Bulk density granulation feature selection method and system based on reasonable particle size principle

Abstract

The application discloses a kind of based on the principle of reasonable granularity bulk density granulation feature selection method and system, the method of the present application includes: data set is preprocessed and density limit parameter and granularity tolerance parameter are set;First layer density clustering is executed to obtain coarse granularity set;Second layer density clustering is executed in each coarse granularity inside traversal candidate neighborhood parameter, and candidate fine granularity division is obtained;The coverage, specificity and homogeneity of each candidate granularity are calculated and comprehensive evaluation index is constructed, and the optimal fine granularity division is selected for each coarse granularity;After merging, final reasonable granularity set is obtained;Attribute importance is calculated based on the set, and feature subset is iteratively selected.The application can effectively process non-convex data structure, reduce neighborhood parameter sensitivity, improve granularity division rationality and feature selection quality by double-layer density granulation and three-dimensional granularity evaluation.

Description

Technical Field

[0001] This invention belongs to the field of data mining and machine learning technology, specifically relating to a method and system for selecting granular features based on the principle of reasonable granularity. It can be used for feature selection, dimensionality reduction and classification modeling of high-dimensional data, and is especially suitable for datasets with non-convex distribution, uneven density distribution or complex structure. Background Technology

[0002] Feature selection is a core technique in data mining and machine learning. Its goal is to select the most relevant subset of features from the original feature set to reduce data dimensionality, computational overhead, and improve the model's generalization performance. With the rapid development of information technology, the size and dimensionality of datasets are constantly increasing, and the "curse of dimensionality" caused by high-dimensional data is becoming increasingly prominent. In many practical applications, such as bioinformatics, image recognition, text classification, and social network analysis, data often contains a large number of redundant and irrelevant features. These features not only increase computational complexity but may also lead to overfitting of classification or prediction models, thereby reducing the model's generalization ability. Therefore, how to efficiently and accurately select the most discriminative feature subset from high-dimensional data has become one of the research hotspots in the field of data mining.

[0003] Existing feature selection methods can generally be categorized into three types: filtering methods, wrapping methods, and embedded methods. Filtering methods independently evaluate the relevance of each feature using statistical metrics (such as mutual information, chi-square test, Fisher Score, etc.), offering high computational efficiency, but neglecting the interactions between features. Wrapping methods evaluate feature subsets by combining search strategies with classifier performance, effectively capturing synergistic effects between features, but incurring high computational costs in high-dimensional data scenarios. Embedded methods integrate feature selection into the model training process, such as Lasso regression and decision trees, achieving both efficiency and effectiveness, but their applicability is limited by specific model structures.

[0004] In recent years, researchers have begun to explore using the structural information of data itself to guide the feature selection process. Cluster analysis, as an unsupervised method for discovering data organization structure, can reveal the distribution patterns and group structures within data. Cluster-based feature selection methods typically first divide the data objects and then evaluate the importance of features based on the clustering results. However, most existing cluster-based feature selection methods rely on clustering algorithms based on center distance, such as K-means and fuzzy C-means. These methods assume that data clusters have a spherical or convex structure. When dealing with real-world data with non-convex distributions such as rings, arcs, stripes, or nested clusters, they often produce incorrect clustering, thus affecting the accuracy of subsequent feature selection.

[0005] Granular computing, as an important research direction in the field of computational intelligence, aims to simulate the human cognitive process from coarse to fine by constructing information granules at different granular levels, thereby handling uncertainties in complex data environments. Information granules are abstract representations of sets of objects with similarity, proximity, or functional correlation. Reasonable information granule construction can effectively reduce problem complexity while maintaining the integrity of the data structure. However, most existing information granule construction methods still rely on convex clustering methods such as K-means or FCM, which are difficult to adapt to the prevalent non-convex data distributions in reality. Some researchers have proposed using density-based clustering methods (such as DBSCAN) to construct information granules. This method identifies cluster structures of arbitrary shapes through density connectivity, giving it a natural advantage in processing non-convex data. However, traditional DBSCAN heavily relies on the reasonable setting of a single neighborhood radius parameter. When there is an uneven density distribution in the dataset, a single parameter cannot adequately account for the density differences in different local regions, easily leading to overly coarse merging or overly fine splitting of information granules.

[0006] The quality evaluation of information granules is one of the key issues in granular computation research. According to the principle of reasonable granulation, a high-quality information granule should simultaneously meet three basic requirements: completeness (the granule should contain enough objects to maintain the statistical significance of the data); specificity (different granules should have clearly distinguishable boundaries); and homogeneity (objects within the same granule should have high consistency). However, existing methods often focus on optimizing one aspect during the granulation process, such as pursuing cluster purity while neglecting coverage, or pursuing inter-granule distinguishability while neglecting intra-granule consistency. How to achieve a balance among these three mutually constraining goals remains a difficult problem that has not yet been effectively solved in granularity construction research.

[0007] In recent years, some studies have attempted to combine feature selection with data organization structure discovery, using feature selection results to guide clustering or to evaluate feature quality using cluster structures. However, most existing methods treat feature selection and granularity construction as two relatively independent stages, lacking a mechanism to directly feed the rationality of the granular structure back to the feature selection process. This leads to two problems: first, the quality of granularity construction is difficult to guarantee effectively; second, the feature selection results lack reflection of the inherent multi-granular structure of the data. Furthermore, existing granularity-based feature selection methods typically employ simple granular representations, making it difficult to characterize the internal structure and inter-granular relationships of non-convex information particles, thus limiting their application effectiveness in complex data scenarios.

[0008] In summary, the existing technology mainly has the following problems and shortcomings: (1) Information particles constructed based on central distance methods such as K-means and FCM are limited by the convex clustering assumption, making it difficult to effectively handle non-convex data structures such as rings, arcs, and stripes, resulting in information particles failing to truly reflect the internal organizational patterns of the data; (2) Although the density granulation method based on DBSCAN can identify arbitrary shape structures, it is extremely sensitive to the single neighborhood radius parameter. It is prone to erroneous merging or over-segmentation in data with uneven density distribution, and lacks the ability to adapt to local structural differences. (3) Existing granulation methods lack a unified and comprehensive evaluation mechanism for coverage, specificity and homogeneity, and cannot guarantee that the constructed information granules simultaneously meet the principle of reasonable granulation. This can easily lead to the mixing of heterogeneous objects due to excessively coarse granulation, or the splitting of homogeneous objects due to excessively fragmented granulation. (4) Existing methods separate the granulation results from the feature selection process and fail to use the rationality of the granulation structure to drive the feature importance assessment, resulting in the selected feature subset lacking the ability to express the inherent multi-granular structure of the data. (5) Existing granulation methods are not robust enough when noise points, boundary samples and local heterogeneous regions exist. They are prone to problems such as noise misjudgment, mixing of heterogeneous objects or excessive splitting of homogeneous objects, which affect the stability and interpretability of information granule structure. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a method and system for selecting features based on the principle of reasonable granularity. By combining two-layer density granulation with a three-dimensional comprehensive evaluation of coverage, specificity, and homogeneity, this invention solves the problems of existing methods, such as difficulty in handling non-convex data, reliance on a single neighborhood parameter, lack of evaluation of reasonable granularity, and separation between granulation and feature selection. This improves the feature selection effect and classification performance of high-dimensional complex data.

[0010] To achieve the above objectives, the present invention provides the following technical solution: This invention first proposes a method for selecting packing density granulation features based on the principle of reasonable granularity, comprising the following steps: S1: Obtain the dataset X to be processed and preprocess the dataset X; S2: Set the maximum density limit parameter for the first-layer density clustering. and particle size tolerance parameter ; S3: Based on the data size of the dataset X and the granularity tolerance parameter Determine the minimum number of neighborhood samples, MinPts, for density clustering; S4: Based on the maximum density limit parameter Given the minimum number of neighborhood samples MinPts, perform a first-level density clustering on the dataset X to obtain one or more coarse-grained sets C1; S5: For each coarse-grained set C1 Construct a candidate neighborhood parameter set E; S6: For each of the aforementioned coarse-grained... Iterate through each neighborhood parameter in the candidate neighborhood parameter set E. In each of the aforementioned coarse-grained Internally, a second layer of density clustering is performed to obtain parameters corresponding to each neighborhood. Candidate fine-grained partition set ; S7: Calculate the candidate fine-grained partition set Each candidate granularity coverage Specificity and homogeneity ; S8: Based on the coverage Specificity and homogeneity Construct comprehensive evaluation indicators Based on the aforementioned comprehensive evaluation indicators Divide the candidate fine-grained set For each of the aforementioned coarse-grained levels Select the optimal fine-grained partition set ; S9: Merge all coarse-grained [variables]. The corresponding optimal fine-grained partition set To obtain the final set of reasonable granularity .

[0011] Furthermore, in step S3, the method for determining the minimum neighborhood sample number MinPts is as follows:

[0012] in: This refers to the particle size tolerance parameter. The number of objects in dataset X.

[0013] Furthermore, in step S7, candidate granularity is calculated. coverage The method is as follows:

[0014]

[0015] in: Candidate granularity; The first in the candidate granularity One object; Representation Object For the Candidate granularity Membership degree; Representation Object To the The distance between the centers of each particle size; Representation Object To the The distance between the centers of each particle size; For fuzzification coefficients, ; Calculate the candidate granularity Specificity The method is as follows:

[0016] in: Indicates candidate granularity The number of objects in the middle; This represents the number of objects in the dataset X; Indicates candidate granularity The normalized value of the size; Calculate candidate granularity homogeneity The method is as follows:

[0017] in: Candidate granularity Entropy; This represents the maximum entropy value.

[0018] Furthermore, in step S8, a comprehensive evaluation index is constructed. The method is as follows:

[0019] in: , and Candidate granularity The coverage, specificity, and homogeneity of the particles; α is the particle size tolerance parameter.

[0020] Furthermore, in step S8, for each coarse-grained... Select the optimal fine-grained partition set The method is as follows: Calculate the candidate fine-grained partition set All fine-grained Comprehensive evaluation indicators The mean of the values ​​is used as the score for the candidate split. ; Traverse all neighborhood parameters Select the score The highest candidate fine-grained partition set is used as the coarse-grained partition set. Optimal fine-grained partition set .

[0021] Furthermore, it also includes: S10: Based on the final reasonable granularity set Calculate the aggregation degree of information granules under attribute subset B. and information particle dispersion And construct a rationality index for a subset of attributes. ; S11: Rationality index based on the aforementioned attribute subset Calculate each candidate attribute Importance It iteratively selects the most important features and adds them to the selected feature set AF until the preset number of features is reached. If the unselected feature set is empty, the final feature subset AF will be output.

[0022] Furthermore, in step S10: Calculate the aggregation degree of information particles The method is as follows:

[0023] in: For the first A set of optimal fine-grained partitions Degree of aggregation; Particle size count; Calculate the information granule discreteness The method is as follows:

[0024] in: The average center of the system; For the first A set of optimal fine-grained partitions Approximate center under attribute subset B; The average center of the system and approximate center The distance between them; Constructing a rationality index for a subset of attributes The method is as follows: .

[0025] Furthermore, in step S11, each candidate attribute is calculated. Importance The method is as follows:

[0026] in: A subset of attributes; To add candidate attributes The rationality index of the subsequent attribute subset; Subset of attributes Reasonableness indicators.

[0027] This invention also proposes a packing density granulation feature selection system based on the principle of reasonable granularity, used to implement the packing density granulation feature selection method based on the principle of reasonable granularity as described above, including: The data acquisition and preprocessing module is used to acquire the dataset X to be processed and perform preprocessing. The parameter setting module is used to set the maximum density limit parameter for the first layer of density clustering. and particle size tolerance parameter And based on the data size of the dataset X and the granularity tolerance parameter Determine the minimum number of neighborhood samples, MinPts; A two-layer packing density granulation module is used to granulate the density based on the maximum density limit parameter. The first layer of density clustering is performed on the dataset X using the minimum neighborhood sample number MinPts to obtain a coarse-grained set C1, and for each coarse-grained sample in the coarse-grained set C1... The second-level density clustering is performed by traversing the candidate neighborhood parameter set E to obtain a candidate fine-grained partition set. ; The reasonable granularity comprehensive evaluation module is used to calculate the candidate fine-grained partition set. Each candidate granularity coverage Specificity and homogeneity And based on the fusion coverage Specificity and homogeneity Comprehensive evaluation indicators Select the optimal fine-grained partition set The final set of reasonable granularities is output after merging. .

[0028] Furthermore, it also includes a density particle feature selection module, which is used to select particles based on the final reasonable particle size set. The degree of aggregation of information particles under the attribute subset B and information particle dispersion To construct rationality index of attribute subset And based on the rationality index of the attribute subset Iteratively select features and output the final feature subset AF.

[0029] The beneficial effects of this invention are as follows: This invention presents a method for selecting packing density granulation features based on the principle of reasonable granulation. Through the synergistic effect of bilayer density granulation and three-dimensional granulation evaluation, it achieves the following technical effects: (1) Breaking through the convexity limitation: Information particles are constructed by using density reachability and density connection relationship, which gets rid of the dependence of traditional K-means, FCM and other methods on the assumption of spherical or convex clustering, and can effectively maintain the original structural form of non-convex data such as ring, arc, and strip; (2) Reduce parameter sensitivity: The first layer coarsening ensures the global density connectivity structure, and the second layer traverses the candidate neighborhood parameters within each coarse-grained layer and adaptively selects the optimal partition by combining the comprehensive evaluation index, which significantly alleviates the problem of traditional DBSCAN being sensitive to a single neighborhood radius. (3) The granularity is reasonable and guaranteed: the three-dimensional indicators of coverage, specificity and homogeneity jointly constrain the formation of granularity, so that the final information granules can not only carry a sufficient number of objects, but also maintain clear inter-granular boundaries and internal consistency, avoiding granularity that is too coarse or too fragmented. (4) Enhanced noise robustness: Density clustering naturally distinguishes core points, boundary points and noise points. Combined with the granularity evaluation index for screening candidate partitions, it effectively suppresses the interference of isolated points and local noise on the final granular structure.

[0030] In addition, the present invention has the advantage of improving the quality of feature selection, namely: based on the calculation of attribute importance based on a reasonable granular structure, the selected feature subset can better reflect the inherent discriminative information of the data, which is conducive to improving the generalization performance and computational efficiency of subsequent classification models. Attached Figure Description

[0031] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a diagram illustrating the overall architecture of the packing density granulation feature selection method based on the principle of reasonable granularity in this invention. Figure 2 This is a flowchart of the packing density granulation feature selection method based on the principle of reasonable particle size of the present invention; Figure 3 For data comparison: (a) Original data; (b) Information granules constructed by DBSCAN; (c) SDG granulation results; Figure 4Illustrations of granulation states under different granularity constraints; (a) using only DBSCAN; (b) small granularity, with parameters set to α = 0.00389 and (c) Large granularity, parameters set to... and ; Figure 5 A schematic diagram illustrating the principle of comprehensive evaluation for reasonable granularity; Figure 6 This is a schematic diagram of the information particle center and auxiliary centers; Figure 7 Flowchart for Density-Gross Selection of Particle Features (DGFS); Figure 8 Experimental results using the SVM classifier; Figure 9 The experimental results are for the Naive Bayes classifier. Figure 10 The experimental results are for the KNN classifier. Figure 11 These are the experimental results using the decision tree classifier. Figure 12 The changes in particle indexes under different parameters are shown in the following figures: (a) 3D bar chart of H value changes; (b) 3D bar chart of T value changes; (c) 3D bar chart of Spec value changes; (d) 3D bar chart of Cov value changes. Figure 13 The average accuracy and variance of each method across 48 experiments; Figure 14 The results are as follows: (a) Comparison of accuracy of raw data method; (b) Comparison of accuracy of SEF method; (c) Comparison of accuracy of WAFS method; (d) Comparison of accuracy of PCA method; (e) Comparison of accuracy of PFS method; (f) Comparison of accuracy of infFS method; (g) Comparison of accuracy of PPFS method; (h) Comparison of accuracy of DGFS method. Figure 15 This is a schematic diagram comparing the prior art with the present invention. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0033] like Figure 1As shown, this embodiment aims to propose a method and system for selecting features based on the principle of reasonable granularity. Taking the dataset to be processed or the decision information system as input, it first uses a first-layer density clustering to obtain a coarse-grained set that maintains the global density connectivity structure. Then, within each coarse-grained set, a second-layer density granulation is performed, traversing the candidate neighborhood radius to form multiple candidate fine-grained partitions. Subsequently, a granularity reasonableness evaluation index is constructed based on coverage, specificity, and homogeneity, and the fine-grained set with the optimal evaluation value is selected as the final granulation result. Finally, the attribute importance is calculated in the attribute space using the granulation result, gradually filtering out the feature subset most relevant to the decision task. This embodiment is based on a collaborative technical solution combining "double-layer density granulation," "reasonable granularity comprehensive evaluation," and "density granular feature selection." The first-layer density granulation ensures the integrity of the overall structure, the second-layer density granulation enhances the distinguishability of local heterogeneous regions, the comprehensive evaluation index constrains the consistency between granularity size and category, and the feature selection step transforms the granular structure into an attribute importance metric, thereby achieving effective dimensionality reduction for high-dimensional data.

[0034] Specifically, such as Figure 2 As shown in the figure, the method for selecting packing density granulation features based on the principle of reasonable granulation in this embodiment includes the following steps.

[0035] S1: Data Acquisition and Preprocessing. Acquire the dataset X to be processed and preprocess the dataset X.

[0036] First, obtain the dataset X or decision information system to be processed. ,in: For a set of objects; For conditional attribute set; This is the set of decision attributes. The set of objects to be processed can be represented as:

[0037] in: Indicates the first One object; This indicates the number of objects. When the data contains decision attributes, these attributes are used to calculate class consistency within the subsequent granularity of computation; when the data does not contain decision labels, pre-clustering, pseudo-label generation, or other approximation methods can be used to estimate class consistency.

[0038] In this embodiment, the method for preprocessing dataset X includes: normalizing each conditional attribute so that attributes with different dimensions are mapped to a unified numerical range. In this embodiment, the Min-Max normalization method is preferably used to map all attributes to a uniform numerical range. Interval. The purpose of normalization is to eliminate the influence of different dimensions on subsequent distance metrics and density granulation results. For decision information systems, decision attributes are retained for subsequent homogeneity evaluation.

[0039] S2: Parameter settings. Set the maximum density limit parameter for the first-layer density clustering. and particle size tolerance parameter .

[0040] in, Used to control the maximum allowed neighborhood distance in the first layer of coarse-grained clustering. The larger the value, the wider the range of objects that the first coarse-grained level can contain, and the larger the size of the coarse-grained set. The smaller the value, the more conservative the first-level clustering result, and the smaller the size of the coarse-grained set. The specific value can be set according to the size and dimensions of the dataset and the actual application requirements.

[0041] Particle size tolerance parameter Used to adjust the weights of specificity and particle size refinement during particle size evaluation. The larger the value, the stronger the constraint of the comprehensive evaluation index on specificity, and the more refined the resulting granularity. In this embodiment, The preferred value range is 0.5 to 1.5, within which a better balance between coverage and specificity can be achieved. The specific value can be determined through experiments based on the data characteristics and classification task requirements.

[0042] S3: Determine the minimum number of neighborhood samples. This is based on the data size of the dataset X and the granularity tolerance parameter. Determine the minimum number of neighborhood samples, MinPts, for density clustering.

[0043] In this embodiment, the method for determining the minimum neighborhood sample number MinPts is as follows:

[0044] in: This refers to the particle size tolerance parameter. The number of objects in dataset X.

[0045] This setting allows the density clustering parameter to be adaptively adjusted according to the sample size, avoiding unstable partitioning caused by a fixed number of neighborhood samples on data of different sizes. For example, when the dataset size is large, MinPts is increased accordingly to ensure the statistical significance of density clustering; when the dataset size is small, MinPts is decreased accordingly to avoid clustering failure due to excessive sparsity.

[0046] S4: Perform the first layer of density granulation based on the maximum density limit parameter. Using the minimum number of neighborhood samples MinPts, perform a first-level density clustering on the dataset X to obtain one or more coarse-grained sets C1.

[0047] In this embodiment, the first layer of density clustering is preferably implemented using the DBSCAN algorithm, as follows:

[0048] in: Represents the first coarse-grained set C1. One coarse grain size; The number of coarse-grained elements in the coarse-grained set C1; This refers to the DBSCAN algorithm.

[0049] Specifically, the first layer of density granulation is used to identify the main density connectivity structure of the data. Since DBSCAN forms clusters based on density reachability and density connectivity, it can maintain the overall outline of non-convex data such as rings and arcs, reducing the risk of incorrect partitioning of non-convex structures by centroid distance-based methods such as K-means and FCM.

[0050] For data with non-convex distribution or complex density connectivity structure, the first layer of density granulation can extract the global density connectivity of the data, forming a coarse-grained set, which lays the foundation for subsequent local refinement.

[0051] S5: Construct a candidate neighborhood parameter set. For each coarse-grained parameter in the coarse-grained set C1... Construct a candidate neighborhood parameter set E.

[0052] For each coarse-grained value obtained in the first layer Construct the candidate neighborhood parameter set E:

[0053] in: It can be determined based on data precision, attribute dimensions, or empirical lower limits; The maximum density limit parameter set in step S2; the preset step size can be set according to actual needs, for example, it can be set to 0.05 or 0.1.

[0054] In this embodiment, the candidate neighborhood parameter set E can be generated using a fixed step size, an adaptive step size based on dimensions, or a method based on neighborhood distance quantiles. Preferably, for low-dimensional data with fewer than 50 features, The step size can be set to 0.05. The value ranges from 0.01 to 0.4; for medium-dimensional data with 50 to 300 features, The step size can be set to 0.05. The value ranges from 0.5 to 0.8; for high-dimensional data with more than 300 features, The step size can be set to 0.1. The value range is from 0.5 to 1.5.

[0055] By traversing multiple candidates within each coarse-grained level This embodiment can search for more suitable density partitioning parameters for different local structures, thereby alleviating the dependence of traditional DBSCAN on a single neighborhood radius.

[0056] S6: Perform the second layer of density granulation. For each of the aforementioned coarse granularities... Iterate through each neighborhood parameter in the candidate neighborhood parameter set E. In each of the aforementioned coarse-grained Internally, a second layer of density clustering is performed to obtain parameters corresponding to each neighborhood. Candidate fine-grained partition set .

[0057]

[0058] in: Represents the candidate fine-grained partition set The first in One candidate fine-grained; Partition the candidate set into fine granularities The number of candidate fine-grained numbers.

[0059] The second layer of density granulation is used to further subdivide potentially heterogeneous regions within the first layer of coarse granulation. This step does not simply pursue the finest possible granularity; rather, it feeds each candidate subdivision result into a subsequent reasonable granularity evaluation process, using coverage, specificity, and homogeneity to jointly determine the reasonableness of the subdivision. Figure 3 As shown.

[0060] like Figure 4 As shown, the second layer of density granulation continues to perform local density refinement within each coarse-grained level to identify potential heterogeneous regions within the coarse-grained level. This structure can improve the ability to characterize local complex structures while maintaining the overall data shape.

[0061] S7: Calculate coverage, specificity, and homogeneity. Calculate the candidate fine-grained partition set. Each candidate granularity coverage Specificity and homogeneity .

[0062] (1) Calculate coverage .

[0063] First, calculate the object. For the Candidate granularity Membership degree:

[0064] in: Representation Object For the Candidate granularity Membership degree; Representation Object To the The distance between the centers of each particle size; Representation Object To the The distance between the centers of each particle size; For fuzzification coefficients, .

[0065] Calculate candidate granularity based on membership degree. coverage The method is as follows:

[0066] in: Candidate granularity; The first in the candidate granularity One object.

[0067] (2) Calculate specificity .

[0068] Calculate the candidate granularity Specificity The method is as follows:

[0069] in: Indicates candidate granularity The number of objects in the middle; This represents the number of objects in the dataset X; Indicates candidate granularity The normalized value of the size. The smaller the granularity, the more specific the information it contains and the stronger its specificity; the larger the granularity, the wider its coverage, but the ability to distinguish will be reduced accordingly.

[0070] (3) Calculate homogeneity .

[0071] set up Indicates the first Among the granularities belonging to the first The number of class objects; Indicates candidate granularity The total number of objects in the middle; m represents the total number of categories; then the candidate granularity. The entropy is defined as:

[0072]

[0073] Calculate candidate granularity based on entropy homogeneity The method is as follows:

[0074] in: Candidate granularity Entropy; This represents the maximum entropy value.

[0075] When objects within a granularity mainly belong to the same category, the entropy value is small and the homogeneity is high; when multiple categories are mixed within a granularity, the entropy value is large and the homogeneity is low.

[0076]

[0077] S8: Construct a comprehensive evaluation index and select the optimal fine-grained division. Based on the coverage... Specificity and homogeneity Construct comprehensive evaluation indicators Based on the aforementioned comprehensive evaluation indicators Divide the candidate fine-grained set For each of the aforementioned coarse-grained levels Select the optimal fine-grained partition set .

[0078] Specifically, based on coverage Specificity and homogeneity Construct comprehensive evaluation indicators The method is as follows:

[0079] in: , and Candidate granularity The coverage, specificity, and homogeneity of the particles; α is the particle size tolerance parameter.

[0080] Comprehensive evaluation indicators Simultaneously, three aspects are constrained: coverage ensures that the information granules have sufficient data carrying capacity; specificity ensures that the information granules have strong distinguishing ability; and homogeneity ensures that the objects within the information granules have high consistency. This avoids both pursuing coverage alone, which leads to overly coarse granularity, and pursuing specificity alone, which leads to overly fragmented granularity.

[0081] In this embodiment, based on comprehensive evaluation indicators Partitioning the candidate set into fine granularities The middle is for each coarse-grained Select the optimal fine-grained partition set The specific method is as follows: Calculate the candidate fine-grained partition set All fine-grained Comprehensive evaluation indicators The mean of the values ​​is used as the score for the candidate split. :

[0082] Traverse all neighborhood parameters Select the score The highest candidate fine-grained partition set is used as the coarse-grained partition set. Optimal fine-grained partition set .

[0083] like Figure 5 As shown, candidate granularity Calculate coverage separately Specificity and homogeneity and through A comprehensive rationality score is obtained, and this score is used as the basis for granularity selection.

[0084] S9: Merge the optimal fine-grained partition set. Merge all the coarse-grained partitions mentioned above. The corresponding optimal fine-grained partition set To obtain the final set of reasonable granularity :

[0085] in: For the final reasonable granularity set The first in Candidate granularity; This represents the final total number of particles.

[0086] Final reasonable granularity set It simultaneously meets the requirements of coverage, specificity, and homogeneity, and can achieve a balance between fully expressing the data structure and maintaining local discriminative ability.

[0087] S10: Calculate the aggregation and dispersion of information granularity. Based on the final reasonable granularity set... Calculate the aggregation degree of information granules under attribute subset B. and information particle dispersion And construct a rationality index for a subset of attributes. .

[0088] (1) Calculate the aggregation degree of information particles .

[0089] For the attribute subset B, the first value obtained from SDG (Stacked Density Granulation) is... A set of optimal fine-grained partitions The degree of aggregation can be calculated based on the average membership degree of the object to that particle size:

[0090] Aggregation degree is used to represent the degree of close dependency between objects within the same information granularity. The higher the value, the more compact the internal structure of the granularity.

[0091] For decision information systems Let attribute subset The overall information granularity aggregation degree of the system Defined as:

[0092] in: For the first A set of optimal fine-grained partitions Degree of aggregation; Particle size count.

[0093] (2) Calculate the information particle dispersion .

[0094] like Figure 6 As shown, for non-convex information particles, FCM can be used to generate several local sub-clusters within the particle size, and the centroid of each sub-cluster can be used to approximate the center of the information particle. Let... For the first The approximate center of each granularity under attribute subset B If the system's average center is used, then the system's information granularity dispersion is... It can be represented as:

[0095] in: The average center of the system; For the first A set of optimal fine-grained partitions Approximate center under attribute subset B; The average center of the system and approximate center The distance between them.

[0096] Discreteness is used to measure the degree of separation between different information particles. Cohesion and dispersion are usually mutually restrictive, so a unified index needs to be constructed to balance the two.

[0097] As attached Figure 4 As shown, for information particles of arbitrary shape, the global center can be approximated by multiple local auxiliary centers, so that non-convex granularity can still participate in the calculation of discreteness and attribute importance.

[0098] (3) Constructing a rationality index for a subset of attributes .

[0099] For attribute subset B, construct a reasonable index for system granularity. The method is as follows:

[0100] in: A larger size indicates a denser internal grain. The larger the value, the more separated the particles. The two are combined to measure the rationality of the information granular structure under attribute subset B.

[0101] S11: Calculate attribute importance and iteratively select features based on the attribute subset rationality index. Calculate each candidate attribute Importance It iteratively selects the most important features and adds them to the selected feature set AF until the preset number of features is reached. If the unselected feature set is empty, output the final feature subset AF, such as... Figure 7 As shown.

[0102] For candidate attribute a, based on the currently selected attribute subset B, the importance of candidate attribute a is defined as follows:

[0103] in: A subset of attributes; To add candidate attributes The rationality index of the subsequent attribute subset; Subset of attributes Reasonableness indicators.

[0104] Calculate the Sig value of each unselected attribute in turn, and add the attribute with the highest importance to the set of selected attributes:

[0105]

[0106] Repeat the above steps until the preset number of features is reached. Alternatively, the set of unselected attributes may be empty. The final output attribute set AF is the feature subset selected in this embodiment.

[0107]

[0108] As attached Figure 5 As shown, DGFS uses the selected feature set AF as a basis, evaluates the improvement of the system granularity after adding candidate features one by one, selects the feature with the largest Sig value, and continues until the preset number of features is reached.

[0109] Since attribute importance is directly driven by the information granular structure formed by SDG, the feature selection result takes into account intra-class compactness, inter-class separability, and complex non-convex data structure. It can effectively remove irrelevant and redundant features and retain key attributes that better reflect the differences in data structure and decision-making.

[0110] In this embodiment, the first and second layer density granulation can be implemented using equivalent density clustering variants of DBSCAN; the distance metric can be selected from Euclidean distance, Manhattan distance, Chebyshev distance, or Minkowski distance depending on the data type; the candidate neighborhood parameter set E can be generated by a fixed step size, an adaptive step size based on dimensions, or a method based on neighborhood distance quantiles; granularity homogeneity can be calculated by real decision labels, manually labeled categories, pre-clustered pseudo-labels, or other category consistency estimation methods.

[0111] This invention also proposes a packing density granularity feature selection system based on the principle of reasonable granularity, used to implement the packing density granularity feature selection method based on the principle of reasonable granularity described in this embodiment. Specifically, the packing density granularity feature selection system based on the principle of reasonable granularity in this embodiment includes a data acquisition and preprocessing module, a parameter setting module, a two-layer packing density granularity module, a reasonable granularity comprehensive evaluation module, and a density particle feature selection module. In this embodiment, the data acquisition and preprocessing module is used to acquire the dataset X to be processed and perform preprocessing; the parameter setting module is used to set the maximum density limit parameter for the first layer of density clustering. and particle size tolerance parameter And based on the data size of the dataset X and the granularity tolerance parameter Determine the minimum number of neighborhood samples, MinPts; the two-layer packing density granulation module is used to determine the maximum density limit parameter. The first layer of density clustering is performed on the dataset X using the minimum neighborhood sample number MinPts to obtain a coarse-grained set C1, and for each coarse-grained sample in the coarse-grained set C1... The second-level density clustering is performed by traversing the candidate neighborhood parameter set E to obtain a candidate fine-grained partition set. The reasonable granularity comprehensive evaluation module calculates the candidate fine-grained partition set. Each candidate granularity coverage Specificity and homogeneity And based on the fusion coverage Specificity and homogeneity Comprehensive evaluation indicators Select the optimal fine-grained partition set The final set of reasonable granularities is output after merging. The density particle feature selection module is used to select particles based on the final reasonable particle size set. The degree of aggregation of information particles under the attribute subset B and information particle dispersion To construct rationality index of attribute subset And based on the rationality index of the attribute subset Iteratively select features and output the final feature subset AF.

[0112] The following section, through specific experiments, further explains the technical effects of the packing density granulation feature selection method and system based on the principle of reasonable particle size in this embodiment.

[0113] (1) Experimental objective.

[0114] To demonstrate that the proposed Packing Density Granulation (SDG) and Density Granular Feature Selection (DGFS) methods in this embodiment can improve the representation ability of complex data structures, reduce the impact of redundant features, enhance classification modeling performance, and improve noise robustness, comparative experiments on public datasets, statistical significance tests, parameter exploration experiments, and robustness experiments were set up according to the experimental section of the paper.

[0115] (2) Experimental design and data sources. To verify the effectiveness of the proposed method in this embodiment, comparative experiments were conducted on 12 publicly available datasets. The datasets covered UCI and Kaggle public data warehouses, encompassing various scenarios including low-dimensional, high-dimensional, small-sample, large-sample, binary classification, and multi-class classification, as shown in Table 1. Before the experiments, all data underwent Min-Max normalization, mapping attributes to the [0,1] interval to eliminate the influence of different units on distance metrics and density granularization results.

[0116] Table 1. Description of Experimental Datasets

[0117] The comparison methods included original features, WAFS, SFE, PFS, infFS, PPFS, and PCA, among other feature selection or dimensionality reduction methods. Feature subsets selected by all methods were input into four classifiers: Naive Bayes, K-Nearest Neighbors, Decision Tree, and Support Vector Machine, and evaluated using 10-fold cross-validation. Evaluation metrics included accuracy, precision, recall, and F1 score.

[0118] (3) Experimental data on classification performance. Classification performance experiments were conducted separately using four classifiers. For example... Figure 8-11 As shown, the experimental results demonstrate that DGFS (Density Granular Feature Selection) outperforms most datasets and classifier combinations, indicating that the information granules constructed by SDG in this embodiment can effectively identify key attributes and reduce the interference of irrelevant or redundant features on the classification model.

[0119] Experimental results show that DGFS performs better on most datasets and classifier combinations. As shown in Table 2, in the decision tree + CHAN scenario, DGFS improves accuracy by 19.34% compared to the original dataset and by 20.45% compared to WAFS; in the KNN + OBE scenario, DGFS improves accuracy by 10.19% compared to the original data and by 25.68% compared to PCA; in the SVM + CRED scenario, DGFS outperforms WAFS by 30.07% and infFS by 24.09%.

[0120] Table 2 Key performance improvements demonstrated in the experiment

[0121] (4) Statistical significance test data. For statistical significance testing, a one-tailed t-test was performed based on the accuracy results of 48 experiments. The hypothesis was: null hypothesis H0, that DGFS is not superior to other methods; alternative hypothesis H1, that DGFS is superior to other methods. The significance level was set at 0.05.

[0122] As shown in Table 3, the p-values ​​for each comparison method are all below 0.05 (original data: 0.0104, SEF: 0.000002, WAFS: 0.000004, PCA: 0.000119, PFS: 0.008464), indicating that the null hypothesis can be rejected in the statistically analyzed experimental comparisons, and the alternative hypothesis that DGFS is superior to the corresponding comparison method can be accepted. This statistically proves that the feature selection method described in this embodiment has a stable performance advantage.

[0123] Table 3. Results of one-tailed t-test

[0124] (5) Parameter exploration experimental data.

[0125] The performance of DGFS is affected by the SDG granularity parameters. As shown in Table 4, this embodiment examines the granularity index as a function of the parameters on the GRID dataset, where: The value range is from 0.5 to 1.5. The value range is from 0.01 to 0.5. For example... Figure 12 As shown, the experiment demonstrates that, The main influence is on the weight of specificity in the overall evaluation value; an appropriate It can better balance coverage and specificity; Directly affects the particle size formation process. If the particle size is too large, the particle size will be too coarse. Smaller granularity allows for more refined division.

[0126] Table 4. Parameter Setting Suggestions and Their Effects

[0127] (6) Experimental data on overall stability and robustness.

[0128] like Figure 13 As shown, this embodiment further summarizes the average accuracy and variance of 48 experiments and evaluates robustness under perturbation conditions. Perturbation settings include: adding 5% Gaussian noise (standard deviation of 5%) and generating 10% missing values ​​through a completely random missing value mechanism. This experiment demonstrates that this embodiment can maintain relatively stable feature selection performance under noisy, missing, or data perturbation scenarios, such as... Figure 14 As shown in Table 5, specifically, under the perturbation conditions of adding 5% Gaussian noise and 10% missing values, the average accuracy of DGFS decreased by only 2.81%, while the average accuracy of PFS decreased by 16.15% after perturbation, proving that this embodiment still has good robustness in incomplete or noisy data environments.

[0129] Table 5. Robustness Experimental Conclusions and Data

[0130] (7) Experimental conclusions.

[0131] 1) Through cross-validation experiments on 12 public datasets and 4 classifiers, DGFS achieves better classification results in most scenarios, proving that the present invention can improve the quality of feature selection by constructing at a reasonable granularity.

[0132] 2) Through one-tailed t-test, the p-values ​​in the statistical comparisons were all below 0.05, proving that the present invention has a statistically significant advantage over the corresponding comparison methods.

[0133] 3) Through parameter exploration experiments, prove the SDG's... and The parameters can control the granularity, coverage, and discrimination capabilities, enabling the present invention to adapt to datasets of different dimensions.

[0134] 4) Through noise and missing value perturbation experiments, the average accuracy of DGFS decreased by only 2.81%, proving that this embodiment still has good robustness in incomplete or noisy data environments.

[0135] In summary, the experimental data demonstrates that the method and system of this embodiment can achieve the invention objectives of parsing complex data structures, filtering key features, improving classification performance, and enhancing disturbance resistance stability.

[0136] The method and system of this embodiment have the following technical effects.

[0137] (1) A two-layer stacked density granulation structure is proposed. This invention differs from directly using a single-layer DBSCAN to output clustering results. Instead, it constructs a stacked density granulation structure of "first-layer coarse-graining + second-layer fine-graining". The first layer is used to extract the global density connectivity of the data, forming a coarse-grained set; the second layer continues to perform local density refinement within each coarse-grained set to identify potential heterogeneous regions within the coarse-grained set. This structure can improve the ability to characterize local complex structures while maintaining the overall data shape.

[0138] (2) It can adapt to non-convex and complex nested data structures. Traditional methods such as K-means and FCM usually rely on the central distance or convex clustering assumptions, which are prone to incorrect partitioning when dealing with non-convex data such as ring-shaped, arc-shaped, strip-shaped, and nested structures. Figure 15 As shown, this invention utilizes relationships such as density reachability and density connectivity to construct information granules, freeing them from the limitations of convex structures and enabling them to more accurately represent the true structure in complex data distributions.

[0139] (3) Alleviating the problem of traditional DBSCAN's sensitivity to a single neighborhood parameter. Traditional DBSCAN usually relies on a fixed neighborhood radius. When data density is uneven, over-merging, over-segmentation, or misjudgment due to noise can easily occur. This invention sets a candidate neighborhood parameter set during the second-layer granulation process, traversing multiple candidate parameters within each coarse-grained level. Furthermore, the optimal fine-grained division is selected through granularity rationality evaluation, thereby reducing the impact of a single parameter setting on the final granulation result.

[0140] (4) Introducing the principle of reasonable granularity as the basis for granularity selection. This invention does not directly determine the final information granule based solely on the density clustering results, but rather introduces the principle of reasonable granularity into the candidate granularity screening process, evaluating each candidate granularity from three aspects: coverage, specificity, and homogeneity. This design provides clear theoretical constraints for the granularity generation process, explaining why information granules are retained and why they have high rationality.

[0141] (5) Construct a comprehensive evaluation index that integrates coverage, specificity, and entropy. The present invention constructs the following comprehensive evaluation index with granularity, which can simultaneously constrain the data carrying capacity, distinguishability, and internal consistency of information granules, avoiding category mixing caused by excessively coarse granularity, and also avoiding structural fragmentation caused by excessively fine granularity.

[0142] (6) Achieving a synergistic balance between completeness, specificity, and homogeneity. This invention ensures that the information granules contain a sufficient number of closely related objects through coverage, that there is a clear distinction between different information granules through specificity, and that the degree of category mixing within the granularity is constrained through entropy and homogeneity. The three types of indicators work together to make the final output information granules more in line with the principle of reasonable granularity, and to achieve a balance between completely expressing the data structure and maintaining local distinguishability.

[0143] (7) It has good noise adaptability. Since the present invention is based on density clustering to construct information particles, it can identify core points, boundary points and noise points; at the same time, it screens reasonable fine-grained structures through the second-layer granulation and comprehensive evaluation mechanism, thus reducing the interference of isolated points, abnormal points or local noise on the final granular structure and improving the stability of information particle construction results.

[0144] (8) Integrating information granule construction with feature selection. This invention not only outputs a reasonable set of granularities, but also further applies the granulation results of packing density to the attribute space, evaluating the importance of attributes through the information granule structure. Specifically, this invention can construct an attribute subset evaluation index based on the degree of aggregation within granularities and the degree of dispersion between granularities, and select features that contribute more to the decision-making task accordingly, thereby achieving the integration of data granulation and feature selection.

[0145] (9) A method for calculating aggregation and dispersion applicable to non-convex granularity is proposed. Addressing the problem that SDG may generate information particles of arbitrary shapes and that traditional centroids are insufficient to accurately describe non-convex granularity, this invention approximates the granularity center using FCM auxiliary centers or local sub-cluster centers, and calculates intra-cluster aggregation and inter-cluster dispersion accordingly. This method can more accurately characterize the spatial relationships between information particles of complex shapes, providing a reliable basis for subsequent attribute importance calculations.

[0146] (10) It has strong interpretability. Each information granule of the present invention can be interpreted by indicators such as coverage, specificity, homogeneity, aggregation degree and dispersion; each selected feature can also be explained by its degree of improvement on the rationality of the system granularity. Therefore, compared with methods that only output clustering labels or dimensionality reduction results, the present invention can provide clearer structural interpretation and attribute contribution interpretation.

[0147] (11) Applicable to data structure parsing of complex information systems. This invention can be used for granular partitioning of ordinary numerical data, as well as for object partitioning, attribute reduction, and feature selection tasks in decision information systems. For data with high-dimensional attributes, mixed categories, significant local density differences, or non-convex structures, this invention can provide a more reasonable information granular construction method and can serve application scenarios such as classification modeling, anomaly detection, knowledge discovery, and data dimensionality reduction.

[0148] (12) It is beneficial to improve the efficiency and stability of subsequent classification modeling. Through the DGFS feature selection process, the present invention can remove irrelevant and redundant features, retain key attributes that better reflect the differences in data structure and decision-making, thereby reducing the computational cost of high-dimensional data processing, mitigating the risk of overfitting, and providing a more compact and efficient input feature space for subsequent classifier training.

[0149] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for selecting packing density granulation features based on the principle of reasonable granularity, characterized in that: Includes the following steps: S1: Obtain the dataset X to be processed and preprocess the dataset X; S2: Set the maximum density limit parameter for the first-layer density clustering. and particle size tolerance parameter ; S3: Based on the data size of the dataset X and the granularity tolerance parameter Determine the minimum number of neighborhood samples, MinPts, for density clustering; S4: Based on the maximum density limit parameter Given the minimum number of neighborhood samples MinPts, perform a first-level density clustering on the dataset X to obtain one or more coarse-grained sets C1; S5: For each coarse-grained set C1 Construct a candidate neighborhood parameter set E; S6: For each of the aforementioned coarse-grained... Iterate through each neighborhood parameter in the candidate neighborhood parameter set E. In each of the aforementioned coarse-grained Internally, a second layer of density clustering is performed to obtain parameters corresponding to each neighborhood. Candidate fine-grained partition set ; S7: Calculate the candidate fine-grained partition set Each candidate granularity coverage Specificity and homogeneity ; S8: Based on the coverage Specificity and homogeneity Construct comprehensive evaluation indicators Based on the aforementioned comprehensive evaluation indicators Divide the candidate fine-grained set For each of the aforementioned coarse-grained levels Select the optimal fine-grained partition set ; S9: Merge all coarse-grained [variables]. The corresponding optimal fine-grained partition set To obtain the final set of reasonable granularity .

2. The method for selecting packing density granulation features based on the principle of reasonable granularity according to claim 1, characterized in that: In step S3, the method for determining the minimum neighborhood sample number MinPts is as follows: in: This refers to the particle size tolerance parameter. The number of objects in dataset X.

3. The method for selecting packing density granulation features based on the principle of reasonable granularity according to claim 1, characterized in that: In step S7, the candidate granularity is calculated. coverage The method is as follows: in: Candidate granularity; The first in the candidate granularity One object; Representation Object For the Candidate granularity Membership degree; Representation Object To the The distance between the centers of each particle size; Representation Object To the The distance between the centers of each particle size; For fuzzification coefficients, ; Calculate the candidate granularity Specificity The method is as follows: in: Indicates candidate granularity The number of objects in the middle; This represents the number of objects in the dataset X; Indicates candidate granularity The normalized value of the size; Calculate candidate granularity homogeneity The method is as follows: in: Candidate granularity Entropy; This represents the maximum entropy value.

4. The method for selecting packing density granulation features based on the principle of reasonable granularity according to claim 1, characterized in that: In step S8, a comprehensive evaluation index is constructed. The method is as follows: in: , and Candidate granularity The coverage, specificity, and homogeneity of the particles; α is the particle size tolerance parameter.

5. The method for selecting packing density granulation features based on the principle of reasonable granularity according to claim 1, characterized in that: In step S8, for each coarse-grained... Select the optimal fine-grained partition set The method is as follows: Calculate the candidate fine-grained partition set All fine-grained Comprehensive evaluation indicators The mean of the values ​​is used as the score for the candidate split. ; Traverse all neighborhood parameters Select the score The highest candidate fine-grained partition set is used as the coarse-grained partition set. Optimal fine-grained partition set .

6. The method for selecting packing density granulation features based on the principle of reasonable granularity according to any one of claims 1-5, characterized in that: Also includes: S10: Based on the final reasonable granularity set Calculate the aggregation degree of information granules under attribute subset B. and information particle dispersion And construct a rationality index for a subset of attributes. ; S11: Rationality index based on the aforementioned attribute subset Calculate each candidate attribute Importance It iteratively selects the most important features and adds them to the selected feature set AF until the preset number of features is reached. If the unselected feature set is empty, the final feature subset AF will be output.

7. The method for selecting packing density granulation features based on the principle of reasonable granularity according to claim 6, characterized in that: In step S10: Calculate the aggregation degree of information particles The method is as follows: in: For the first A set of optimal fine-grained partitions Degree of aggregation; Particle size count; Calculate the information granule discreteness The method is as follows: in: The average center of the system; For the first A set of optimal fine-grained partitions Approximate center under attribute subset B; The average center of the system and approximate center The distance between them; Constructing a rationality index for a subset of attributes The method is as follows: 。 8. The method for selecting packing density granulation features based on the principle of reasonable granularity according to claim 6, characterized in that: In step S11, each candidate attribute is calculated. Importance The method is as follows: in: A subset of attributes; To add candidate attributes The rationality index of the subsequent attribute subset; Subset of attributes Reasonableness indicators.

9. A packing density granularity feature selection system based on the principle of reasonable granularity, used to implement the packing density granularity feature selection method based on the principle of reasonable granularity as described in any one of claims 1-8, characterized in that: include: The data acquisition and preprocessing module is used to acquire the dataset X to be processed and perform preprocessing. The parameter setting module is used to set the maximum density limit parameter for the first layer of density clustering. and particle size tolerance parameter And based on the data size of the dataset X and the granularity tolerance parameter Determine the minimum number of neighborhood samples, MinPts; A two-layer packing density granulation module is used to granulate the density based on the maximum density limit parameter. The first layer of density clustering is performed on the dataset X using the minimum neighborhood sample number MinPts to obtain a coarse-grained set C1, and for each coarse-grained sample in the coarse-grained set C1... The second-level density clustering is performed by traversing the candidate neighborhood parameter set E to obtain a candidate fine-grained partition set. ; The reasonable granularity comprehensive evaluation module is used to calculate the candidate fine-grained partition set. Each candidate granularity coverage Specificity and homogeneity And based on the fusion coverage Specificity and homogeneity Comprehensive evaluation indicators Select the optimal fine-grained partition set The final set of reasonable granularities is output after merging. .

10. The packing density granulation feature selection system based on the principle of reasonable granularity according to claim 9, characterized in that: It also includes a density particle feature selection module, which is used to select particles based on the final reasonable particle size set. The degree of aggregation of information particles under the attribute subset B and information particle dispersion To construct rationality index of attribute subset And based on the rationality index of the attribute subset Iteratively select features and output the final feature subset AF.

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