Scatter plot overdraw solution effectiveness evaluation method

Abstract

The application provides a method for evaluating the effectiveness of a scatter plot overdraw solution, comprising obtaining scatter plot data before and after scatter plot layout, calculating the overlap degree between different data points after scatter plot layout, and the feature retention degree of the feature retention condition of the scatter plot after layout; the feature retention degree includes a plurality of specific feature retention indicators for evaluating the specific feature retention condition of the scatter plot and a comprehensive feature retention rate for comprehensively evaluating the feature retention condition of the scatter plot. The application provides a complete set of node displacement method effective evaluation indicators based on visual tasks, so that there is no excessive correlation calculation between different indicators, the probability of repeated data operation is reduced, and the effectiveness of data point displacement is systematically evaluated from the retention conditions of a plurality of specific features.

Description

Technical Field

[0001] This invention relates to the field of scatter plot overdraw evaluation technology, and more specifically to a method for evaluating the effectiveness of scatter plot overdraw solutions. Background Technology

[0002] Overdrawing data points is a common problem in data visualization. For example, when a dataset has a large number of points and large visual nodes, overlapping data points often occur, leading to many visualization problems. Specifically, overdrawing makes it difficult to obtain the location, number, and distribution of points, resulting in information loss; it also reduces the readability and interpretability of charts.

[0003] In the fields of graph layout and information visualization, node displacement is a widely used and typical method. This method alleviates over-drawing by changing the spatial position of nodes to minimize their overlap in the visual space. To improve visibility, researchers have proposed many node displacement methods, which are generally classified into three categories based on whether the size, shape, and possible placement of the nodes are fixed during displacement: node scattering, subspace mapping, and dynamic space partitioning.

[0004] Node scattering spreads a set of visible nodes of a given size and shape out of their original positions to avoid overlap, such as PFS, VPSC, PRISM, GTree, and RWordle-L. Subspace mapping methods consist of two independent steps: spatial partitioning and subspace matching. First, the scatter plot coverage area is divided into a series of spatially exclusive subspaces, without considering any data information. Then, data points are mapped to subspaces by matching the spatial nearest neighbors between subspaces and between data points, such as DGrid, HaGrid, IsoMatch, PRSP, and generalized scatter plots. Dynamic spatial partitioning methods determine the size, shape, and position of nodes dynamically, such as CVT and Nmap.

[0005] In addressing the overdraw problem, the displacement of nodes (data points) inevitably leads to the loss of some original information. Specifically, modifications to the underlying data pose a risk of both shape and density distribution distortion in such methods, impacting scatter plot visualization tasks such as cluster recognition and shape recognition.

[0006] Therefore, evaluating the effectiveness of various node displacement methods is an important issue. Previous literature has proposed many evaluation methods, including overlap indices, relative position preservation indices, displacement indices, and global shape indices. Among them, the overlap index can calculate the overlap rate of the scatter plot to characterize the degree of overlap; the relative position preservation index is used to measure whether the relative orientation of point pairs in the previous and subsequent scatter plots remains consistent; the displacement index is used to evaluate the relative displacement distance of points; the global shape index can capture the initial global shape and evaluate its preservation degree; and there is also the layout diffusion index, which is used to limit the minimum size of the scatter plots to avoid creating unreadable markers and large areas that result in no markers.

[0007] Existing evaluation methods generally involve simple combinations of the aforementioned indicators, which presents several problems: the evaluation schemes are often unsystematic, leading to confusion regarding the relationships between different indicators, and the high degree of correlation between different indicators results in redundancy. For example, both the global shape preservation indicator and the layout diffusion indicator involve the ratio of the area before and after the scatter plot layout.

[0008] Secondly, several metrics have low correlation with the visual performance of scatter plots, affecting the visual effectiveness of the scatter plots. Furthermore, there are no corresponding metrics to represent the density preservation between arbitrary combinations of scatter points after layout, the clustering of similar data points, and the current state identification of data points, resulting in incomplete existing metrics. Summary of the Invention

[0009] In view of this, the problem to be solved by the present invention is to provide an evaluation method for the effectiveness of the scatter plot over-drawing solution. It provides a complete set of effective evaluation indicators for node displacement methods based on visual tasks, so that there is no excessive correlation calculation between different indicators, reducing the probability of data duplication calculation, and systematically evaluating the displacement effectiveness of data points from the preservation of multiple specific features.

[0010] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0011] An evaluation method for the effectiveness of a scatter plot overdraw solution includes acquiring scatter plot data before and after scatter plot layout, calculating the degree of overlap between different data points after scatter plot layout and the degree of feature preservation of the scatter plot after layout.

[0012] The degree of feature preservation includes several specific feature preservation indicators for evaluating the preservation of specific features in a scatter plot, and a comprehensive feature preservation rate for comprehensively evaluating the preservation of features in a scatter plot.

[0013] Furthermore, the method for obtaining the comprehensive feature retention rate is as follows: several angle axes with different tilt angles are set, and data points are arranged according to the projection positions of the data points before and after the layout on the angle axes. The Kendall similarity of the data points arranged before and after the layout of each angle axis is calculated, and the average Kendall similarity value of all angle axes is defined as the comprehensive feature retention rate.

[0014] Furthermore, the specific feature preservation indicators include displacement minimization and k-nearest neighbor retention rate determined based on local features, density retention rate and shape retention rate determined based on global features, so as to judge the feature preservation of the scatter plot layout from four perspectives respectively.

[0015] The displacement minimization is used to represent the moving distance value of all scatter plots after the scatter plot layout. The k-nearest neighbor retention rate is used to represent the retention of the types and number of neighboring data points of each data point after the layout. The density retention rate is used to measure the density retention of scatter points in any region after the scatter plot layout. The shape retention rate is used to measure the contour retention of several data points after the layout.

[0016] Furthermore, the method for obtaining the minimum displacement value is as follows: adjust the scaling ratio of the scatter plot before layout so that its size is the same as that of the scatter plot after layout, and calculate and align the center coordinates of the scatter plots before and after layout.

[0017] Calculate the distance between corresponding data points before and after the layout of all data points in the scatter plot, and obtain the average value of all data point distances.

[0018] Furthermore, the method for obtaining the k-nearest neighbor retention rate is as follows: set a judgment data point, use the VP-Tree algorithm to determine several neighbor data points that are close to the judgment data point, obtain the types and corresponding quantities of several neighbor data points before and after the layout, and determine the neighbor retention rate based on the retention of the types and quantities of neighbor data points before and after the layout of the judgment data point.

[0019] The average nearest neighbor retention rate for all data points is the k-nearest neighbor retention rate.

[0020] Furthermore, the number of adjacent data points is set to be the same before and after the layout.

[0021] Furthermore, the density retention rate is obtained by: obtaining the average Euclidean distance of all data points before and after layout and defining it as the regional density of the data point; arranging the data points before and after layout according to the regional density; and then taking the quantile of the data point position. The average value of the difference between the quantiles of all data points before and after layout is defined as the density retention rate.

[0022] Furthermore, the method for obtaining the shape retention rate is as follows: set a data point as the center data point, construct several standard graphics of different sizes and dimensions around the geometric center of the center data point, obtain several data points in the original scatter plot that are closest to the outline of the standard graphics and generate a measurement point group, calculate the dissimilarity between the graphic formed by the measurement point group in the scatter plot after layout and the standard graphics, and define the average value of all standard graphics as the shape retention rate.

[0023] Furthermore, the standard graphic can be either a circle or a polygon.

[0024] Furthermore, the degree of overlap includes an overlap rate, which is obtained by: combining data points in the scatter plot after layout into pairs, calculating the overlap area between the combined data points, dividing by the area of ​​the smallest data point in the combination to generate an overlap value, and calculating the average of all overlap values ​​as the overlap rate of the scatter plot.

[0025] The advantages and positive effects of this invention are:

[0026] By setting up a complete set of node displacement methods based on visual tasks, effective evaluation indicators are obtained. These indicators include the degree of overlap of the data graph before and after its layout (before and after changing the spatial position of the nodes), displacement minimization, k-nearest neighbor retention rate, density retention rate, shape retention rate, and comprehensive feature retention rate. The visualization of the data graph before and after its layout and the retention of data features are evaluated from multiple specific data point features. This avoids excessive correlation calculations between different indicators, reduces the probability of data duplication, and systematically evaluates the effectiveness of data point displacement from the retention of multiple specific features.

[0027] The density retention rate index is obtained by using the difference in quantiles of data points, which avoids the influence of regional division and regional density ranking, thus improving the accuracy of evaluating the density retention rate.

[0028] The shape retention rate index assesses the external shape retention of data by calculating the average distance value of the measurement point group before layout and judging the difference between the average distance value of all data points in the measurement point group after layout. It also includes an examination of the semantic structure shape (cluster shape) within the distribution. Attached Figure Description

[0029] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0030] Figure 1 This is an overall structural diagram of a method for evaluating the effectiveness of a scatter plot overdrawing solution according to the present invention;

[0031] Figure 2 This is a schematic diagram of the overlap rate principle of an evaluation method for the effectiveness of a scatter plot overdrawing solution according to the present invention.

[0032] Figure 3 This is a displacement minimization principle diagram of an evaluation method for the effectiveness of a scatter plot overdrawing solution according to the present invention;

[0033] Figure 4 This is a schematic diagram of the k-nearest neighbor preservation principle of an evaluation method for the effectiveness of a scatter plot overdrawing solution according to the present invention.

[0034] Figure 5 This is a density retention principle diagram of an evaluation method for the effectiveness of a scatter plot overdrawing solution according to the present invention.

[0035] Figure 6 This is a schematic diagram of the shape retention principle of an evaluation method for the effectiveness of a scatter plot overdraw solution according to the present invention;

[0036] Figure 7 This is a schematic diagram of the comprehensive feature retention principle of an evaluation method for the effectiveness of a scatter plot overdrawing solution according to the present invention. Detailed Implementation

[0037] 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, and 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.

[0038] It should be noted that when a component is described as "fixed to" another component, it can be directly on the other component or may have a component in between. When a component is described as "connected to" another component, it can be directly connected to the other component or may have a component in between. When a component is described as "set on" another component, it can be directly set on the other component or may have a component in between. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0039] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0040] This invention provides a method for evaluating the effectiveness of a scatter plot overdraw solution. After collecting large amounts of data, to facilitate understanding the relationships between similar and dissimilar data, a large number of different types of data are typically represented as scatter plots. However, the close proximity of data values ​​can lead to an over-dense arrangement of many scatter points, resulting in overdrawing and affecting the visibility of the scatter plot. A common solution is to perform a secondary layout (moving data points) of the scatter plot to ensure the effectiveness of the data's information content while improving its visibility.

[0041] However, when the data is actually rearranged, the arrangement of the scattered points will inevitably change, affecting the validity of the data. Establishing a set of evaluation criteria can assess the effectiveness of the layout from multiple perspectives.

[0042] Taking a scatter plot as an example, the method for obtaining its indicators is as follows: Figure 1 and Figure 2 As shown, the overlap rate between data points after the scatter plot layout is obtained. The overlap rate is determined by judging the overlap between any two data points to determine the visibility of the data after the scatter plot layout. The higher the overlap rate, the more overlapping data points there are, and the lower the data visibility; conversely, the lower the overlap rate, the higher the data visibility.

[0043] The method for obtaining the overlap rate is as follows: after layout, the data points in the scatter plot are paired, and the overlap area between the two data points in the pair is obtained. The ratio of the overlap area to the area of ​​the smaller data point in the pair is the overlap value between the two data points, and the average of the overlap values ​​of all pairs is defined as the overlap rate of the scatter plot.

[0044] OL is used to represent the overlap rate after scatter plot layout. The specific formula for calculating the overlap rate is:

[0045]

[0046] in, Represents a data point in the combination The area of ​​one, the area of ​​the other is used express, Representing data points With data points The overlapping area, where n represents the number of data points in the scatter plot.

[0047] like Figure 1 To determine the validity of data after scatter plot layout, feature preservation indices are obtained before and after scatter plot layout. These indices consist of five metrics: density preservation rate, shape preservation rate, k-nearest neighbor preservation rate, displacement minimization, and comprehensive feature preservation rate.

[0048] like Figure 3As shown, displacement minimization is used to represent the displacement of all data points after the scatter plot is laid out. It can determine the average displacement of all data points at a micro level (displacement characteristics) to judge the preservation of the overall characteristics of the scatter plot. The theory is: if the relative displacement is smaller when two pictures are placed in basically the same proportion and position, it means that the overall position has not changed much and the overall characteristics are well preserved.

[0049] The method for obtaining the displacement value is as follows: Adjust the scaling ratio of the scatter plot before layout to make it the same size as the scatter plot after scaling, and then align the centers of the two scatter plots (scatter plots are usually distributed on a rectangular plane). Calculate the distance values ​​between corresponding data points before and after layout, and define the average of the distance values ​​of all data points as the overall displacement value of the scatter plot.

[0050] The specific calculation process is as follows:

[0051] A is the original scatter plot. After layout, the scattered diagram is set as follows: and Scatter plot after layout Given the width and height, scale A proportionally to the width and height. After the bounding boxes occupy the same area, align their centers. and For any data point in A Coordinates after scaling and translation and This represents the offset of the center point.

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] This patent uses indicators To measure the degree of displacement of all scattered points, The closer to 0, the smaller the displacement of the scatter plot. n represents the number of scatter plot points. express One of the scattered points. The specific calculation process is as follows:

[0058]

[0059] like Figure 4As shown, the k-nearest neighbor retention rate is used to represent the retention of the types and number of neighboring data points after each data point is laid out, in order to evaluate the retention of the relative positions of different types of data points within a scatter plot. The theory is that the overlap of the nearest neighbor set is used to represent the change in the relative position of each point after transformation, thus reflecting the structural retention of adjacent points. It is mainly used to display the retention of embedding features between different types of data.

[0060] The technical method is as follows: Select the same judgment data point in the scatter plot before and after layout, and use the VP-Tree algorithm to calculate several nearest neighbor data points of the judgment data point before and after layout. The data points contained in the two dashed circles in the figure are the nearest neighbor data points before and after layout, respectively. Using the Euclidean distance between coordinates (the actual distance between data points) as the standard, the distance and type between the judgment data point and the nearest neighbor data points before and after layout are calculated respectively.

[0061] Obtain the K nearest neighbor data points of the judgment data point before and after layout. Calculate the number of the same type of neighbor data points among these K nearest neighbor data points before and after layout, and divide by the K value to determine the retention rate of the neighbor data point types for a single judgment data point after layout. Calculate the K nearest neighbor retention probability for all data points in the scatter plot. The average of the K nearest neighbor retention probabilities for all data points is the k nearest neighbor retention rate of the scatter plot.

[0062] The specific calculation process is as follows:

[0063] A is the original scatter plot. This is a scatter plot after layout, in A and Select the judgment data points respectively and Using the Euclidean distance (the actual distance between data points) between the nearest neighbor data point and the center data point as the standard, and through the VP-Tree algorithm, several nearest neighbor data points (each containing several types of data points) are obtained, and then determined... and Its corresponding nearest neighbor data point set, and denoted as and K represents the number of nearest neighbor data points, using the metric To characterize the K-nearest neighbor level, The closer it is to 1, the lower the number of changes in the types of the central data point's nearest neighbors, and the better the retention of the nearest neighbors after the layout. The calculation formula is:

[0064]

[0065] Therefore, the two indicators of displacement minimization and k-nearest neighbor retention rate determine the retention of scattered point characteristics after layout based on specific features (movement distance characteristics, types and number of neighboring data points).

[0066] like Figure 5 As shown, density retention rate measures how well the density of scatter points is maintained within any region after a scatter plot has been laid out. This density value is unaffected by region division and efficiently and accurately determines the degree to which the density of data points is maintained across all regions of the scatter plot after layout. The theory is that if the relative density order of points in two scatter plots is well maintained, then the global density retention of these two scatter plots will be good.

[0067] The technical method is as follows: Calculate the average Euclidean distance of all data points before and after layout, and use this distance as the region density of that point. Arrange the data points sequentially according to their Euclidean distance values ​​to generate separate density sequences for the data points before and after layout. Obtain the quantiles of corresponding data points before and after layout (total data points as the denominator, and the arrangement position as the numerator), calculate the difference in quantiles for the same data point before and after layout, and define the average of these differences to represent the density retention of the scatter plot after layout.

[0068] Alternatively, several data points can be selected, and the average of the quantile differences among these data points can be calculated to represent the density preservation of the data points. This allows for the assessment of density changes among the selected data points.

[0069] The specific calculation process is as follows:

[0070] For each point in A and A', the average Euclidean distance of KNN is used as the region density for each data point. The region density values ​​represented by all points in A and A' are then arranged in ascending order to obtain the density sorting sequences of the two scatter plots. (Specific data point) The quantiles of the two sorted sequences are respectively and , where n represents the number of data points in the scatter plot. The density preservation metric DP is used to characterize the density preservation feature; the closer the DP value is to 0, the better the density feature is preserved.

[0071]

[0072] like Figure 6 As shown, shape retention rate is used to represent the preservation of the outlines of several data points and the change in distance from the center point of the scatter plot before and after layout. It is mainly used to represent the layout changes between data points after layout. The theory is: the smaller the deformation of a set of standard shapes in the original scatter plot after layout, the better the shape retention rate.

[0073] The calculation method is as follows: An arbitrary point is selected as the data point. A standard shape is constructed around this data point; the standard shape can be a circle or a polygon. Next, a set of data points that can describe the outline of the standard shape is found in the original scatter plot. These data points are defined as a set of measurement points. The dissimilarity between the shape formed by the measurement point set in the new scatter plot and the standard shape is calculated. The average dissimilarity ranges from 0 to positive infinity; the smaller the average dissimilarity, the better the shape is preserved.

[0074] The specific calculation process is as follows:

[0075] Set the original scatter plot as follows: In a scatter plot, a central data point is identified. Using this central data point as the geometric center of a polygon, each data point within the measurement point group is determined. Its x-coordinate is... , It is the first item The last item is The tolerance is The arithmetic sequence is given by m, where m is the distance from the center data point. The ordinate is... , It is the first item The last item is The tolerance is The arithmetic sequence, where p is the number of angles at the center data point. These are the coordinates of the measurement point group.

[0076] Random selection (The radius of the corresponding circle), for the set of coordinates containing it. (The coordinates of all data points passing through the circle in the diagram), find the points in A that are closest to these coordinates to form a measurement point group, and denote the mapping point set of this measurement point group in A' as . Seeking The distance of each point from the center of A' The SP metric is used to characterize shape retention features. for middle The average value, SP is the average value of ... The variance-based evaluation index is used; the closer SP is to 0, the better the structural characteristics are preserved.

[0077]

[0078] Therefore, the effectiveness of the layout can be assessed by using density retention rate (calculating the density retention rate of all data points in the scatter plot) and shape retention rate to evaluate the retention of global features in the scatter plot.

[0079] like Figure 7As shown, the overall feature retention rate is used to measure the average similarity between the new scatter plot and the original scatter plot from multiple (physical) observation angles after layout. The overall feature retention rate can be used as a comprehensive indicator of four metrics: density retention rate, shape retention rate, k-nearest neighbor retention rate, and displacement minimization. The theoretical basis of overall similarity is that if two scatter plots are very similar when observed from all angles, then they are very similar overall.

[0080] The calculation method is as follows: Obtain scatter plots before and after layout. The scatter plots are divided into several data point groups, and the data points within each group are projected onto different angular axes. The data points are then arranged sequentially based on their projection positions. The Kendall similarity of each data point group between its corresponding two scatter plots is calculated, and the Kendall similarity of all data groups is also calculated. The Kendall similarity ranges from -1 to 1. The higher the average Kendall similarity of all data point groups, the better the overall reconstruction quality.

[0081] The specific calculation process is as follows:

[0082] On the scatter plot, set the x-axis and y-axis vertically, with the positive x-axis pointing to the direction of 0 radians and the positive y-axis pointing to the positive direction of the number line. From 0 to... Every range Set a projection axis j, and and The data points are projected onto each axis. For projection axis j, the index sequence before and after the layout consists of the data point indices. and This patent uses the metric OP to calculate the average similarity across various dimensions, where... It is a sequential logarithm (the projected position moves forward after layout). It is the reverse logarithm (the projected position moves forward after layout). The value range is [-1, 1]. The closer the OP value is to 1, the better the overall similarity.

[0083]

[0084]

[0085]

[0086] The evaluation framework consisting of the six metrics proposed above basically covers the quantitative evaluation of feature preservation of two scatter plots and the overlap rate of a single scatter plot, providing a framework for evaluating the nodal displacement method of scatter plots and scatter plots. Figure 1 Consistency testing provides the technical basis for quantitatively and comprehensively assessing the universality of scatter plot distribution consistency, improving the reliability of the results and facilitating layout adjustments based on the aforementioned indicators to enhance layout effectiveness.

[0087] The embodiments of the present invention have been described in detail above, but the content described is only a preferred embodiment of the present invention and should not be considered as limiting the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of this patent.

Claims

1. A method for evaluating the effectiveness of a scatter plot overdraw solution, the method comprising: receiving a scatter plot overdraw solution; and evaluating the effectiveness of the scatter plot overdraw solution. The application relates to a method for evaluating the layout of a scatter diagram, comprising the following steps: acquiring scatter diagram data before and after the layout of the scatter diagram, calculating the overlap rate between data points after the layout of the scatter diagram based on the scatter diagram data, judging the overlap between any two data points according to the overlap rate to determine the visibility of the data after the layout of the scatter diagram, calculating the feature retention degree of the scatter diagram after the layout based on the scatter diagram data to judge the validity of the data after the layout of the scatter diagram, wherein the feature retention degree comprises a plurality of specific feature retention indexes and a comprehensive feature retention rate, the comprehensive feature retention rate is acquired by arranging data points according to the projection positions of the data points on angle axes with different angles before and after the layout, calculating the Kendall similarity of the arranged data points before and after the layout of each angle axis, and defining the average Kendall similarity value of all the angle axes as the comprehensive feature retention rate, the specific feature retention indexes comprise displacement minimization and k-neighborhood retention rate determined according to local features, density retention rate and shape retention rate determined according to global features, and the feature retention situation of the scatter diagram layout is judged from four aspects, the displacement minimization is used for representing the moving distance value of all the scatter diagrams after the layout, the k-neighborhood retention rate is used for representing the retention situation of the category and quantity of the neighborhood data points of each data point after the layout, the density retention rate is used for measuring the density retention situation of the scatter points in any region after the layout of the scatter diagram, and the shape retention rate is used for measuring the contour retention situation of a plurality of data points after the layout.

2. The method of claim 1, wherein the method of evaluating the effectiveness of the scatter plot overdraw solution is characterized by, the displacement minimization value is acquired by adjusting the scaling ratio of the scatter diagram before the layout to make the size of the scatter diagram before the layout same as that after the layout, and aligning the center coordinates of the scatter diagrams before and after the layout, the distance value between the corresponding data points of all the data points in the scatter diagram before and after the layout is calculated, and the average value of all the distance values is acquired.

3. The method of claim 2, wherein the method of evaluating the effectiveness of the scatter plot overdraw solution is characterized by, the k-neighborhood retention rate is acquired by setting a judgment data point, determining a plurality of neighborhood data points adjacent to the judgment data point by using a VP-Tree algorithm, acquiring the category and corresponding quantity of the neighborhood data points before and after the layout, and determining the neighborhood retention rate according to the retention situation of the category and quantity of the neighborhood data points of the judgment data point before and after the layout, the average value of the neighborhood retention rates of all the data points is the k-neighborhood retention rate.

4. The method of claim 3, wherein the method further comprises: the number of the neighborhood data points before and after the layout is the same.

5. The method of claim 4, wherein the method further comprises: the density retention rate is acquired by acquiring the average Euclidean distance of all the data points before and after the layout and defining the region density of the data points, arranging the data points before and after the layout according to the region density, and acquiring the quantile of the data point positions, and the average value of the difference values of the quantiles of all the data points before and after the layout is defined as the density retention rate.

6. The method of claim 5, wherein the method further comprises: the shape retention rate is acquired by setting a data point as a center data point, constructing a plurality of standard graphs with different sizes and dimensions based on the geometric center of the center data point, acquiring a plurality of data points most close to the contours of the standard graphs in the original scatter diagram and generating a group of measurement points, calculating the dissimilarity between the graphs formed by the group of measurement points in the scatter diagram after the layout and the standard graphs, and defining the average value of all the standard graphs as the shape retention rate.

7. The method of claim 6, wherein the method further comprises: The standard graph can be a circle or a polygon.

8. The method of claim 1, wherein the method is effective for evaluating the effectiveness of a scatter plot overdraw solution. The method for obtaining the overlap rate is: obtaining two-by-two combination of data points in the layouted scatter plot, calculating the overlap area between the combined data points, and dividing by the smallest data point area in the combination to generate an overlap value, and calculating the average of all overlap values as the overlap rate of the scatter plot.

Images