Non-uniform data clustering method based on convex hull optimization
By introducing convex hull calculation and abandonment mechanisms into the clustering method, optimizing the clustering center and boundaries, the boundary recognition and efficiency problems of traditional methods when processing non-uniform data are solved, and more accurate and stable clustering results are achieved.
Patent Information
- Application Number
- CN202411636442.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-15
- Publication Date
- 2025-03-07
AI Technical Summary
Traditional clustering methods encounter challenges in dealing with non-uniform or complex data sets, fail to accurately identify the natural boundaries of the data, and the efficiency decreases in high-dimensional data, affecting the quality and availability of clustering results.
The clustering method based on convex hull optimization is adopted, and the clustering center and boundaries are gradually optimized by randomly selecting the clustering center, calculating the abandoned probability and discarding data points that deviate from the center of mass, calculating the convex hull of each cluster as the boundary, and re-dividing the clustering of abandoned points, until the clustering tends to stabilize.
This method can more accurately define and identify cluster boundaries in non-uniform data sets, improve the clarity of clustering results and the rationality of the attribution of data points, and enhance the overall effect and application value of the clustering algorithm.
Smart Images
Figure CN119577490A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a clustering method for non-uniform data based on convex hull optimization, and belongs to the technical field of data processing. Background Art
[0002] At present, in the field of data processing, clustering is a common data analysis method, which is used to divide the data set into several groups or classes, so that the data points in the same group have high similarity, while the data points in different groups have low similarity. Traditional clustering methods usually rely on specified rules or distances to group data, but these methods often encounter challenges when dealing with non-uniform or complex distribution data sets. For example, they may not be able to accurately identify the natural boundaries of the data, or their efficiency decreases when the data dimension is high, affecting the quality and usability of the clustering results. In addition, some commonly used algorithms are extremely sensitive to the setting of initial parameters, and the instability of the results may result if they are not careful. More importantly, traditional methods often ignore the complexity of the internal structure of the data, such as the non-convex shape of similar data points in multidimensional space, which makes simple distance calculations insufficient to capture the true inter-class relationship. Summary of the invention
[0003] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a clustering method for non-uniform data based on convex hull optimization, which can not only effectively process high-dimensional data and complex data distribution, but also accurately divide the clustering boundaries by calculating the convex hull of data points, thereby improving the accuracy and efficiency of clustering.
[0004] In order to solve the above technical problems, the technical solution of the present invention is: a clustering method for non-uniform data based on convex hull optimization, the steps of the method include:
[0005] S1: Randomly select cluster centers in the data set and initialize clustering of the data set based on Euclidean distance; one cluster center corresponds to one cluster;
[0006] S2: Discard the data points that are far away from the centroid of the cluster according to the discard probability formula, i.e., the discarded points, and re-update the centroid position of each cluster;
[0007] S3: Calculate the convex hull for each cluster's undiscarded data points and define it as the cluster boundary;
[0008] S4: Recalculate the distances from the abandoned points to the boundaries of each cluster, and divide the abandoned points into the clusters corresponding to the nearest cluster boundaries;
[0009] S5: Repeat steps S2 to S5 until all clusters become stable.
[0010] Further, in step S1,
[0011] Randomly select an equal number of cluster centers according to the number of clusters required;
[0012] Then iterate: calculate the Euclidean distance from each data point to the cluster center, assign the data point to the nearest cluster center, and update the cluster center of each cluster to the mean of its internal points; until the position of the cluster center is stable, the clustering is initialized.
[0013] Further, in step S2,
[0014] The abandonment probability formula is:
[0015]
[0016] Among them, p is the probability of a data point being abandoned, d j Represents the Euclidean distance from the data point in the cluster to the cluster centroid, d min With d max They represent the Euclidean distance from the nearest data point to the cluster centroid and the Euclidean distance from the farthest point to the cluster centroid, respectively.
[0017] Further, in step S5, the method for determining whether the cluster is stable includes: the convex hull boundary of the cluster does not change and / or the data points in the cluster do not change.
[0018] After adopting the above technical solution, the present invention has the following beneficial effects:
[0019] First, by introducing convex hull calculation, the present invention can more accurately define and identify cluster boundaries in non-uniform data sets, especially in the case of complex and approximately polyhedral data distribution. This method improves the clarity of clustering results and makes the attribution of data points more reasonable, thereby improving the overall effect and application value of clustering algorithms.
[0020] Secondly, by optimizing the selection and iteration process of cluster centers and introducing a data point discarding mechanism, the present invention improves the stability and robustness of the clustering process. BRIEF DESCRIPTION OF THE DRAWINGS
[0021] Figure 1 A schematic diagram of a clustering method for non-uniform data based on convex hull optimization of the present invention;
[0022] FIG. 2( a ) is a test result of the clustering method of the present invention based on convex hull optimization for non-uniform data Figure 1 ;
[0023] FIG2( b ) is a second test result diagram of the clustering method for non-uniform data based on convex hull optimization of the present invention;
[0024] FIG2( c ) is a third test result diagram of the clustering method for non-uniform data based on convex hull optimization of the present invention;
[0025] FIG. 2( d ) is a fourth test result diagram of the clustering method for non-uniform data based on convex hull optimization of the present invention. DETAILED DESCRIPTION
[0026] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments in conjunction with the accompanying drawings.
[0027] like Figure 1 As shown, a clustering method for non-uniform data based on convex hull optimization, the steps of the method include:
[0028] S1: Randomly select cluster centers in the data set and initialize clustering of the data set based on Euclidean distance; one cluster center corresponds to one cluster;
[0029] S2: Discard the data points that are far away from the centroid of the cluster according to the discard probability formula, i.e., the discarded points, and re-update the centroid position of each cluster;
[0030] S3: Calculate the convex hull for each cluster's undiscarded data points and define it as the cluster boundary;
[0031] S4: Recalculate the distances from the abandoned points to the boundaries of each cluster, and divide the abandoned points into the clusters corresponding to the nearest cluster boundaries;
[0032] S5: Repeat steps S2 to S5 until all clusters become stable.
[0033] In this embodiment, the cluster centroid refers to the component average of all data points in each cluster in each dimension; the convex hull refers to the smallest convex polygon surrounding all points in the cluster, and all internal angles are less than or equal to 180 degrees.
[0034] Further, in step S1,
[0035] Randomly select an equal number of cluster centers according to the number of clusters required;
[0036] Then iterate: calculate the Euclidean distance from each data point to the cluster center, assign the data point to the nearest cluster center, and update the cluster center of each cluster to the mean of its internal points; until the position of the cluster center is stable, the clustering is initialized.
[0037] Further, in step S2,
[0038] The abandonment probability formula is:
[0039]
[0040] Among them, p is the probability of a data point being abandoned, d jRepresents the Euclidean distance from the data point in the cluster to the cluster centroid, d min With d max They represent the Euclidean distance from the nearest data point to the cluster centroid and the Euclidean distance from the farthest point to the cluster centroid, respectively.
[0041] Further, in step S5, the method for determining whether the cluster is stable includes but is not limited to: the convex hull boundary of the cluster does not change, and the data points in the cluster do not change.
[0042] The specific flow chart of this embodiment is as follows Figure 1 As shown, in Figure 1 In the figure, the upper dashed box shows the initialization of the clustering method based on Euclidean distance, and the lower dashed box shows the operation process of the clustering method based on convex hull. The left picture in the lower dashed box shows the result of the initialization of the clustering method based on Euclidean distance; in the second left picture, the gray points are the data points discarded from the red cluster in the first left picture under ideal conditions, waiting to be reassigned to the cluster; in the third left picture, the convex hulls of the blue cluster and the red cluster are calculated respectively, which are defined as the cluster boundaries; in the second right picture, a and b are the shortest distances from the gray point to the boundaries of the blue and red clusters respectively; in the first right picture, after comparing a and b, the gray point is closer to the blue cluster, so it is assigned to the blue cluster.
[0043] The test results on two-dimensional data are as follows Figure 2(a) to Figure 2(d) As shown, points of the same color belong to one cluster and the red X is the cluster center. In the test results of Figure 2(a) and Figure 2(c), the point categories between different clusters are relatively vague, and it is impossible to significantly distinguish the advantages and disadvantages of the method of this embodiment and the traditional method. In the test results of Figure 2(b), the method of this embodiment is exactly the same as the result of the traditional algorithm. In the test results of Figure 2(d), the method of this embodiment is more accurate for the points on the cluster boundary. It can be seen that when it is difficult to accurately divide the cluster boundaries of polyhedral geometric bodies in the face of complex distributions, the method of this embodiment has certain advantages.
[0044] The specific embodiments described above further illustrate the technical problems, technical solutions and beneficial effects solved by the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.
Claims
1. A clustering method for non-uniform data based on convex hull optimization, characterized in that: The steps of the method include: S1: Randomly select cluster centers in the data set and initialize clustering of the data set based on Euclidean distance; one cluster center corresponds to one cluster; S2: Discard the data points that are far away from the centroid of the cluster according to the discard probability formula, i.e., the discarded points, and re-update the centroid position of each cluster; S3: Calculate the convex hull for each cluster's non-discarded data points and define it as the cluster boundary; S4: Recalculate the distances from the abandoned points to the boundaries of each cluster, and divide the abandoned points into the clusters corresponding to the nearest cluster boundaries; S5: Repeat steps S2 to S5 until all clusters become stable.
2. The clustering method according to claim 1, characterized in that: In step S1, Randomly select an equal number of cluster centers according to the number of clusters required; Then iterate: calculate the Euclidean distance from each data point to the cluster center, assign the data point to the nearest cluster center, and update the cluster center of each cluster to the mean of its internal points; until the position of the cluster center is stable, the clustering is initialized.
3. The clustering method according to claim 1, characterized in that: In step S2, The abandonment probability formula is: Among them, p is the probability of a data point being abandoned, d j Represents the Euclidean distance from the data point in the cluster to the cluster centroid, d min With d max They represent the Euclidean distance from the nearest data point to the cluster centroid and the Euclidean distance from the farthest point to the cluster centroid, respectively.
4. The clustering method according to claim 1, characterized in that: In step S5, the method for determining whether the cluster is stable includes: the convex hull boundary of the cluster does not change and / or the data points in the cluster do not change.