A large-scale scatter plot de-overlapping method based on circle stacking

Abstract

The present invention provides a large-scale scatter plot de-overlapping method and system based on circle stacking, belonging to the field of data processing technology, and specifically comprising: expanding nodes in a scatter plot that overlap in a visualization space due to having the same coordinates into a leaf sequence, and dividing the visualization space into square grids, allocating placeholder nodes and data nodes to each grid on the principle of area equality and no loss of data points, calculating the distance and angle of each node relative to the center of a canvas based on a circle stacking layout algorithm, placing each node in ascending order of its distance along a target angle to the contour edge of a node pile formed by placed nodes, filtering nodes that should not be rendered, and constructing a scatter plot of the visualization space, and when a user uses an interactive tool to interact with data, performing data enhancement processing on the visualization space of the scatter plot according to the mutually exclusive radius and movement strategy of different nodes, thereby improving the visualization processing effect of the scatter plot.

Description

Technical Field

[0001] The invention belongs to the technical field of data processing, and in particular relates to a large-scale scatter plot de-overlapping method based on circle stacking. Background Art

[0002] With the advent of the big data era, visualization has become an important analytical tool in today's world due to its intuitiveness and flexibility. As an important visualization technology, scatter plots are often used to analyze high-dimensional data and reveal data patterns such as clusters, trends, correlations, and outliers in big data due to their ease of use and excellent performance. However, for scatter plots, the growth of data scale has brought about the problem of over-drawing, that is, a large number of data nodes representing individuals overlap. This will seriously interfere with people's observation of the underlying data distribution, damage the readability and effectiveness of scatter plots, and make various visual tasks impossible to carry out.

[0003] To solve the above technical problems, in the existing technical solution, the paper "Data Sampling in Multi-view and Multi-class Scatterplots via Set Cover Optimization" divides the data set into multiple subsets in space by using the Z-order space filling curve, samples a data point in each subset, and models the sampling problem as a set cover optimization problem, which better achieves the preservation of class relative density. However, it is not difficult to find through analysis that there are the following technical problems:

[0004] Existing scatter plot de-overlapping methods cannot accurately express the distribution of intrinsic data while strictly ensuring that nodes do not overlap, and have certain limitations. In addition, previous methods have not considered further visual enhancement through interaction on the existing mitigation results, and cannot guarantee the effectiveness of scatter plot visualization analysis.

[0005] In view of the above technical problems, the present invention provides a large-scale scatter plot de-overlapping method based on circle stacking. Summary of the invention

[0006] The object of the present invention is to provide a large-scale scatter plot de-overlapping method based on circle stacking.

[0007] In order to solve the above technical problems, the present invention provides a large-scale scatter plot de-overlapping method based on circle stacking, which is characterized by specifically comprising:

[0008] Divide the visualization space into square grids, fill each grid with circles, and assign placeholder nodes and data nodes to each grid on the principle of equal area and no missing data points;

[0009] The circle stacking-based layout algorithm calculates the distance and angle of each node relative to the center of the canvas, and places each node in ascending order of its distance along the target angle to the edge of the outline of the node pile formed by the placed nodes, filters out the nodes that should not be rendered, and constructs a scatter plot of the visualization space;

[0010] The mutually exclusive radius and movement strategy when zooming using the interactive tool are determined according to the node type, and when the user uses the interactive tool to interact with data, data enhancement processing is performed on the visualization space of the scatter plot according to the mutually exclusive radius and movement strategy of different nodes.

[0011] A further technical solution is to fill each grid with a circle, specifically including:

[0012] The number of data points of the grid is obtained, and the number of circles of the grid is determined according to the number of data points and a preset number threshold.

[0013] A further technical solution is that the radius of the circle of each grid is equal.

[0014] A further technical solution is that the angle is the angle between a line connecting the node and the center of the canvas and the positive direction of the x-axis.

[0015] A further technical solution is that the types of the nodes include high-density control points and low-density control points.

[0016] A further technical solution is that, when the type of the node is a high-density control point, the zoom movement strategy of the interactive tool is:

[0017] Determining a movement curve of the node according to the relative density and radius of the node;

[0018] Taking the moving curve as a constraint condition, during the zoom control process of the interactive tool, the node is controlled to be zoomed in accordance with the moving curve.

[0019] The beneficial effects of the present invention are:

[0020] (1) Provides a new paradigm for the design of scatter plot de-overlapping algorithms:

[0021] Starting from analyzing the reasons why the previous methods were not effective, this paper emphasizes the importance of unifying the granularity of data space and visualization space information and formalizes the relationship of unity of opposites. Based on this description, the de-overlapping problem is formalized as an optimization problem with node mutual exclusion and spatial bijection as constraints and the goal of perceiving the distribution consistency of the optimal solution.

[0022] (2) High computational efficiency:

[0023] The present invention improves the previous circle stacking algorithm. Since the traditional circle stacking algorithm may face a problem of high computational complexity when processing large-scale data, resulting in a long running time, the present invention introduces a data-independent truncation threshold, which significantly improves the computational efficiency of the stacking algorithm, and it only takes 1 second to stack 100,000 nodes.

[0024] (3) Extremely high visual quality:

[0025] The grid division strategy in the data transcription method proposed by the present invention and the strategy of maintaining the relative positions of nodes during stacking can better maintain global and local features. The present invention achieves optimal or near-optimal results in k-nearest neighbor preservation, displacement minimization, shape preservation, and density preservation.

[0026] (4) Better support for high dynamic range data:

[0027] Existing technical solutions do not support this type of scatter plot well. Extremely high-density areas often result in a very small default stacking radius, which will seriously damage the visual quality of the entire scatter plot. This paper achieves a controllable balance between strictly maintaining relative density and high visual quality through rendering radius configuration guided by safe interaction.

[0028] Other features and advantages will be described in the following description, and part of them will become obvious from the description, or be understood by practicing the invention. The purpose and other advantages of the invention are realized and obtained by the structures particularly pointed out in the description and the drawings.

[0029] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The above and other features and advantages of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings.

[0031] Figure 1 This is a flow chart of a large-scale scatter plot de-overlapping method based on circle stacking according to Example 1.

[0032] Figure 2 This is a flowchart of the data transcription algorithm based on analytic geometry in Example 1.

[0033] Figure 3 This is a flowchart of the circle stacking-based layout algorithm in Example 1.

[0034] Figure 4 This is a flowchart of placing each node to the edge of the outline of the node pile formed by the placed nodes in Example 1.

[0035] Figure 5 This is a graph of the radius configuration model in Example 1.

[0036] Figure 6 This is a diagram verifying the effect of the radius configuration scheme in Example 1.

[0037] Figure 7 It is a schematic diagram showing that the radius configuration scheme in Example 1 effectively supports interaction.

[0038] Figure 8 This is a diagram verifying the effect of mode enhancement in Example 1. DETAILED DESCRIPTION

[0039] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that the present invention will be comprehensive and complete and fully convey the concepts of the example embodiments to those skilled in the art. The same reference numerals in the figures represent the same or similar structures, and thus their detailed description will be omitted.

[0040] The terms "a", "an", "the", and "said" are used to indicate the presence of one or more elements / components / etc.; the terms "comprising" and "having" are used to express an open-ended inclusive meaning and mean that additional elements / components / etc. may be present in addition to the listed elements / components / etc.

[0041] With the advent of the big data era, visualization has become an important analytical tool in today's world due to its intuitiveness and flexibility. As an important visualization technology, scatter plots are often used to analyze high-dimensional data and reveal data patterns such as clusters, trends, correlations, and outliers in big data due to their ease of use and excellent performance. However, for scatter plots, the growth of data scale has brought about the problem of over-drawing, that is, a large number of data nodes representing individuals overlap. This will seriously interfere with people's observation of the underlying data distribution, damage the readability and effectiveness of scatter plots, and make various visual tasks impossible to carry out.

[0042] To solve the problem of over-drawing of scatter plots, researchers in the field of visualization have made many explorations. Existing technical solutions can be divided into the following three categories according to the level at which their core operations occur:

[0043] The first category is data space methods, which only involve data transformation without performing any operations on primitives. The representative of this type of method is the data reduction method, which reduces the data points and thus reduces the visual units that need to be drawn in the visual space to alleviate overdrawing. For example, Hu et al. used the Z-order space filling curve to divide the data set into multiple subsets in space, sampled a data point in each subset, and modeled the sampling problem as a set cover optimization problem, which better achieved the maintenance of class relative density; Chen et al. proposed a pyramid-based sampling technology, which achieved the coordinated coexistence of data relative density maintenance and outlier retention by balancing density maps and visual maps layer by layer at multiple levels of abstract scales. Although this type of method can alleviate the overlap problem to a certain extent, it abandons some data points and pursues different sampling characteristics, resulting in a certain degree of data loss and data bias. More importantly, this type of method strictly opposes reducing overlap and reducing data loss, ignoring the fact that under the premise of allowing slight changes in node positions, there is a great room for easing the contradiction between the two.

[0044] The second category is visualization space methods, which only involve visual encoding and view transformation, not data transformation. Representatives of this type are appearance adjustment methods and node displacement methods. For example, Micallef et al. designed a cost function based on several metrics to simulate human perception. This function can be used to optimize scatter plots by customizing parameters for different tasks; Cutura R et al. used space filling lines to divide the space and used heuristic algorithms for subspace matching. This type of method only seeks to alleviate the overlap of visual nodes without maintaining the intrinsic data distribution as a constraint, losing the unity of the two spaces in information transmission, and the layout distortion is high.

[0045] The third type of method is the hybrid space method, which performs abstract operations in both data space and visualization space. This type of method usually ignores the individual information of data points at the data level and instead counts the aggregate information of local areas. At the visual level, it usually abandons the display of individual nodes and replaces them with pixels or regions with higher abstraction. For example, Li et al. used kernel density estimation to infer the density of any position in the space and proposed a multi-class contour visualization framework to help users choose appropriate design parameters to express density distribution; Gansner ER et al. proposed a mosaic-based boundary construction technology, first constructing Voronoi space divisions with all data points, and then coloring the Voronoi grids of the same class with the same color. This type of method loses the mapping relationship between individual data details and visual units and data points, and the abstract scheme often needs to be frequently adjusted according to the task.

[0046] In summary, existing scatter plot de-overlapping methods cannot accurately express the distribution of intrinsic data while strictly ensuring that nodes do not overlap, and each has its own limitations. In addition, previous methods have not considered further visual enhancement through interaction on the existing mitigation results. This problem urgently needs a visualization solution with better performance.

[0047] Example 1

[0048] In order to solve the above technical problems, Figure 1 As shown, the present invention provides a large-scale scatter plot de-overlapping method based on circle stacking, which is characterized by specifically comprising:

[0049] Divide the visualization space into square grids, fill each grid with circles, and assign placeholder nodes and data nodes to each grid on the principle of equal area and no missing data points;

[0050] Furthermore, each grid is filled with circles, including:

[0051] The number of data points of the grid is obtained, and the number of circles of the grid is determined according to the number of data points and a preset number threshold.

[0052] like Figure 2 As shown, the recording medium of the analytical space is an algebraic representation, which is a transition and does not require actual drawing. The implementation scheme of this step is to configure the actual drawing radius (i.e., rendering radius) and the placeholder radius (i.e., stacking radius) for the data points. The specific steps are as follows:

[0053] Expand the points that overlap in data space due to having the same coordinates into leaf order;

[0054] Divide the space into a square grid (grid size is a parameter)

[0055] Fill each grid with circles. The filling rule is: a grid containing num data points will be filled with max(k,num) circles, and the radius of each circle is equal. (The threshold k is a parameter).

[0056] The circle stacking-based layout algorithm calculates the distance and angle of each node relative to the center of the canvas, and places each node in ascending order of its distance along the target angle to the edge of the outline of the node pile formed by the placed nodes, filters out the nodes that should not be rendered, and constructs a scatter plot of the visualization space;

[0057] Furthermore, the radius of the circle of each grid is equal.

[0058] Specifically, the angle is the angle between a line connecting the node and the center of the canvas and the positive direction of the x-axis.

[0059] It should be noted that the placement along the target angle to the edge of the outline of the node pile formed by the placed nodes specifically includes:

[0060] A group of circles connected end to end on the edge of the node heap outline is called a front chain, which is maintained using a bidirectional circular linked list. The initial value of the front chain is three circles closest to the center of the canvas that are tangent to each other around the center of the canvas.

[0061] Traverse the entire front chain to find the node on the chain with the smallest target angle difference with the node, record it as the screening node, and determine whether the node and the screening node meet the mutual exclusion requirement. If so, use the current position of the node as the placement position, if not, proceed to the next step;

[0062] With the screening node as the center and a preset length as the window, all node positions are detected in sequence in the order away from the screening node until a node position that meets the requirements is found and the node is placed at the node position.

[0063] Further, determining whether the node and the screening node meet the mutual exclusion requirement specifically includes:

[0064] When the current position of the node intersects with the screening node, it is determined that the node and the screening node do not meet the mutual exclusion requirement.

[0065] like Figure 3 As shown, this is the mutually exclusive layout algorithm based on circle stacking of the present application. This step is the core method of the present invention, and its purpose is to visualize the nodes without overlapping and with high fidelity. This algorithm uses a stacking method to visualize the analytical space obtained in step 1 with high fidelity. Compared with the aforementioned existing de-overlapping scheme, this algorithm has excellent computational performance, high fidelity, and strict mutual exclusion. The circle stacking algorithm of this step is improved on the original circle stacking method, and attention is paid to maintaining the relative position of the nodes during the stacking process.

[0066] Let the algorithm input be the analytical space, and the detailed steps of the algorithm are as follows:

[0067] ① Calculate the distance and angle of each node relative to the center of the canvas. The angle is the angle between the line connecting the node and the center of the canvas and the positive direction of the x-axis, which is called the target angle.

[0068] ② If Figure 4As shown, it is a flowchart for placing each node to the edge of the outline of the node pile formed by the placed nodes. Specifically, in this step, a group of circles connected end to end on the edge of the outline of the current node pile is called the front chain, which is maintained using a bidirectional circular linked list. The initial value of the front chain is the three circles closest to the center of the canvas, which are tangent to each other around the center of the canvas. The ideal position of node n is the position with the smallest possible difference from its target angle and is only tangent to two nodes on the front chain without intersecting with any node. This meets the requirements of close arrangement and strict mutual exclusion. Assuming that the two nodes that are finally tangent to node n are called n1 and n2, the placement method (i.e., the method of finding n1 and n2) is as follows:

[0069] 1) Traverse the entire front chain to find the node on the chain with the smallest angle difference with the target node n, denoted as

[0070] 2) If the node already meets the mutual exclusion requirement, then That is n1, The next or previous node is n2; if the ideal position generated by this node intersects with other nodes on the chain, go to step 3);

[0071] 3) as the center, the length 2th is the window, follow the distance Detect all the<n1,n2> Yes, until a target that satisfies the requirement is found (if the target with relaxed conditions is still not found in the truncation window<n1,n2> By default, the position with the smallest overlap is selected as the final position of n) where the 2th position is fixed to 50 (experience value, no adjustment required)

[0072] ③Filter the placeholder nodes that should not be rendered to obtain a new scatter plot layout result.

[0073] The mutually exclusive radius and movement strategy when zooming using the interactive tool are determined according to the node type, and when the user uses the interactive tool to interact with data, data enhancement processing is performed on the visualization space of the scatter plot according to the mutually exclusive radius and movement strategy of different nodes.

[0074] Specifically, the types of nodes include high-density control points and low-density control points.

[0075] Furthermore, the mutually exclusive radius of scaling of the node is determined according to an interval formed by the stacking radius and the drawing radius of the node.

[0076] Specifically, the drawing radius is the global minimum value of the stacking radius of the node.

[0077] Furthermore, when the type of the node is a high-density control point, the zoom movement strategy of the interactive tool is:

[0078] Determining a movement curve of the node according to the relative density and radius of the node;

[0079] Taking the moving curve as a constraint condition, during the zoom control process of the interactive tool, the node is controlled to be zoomed in accordance with the moving curve.

[0080] Furthermore, when the type of the node is a low-density control point, the zoom movement strategy of the interactive tool is:

[0081] Determining a movement curve of the node according to the relative density and radius of the node;

[0082] The moving curve is used to divide the quadrant space into a safe area and a non-safe area, and during the zoom control process of the interactive tool, the node is controlled to perform zoom control in the safe area.

[0083] The purpose of this step is to achieve interactive scatter plot visual enhancement that supports safe interaction. For any node, the radius can be adjusted between the default drawing radius and the stacking radius without worrying about node overlap, that is, this interval is the radius safety interval. The x-axis and y-axis of the configuration model of the radius of each node in this safety interval represent the relative density and radius of the node, respectively. The red decreasing curve is the stacking radius curve, and the safety lower bound in the figure is the stacking radius lower bound. The safety lower bound straight line, the stacking radius curve, and the drawing radius curve divide the entire quadrant into overlapping areas and non-overlapping areas.

[0084] Figure 5 A black drawing radius curve is created for high-density control points and low-density control points, which determines the drawing radius of nodes at each density. High-density control points can only slide along the stacked radius curve, while low-density control points can move freely in the non-overlapping area of ​​the graph.

[0085] This radius configuration method can significantly enhance the patterns in the semantic space. Figure 6 Sub-figures (a) and (b) of the figure show the rendering results using the default drawing radius and the adjusted drawing radius, respectively. By simply moving the high-density control points to the left, the visual quality of the high dynamic range dataset is greatly improved; by simply moving the low-density control points upward, the visual significance of the outliers is significantly improved. In addition, Figure 7 As shown, the radius configuration method supports viewing details through geometric zooming, which can show rich and comprehensive details at the micro level, greatly improving the efficiency of interactive exploration of semantic space.

[0086] Figure 8The comparison in the first column shows that the present invention can accurately reproduce the global features of the original data set, including density distribution and structural shape. The slight texture presented in the new scatter plot proves that the present invention can reproduce hidden data patterns and details.

[0087] Regarding the parameters that appear in the present invention: the lower limit k of the number of nodes in the grid, the grid size size, and the sampling rate α (non-direct parameter), we conducted experiments on density preservation, shape preservation, k-nearest neighbor preservation, and displacement minimization and found that the effects of all parameters are relatively slight and monotonous, that is, the present invention has good robustness, and the parameter adjustment is controllable and predictable.

[0088] Based on the above embodiments, the following technical effects are expected to be achieved:

[0089] (1) Provides a new paradigm for the design of scatter plot de-overlapping algorithms:

[0090] Starting from analyzing the reasons why the previous methods were not effective, this paper emphasizes the importance of unifying the granularity of data space and visual space information and formalizes the relationship of unity of opposites. Based on this description, the de-overlapping problem is formalized as an optimization problem with node mutual exclusion and spatial bijection as constraints and the distribution consistency of the perceived optimal solution as the goal.

[0091] (2) High computational efficiency:

[0092] The present invention improves the previous circle stacking algorithm. Since the traditional circle stacking algorithm may face a problem of high computational complexity when processing large-scale data, resulting in a long running time, the present invention introduces a data-independent truncation threshold, which significantly improves the computational efficiency of the stacking algorithm. Stacking 100,000 nodes only takes about 1 second on an ordinary PC.

[0093] (3) Extremely high visual quality:

[0094] The grid division strategy in the data transcription method proposed by the present invention and the strategy of maintaining the relative positions of nodes during stacking can better maintain global and local features. The present invention achieves optimal or near-optimal results in k-nearest neighbor preservation, displacement minimization, shape preservation, and density preservation.

[0095] (4) Better support for high dynamic range data:

[0096] High dynamic range is a common distribution characteristic of large-scale scatter plots. In this type of distribution, there are both extremely high-density areas and sparse outliers, and the range of local density values ​​may span several orders of magnitude. Existing technical solutions do not support this type of scatter plot well. Extremely high-density areas often lead to a very small default stacking radius, which will seriously damage the visual quality of the entire scatter plot. This paper achieves a controllable balance between strictly maintaining relative density and high visual quality through the rendering radius configuration guided by safe interaction.

[0097] In the description of this specification, the description of the terms "one embodiment", "a preferred embodiment", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiment of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0098] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A large-scale scatter plot de-overlapping method based on circle stacking, characterized in that: Specifically include: Divide the visualization space into square grids, fill each grid with circles, and assign placeholder nodes and data nodes to each grid on the principle of equal area and no missing data points; The circle stacking-based layout algorithm calculates the distance and target angle of each node relative to the center of the canvas, and places each node along the target angle in ascending order of its distance to the edge of the outline of the node pile formed by the placed nodes, filters out the nodes that should not be rendered, and constructs a scatter plot of the visualization space; Determine the mutually exclusive radius and movement strategy when zooming using the interactive tool according to the node type, and perform data enhancement processing on the visualization space of the scatter plot according to the mutually exclusive radius and movement strategy of different nodes when the user uses the interactive tool to interact with data; Fill each grid with circles, including: Obtaining the number of data points of the grid, and determining the number of circles of the grid according to the number of data points and a preset number threshold; Fill each grid with circles. The filling rule is: a grid containing num data points will be filled with max(k,num) circles. The radius of each circle is equal. The threshold k is a parameter. Place the nodes along the target angle to the edge of the node pile formed by the placed nodes, including: A group of circles connected end to end on the edge of the node heap outline is called a front chain, which is maintained using a bidirectional circular linked list. The initial value of the front chain is three circles closest to the center of the canvas that are tangent to each other around the center of the canvas. Traverse the entire front chain to find the node on the chain with the smallest target angle difference with the node, record it as the screening node, and determine whether the node and the screening node meet the mutual exclusion requirement. If so, use the current position of the node as the placement position, if not, proceed to the next step; Taking the screening node as the center and a preset length as the window, all node positions are detected in order of distance from the screening node until a node position that meets the requirements is found and the node is placed at the node position; Determining whether the node and the screening node meet the mutual exclusion requirement specifically includes: When the current position of the node intersects with the screening node, it is determined that the node and the screening node do not meet the mutual exclusion requirement.

2. The large-scale scatter plot de-overlapping method based on circle stacking as claimed in claim 1, characterized in that: The radius of the circle of each grid is equal.

3. The large-scale scatter plot de-overlapping method based on circle stacking as claimed in claim 1, characterized in that: The target angle is the angle between the line connecting the node and the center of the canvas and the positive direction of the x-axis.

4. The large-scale scatter plot de-overlapping method based on circle stacking as claimed in claim 1, characterized in that: The types of nodes include high-density control points and low-density control points.

5. The large-scale scatter plot de-overlapping method based on circle stacking as claimed in claim 1, characterized in that: The mutually exclusive radius of scaling of the node is determined according to an interval formed by a stacking radius and a drawing radius of the node.

6. The large-scale scatter plot de-overlapping method based on circle stacking as claimed in claim 5, characterized in that: When the type of the node is a high-density control point, the zoom movement strategy of the interactive tool is: Determining a movement curve of the node according to the relative density and radius of the node; Taking the moving curve as a constraint condition, during the zoom control process of the interactive tool, the node is controlled to be zoomed in accordance with the moving curve.

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