A high-efficiency granulocyte generation method based on principal component analysis
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHONGQING UNIV OF POSTS & TELECOMM
- Filing Date
- 2026-02-11
- Publication Date
- 2026-06-02
Smart Images
Figure CN122132824A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of quantum computing and relates to an efficient particle generation method based on principal component analysis. Background Technology
[0002] With the rapid development of information technology, the scale of data has exploded. In the field of machine learning, how to efficiently process large-scale data has become a core challenge. Particle-sphere computing, as an efficient computing paradigm that simulates the human mechanism of prioritizing large-scale cognition, successfully reduces the complexity of computational tasks from sample-scale dependent to particle-sphere-scale dependent by adaptively generating hyperspheres, i.e., particles, to cover and represent the data space. However, existing particle-sphere generation algorithms mainly rely on Euclidean distance metrics and simple radius constraints, which face serious challenges when processing data with complex geometric structures.
[0003] On the one hand, to meet strict radius or consistency constraints, existing algorithms often tend to over-segment data into a large number of tiny redundant spheres, leading to a decrease in compression ratio and an increase in subsequent computational burden. On the other hand, during initialization and splitting, outliers and boundary noise often affect the centroid position and splitting direction, resulting in a decrease in the quality of the generated spheres. Especially in scenarios requiring extremely high computational resource efficiency, such as quantum machine learning tasks in the era of Noisy Intermediate-Scale Quantum (NISQ), where qubit and circuit depth resources are extremely limited, how to generate a set of spheres that is as small as possible but can accurately represent the distribution of the original data is a pressing technical problem that needs to be solved.
[0004] The main shortcomings of existing technologies lie in their low data representation efficiency, failing to ensure accuracy while avoiding over-segmentation and noise interference. Therefore, there is an urgent need in this field for a robust and efficient particle generation method that can incorporate data geometric features to improve the efficiency and accuracy of large-scale data processing. Summary of the Invention
[0005] In view of this, the purpose of this invention is to provide an efficient particle generation method based on principal component analysis.
[0006] To achieve the above objectives, the present invention provides the following technical solution: An efficient granule generation method based on principal component analysis, comprising the following steps: S1: The original dataset is initialized using a parallel sampling strategy to generate an initial set of particles; S2: Calculate the splitting gain for each particle in the current particle set and determine the splitting threshold; S3: Traverse the set of particles and for target particles that meet the splitting threshold, calculate their optimal splitting direction based on PCA; S4: Based on the optimal splitting direction, split the target particle into two sub-particles and update the particle set; S5: Repeat steps S2 to S4 until no more particles meet the splitting condition, and output the final set of particles.
[0007] Furthermore, in step S1, generating the initial set of spheres specifically includes the following steps: S11: Set the initial target number of balls to [value]. ,in n This represents the total number of samples in the dataset. S12: Initialize the candidate center set based on the minimum squared distance from each sample point to the current candidate center. Constructing a normalized probability distribution ; S13: Based on the probability distribution, independently sample multiple sample points and add them to the candidate center set, repeating this sampling process multiple times; S14: Select centers by applying the k-means++ algorithm to the candidate center set. One of the most representative centers; S15, assign each sample point in the dataset to the nearest center to form an initial set of spheres, and calculate the center of each sphere. c and radius r .
[0008] Furthermore, in step S2, calculating the splitting gain and determining the splitting threshold specifically includes the following steps: S21: Define the split gain The formula is the decrease in the sum of squares (SSE) within the cluster before and after granular GB splitting. , where SSE represents the sum of squares within the cluster; S22: Calculate the splitting gain of all spheres in the initial sphere set and obtain the maximum gain value. ; S23: Set the splitting threshold ,in This is the preset relative gain coefficient.
[0009] Furthermore, in step S3, calculating the optimal splitting direction based on PCA specifically includes the following steps: S31: For the target particle to be split, calculate the distance from all sample points inside it to the center of the particle; S32: Select the frontmost element closest to the center. The proportion of sample points is used as the core sample set, where This is a preset proportional coefficient; S33: Perform PCA analysis on the core sample set to extract the first principal component eigenvector corresponding to the largest eigenvalue. As the main direction.
[0010] Furthermore, in step S4, splitting the target particle into two sub-particles specifically includes: Construct a feature vector that passes through the center of the sphere and is perpendicular to the first principal component. The hyperplane is used to divide the sample within the target particle into two subsets, forming two new sub-particles.
[0011] Furthermore, the relative gain coefficient It is used to achieve a balance between data representation accuracy and particle count.
[0012] Furthermore, the proportionality coefficient Used to filter boundary noise and outliers.
[0013] Furthermore, in S5, the splitting condition is that the splitting gain of no granules is greater than the splitting threshold. .
[0014] The beneficial effects of this invention are as follows: (1) This invention employs a coarse-to-fine splitting strategy guided by PCA, resulting in a significantly smaller number of generated spheres compared to traditional methods while maintaining data coverage accuracy. The parallel sampling initialization and adaptive splitting threshold mechanisms in the technical solution ensure that the sphere generation process only refines necessary regions, avoiding redundant segmentation of flat areas. This directly reduces the computational burden of subsequent data processing tasks, making it particularly suitable for large-scale datasets. Experimental results show that the number of spheres generated by this invention can be reduced by approximately 30%-50% while maintaining a similar representational accuracy to the original data, thus demonstrating a significant advantage in resource-constrained environments.
[0015] (2) Traditional methods rely on Euclidean distance and simple radius constraints, making it difficult to capture nonlinear data distributions. This invention introduces a PCA splitting mechanism, extracting the principal direction of the data (the first principal component feature vector) as the splitting axis, so that the sphere partitioning naturally conforms to the geometric distribution of the data. For example, in data with spiral or concentric circle structures, the spheres will split along the direction of maximum change, avoiding invalid segmentation in simple structural regions. This adaptive partitioning ensures that the sphere set accurately characterizes the topological features of the data. The spheres generated on complex datasets are more densely packed at boundaries and in regions of density variation, while maintaining a larger volume in flat regions, thus achieving better data fitting results.
[0016] (3) The core sample set mechanism in the technical solution filters out samples far from the center of the grain, eliminating the interference of boundary noise and outliers on the splitting direction. Compared with traditional methods that directly use all samples to calculate the principal direction, this invention performs PCA analysis only based on core samples, ensuring that the splitting axis stably reflects the mainstream distribution of the data. This design significantly improves the stability of the algorithm on noisy datasets, such as... Figure 3 As shown, the core sample set (blue dots) is unaffected by edge noise, and the splitting direction accurately aligns with the data extension trend. This makes the present invention more practical in real-world scenarios (such as medical data or sensor data).
[0017] (4) By iterative split gain calculation and threshold control, the present invention dynamically balances the relationship between data representation accuracy and the number of particles, thus avoiding the waste of computing resources.
[0018] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description
[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is an overall flowchart of the method in the embodiments of the present invention; Figure 2 This is a process diagram of generating the initial particle geometry through a sampling strategy in this invention; Figure 3 This is a diagram illustrating the process of splitting two daughter particles using PCA in this invention. Figure 3 (a) is a schematic diagram of the distribution of parent particle samples; Figure 3 (b) is a schematic diagram of the core sample set and PCA main direction extraction; Figure 3 (c) is a schematic diagram of hyperplane splitting and daughter particle formation; Figure 4 This is a diagram showing the results of generating spheres on two common clustering datasets in this invention. Detailed Implementation
[0020] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.
[0021] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.
[0022] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.
[0023] Please see Figures 1-4 This is a highly efficient spheroid generation method based on principal component analysis. According to... Figure 1 The method includes the following steps: S1: Initialize the original dataset using a parallel sampling strategy to generate an initial set of particles. This step corresponds to... Figure 2 The initialization process shown aims to quickly construct an initial sphere that can cover the global contour of the data. Specifically, for a given set of data containing... For a large dataset of samples, the initial target number of balls is first set. The algorithm does not use a simple one-time random selection, but rather an iterative oversampling mechanism. Specifically, as... Figure 2 As shown, the candidate center set is first initialized as a single point. In each iteration, the non-center point in the dataset is computed. Shortest distance to the current candidate center set Based on this, a normalized probability distribution is constructed. Based on this probability distribution, multiple new sample points are independently sampled in each round and added to the candidate set. After a finite number of sampling rounds, the k-means++ algorithm is applied to refine the candidate set to... The most representative center is determined, and all sample points in the dataset are assigned to the nearest center to form an initial set of spheres. The center and radius of each sphere are calculated.
[0024] S2: Calculate the splitting gain for each sphere in the current sphere set and determine the splitting threshold. The initially generated spheres may be too coarse to accurately characterize local details. This step uses the reduction in the sum of squares within the cluster (SSE) as a metric for the necessity of splitting. Specifically, for any sphere GB, it is assumed that it splits into two sub-spheres. and Define split gain for The SSE measures the compactness of the spheres. The system first calculates the maximum potential gain for all spheres in the initial sphere set. And set an adaptive split threshold. ,in This is a preset relative gain coefficient (e.g., 0.01). Only when the splitting gain of a single particle is greater than... Only then will subsequent splitting operations be performed.
[0025] S3: Traverse the set of particles. For target particles that meet the splitting threshold, calculate their optimal splitting direction based on principal component analysis. For example... Figure 3 As shown, to improve the robustness of the algorithm in noisy environments, this step introduces a principal component analysis mechanism based on the core sample set. Specifically, as... Figure 3 As shown in (a) and 3(b), for the parent sphere to be split, the distance from all samples within it to the center is first calculated, and only the samples closest to the center are selected. A proportion (e.g., 90%) of the sample points constitute the core sample set (e.g.) Figure 3 (as shown by the blue dots in (b)), while samples at the edges are temporarily excluded as potential noise or outliers. Subsequently, PCA analysis is performed on the core sample set to extract the first principal component eigenvector e1 corresponding to the largest eigenvalue as the optimal splitting direction. (See also...) Figure 3 As shown in (b), this direction accurately captures the main extension direction of the data distribution without being affected by edge noise.
[0026] S4: Based on the optimal splitting direction, split the target particle into two sub-particles and update the particle set. This step utilizes the principal direction obtained from S3 to perform geometric partitioning. Specifically, as follows: Figure 3As shown in (b) and 3(c), a hyperplane is constructed that passes through the center of the particle and is perpendicular to the first principal component eigenvector e1. This hyperplane is used to divide all samples within the target particle into two subsets. Based on these two subsets, new centroids and radii are calculated respectively, forming two new sub-particles. and (like Figure 3 (c) shows that the original parent particle is replaced by these two child particles in the particle set. This partitioning along the direction of maximum data variation minimizes intra-cluster variance.
[0027] S5: Repeat steps S2 to S4 until no more particles satisfy the splitting condition, then output the final set of particles. The algorithm iteratively executes the above-described process of calculating gain, determining the threshold, and PCA-guided splitting until the potential splitting gain of all granules is lower than the threshold. .like Figure 4 The image shows the final particle sphere generation results of the method of this invention on two datasets with complex geometric structures. It can be seen that in regions with flat data distribution, the generated particles are larger; while in regions with complex data structures or varying density (such as the junctions of spiral arms or the gaps between concentric circles), the generated particles are smaller and denser. This indicates that the efficient particle sphere set generated by this invention can accurately maintain the nonlinear topological structure and distribution characteristics of the original data while significantly compressing the data size.
[0028] Example 1: Generation of spheres on a synthetic two-dimensional spiral dataset This embodiment uses a synthetic two-dimensional spiral dataset to simulate data with complex geometric structures, commonly found in pattern recognition and clustering tasks. The dataset contains 1000 sample points forming a double helix structure, designed to test the invention's adaptability to nonlinear distributions.
[0029] Implementation process: Initialization (S1): Set the initial target number of balls. ≈32. A parallel sampling strategy is adopted, generating candidate centers through iterative oversampling, and finally applying k-means++ to select 32 centers, forming an initial set of spheres. The center and radius of each sphere are calculated to ensure coverage of the global contour of the data.
[0030] Split gain calculation (S2): Define split gain To calculate the reduction in the sum of squares (SSE) within the cluster, calculate the gain of all spheres and obtain the maximum value. Set the relative gain coefficient. =0.01, splitting threshold .
[0031] PCA splitting (S3 and S4): For gains exceeding The particles are selected from the core sample set (proportion coefficient). =0.9), PCA analysis was performed to extract the first principal component direction. Build vertically Hyperplane splitting spheres, for example at the bend of the helical arm, with the splitting axis along the data extension direction, generate compact subspheres.
[0032] Iteration (S5): Repeat the splitting until convergence, and output the final set of particles.
[0033] Results Analysis: This embodiment generates approximately 50-60 spheres, significantly fewer than traditional methods (typically exceeding 100). The spheres are small and densely packed in the helical arm region, and larger in the central region, precisely fitting the data structure. For example... Figure 4 As shown, this method avoids over-segmentation while preserving the spiral topology, verifying the invention's efficient representation capability for complex geometry.
[0034] Example 2: Data Compression Application on Real-World Image Datasets This embodiment uses the MNIST handwritten digit dataset (a subset). n =5000 samples), applied to image data compression tasks, to test the efficiency of the present invention in processing high-dimensional data.
[0035] Implementation process: Initialization (S1): Treat image data as high-dimensional vectors (each image is 28x28 pixels = 784 dimensions). Setting... By initializing the particle set through parallel sampling, computational overhead is reduced.
[0036] Threshold control (S2): Calculate the split gain and set... =0.05 to accommodate high-dimensional noise and ensure that splitting only occurs in structurally complex regions.
[0037] Noise robustness treatment (S3): For each particle, use =0.85 filters boundary noise (such as image edge pixels), and calculates the PCA principal direction based on the core sample set. For example, in the intersection area of the digit "8", the PCA direction extends along the stroke to avoid splitting deviation caused by noise.
[0038] Splitting and updating (S4): Split the spheres along the principal direction and iterate until convergence.
[0039] Results Analysis: This invention generates approximately 100 spheres, achieving a 30% improvement in compression ratio compared to traditional methods, with a reconstruction error of less than 5%. The spheres are densely distributed at the boundaries of digital strokes and sparsely distributed in flat background areas, demonstrating adaptive compression. This method provides an efficient solution for image storage and transmission, particularly suitable for resource-constrained edge computing devices.
[0040] Example 3: Resource optimization scenario in quantum machine learning This embodiment simulates a machine learning task in the era of noisy, medium-scale quantum NISQ, using a synthetic quantum state dataset ( n =2000 samples), to test the performance of the present invention in a resource-constrained environment.
[0041] Implementation process: Efficient initialization (S1): Setting ≈45, initial spheres are generated quickly through parallel sampling, reducing the occupancy of qubits.
[0042] Dynamic threshold (S2): Setting =0.005, strictly limiting the number of splits to balance accuracy and computational depth.
[0043] PCA-guided splitting (S3): Addresses decoherence noise in quantum data using... =0.95 filters outoutliers to ensure PCA direction stability. For example... Figure 3 As shown, the core sample set excludes noise interference, and the split axes are aligned with the principal components of the data.
[0044] Iterative optimization (S4 and S5): After splitting, the set of particles is updated, and the final output is about 60 particles for subsequent quantum clustering algorithms.
[0045] Results Analysis: This invention reduces computational complexity from... O ( n ) down to O ( m )( m (The number of spheres is reduced), and the quantum circuit depth is reduced by 40%. In quantum hardware simulations, the sphere set accurately characterizes the quantum state distribution with a lower error rate than traditional methods. This demonstrates the practical value of this invention in NISQ scenarios and provides a scalable data preprocessing tool for quantum machine learning.
[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A highly efficient granule generation method based on principal component analysis, characterized in that: The method includes the following steps: S1: The original dataset is initialized using a parallel sampling strategy to generate an initial set of particles; S2: Calculate the splitting gain for each particle in the current particle set and determine the splitting threshold; S3: Traverse the set of particles and for target particles that meet the splitting threshold, calculate their optimal splitting direction based on PCA; S4: Based on the optimal splitting direction, split the target particle into two sub-particles and update the particle set; S5: Repeat steps S2 to S4 until no more particles meet the splitting condition, and output the final set of particles.
2. The efficient pellet generation method according to claim 1, characterized in that: In step S1, generating the initial set of particles specifically includes the following steps: S11: Set the initial target number of balls to [value]. ,in n This represents the total number of samples in the dataset. S12: Initialize the candidate center set based on the minimum squared distance from each sample point to the current candidate center. Constructing a normalized probability distribution ; S13: Based on the probability distribution, independently sample multiple sample points and add them to the candidate center set, repeating this sampling process multiple times; S14: Select centers by applying the k-means++ algorithm to the candidate center set. One of the most representative centers; S15, assign each sample point in the dataset to the nearest center to form an initial set of spheres, and calculate the center of each sphere. c and radius r .
3. The efficient pellet generation method according to claim 1, characterized in that: In step S2, calculating the splitting gain and determining the splitting threshold specifically includes the following steps: S21: Define the split gain The formula is the decrease in the sum of squares (SSE) within the cluster before and after granular GB splitting. , where SSE represents the sum of squares within the cluster; S22: Calculate the splitting gain of all spheres in the initial sphere set and obtain the maximum gain value. ; S23: Set the splitting threshold ,in This is the preset relative gain coefficient.
4. The efficient pellet generation method according to claim 1, characterized in that: In step S3, calculating the optimal splitting direction based on PCA specifically includes the following steps: S31: For the target particle to be split, calculate the distance from all sample points inside it to the center of the particle; S32: Select the frontmost element closest to the center. The proportion of sample points is used as the core sample set, where This is a preset proportional coefficient; S33: Perform PCA analysis on the core sample set to extract the first principal component eigenvector corresponding to the largest eigenvalue. As the main direction.
5. The efficient pellet generation method according to claim 1, characterized in that: In step S4, splitting the target particle into two sub-particles specifically includes: Construct a feature vector that passes through the center of the sphere and is perpendicular to the first principal component. The hyperplane is used to divide the sample within the target particle into two subsets, forming two new sub-particles.
6. The efficient pellet generation method according to claim 3, characterized in that: The relative gain coefficient It is used to achieve a balance between data representation accuracy and particle count.
7. The efficient pellet generation method according to claim 4, characterized in that: The proportionality coefficient Used to filter boundary noise and outliers.
8. The efficient pellet generation method according to claim 1, characterized in that: In step S5, the splitting condition is that the splitting gain without any granules is greater than the splitting threshold. .