Granulocyte density peak clustering method based on dynamic threshold value numerical p system

Abstract

The application discloses a granular ball density peak clustering method based on a dynamic threshold numerical neural P system, and comprises the following steps: step S1, constructing a dynamic threshold numerical neural P system parallel computing model, wherein the dynamic threshold numerical neural P system is composed of a numerical object set, a multi-channel set, a neuron with a dynamic threshold function, a synapse structure, an input neuron and an output neuron; and step S2, preprocessing a data set to be clustered, and inputting the data set into the constructed dynamic threshold numerical neural P system.The application has the beneficial effect that the multi-granularity self-adaptive idea of natural granular balls is introduced, the radius value of the granular ball is used to replace the global cut-off distance parameter of the traditional DPC, the density calculation is completely self-adaptive to the local distribution characteristics of data, manual parameter setting is not needed, and the automation of the clustering process is realized.

Description

Technical Field

[0001] This invention relates to the field of membrane computing technology, specifically to a particle sphere density peak clustering method based on a dynamic threshold numerical neural P-system. Background Technology

[0002] Membrane computing is an emerging computational paradigm, first proposed in 1998. These different computational models are collectively referred to as P-systems. P-systems can be broadly classified into three main types: cell-like P-systems, tissue-like P-systems, and neural P-systems. In recent years, various P-systems have attracted widespread attention due to their advantages and characteristics, achieving remarkable results in both theoretical research and applications.

[0003] Cluster analysis, as an unsupervised learning method in data mining, plays a crucial role in data mining by discovering latent knowledge and revealing hidden patterns in data. Clustering algorithms have been widely applied in fields such as pattern recognition, anomaly detection, recommender systems, customer classification, medical diagnosis, image segmentation, and fault detection.

[0004] In 2014, Science magazine published a novel density-based clustering method called Fast Search Discovery Density Peaks (DPC) clustering algorithm. The core assumption of this algorithm is that cluster centers are points with high local density surrounded by points of lower density, and these centers are relatively far apart. The DPC algorithm does not require pre-determining the number of clusters; cluster centers can be intuitively selected from its proposed two-dimensional decision graph, and it can detect clusters of arbitrary shapes. In addition to the original DPC algorithm, existing technologies have developed improved methods such as the Natural Particle Spherical Clustering algorithm to enhance clustering performance.

[0005] However, existing technologies still have several shortcomings in practical applications, specifically: First, the original DPC algorithm requires manual setting of the global cutoff distance parameter, which directly determines the calculation method of local density and thus significantly affects the clustering results. Since there is a lack of objective and automated parameter determination criteria, users usually rely on experience to repeatedly debug, making it difficult to obtain stable and reliable clustering results. Second, the original DPC algorithm uses a single-chain propagation strategy to assign non-central points. Once a non-central point is incorrectly assigned to a cluster, the error will spread downstream along the propagation chain, producing a chain of errors similar to the domino effect, which leads to a significant decrease in clustering accuracy. Third, traditional DPC algorithms use individual data points as the basic clustering unit, making them highly sensitive to noise and outliers. Furthermore, when processing large-scale datasets, the point-to-point distance calculation method results in high algorithm complexity, limiting its efficiency in massive data scenarios. Fourth, traditional neural P systems mainly focus on theoretical research into their computational completeness and computational capabilities, lacking specialized designs for specific application tasks (such as cluster analysis). Furthermore, neural P systems use symbolic impulses as information transmission carriers, making them inherently suitable for discrete symbolic processing. They suffer from discontinuity defects when processing continuous numerical data, making them difficult to directly and effectively apply to practical continuous data clustering problems.

[0006] Therefore, to address the aforementioned technical issues, it is necessary to provide a particle sphere density peak clustering method based on a dynamic threshold numerical neural P system. Summary of the Invention

[0007] To address the shortcomings of the existing technology, the purpose of this invention is to provide a particle sphere density peak clustering method based on a dynamic threshold numerical neural P system, in order to solve the problems mentioned in the background technology.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: This invention provides a particle spherical density peak clustering method based on a dynamic threshold numerical neural P-system. In one or more embodiments of the present invention, the following steps are included: Step S1: Construct a parallel computing model for a dynamic threshold numerical neural P system. The dynamic threshold numerical neural P system consists of a set of numerical objects, a multi-channel set, neurons with dynamic threshold function, synaptic structures, input neurons, and output neurons. Step S2: Preprocess the dataset to be clustered by inputting the dataset into the constructed dynamic threshold numerical neural network P system; Step S3: Generate natural particle spheres using the natural neighbor search algorithm. Use natural particle spheres as the basic unit of clustering. Each natural particle sphere is described by its centroid and radius. Step S4: Based on the idea of ​​density peak, calculate the local density and relative distance of each natural particle sphere. The local density calculation formula uses the radius value of the particle sphere instead of the traditional cutoff distance parameter. Step S5: Calculate the decision value of each natural particle based on local density and relative distance, and select the natural particles with the largest decision values ​​as the initial cluster centers; Step S6: Assign the natural particles that were not selected as cluster centers to the nearest cluster centers to form the initial clusters; Step S7: Iteratively optimize the initial clustering, calculate the segmentation threshold based on the statistical characteristics of the radius of the particles within the cluster, and perform splitting and merging operations on the particles that meet the conditions until the data point labels no longer change; Step S8: Output the final clustering result through the output neuron.

[0009] In one or more embodiments of the present invention, the dynamic threshold numerical neural network P system is a distributed system of degree m, where m ≥ 1.

[0010] In one or more embodiments of the present invention, the natural particle spheres in step S3 are generated based on the definition of natural neighborhood. The natural neighborhood is a stable neighborhood structure that does not require preset parameters and is determined by the multi-layer nearest neighbor and reverse nearest neighbor of the sample point. A single natural particle sphere contains the sample point and all its natural neighbors, and is uniquely characterized by its centroid coordinates and radius.

[0011] In one or more embodiments of the present invention, the local density of the natural particle sphere in step S4 is calculated by the centroid spacing of the particle sphere, the number of data points inside the particle sphere, and the radius of the particle sphere. The relative distance is the minimum distance from the current natural particle to the center of mass of all natural particles with a density higher than itself.

[0012] In one or more embodiments of the present invention, the segmentation threshold in step S7 is calculated from the statistical characteristics of the radii of all natural particles within the cluster; A splitting operation is triggered when the difference in the radius of natural spheres within a cluster exceeds the splitting threshold. During the splitting process, the point with the most natural neighbors within the particle sphere is selected as the representative point of the dense region, and the point with the fewest natural neighbors is selected as the representative point of the sparse region. The dense region and the sparse region are divided according to the distance of the sample point to the two representative points.

[0013] In one or more embodiments of the present invention, after the natural particle spheres split, the particle spheres corresponding to the dense regions are retained in the original cluster, and the particle spheres corresponding to the sparse regions are separated and assigned to the cluster where the nearest cluster center is located. This process is repeated until the data point labels are stable.

[0014] In one or more embodiments of the present invention, the particle sphere density peak clustering algorithm is placed within the operational framework of a dynamic threshold numerical neural network P-system, resulting in a GBDP-DTNNP system model with a degree of 9. The GBDP-DTNNP system model is defined as follows:

[0015] in, It is a collection of numerical objects. In the GBDP-DTNNP algorithm, it represents the input dataset and its evolutionary form. The object's form changes with the neuron's processing stage, and its initial state is... , representing the original sample points, and the running status is ; This represents the set of intrasynaptic channels connecting adjacent neurons, where... The set of positive integers; The term refers to neurons in a system, which are defined as follows: The specific components include: The numerical object input by the neuron can be specifically interpreted as the center of mass of a natural sphere in the GBDP-DTNNP algorithm. ,radius Density value Relative distance and decision value ; The dynamic threshold calculated based on the numerical object can be specifically interpreted in the GBDP-DTNNP algorithm as follows: selecting the highest density value point one by one during the cluster center selection phase; selecting the relative distance between a non-cluster center point and its nearest center point; and calculating the segmentation threshold based on the numerical object during cluster splitting and merging. ; Represents neurons The finite set of rules in includes: This rule is used to abstract data objects into a dynamic threshold judgment form. In the GBDPC-DTNNP algorithm, it can be specifically interpreted as the center of mass of a natural sphere. ,radius ,density Relative distance and decision value The calculation process; like Then rule 2 is triggered, and the channel is used. The output is passed to the next neuron. In the GBDPC-DTNNP algorithm, this can be specifically interpreted as the process of selecting the cluster center sphere with the highest decision value and assigning it to non-center points, and the process of dividing and merging spheres based on the division threshold. Determine the process of particle spheres being split and two particles merging; like Then rule 3 is triggered, and the channel is used. The output to the next neuron, in the GBDPC-DTNNP algorithm, can be specifically interpreted as the separation process between core and non-core points and the failure to meet the segmentation threshold. The process of non-merging particles and two non-merging particles; This represents the synaptic structure between neurons, denoted as . Records intermediate between neurons and The synapses between, among which ; and These refer to the input neuron and the output neuron, respectively, which are the input of data and the output of clustering results.

[0016] The beneficial effects of this invention are as follows: 1. By introducing the multi-grain size adaptive concept of natural spheres, the radius value of the spheres is used to replace the global cutoff distance parameter of the traditional DPC, so that the density calculation is fully adaptive to the local distribution characteristics of the data, without the need for manual parameter setting, thus realizing the automation of the clustering process; 2. Using natural spheres as the basic clustering unit, the natural neighbor structure of the spheres effectively avoids the chain reaction caused by single-point misassignment, significantly improving the robustness and accuracy of the clustering results.

[0017] 3. By defining a dynamic segmentation threshold using the statistical characteristics of the particle sphere radius within the cluster, and effectively eliminating underfitting and overfitting phenomena through the division and redistribution of dense and sparse regions, better clustering results are obtained. 3. The GBDP algorithm is fully mapped to the parallel computing framework of the DTNNP system and executed thereon, utilizing the distributed parallel architecture of the neural P system to accelerate computation. Experiments show that the time complexity of the algorithm can be significantly reduced as the number of processors increases, providing technical support for large-scale data processing and real-time clustering applications. 4. The neural P system was applied to clustering analysis tasks, and a complete clustering algorithm solution was constructed, which can be applied to multiple practical fields such as medical diagnosis and image segmentation. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is an example diagram of a particle sphere density peak clustering method based on a dynamic threshold numerical neural P-system in one embodiment of the present invention; Figure 2 This is a flowchart illustrating the operation of a particle density peak clustering method based on a dynamic threshold numerical neural P-system in one embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the true cluster shape of the synthetic dataset; Figure 4This is a comparison chart of the results on the Aggregation synthetic dataset; Figure 5 The comparison results are shown on the Spiral synthetic dataset; Figure 6 The comparison results are shown on the R15 synthetic dataset; Figure 7 This is a comparison of the results on the Heartshapes synthetic dataset; Figure 8 The comparison results are shown in the Flame synthetic dataset. Figure 9 This is a comparison of results on a path-based synthetic dataset; Figure 10 This is a comparison chart of results on the Compound synthetic dataset; Figure 11 The comparison results are shown on the Dountcurves synthetic dataset. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] A particle spherical density peak clustering method based on a dynamic threshold numerical neural network P-system according to an embodiment of the present invention includes the following steps: Step S1: Construct a parallel computing model for a dynamic threshold numerical neural P system. The dynamic threshold numerical neural P system consists of a set of numerical objects, a multi-channel set, neurons with dynamic threshold function, synaptic structures, input neurons, and output neurons. Step S2: Preprocess the dataset to be clustered by inputting the dataset into the constructed dynamic threshold numerical neural network P system; Step S3: Generate natural particle spheres using the natural neighbor search algorithm. Use natural particle spheres as the basic unit of clustering. Each natural particle sphere is described by its centroid and radius. Step S4: Based on the idea of ​​density peak, calculate the local density and relative distance of each natural particle sphere. The local density calculation formula uses the radius value of the particle sphere instead of the traditional cutoff distance parameter. Step S5: Calculate the decision value of each natural particle based on local density and relative distance, and select the natural particles with the largest decision values ​​as the initial cluster centers; Step S6: Assign the natural particles that were not selected as cluster centers to the nearest cluster centers to form the initial clusters; Step S7: Iteratively optimize the initial clustering, calculate the segmentation threshold based on the statistical characteristics of the radius of the particles within the cluster, and perform splitting and merging operations on the particles that meet the conditions until the data point labels no longer change; Step S8: Output the final clustering result through the output neuron.

[0022] Furthermore, such as Figure 1 As shown, the dynamic threshold numerical neural network P system is a distributed system of degree m, where m ≥ 1. The formal definition of a distributed dynamic threshold numerical neural network P system of degree m is:

[0023] in, It is a collection of numerical objects. It represents the collection of channels connecting the synapses of adjacent neurons.

[0024] in, Represents the set of positive integers. The term "neuron" refers to a cell in a system, and is defined as follows: The specific components include: , It is a numerical object input by neurons; , It is a dynamic threshold calculated based on the numerical object; , Represents neurons The finite set of rules in includes: Neuron The rules in the document are used to abstract data objects into a dynamic threshold judgment form; ,like Then rule 2 is triggered, and the channel is used. Output to the next neuron; ,like Then rule 3 is triggered, and the channel is used. Output to the next neuron; This represents the synaptic structure between neurons, denoted as . Records intermediate between neurons and The synapses between, among which ; and These refer to the input neurons and the output neurons, respectively.

[0025] like Figure 1 As shown, The input is from the output neuron The transmitted data signal executed the prescribed procedure. That is, numerical rules are processed by functions and the processed result is output to the next neuron in the form of numerical impulses; The input is The emitted numerical signal is processed according to a dynamic threshold, and the processed numerical signal is output to the neuron cell. and middle, and These are input neurons and output neurons, respectively.

[0026] The input is from the output neuron The transmitted data signal executed the prescribed procedure. That is, numerical rules are processed by functions and the processed result is output to the next neuron in the form of numerical impulses; The input is The emitted numerical signal is processed according to a dynamic threshold, and the processed numerical signal is output to the neuron cell. and middle, and These are input neurons and output neurons, respectively.

[0027] Furthermore, this embodiment uses natural spheres as the basic unit of clustering. Natural spheres are generated by a natural neighborhood search algorithm. The definitions of natural neighborhood and natural sphere are as follows: Definition 1 (Natural Neighborhood): For any Its natural neighborhood It is a stable neighborhood structure obtained through the natural neighbor search algorithm, requiring no preset parameters. Its expression is:

[0028] in For sample points The Floor neighbor, Reverse nearest neighbor, This represents the number of layers when the search is stable.

[0029] Definition 2 (Natural Sphere): Each object and its natural neighbors are considered as a sphere, serving as the basic unit of clustering for sample points. Its natural granular spheres From the center of mass and radius Described as:

[0030] After determining the natural particle sphere for each point, this invention, based on the concept of density peaks, uses the natural particle sphere instead of the original single sample point as the central particle sphere for clustering. The definition of the density peak natural particle sphere is as follows: Definition 3 (Density Peak Natural Particle Sphere): For those satisfying The K objects with the maximum value (the preset number of cluster centers), the set of cluster centers that caused the incident is: .

[0031] Utilizing the radius value of natural particle spheres and replacing the traditional DPC global cutoff distance This is to accommodate the density distribution of natural granules. The local density formula for natural granules is as follows:

[0032] in The distance between the centers of mass of different natural spheres. Natural granular spheres The number of data points within.

[0033] The relative distance between natural granules is determined by calculating the distance to the center of mass of the natural granule, which has a higher density than itself. The formula is as follows:

[0034] This embodiment still uses the traditional density peak clustering algorithm to calculate the decision value, and the formula is as follows:

[0035] For particles that are not selected as cluster centers, this embodiment merges them into the nearest density peak particle that has been identified as a cluster center, forming an initial cluster. The initial clustering process is now complete.

[0036] Furthermore, for the initial clusters formed through the initial clustering process, this embodiment defines a natural particle spherical cluster as follows: Definition 4 (Natural Particle Cluster): The set of all natural particle clusters contained in a cluster is Its definition is: The iterative process of forming natural spheres from the initial clustering consists of two parts: sphere splitting and sphere merging. Natural spheres formed from objects within a cluster should have a uniform size. There are three reasons why the radius of the formed spheres might be too large: firstly, edge objects are contained within the same sphere; secondly, edge objects from another cluster are contained within the sphere; and thirdly, noisy objects are contained within the sphere. Therefore, it is necessary to adjust the spheres in the cluster to ensure tight connections between points. For the iterative splitting process, this invention defines the criterion for determining whether a natural sphere has splitted as a splitting threshold. The statistical properties of the particle sphere radius within the cluster are used to define it as follows:

[0037] If the radius difference of the natural spheres within the cluster is too large, that is, if the condition is met... If a certain condition is met, a split is triggered. For a sphere to be split, if it contains few neighboring objects, it means it may be located in an edge cluster or is itself a noise point. The more sample points it contains, the closer the natural particle sphere is to the central cluster. Therefore, this invention selects two representative points to split natural particle spheres that meet the conditions. The representative points for dense and sparse regions are defined as follows: Definition 5 (Representative Point): When satisfying In a natural sphere of particles, the representative point of a dense region is selected as the point with the most natural neighbors, i.e. Similarly, the representative point of a sparse region is selected as the point with the fewest natural neighbors, i.e. .

[0038] For the regions generated by segmentation, this invention divides dense and sparse regions based on the distances of points within the natural particle spheres to representative points in dense and sparse regions, thereby determining the sample points contained in the two segmented particle spheres. Definition 6 (Dense Regions and Sparse Regions): In a natural particle sphere, sample points that are closer to the representative point of a dense region are classified as dense regions. Sample points that are closer to the representative points of the sparse region are classified as sparse regions. The expression is:

[0039] After a natural particle sphere splits into sparse and dense regions, its neighborhood information becomes more stable, and its radius becomes smaller. For the sparse and dense regions formed by the split, this invention treats the dense region as a new particle sphere within the initial cluster and excludes the sparse region from the initial cluster, so as to improve the final clustering effect in the subsequent merging process.

[0040] After the natural particle sphere segmentation process is completed, the present invention can obtain an initial cluster composed of particles with uniform volume and new particles composed of sparse regions separated from the initial clusters through the segmentation process. For the aforementioned new particles, the present invention assigns them to the cluster containing the nearest cluster center and performs a new round of iteration.

[0041] The criterion for determining whether the iteration process has stopped is whether all natural spheres have common neighbors during the computation. After the iteration stops, the number of data points is greater than... Natural granular particles are considered as a cluster, while the number of data points is less than [a certain value]. The particles will be assigned to the clusters that are closest to them, and finally all the merged clusters will be used as the final output of the clustering.

[0042] Furthermore, the particle density peak clustering algorithm is placed within the operational framework of a dynamic threshold numerical neural network P-system, resulting in a GBDP-DTNNP system model with a degree of 9. The GBDP-DTNNP system model is defined as follows:

[0043] in, It is a collection of numerical objects, specifically representing the input dataset and its evolutionary form in the GBDP-DTNNP algorithm. The object's form changes with the neuron's processing stage. Its initial state is... This represents the original sample points, and the running status is... ; This represents the set of intrasynaptic channels connecting adjacent neurons, where... The set of positive integers; The term "neuron" refers to a cell in a system, and is defined as follows: The specific components include: The numerical object input by the neuron can be specifically interpreted as the center of mass of a natural sphere in the GBDP-DTNNP algorithm. ,radius Density value Relative distance and decision value ; The dynamic threshold calculated based on the numerical object can be specifically interpreted in the GBDP-DTNNP algorithm as follows: selecting the highest density value point one by one during the cluster center selection phase; selecting the relative distance between a non-cluster center point and its nearest center point; and calculating the segmentation threshold based on the numerical object during cluster splitting and merging. ; Represents neurons The finite set of rules in includes: This rule is used to abstract data objects into a dynamic threshold judgment form. In the GBDPC-DTNNP algorithm, it can be specifically interpreted as the center of mass of a natural sphere. ,radius ,density Relative distance and decision value The calculation process; like Then rule 2 is triggered, and the channel is used. The output is passed to the next neuron. In the GBDPC-DTNNP algorithm, this can be specifically interpreted as the process of selecting the cluster center sphere with the highest decision value and assigning it to non-center points, and the process of dividing and merging spheres based on the division threshold. Determine the process of particle spheres being split and two particles merging; like Then rule 3 is triggered, and the channel is used. The output to the next neuron, in the GBDPC-DTNNP algorithm, can be specifically interpreted as the separation process between core and non-core points and the failure to meet the segmentation threshold. The process of non-merging particles and two non-merging particles; This represents the synaptic structure between neurons, denoted as . Records intermediate between neurons and The synapses between, among which .

[0044] and These refer to the input neuron and the output neuron, respectively, which are the input of data and the output of clustering results.

[0045] like Figure 2 As shown, the operating steps of GBDPC-DTNNP are as follows: The dataset consists of input neurons After being input into the membrane system, all sample points are transmitted to the neuron cells via synapses in the form of numerical signals. In neurons Triggering rules Then, the calculated sample points and their corresponding natural particle sphere information will be... Input to nerve cells middle.

[0046] Furthermore, neurons Received information about natural granular balls. Its specific content is as follows In nerve cells Triggering rules Calculate density Relative distance and decision value After the calculation is complete, information including the particle spheres and decision values ​​will be provided. Transmitted to neurons via synapse middle.

[0047] Neuron cells Based on the input signal, i.e., receiving relevant information about the natural particle spheres and decision values. Implement dynamic threshold rules Among them, dynamic threshold For decision value Natural granular spheres, and related information Through the passage Output to neurons In the middle, for decision value Natural granular spheres, and related information Through the passage Output to neurons .

[0048] In neurons In the process, the particles identified as cluster centers are subject to regulations. Marked as the A cluster is formed, and the data is input into the neuron cells. In neurons In the process, the particles that are determined to be non-cluster centers are subject to the following rules. It identifies the nearest natural particle sphere that is the cluster center and then outputs it to the neuron. middle.

[0049] In neurons In the middle, natural spheres without cluster centers With natural granular spheres labeled as cluster centers Execution rules Initial clusters are formed, where It is all natural spheres that are far from the cluster center. The most recent collection of pellets.

[0050] In neurons In China, for For all particles, apply the dynamic threshold rule. ,in To determine the segmentation threshold, for those that satisfy... The granules were identified as needing to be segmented and passed through the channel. Sent to neurons In the middle; for satisfying The granular particles were determined to be unsplitting, passing through the channel. Sent to neurons middle.

[0051] In neurons In the middle, the execution rules ,in That is, to put the pellets into balls A sphere that splits into sparse regions, for Retain the clustering information in the original dataset. Send to neurons In China; for Generate new particle information And send it to the neuron cells middle; In neurons In this context, the following rules apply:

[0052] Identify the final cluster to which the segmented sparse region particles belong, and use the final label information as the clustering result and neurons. The clustering information is returned to the neuron as the result of a new round of iteration. Iterate through the data points until the labels no longer change.

[0053] At this point, the DTNNP system terminates its operation and removes the neurons from their current state. The results, as the final clustering results, are obtained through neuronal cells. Output.

[0054] Taking patient classification in medical diagnosis as an example, the specific application process of this invention is as follows: First, collect patients' clinical data, including various physiological indicators (such as age, blood pressure, blood sugar, blood lipids, etc.), to form a multi-dimensional dataset. Treat each patient as a sample point, and all patient data constitute the dataset to be clustered.

[0055] Next, the dataset is input into the constructed DTNNP system. The system automatically generates natural spheres using a natural neighbor search algorithm, with each sphere representing a group of patients with similar clinical characteristics.

[0056] The system then automatically identifies density peak particle spheres as cluster centers, which represent typical patient types. For example, it may identify typical patient types such as "hypertension risk group," "diabetes risk group," and "healthy control group."

[0057] Next, the system assigns other patients to their respective typical patient types, forming initial patient clusters. For patients in borderline states, the system refines the classification through a particle sphere splitting and merging mechanism to ensure accuracy.

[0058] Finally, the system outputs patient clustering results to assist doctors in making clinical decisions. This method can automatically discover potential patterns within patient populations, providing data support for personalized medicine and precision treatment.

[0059] like Figures 3 to 11 As shown, the clustering algorithm was simulated and tested using MATLAB 2022a software in an environment with a hardware configuration of 13th Gen Intel Core i5-13500HX processor and Windows 11 64-bit operating system.

[0060] The experiment selected eight synthetic datasets (including Aggregation, Spiral, R15, Heartshapes, Flame, Pathbased, Compound, and Dountcurves) and seven real-world datasets from the UCI database (including Iris, Seeds, Wine, Ecoli, Thyroid, Dematology, and Segmentation). Comparison algorithms included K-means clustering, DBSCAN clustering, DPC, NGBC, and DPC-DBFN. Three external evaluation metrics for clustering—adjusted Rand index, normalized mutual information, and the Falks-Mass index—were used for evaluation.

[0061] In experiments on synthetic datasets, the GBDP-DTNNP algorithm achieved excellent performance on all synthetic datasets. In particular, it achieved perfect scores on all three metrics of the dountcurves, path-based, spiral, flame, and heartshapes datasets. In contrast, DPC's ARI score on dountcurves was only 0.7137, and K-means's ARI score on spiral was only 0.1659, demonstrating the significant advantage of this invention in handling complex shape data.

[0062] In real-world dataset experiments, the GBDP-DTNNP algorithm achieved best or near-best results on almost every metric across all datasets. On the Iris dataset, GBDP-DTNNP achieved ARI 0.9673, NMI 0.9040, and FMI 0.8846, outperforming all compared algorithms. On the Seeds dataset, GBDP-DTNNP achieved the best ARI and NMI scores. On the Wine dataset, GBDP-DTNNP achieved the best FMI score of 0.8649. These results demonstrate that the present invention possesses good generalization ability and stable clustering performance.

[0063] Experimental results show that the GBDP-DTNNP algorithm outperforms existing technologies in terms of clustering accuracy, automation, and robustness, especially in handling datasets with complex shapes and uneven density. It has reached the technological maturity for application in real-world scenarios.

[0064] Obviously, the above-described embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A particle spherical density peak clustering method based on a dynamic threshold numerical neural network P system, characterized in that, Includes the following steps: Step S1: Construct a parallel computing model for a dynamic threshold numerical neural P system. The dynamic threshold numerical neural P system consists of a set of numerical objects, a multi-channel set, neurons with dynamic threshold function, synaptic structures, input neurons, and output neurons. Step S2: Preprocess the dataset to be clustered by inputting the dataset into the constructed dynamic threshold numerical neural network P system; Step S3: Generate natural particle spheres using the natural neighbor search algorithm. Use natural particle spheres as the basic unit of clustering. Each natural particle sphere is described by its centroid and radius. Step S4: Based on the idea of ​​density peak, calculate the local density and relative distance of each natural particle sphere. The local density calculation formula uses the radius value of the particle sphere instead of the traditional cutoff distance parameter. Step S5: Calculate the decision value of each natural particle based on local density and relative distance, and select the natural particles with the largest decision values ​​as the initial cluster centers; Step S6: Assign the natural particles that were not selected as cluster centers to the nearest cluster centers to form the initial clusters; Step S7: Iteratively optimize the initial clustering, calculate the segmentation threshold based on the statistical characteristics of the radius of the particles within the cluster, and perform splitting and merging operations on the particles that meet the conditions until the data point labels no longer change; Step S8: Output the final clustering result through the output neuron.

2. The particle spherical density peak clustering method based on a dynamic threshold numerical neural network P system as described in claim 1, characterized in that, The dynamic threshold numerical neural network P system is a distributed system of degree m, where m ≥ 1.

3. The particle spherical density peak clustering method based on a dynamic threshold numerical neural network P system as described in claim 1, characterized in that, In step S3, the natural particle spheres are generated based on the definition of natural neighborhood. Natural neighborhood is a stable neighborhood structure that does not require preset parameters and is determined by the multi-layer nearest neighbor and reverse nearest neighbor of the sample point. A single natural particle sphere contains the sample point and all its natural neighbors, and is uniquely characterized by its centroid coordinates and radius.

4. The particle spherical density peak clustering method based on a dynamic threshold numerical neural network P system as described in claim 1, characterized in that, In step S4, the local density of the natural particle sphere is calculated by the centroid spacing of the particle sphere, the number of data points inside the particle sphere, and the radius of the particle sphere. The relative distance is the minimum distance from the current natural particle to the center of mass of all natural particles with a density higher than itself.

5. The particle spherical density peak clustering method based on a dynamic threshold numerical neural network P system as described in claim 1, characterized in that, In step S7, the segmentation threshold is calculated based on the statistical characteristics of the radii of all natural particles within the cluster. A splitting operation is triggered when the difference in the radius of natural spheres within a cluster exceeds the splitting threshold. During the splitting process, the point with the most natural neighbors within the particle sphere is selected as the representative point of the dense region, and the point with the fewest natural neighbors is selected as the representative point of the sparse region. The dense region and the sparse region are divided according to the distance of the sample point to the two representative points.

6. The particle spherical density peak clustering method based on a dynamic threshold numerical neural network P system as described in claim 5, characterized in that, After the natural particle spheres split, the particle spheres corresponding to the dense regions are retained in the original clusters, while the particle spheres corresponding to the sparse regions are separated and assigned to the clusters containing the nearest cluster centers. This process is repeated until the data point labels are stable.

7. The particle spherical density peak clustering method based on a dynamic threshold numerical neural network P system as described in claim 1, characterized in that, By placing the particle density peak clustering algorithm within the operational framework of a dynamic threshold numerical neural network P-system, a GBDP-DTNNP system model with a degree of 9 is presented. The GBDP-DTNNP system model is defined as follows:

8. Among them, It is a collection of numerical objects. In the GBDP-DTNNP algorithm, it represents the input dataset and its evolutionary form. The object's form changes with the neuron's processing stage, and its initial state is... , representing the original sample points, and the running status is ; This represents the set of intrasynaptic channels connecting adjacent neurons, where... The set of positive integers; The term refers to neurons in a system, which are defined as follows: The specific components include: The numerical object input by the neuron can be specifically interpreted as the center of mass of a natural sphere in the GBDP-DTNNP algorithm. ,radius Density value Relative distance and decision value ; The dynamic threshold calculated based on the numerical object can be specifically interpreted in the GBDP-DTNNP algorithm as follows: selecting the highest density value point one by one during the cluster center selection phase; selecting the relative distance between a non-cluster center point and its nearest center point; and calculating the segmentation threshold based on the numerical object during cluster splitting and merging. ; Represents neurons The finite set of rules in includes: This rule is used to abstract data objects into a dynamic threshold judgment form. In the GBDPC-DTNNP algorithm, it can be specifically interpreted as the center of mass of a natural sphere. ,radius ,density Relative distance and decision value The calculation process; like Then rule 2 is triggered, and the channel is used. The output is passed to the next neuron. In the GBDPC-DTNNP algorithm, this can be specifically interpreted as the process of selecting the cluster center sphere with the highest decision value and assigning it to non-center points, and the process of dividing and merging spheres based on the division threshold. Determine the process of particle spheres being split and two particles merging; like Then rule 3 is triggered, and the channel is used. The output to the next neuron, in the GBDPC-DTNNP algorithm, can be specifically interpreted as the separation process between core and non-core points and the failure to meet the segmentation threshold. The process of non-merging particles and two non-merging particles; This represents the synaptic structure between neurons, denoted as . Records intermediate between neurons and The synapses between, among which ; and These refer to the input neuron and the output neuron, respectively, which are the input of data and the output of clustering results.

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