An efficient boundary detection method based on angle entropy weighted spring network
By using an angle entropy weighted spring network model, the problems of misjudgment and computational burden in boundary point identification in high-dimensional data are solved, achieving efficient boundary detection and improving clustering accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTH CHINA UNIV OF WATER RESOURCES & ELECTRIC POWER
- Filing Date
- 2026-04-28
- Publication Date
- 2026-05-29
AI Technical Summary
Existing technologies struggle to accurately identify boundary points at cluster boundaries in high-dimensional and complex data, leading to decreased clustering accuracy. Furthermore, traditional methods suffer from misjudgment and excessive computational burden in boundary point identification.
An angle entropy-weighted spring network model is adopted. The resultant force is calculated by simulating the spring connection between data points as the basic boundary score. The angle entropy-weighted basic boundary score is used to distinguish the boundary points from the internal points. The boundary points are selected by combining local dimensionality reduction and preset threshold.
It effectively distinguishes between boundary points and interior points, improves clustering results, reduces computational complexity, and achieves efficient boundary detection.
Smart Images
Figure CN122115490A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of image boundary detection technology, and in particular to an efficient boundary detection method based on an angle entropy weighted spring network. Background Technology
[0002] Clustering analysis is an important technique in unsupervised learning, widely used in image segmentation and pattern recognition. However, when faced with massive amounts of high-dimensional and structurally complex data, traditional clustering methods often suffer from decreased clustering accuracy because they cannot accurately identify the boundary points at the intersections of clusters. Boundary points have low neighborhood density and divergent orientations, making them prone to misclassification into adjacent clusters, resulting in cluster overlap and blurred boundaries, which becomes a key obstacle to improving clustering performance.
[0003] Existing boundary point detection methods mainly fall into two categories. Density-based methods rely on preset density thresholds, which can easily misclassify true boundary points in low-density areas as noise or vice versa in high-density areas, especially when the density distribution is uneven. Geometrically based methods require calculating the orientation distribution in high-dimensional space, with the computational burden increasing dramatically with dimensionality, making them unsuitable for real-time processing. Due to these limitations in boundary point identification, when the similarity between data points is extremely high, the number of misclassified points in the inter-cluster boundary regions increases significantly, further exacerbating cluster overlap and affecting the reliability of clustering results. Summary of the Invention
[0004] In view of this, the present invention proposes an efficient boundary detection method based on an angle entropy weighted spring network to solve the problem of limited boundary point detection performance caused by heterogeneous density, boundary ambiguity and noise in the prior art.
[0005] The specific technical solution of this invention is as follows: An efficient boundary detection method based on an angle entropy weighted spring network includes: For each data point in the dataset, search for its multiple nearest neighbors; Calculate the elastic force of each nearest neighbor to the current data point, with the elastic force based on Hooke's law to simulate the spring connection; Calculate the resultant force of all elastic forces as the basic boundary fraction; Calculate the angle entropy of the current data point. The angle entropy quantifies the direction distribution based on the angle information of the nearest neighbor distribution. The final boundary score is obtained by weighting the basic boundary scores using angular entropy; Boundary detection is completed by selecting boundary points using a preset threshold.
[0006] Specifically, the calculation of elastic force includes: defining the actual distance as the Euclidean distance between data points; defining the natural length as a multiple of the actual distance; defining the spring constant as inversely proportional to the actual distance; and, according to Hooke's Law, the magnitude of the elastic force is a constant, and its direction is from the neighbor to the current point.
[0007] Specifically, the calculation of angle entropy includes: for two-dimensional data, directly calculating the angle of the nearest neighbor relative to the current point; for high-dimensional data, first performing local dimensionality reduction to two-dimensional space, and then calculating the angle; dividing the angle space into multiple sector regions and counting the number of nearest neighbors in each region; calculating the empirical probability of the angle distribution and performing smoothing; calculating the angle entropy based on the Shannon entropy formula and performing normalization.
[0008] Specifically, the weighted basic boundary scores use a weighting factor, which is defined as the directional concentration, where the directional concentration is 1 minus the normalized angular entropy.
[0009] Specifically, selecting boundary points by setting a preset threshold includes: sorting the final boundary scores in descending order; calculating the threshold based on a given percentile; and defining points whose final boundary scores are greater than the threshold as boundary points.
[0010] Specifically, local dimensionality reduction is performed using principal component analysis, which projects high-dimensional data onto the first two principal components to calculate the angle.
[0011] Specifically, a spatial index structure is used to accelerate distance calculation and nearest neighbor search.
[0012] Specifically, the method has a linear time complexity.
[0013] Specifically, the multiple of the natural length is set to a value less than 1 to simulate spring tension.
[0014] Specifically, the number of multiple sector regions is a fixed value.
[0015] The beneficial effects of this invention are as follows: 1. By treating each data point as a network node and simulating the connection of springs to calculate the resultant force as the basic boundary fraction, the degree of local imbalance of the point can be effectively reflected, thereby distinguishing the boundary point from the internal point.
[0016] 2. Calculating the angular entropy based on the nearest neighbor distribution angle information and weighting the basic boundary score can amplify the features of boundary points and suppress the features of internal points, making the features of boundary points more prominent.
[0017] 3. Choosing a stiffness coefficient inversely proportional to distance reduces the influence of distant neighbors, making the elasticity calculation more consistent with the actual data distribution.
[0018] 4. The angle is calculated after performing local dimensionality reduction processing (PCA) on high-dimensional data, which solves the problem that the angle cannot be directly calculated from high-dimensional data and facilitates the quantification of neighbor direction information.
[0019] 5. By selecting boundary points using thresholds, boundary points can be accurately filtered out from the data to complete the boundary detection task. Attached Figure Description
[0020] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0021] Figure 1 This is a schematic diagram of the resultant force vector field of the present invention; Figure 2 This is a schematic diagram illustrating the angular distribution differences between the boundary points and interior points of the present invention. Figure 3 This is a schematic diagram of the angular entropy distribution of boundary points and interior points of the present invention; Figure 4 The flowchart of the algorithm of this invention shows the visualization process of the entire boundary point detection, using the Aggregation dataset as an example; where (a) is the original data distribution; (b) is a schematic diagram of the connection of the virtual spring network; (c) is the basic boundary score of each point, which is the resultant force of the elastic forces of its neighbors; (d) is the heatmap of the angle entropy value of each point; (e) is the final boundary score of each point after weighting by angle entropy; and (f) is the effect diagram of boundary point detection using threshold. Detailed Implementation
[0022] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
[0023] This invention proposes an efficient boundary detection method based on angle entropy weighted spring network (AEWSNBD). This method treats each data point as a network node, constructing a data elasticity model. First, the method simulates the elastic force generated by connecting two data points with a spring, treating each data point as an object subjected to different degrees of tension, and calculating the resultant force as the basic boundary score. Then, it calculates the angle entropy based on the angle information of the nearest neighbors, and uses the angle entropy to weight the basic boundary score to obtain the final boundary score. Finally, a threshold is used to select boundary points. Based on this characteristic, the method can effectively detect boundary points.
[0024] In the boundary detection method of the present invention, for points ,That Nearest neighbors can be represented as: (1) Equivalent to: (2) Shannon entropy is a core concept in information theory, used to quantify the uncertainty or information content of a random variable. For a discrete random variable... Take its value The corresponding probability distribution is ,in Then the formula for calculating Shannon entropy is: (3) In the spring network model, the spring network is parameterized, specifically treating each data point as a network node, and its k nearest neighbors are connected through virtual springs, based on Hooke's Law: Definition 1 (Actual Distance): Actual distance is the Euclidean distance between data points.
[0025] (4) Definition 2 (Natural Length): (5) parameter Controlling the degree of spring relaxation, when When the spring's natural length is less than the actual distance, a pulling force is generated; when Thrust is generated at that time, and this algorithm uses There is tension between the simulated data.
[0026] Definition 3 (Stiffness Coefficient): (6) Choosing a spring constant inversely proportional to distance reduces the influence of distant neighbors. Then, according to Hooke's Law, the spring force between data network nodes is: (7) (8) It can be observed that the magnitude of the force is a constant, only related to... It is related to, but independent of, distance. The direction of the force vector is from... point to : (9) The complete resultant force vector is: (10) point The total net force acting on it is the vector sum of the elastic forces of its neighbors: (11) like Figure 1 The figure shows the resultant force vector field.
[0027] Definition 4 (Basic Boundary Fraction): The magnitude of the resultant elastic force acting on all neighbors is defined as the basic boundary fraction. (12) in yes The Each component, its physical meaning is reflected in the point. The degree of local imbalance. The forces in each direction at the internal points are basically balanced. Approaching zero; the boundary point force mainly comes from one side. Larger.
[0028] According to the definition of Shannon entropy, in order to quantify the amount of information in the direction of neighbors, the angular information of the neighbor distribution is introduced into the entropy to quantify the difference in the neighbor distribution between boundary points and interior points. The specific calculation process is as follows: For 2D data, the angles of neighbors relative to the current point are calculated, along with their relative position vectors and angles: (13) (14) For high-dimensional data, angles cannot be calculated directly. Local dimensionality reduction (PCA) of the neighbors is required before calculating the 2D angle. (15) (16) To facilitate observation of the distribution of neighboring angles, the angles are mapped onto a circle, and then the angle space is divided into M equal-sized sector regions. Figure 2 This demonstrates the difference between boundary points and interior points in terms of neighbor angles. It is clear that the neighbor angles of boundary points are distributed on the same side, while the neighbor angles of interior points are more evenly distributed.
[0029] (17) (18) Count the number of neighbors within each sector interval and calculate the empirical probability of the angular distribution: (19) (20) To avoid extreme cases, smoothing is necessary: ; (twenty one) The difference in angular distribution between boundary points and interior points is as follows: Figure 2 As shown.
[0030] Definition 5 (Angle Entropy): Shannon entropy based on angle information is defined as angle entropy: ; (twenty two) Normalize the angle entropy to Interval: ; (twenty three) The angular entropy distribution of boundary points and interior points is as follows Figure 3 As shown.
[0031] Due to the distribution characteristics of boundary points and interior points, interior points have neighbors located in all directions, resulting in a smaller net elastic force, dispersed angular directions, and a larger angular entropy; boundary points, on the other hand, tend to have neighbors located on one side, resulting in a larger net elastic force, concentrated angular directions, and a smaller angular entropy. To amplify the features of boundary points and suppress the features of interior points, an angular entropy weighting strategy is proposed, defining a weighting factor. : ; (twenty four) in Defined as directional concentration, the final boundary score is obtained through weighting factors.
[0032] Definition 6 (Final Boundary Score): (25) After weighting by angular entropy, the boundary scores of interior points remain basically unchanged, while the boundary scores of boundary points are doubled. This ensures that the features of boundary points are amplified while the features of interior points are suppressed.
[0033] The boundary points are selected as follows: sort the final boundary scores in descending order of their powers, given the percentiles. Calculate the threshold: (26) (27) Will Defined as a boundary point.
[0034] Figure 4 The entire boundary point detection process is visualized using the Aggregation dataset as an example.
[0035] The pseudocode for the algorithm of this invention is as follows: To evaluate the computational efficiency of the algorithm, we need to analyze its time complexity, which can be divided into the following parts: (28) in , , , These represent the calculation of distance. The time required for nearest neighbor search and elasticity calculation, angle entropy calculation, and boundary sorting.
[0036] Distance calculation is accelerated using a KD-tree, with a time complexity of O(n log n). According to formulas (1) and (11), the time complexity of k-nearest neighbor search and elastic force calculation is... ; Calculating the angular entropy according to formula (19) requires The time complexity is O(n); finally, the boundary scores are sorted to distinguish between boundary points and interior points, with a time complexity of O(n). In summary, the total time complexity of the AESN algorithm is: (29) The beneficial effects of this invention are as follows: 1. A spring network model based on Hooke's Law is proposed, which treats data points as objects subjected to different degrees of tension in the network nodes, and calculates the resultant force on the nodes in the spring network as the standard for boundary scoring.
[0037] 2. Based on the concept of Shannon entropy, angular entropy is proposed to quantify the directional differences in the distribution of nearest neighbor data points. High-dimensional data is mapped to a two-dimensional angular space through local dimensionality reduction, and angular entropy is used to distinguish the neighbor distribution characteristics of boundary points and internal points.
[0038] 3. By constructing a weighting factor using angular entropy, the basic boundary scores are weighted, amplifying the local imbalance features of boundary points and suppressing the balanced distribution features of internal points, thereby improving the discriminative power of boundary detection.
[0039] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. An efficient boundary detection method based on an angle entropy weighted spring network, characterized in that, include: For each data point in the dataset, search for its multiple nearest neighbors; Calculate the elastic force of each nearest neighbor to the current data point, the elastic force being based on Hooke's law to simulate a spring connection; Calculate the resultant force of all elastic forces as the basic boundary fraction; Calculate the angle entropy of the current data point, where the angle entropy quantifies the direction distribution based on the angle information of the nearest neighbor distribution; The final boundary score is obtained by weighting the basic boundary scores using angular entropy; Boundary detection is completed by selecting boundary points using a preset threshold.
2. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 1, characterized in that, The calculation of the elastic force includes: defining the actual distance as the Euclidean distance between data points; defining the natural length as a multiple of the actual distance; defining the spring constant as inversely proportional to the actual distance; and, according to Hooke's Law, the magnitude of the elastic force is a constant, and its direction is from the neighbor to the current point.
3. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 1, characterized in that, The calculation of the angle entropy includes: for two-dimensional data, directly calculating the angle of the nearest neighbor relative to the current point; for high-dimensional data, first performing local dimensionality reduction to two-dimensional space, and then calculating the angle; dividing the angle space into multiple sector regions and counting the number of nearest neighbors in each region; calculating the empirical probability of the angle distribution and performing smoothing; calculating the angle entropy based on the Shannon entropy formula and performing normalization.
4. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 1, characterized in that, The weighted basic boundary score uses a weighting factor, which is defined as directional concentration, where directional concentration is 1 minus the normalized angular entropy.
5. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 1, characterized in that, The step of selecting boundary points by a preset threshold includes: sorting the final boundary scores in descending order; calculating the threshold based on a given percentile; and defining points whose final boundary scores are greater than the threshold as boundary points.
6. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 3, characterized in that, The local dimensionality reduction process is specifically principal component analysis, which projects the high-dimensional data onto the first two principal components to calculate the angle.
7. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 1, characterized in that, Spatial indexing structures are used to accelerate distance calculation and nearest neighbor search.
8. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 1, characterized in that, The time complexity of the method is linear.
9. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 2, characterized in that, The multiple of the natural length is set to a value less than 1 to simulate spring tension.
10. The efficient boundary detection method based on angle entropy weighted spring network as described in claim 3, characterized in that, The number of the multiple sector regions is a fixed value.