 2], where n is the number of scatter plots in the original point cloud dataset, m represents the number of points in each scatter plot, and 2 represents that the coordinates of each scatter plot are two-dimensional.

[0023] In step S2 of the present invention, the format of the sampled dataset P is [n, t, 2], where t represents the number of points in each scatter plot after sampling.

[0024] In step S5, the similarity calculation formula is:

[0025]

[0026] Where a and b are both k-dimensional feature vectors, and a∈H, b∈H'.

[0027] In step S6, the expression for the contrast loss function L is:

[0028]

[0029] In this dataset, P contains n scatter plots, and P' represents the corresponding set of n augmented scatter plots. x represents a scatter plot in P. For each x, there is a corresponding x+∈P', which is its augmented scatter plot in the augmented set P'. Each scatter plot x has one positive pair (x, x+). Since x-∈P∪P' (x-≠x and x-≠x+), each scatter plot x has 2n-2 negative pairs (x, x-). In the formula, g() represents the scatter plot feature extraction function, i.e., PointNet; sim() calculates the similarity between the extracted features.

[0030] A terminal device includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program to implement the steps of the method described above.

[0031] A computer-readable storage medium having a computer program / instructions stored thereon; when the computer program / instructions are executed by a processor, they implement the steps of the method described above in this invention.

[0032] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention utilizes PointNet for comparative learning training on two-dimensional point clouds. Using point cloud data as input allows the measurement results to be independent of the scatter plot visualization, enabling the network to learn the features of the scatter data itself. Sampling operations allow irregular point cloud data to better cooperate with PointNet. Different data augmentation operations guide the network's learning direction to measure the similarity of the scatter plot in different dimensions. This invention does not require labeled data, perfectly solving the problems of high cost of manually obtaining labels and biased results caused by different subjective judgments of different people. Attached Figure Description

[0033] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0034] Figure 2 This refers to the change in the loss function value during training in Embodiment 1 of the present invention;

[0035] Figures 3(a) and 3(b) show the changes in Top1 and Top5 accuracy during training in Embodiment 1 of the present invention, respectively. Detailed Implementation

[0036] 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.

[0037] In this document, the terms "first," "second," and other similar words are not intended to imply any order, quantity, or importance, but are merely used to distinguish different elements. The terms "one," "a," and other similar words are not intended to indicate the existence of only one of the stated things, but rather that the description pertains to only one of the two stated things, which may include one or more. The terms "comprising," "including," and other similar words are intended to indicate a logical relationship, not a spatial relationship. For example, "A includes B" means that logically B belongs to A, not that spatially B is located inside A. Furthermore, the meanings of the terms "comprising," "including," and other similar words should be considered open-ended, not closed. For example, "A includes B" means that B belongs to A, but B does not necessarily constitute all of A; A may also include other elements such as C, D, and E.

[0038] Example 1

[0039] Embodiment 1 of the present invention provides a scatter plot similarity measurement method based on contrastive learning, comprising the following steps:

[0040] S1. Obtain the original point cloud dataset S for multiple scatter plots;

[0041] S2. Sample each scatter plot in the dataset S obtained in step S1 to obtain the sampled dataset P;

[0042] S3. Perform data augmentation on each scatter plot in the dataset P obtained in step S2 to obtain the augmented dataset P';

[0043] S4. Input dataset P and dataset P' into PointNet for feature extraction, and obtain feature sets H and H' respectively;

[0044] S5. Calculate the similarity Sim(H,H′) between the feature sets H and H′ obtained in step S4 to obtain the similarity matrix V;

[0045] S6. Calculate the contrast loss L using the similarity matrix V obtained in step S5;

[0046] S7. Minimize the contrast loss L obtained in step S6, and optimize the parameters of the entire network;

[0047] S8. Iterate from S4 to S7 repeatedly until the preset number of iterations K is reached or the contrast loss L no longer decreases;

[0048] S9. Separate the part of the contrastive learning network that can extract scatter plot features to obtain a scatter plot feature extraction network N;

[0049] S10. Use the network N obtained in step S9 to extract features from the scatter plot, and calculate the similarity between scatter plots by the distance between features.

[0050] The data in the original dataset obtained in step S1 can be any combination of two dimensions of high-dimensional data, or it can be high-dimensional data reduced to two dimensions. A high-dimensional dataset can be used to generate multiple scatter plots through different combinations of dimensions, or through different dimensionality reduction methods and parameters. Regardless of the method used, each scatter plot in the dataset corresponds to a two-dimensional point cloud. Therefore, the dataset format is [n, m, 2], where n represents the number of scatter plots, m represents the number of points in each scatter plot, and 2 indicates that the coordinates of each scatter plot are two-dimensional. It is important to note that the value of m may differ for each scatter plot. If the scatter plots are generated from the same high-dimensional data, the value of m will be the same; if the scatter plots are generated from different high-dimensional data, the value of m may be different.

[0051] Steps S2 to S8 constitute a complete comparative learning process. Sampling in step S2 aligns the number of points in the scatter plots, allowing the entire dataset to be simultaneously fed into PointNet in step S4; it also reduces data dimensionality, decreasing the overall network complexity. The sampled dataset is formatted as [n, t, 2], where n represents the number of scatter plots, t indicates that each scatter plot contains t points, and 2 indicates that the coordinates of each scatter plot are two-dimensional.

[0052] Different sampling methods can be selected based on different task requirements. For example, blue noise sampling can be used to measure perceptual similarity, which can ensure that the sampled data retains the overall shape of the original data as much as possible.

[0053] Data augmentation in step S3 is crucial for the contrastive learning network to learn the desired features. The appropriate data augmentation operation and its degree must be selected based on the task requirements. For example, to measure perceptual similarity, data augmentation operations such as rotation, translation, and shuffling are needed; furthermore, data augmentation is key to the network's high scalability. Similarly, if one wants to measure perceptual similarity while also ensuring high similarity between scatter plots with different coordinate axis selections, coordinate axis transformation can be incorporated into the data augmentation. This transformation simply requires swapping the order of the x and y coordinates during the parsing of the scatter plot data.

[0054] PointNet, used in step S4, is a commonly used feature extractor in the point cloud field. To ensure the stability of multi-dimensional point clouds acquired from different viewpoints, it incorporates a feature space alignment network. However, in two-dimensional point clouds, since there is only one viewpoint, feature space alignment is unnecessary, and this alignment network can negatively impact the final performance of contrastive learning. Therefore, this embodiment optimizes it to better support two-dimensional point clouds. The extracted feature sets H and H' are in the format [n,k], where n represents the number of scatter plots and k represents the dimension of the features.

[0055] The similarity matrix in step S5 is calculated using the following cosine similarity:

[0056]

[0057] Here, a and b are both k-dimensional feature vectors, and a∈H, b∈H'.

[0058] The contrast loss in step S6 is the following InfoNCE loss:

[0059]

[0060] Where n is the number of scatter plots in dataset P, and x represents a scatter plot in P; for each x, there is a corresponding xi. + Let x ∈ P' be the augmented scatter plot of x in the augmented set P', where each scatter plot x has one positive pair (x, x). + );x - ∈P∪P', x - ≠x and x - ≠x + Each scatter plot x has 2n-2 negative pairs (x, x). - The function g() represents the scatter plot feature extraction function, i.e., PointNet; the function sim() calculates the similarity between the extracted features.

[0061] Minimizing the InfoNCE loss in step S7 aims to make the distance between positive pairs closer and the distance between negative pairs farther and farther.

[0062] The part in step S9 that extracts the scatter plot features is the sampling in step S2 and the PointNet in step S4 after the iteration is completed.

[0063] The similarity calculated in step S10 is also cosine similarity.

[0064] Compared to traditional scatter plot similarity measurement methods, this invention can measure similarity in dimensions that are difficult to calculate using traditional methods, such as perceptual similarity. Compared to other deep learning methods, this invention does not require labeled data, perfectly solving the problems of high costs associated with manually obtaining labels and biases caused by differing subjective judgments from different individuals. Furthermore, through sampling operations, the dimensionality of the network input data can be reduced to 200*2 (coordinates of 200 points), while the dimensionality of other image-based network input data is generally 256*256 (the size of the scatter plot canvas). This significantly reduces the complexity of the entire network and accelerates the training speed. Flexible data augmentation operations make the network used in this embodiment highly scalable; when similarity needs to be measured, only the corresponding data augmentation operation needs to be added.

[0065] This invention, based on a contrastive learning model framework, uses PointNet as a feature extractor and incorporates sampling operations to present a novel method for measuring scatter plot similarity. By leveraging PointNet for contrastive learning training on a two-dimensional point cloud, and using point cloud data as input, the measurement results become independent of the scatter plot's visual representation, allowing the network to learn the inherent features of the scatter data itself. Sampling operations enable irregular point cloud data to better align with PointNet. Different data augmentation operations guide the network's learning direction to measure the similarity of scatter plots across different dimensions.

[0066] This embodiment compares the method with two classic methods: Scagnostics, based on point cloud data, and HOG, based on image data. Because other deep learning methods suffer from data loss, their algorithms cannot be reproduced, making direct comparison impossible. However, this embodiment still offers significant advantages over other deep learning methods. Embodiment 1 of this invention outperforms the other two methods in measuring perceptual similarity.

[0067] For a given scatter plot, choosing different coordinate axes will result in two scatter plots that appear different. However, they are actually scatter plots generated from the same data point and should be highly similar.

[0068] from Figure 2 It can be seen that the loss function value of Embodiment 1 of the present invention is steadily decreasing. This indicates that the distance between positive example pairs is getting closer and closer, while the distance between negative example pairs is getting farther and farther, and the entire network is steadily optimizing in the desired direction.

[0069] As can be seen from Figures 3(a) and 3(b), the accuracy of Embodiment 1 of the present invention increases with the number of iterations. The Topk accuracy is defined as follows: if an enhanced scatter plot appears among the top k most similar scatter plots, then the scatter plot data is considered correct. The proportion of correct data to all data is the Topk accuracy. Here, k takes values ​​of 1 and 5, representing Top1 accuracy and Top5 accuracy, respectively. The Top1 accuracy in Figure 3(a) is not very high, indicating that Embodiment 1 of the present invention does not overfit. This is because there are still some differences between the enhanced data and the original data, and there may be some data in the dataset that are more similar to the original data. Therefore, the similarity between the enhanced data and the original data is not necessarily the highest, so the Top1 accuracy cannot be too high. However, the Top5 accuracy in Figure 3(b) is very high, indicating that the similarity measurement effect of the present invention is very good. This is because the similarity between the enhanced data and the original data is higher than the similarity between most data in the dataset and the original data.

[0070] Example 2

[0071] 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.

[0072] 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.

[0073] 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.

[0074] 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.

[0075] Example 3

[0076] 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.

[0077] 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.

[0078] 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.

[0079] 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.

[0080] 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.

[0081] 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.

[0082] 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.

[0083] The references cited in this invention are as follows:

[0084] [1]TATU A,ALBUQUERQUE G,EISEMANN M,et al.Combining automated analysis and visualization techniques for effective exploration of high-dimensionaldata[C] / / 2009IEEE Symposium on Visual Analytics Science and Technology.IEEE,2009:59-66.

[0085] [2]LEHMANN DJ,ALBUQUERQUE G,EISEMANN M,et al.Selecting coherent andrelevant plots in large scatterplot matrices[C] / / Computer Graphics Forum:volume 31.Wiley Online Library,2012:1895-1908.

[0086] [3]SHAO L,BEHRISCH M,SCHRECK T,et al.Guided sketching for visualsearch and exploration in large scatter plot spaces.[C] / / EuroVA@EuroVis.2014.

[0087] [4]WILKINSON L,ANAND A,GROSSMAN R.Graph-theoretic scagnostics[C] / / Information Visualization,IEEE Symposium on.IEEE Computer Society,2005:21-21.

[0088] [5]SIPS M,NEUBERT B,LEWIS J P,et al.Selecting good views of high-dimensional data using class consistency[C] / / Computer Graphics Forum:volume28.Wiley Online Library,2009:831-838.

[0089] [6]RESHEF D N,RESHEF Y A,FINUCANE H K,et al.Detecting novelassociations in large data sets[J].science,2011,334(6062):1518-1524.

[0090] [7]MA Y,TUNG AK,W ANG W,et al.Scatternet:A deep subjective similaritymodel for visual analysis

[0091] of scatterplots[J].IEEE transactions on visualization and computergraphics,2018,26(3):1562-1576.

[0092] [8] L,ZOU Y, M,et al.Learning a perceptualquality metric for correlation in scatterplots[J].VMV 2019-Vision,Modelingand Visualization,2019。

Claims

1. A scatter plot similarity measurement method, characterized in that, Includes the following steps: S1. Obtain the original point cloud dataset S of multiple scatter plots; S2. Sample each scatter plot in the original point cloud dataset S to obtain the sampled dataset P; S3. Perform data augmentation on each scatter plot in the dataset P to obtain the augmented dataset P'; S4. Using the dataset P and the augmented dataset P' as inputs to the PointNet network, extract the features of the dataset P and the augmented dataset P' to obtain the first feature set H and the second feature set H'. S5. Calculate the similarity between the first feature set H and the second feature set H' to obtain the similarity matrix V; S6. Calculate the contrast loss function L of the PointNet network using the similarity matrix V; S7. Minimize the contrast loss function L to optimize the parameters of the PointNet network; S8. Repeat steps S4 to S7. When the preset number of iterations is reached or the contrast loss function L converges, the feature extraction network of the scatter plot is obtained. S9. Separate the part of the contrastive learning network that can extract scatter plot features to obtain a scatter plot feature extraction network N; S10. Use the network N obtained in step S9 to extract features from the scatter plot, and calculate the similarity between scatter plots by the distance between features.

2. The scatter plot similarity measurement method according to claim 1, characterized in that, The feature extraction network of the scatter plot is used to extract features from the scatter plot, and the distance between the features is calculated to obtain the similarity between the scatter plots.

3. The scatter plot similarity measurement method according to claim 1, characterized in that, In step S1, the original point cloud dataset S is in the format [n, m, 2], where n is the number of scatter plots in the original point cloud dataset, m represents the number of points in each scatter plot, and 2 represents that the coordinates of each scatter plot are two-dimensional.

4. The scatter plot similarity measurement method according to claim 3, characterized in that, In step S2, the format of the sampled dataset P is [n, t, 2], where t represents the number of points in each scatter plot after sampling.

5. The scatter plot similarity measurement method according to claim 1, characterized in that, In step S5, the similarity calculation formula is: Here, a and b are both k-dimensional feature vectors, and a∈H, b∈H'.

6. The scatter plot similarity measurement method according to claim 1, characterized in that, In step S6, the expression for the contrast loss function L is: Where n is the number of scatter plots in dataset P, and x represents a scatter plot in P; for each x, there is a corresponding xi. + Let x ∈ P' be the augmented scatter plot of x in the augmented set P', where each scatter plot x has one positive pair (x, x). + );x - ∈P∪P', x - ≠x and x - ≠x + Each scatter plot x has 2n-2 negative pairs (x, x). - The function g() represents the scatter plot feature extraction function, i.e., PointNet; the function sim() calculates the similarity between the extracted features.

7. A terminal device, comprising a memory, a processor, and a computer program stored in the memory; characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program / instructions stored thereon; characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 6.

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