Customer data analysis method and system

Abstract

The invention provides a customer data analysis method and system, and the method specifically comprises the steps: calculating a behavior drift vector for each customer, adaptively determining a neighborhood cardinal number k value from a preset candidate set for each data point, and calculating the core distance of each data point; constructing a minimum spanning tree of the customer data according to the corrected mutual reachable distance, and generating a clustering hierarchical tree; for each potential cluster in the clustering hierarchical tree, the life cycle persistence of the cluster is calculated by using the structure information of the cluster in the clustering hierarchical tree, and the life cycle persistence and the value grade aggregation values of all clients in the cluster are fused to calculate a service stability score; and according to the service stability score and a preset minimum cluster scale threshold value, extracting a customer grouping result from the clustering hierarchical tree, and identifying data points which do not belong to any group as noise points.

Description

Technical Field

[0001] This application belongs to the field of data analysis, and in particular relates to a customer data analysis method and system. Background Technology

[0002] Customer segmentation is crucial for modern enterprises to conduct refined operational management such as precision marketing, personalized recommendations, credit assessment, and churn prediction. By clustering massive amounts of customer data, enterprises can identify customer groups with similar characteristics and behavioral patterns, thereby formulating differentiated service strategies. Commonly used customer segmentation methods include K-Means and DBSCAN. However, the K-Means algorithm requires pre-specifying the number of clusters and is sensitive to initial centers, making it difficult to handle non-convex clusters. While DBSCAN can discover clusters of arbitrary shapes and identify noise, its performance is highly dependent on two global parameters: the neighborhood radius Eps and the minimum number of points MinPts, often resulting in poor performance with complex customer datasets of uneven density. Furthermore, when measuring customer similarity, it often only considers the proximity of data features, ignoring important business dimensions such as customer value levels and inherent connections between customers, thus limiting the business interpretability and practicality of the segmentation results. Improved clustering algorithms, such as the Hierarchical Density Clustering Algorithm (HDBSCAN), avoid setting the Eps parameter by constructing a hierarchical clustering structure and can better adapt to data distributions with uneven density. However, they still have shortcomings in interpretability and clustering accuracy. Summary of the Invention

[0003] In response to the problems mentioned in the background art, in a first aspect, the present invention provides a customer data analysis method, comprising the following steps: Acquire raw customer data collected at at least two preset time points; calculate a behavioral drift vector for each customer based on the direction and magnitude of changes in data characteristics of the same customer between the two time points; The customer distance is obtained using the original customer data and the drift vector. Based on the customer distance and the determined neighborhood cardinality k, the core distance of each data point is calculated. The mutual reachability distance between any two data points is calculated based on the core distance and customer distance. If there is a customer relationship between the two data points, the mutual reachability distance is adjusted. Construct a minimum spanning tree for customer data based on the corrected mutual reachability distance, and generate a clustering hierarchy tree; for each potential cluster in the clustering hierarchy tree, calculate the cluster's lifecycle durability using the cluster's structural information in the clustering hierarchy tree, and combine the lifecycle durability with the aggregated value of the value level of all customers in the cluster to calculate the business stability score. Based on the business stability score and the preset minimum cluster size threshold, customer grouping results are extracted from the clustering hierarchy tree, and data points that do not belong to any group are identified as noise points.

[0004] In a second aspect, the present invention provides a customer data analysis system, comprising the following modules: The data acquisition module is used to acquire raw customer data collected at at least two preset time points; and to calculate a behavioral drift vector for each customer based on the direction and magnitude of the data feature changes of the same customer between the two time points. The distance calculation module is used to obtain the customer distance using the original customer data and the drift vector, and to calculate the core distance of each data point based on the customer distance and the determined neighborhood cardinality k value. The reachability calculation module is used to calculate the mutual reachability distance between any two data points based on the core distance and the customer distance. If there is a customer relationship between the two data points, the mutual reachability distance is corrected. The cluster partitioning module is used to construct a minimum spanning tree of customer data based on the corrected mutual reachability distance, and generate a clustering hierarchy tree; for each potential cluster in the clustering hierarchy tree, the cluster's lifecycle durability is calculated using the cluster's structural information in the clustering hierarchy tree, and the lifecycle durability is fused with the aggregated value of the value level of all customers in the cluster to calculate the business stability score. The result output module is used to extract customer clustering results from the clustering hierarchy tree based on the business stability score and the preset minimum cluster size threshold, and to identify data points that do not belong to any cluster as noise points.

[0005] This invention proposes a novel method for calculating customer distance, integrating not only static customer attributes but also the evolutionary trends of customer behavior over time, the customer's own commercial value level, and inherent social or business connections between customers into the similarity measurement. Furthermore, when selecting the final effective customer group, this invention combines the topological stability of the cluster with the aggregate value of all members within that cluster to form a comprehensive business stability score. This ensures that the final output customer group is not only stable in data distribution but also commercially valuable, avoiding the problem of pseudo-customer groups that may arise from traditional methods but have stable structures but low commercial value. Attached Figure Description

[0006] Figure 1 A flowchart for customer data analysis methods; Figure 2 A schematic diagram for calculating the behavior drift vector; Figure 3 This is a schematic diagram of a minimum spanning tree; Figure 4This is a schematic diagram of a clustering hierarchy tree. Detailed Implementation

[0007] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use, and processing of related data must comply with relevant laws, regulations, and standards, and corresponding operation entry points are provided for users to choose to authorize or refuse.

[0008] like Figure 1 The customer data analysis method shown includes the following steps: Step 1: Obtain raw customer data collected at at least two preset time points; calculate a behavioral drift vector for each customer based on the direction and magnitude of changes in data characteristics of the same customer between the two time points; Two preset time points, such as the beginning and end of the year, are used to extract customer data from the enterprise customer relationship management system (CRM) and transaction database. Numerical features can include age, annual income, and total spending in the past year; categorical features can include occupation and gender; customer value levels can be divided into high-value, medium-value, and low-value; and customer relationships can include family member relationships and referral / referred relationships. These relationships are stored in a graph structure or a list of relationship pairs. Categorical features are converted to numerical form using one-hot encoding, and then all numerical features are subjected to min-max normalization. For customer i, its feature vector at time point t1 is... The eigenvector at time point t2 is Then the customer's behavior drift vector Vi is calculated by vector subtraction, that is... .

[0009] Step 2: Use the original customer data and the drift vector to obtain the customer distance, and calculate the core distance of each data point based on the customer distance and the determined neighborhood cardinality k value; The normalized multidimensional feature space is divided into a hypercube grid. The number of data points falling into each grid cell is counted as the local density of that cell. A candidate set of neighborhood cardinality is preset, for example, {5, 10, 20}. For any data point p, a value k is assigned to it according to the local density of its grid cell using a preset mapping rule. For example, points in the highest density region correspond to k=20, points in the medium density region correspond to k=10, and points in the lowest density region correspond to k=5. For each data point p, its specific neighborhood cardinality determined in the previous step is used. Among all its neighbors, find the customer distance Dfinal to rank in the top 10. The distance between the neighbors of data point p is the core distance of data point p. .

[0010] Step 3: Calculate the mutual reachability distance between any two data points based on the core distance and customer distance. If there is a customer relationship between the two data points, then adjust the mutual reachability distance. For data points a and b, their mutual reachability mreach(a,b) is calculated as follows: , and The maximum of the three. Query the pre-stored customer relationship data. If a relationship is found between a and b, multiply their mutual reachability distance by a relationship decay factor less than 1, such as 0.5, to obtain the corrected mutual reachability distance. Otherwise, its value remains unchanged.

[0011] Step 4: Construct a minimum spanning tree for customer data based on the corrected mutual reachability distance, and generate a clustering hierarchy tree; for each potential cluster in the clustering hierarchy tree, calculate the cluster's lifecycle durability using the cluster's structural information in the clustering hierarchy tree, and combine the lifecycle durability with the aggregated value of the value level of all customers in the cluster to calculate the business stability score. Treat all customer data points as vertices of a graph, and use the adjusted reachability distance between any two vertices as the edge weight. Apply Prim's algorithm or Kruskal's algorithm to find the tree connecting all vertices in this fully weighted graph that has the minimum total weight; this is the minimum spanning tree (MST). Figure 3 As shown. Then, the edges of the minimum spanning tree are sorted in descending order of weight, and edges are removed one by one. Each removal will split a connected component into two or more. The hierarchical structure formed by this process is the clustering hierarchy tree, as shown. Figure 4 As shown. In the clustering hierarchy tree, the lifetime durability of each cluster is obtained using the standard stability calculation method in the HDBSCAN algorithm, that is, the lifetime durability of all points within the cluster. Value minus the time of cluster birth The sum after the value, where This is the reciprocal of the reachability distance. Simultaneously, the value level values ​​of all customers within the cluster are summed to obtain the aggregated value. The lifecycle durability and aggregated value are then combined using a weighted summation method to form a business stability score; for example, Business Stability Score = Weight. ×Lifetime Durability + Weight × Value aggregation value.

[0012] Step 5: Based on the business stability score and the preset minimum cluster size threshold, extract the customer grouping results from the clustering hierarchy tree, and identify data points that do not belong to any group as noise points.

[0013] A minimum cluster size, such as 5, is set, and all potential clusters with fewer than 5 members are removed from the clustering hierarchy tree. Then, the remaining clusters are selected using a traversal strategy from leaf nodes to the root node: if a parent cluster's business stability score is higher than the sum of the business stability scores of all its child clusters, then that parent cluster is selected as a final cluster; otherwise, its child clusters are retained for the next round of comparison. This process is iterated until the root node is reached, resulting in a set of non-overlapping clusters with the highest total business stability score, which are then used as the final customer clusters. All data points not included in any final cluster are marked as noise points.

[0014] In an optional embodiment, obtaining the customer distance using the original customer data and the drift vector specifically involves: For any two customers i and j, calculate the Gower distance based on numerical and categorical features as the initial mixture distance; Calculate the cosine of the angle between the behavior drift vectors and obtain the directional consistency coefficient; Obtain their customer value level and calculate the value modulation factor; The customer distance is obtained based on the initial mixing distance, the adjustment term based on the directional consistency coefficient, and the value modulation factor.

[0015] For customers i and j, the initial mixing distance is calculated using the Gower distance. Calculate the cosine of the angle between its behavior drift vectors Vi and Vj. 1 indicates that the directions are exactly the same, -1 indicates that the directions are exactly opposite, and 0 indicates that the directions are orthogonal. For example, The directional consistency coefficient is obtained. High, medium, and low value levels are mapped to values ​​of 3, 2, and 1 respectively, denoted as... and Using an exponential decay function as a nonlinear value modulation function, such as the modulation factor. ,in and These are the quantitative value levels for customers i and j, respectively. To pre-determine positive weights, customer distance .

[0016] Taking customers i and j as examples, their static characteristics include age (e.g., 35 and 40 years old) and membership type (e.g., gold and silver cards). Gower distance provides an initial similarity measure; let's assume the initial mixed distance is 0.4. Simultaneously, their behavioral drift vectors are calculated. If two vectors are close in direction (e.g., a cosine of their angle is 0.9), it indicates a high degree of consistency in their behavioral trends, and they should be placed closer together in the final distance. Assuming customer i has a five-star value rating and customer j has a three-star rating, a significant difference in ratings can be addressed. A value modulation factor, such as 1 + (absolute value difference / maximum rating), yields 1.4. This factor amplifies the distance between customers with different value ratings. The final customer distance combines these three factors. For example, the initial mixed distance of 0.4 is multiplied by an adjustment term based on directional consistency (e.g., 1 + 0.9), and then multiplied by the value modulation factor of 1.4. In this way, the final distance reflects not only the similarity of customers' static attributes but also the consistency of their behavioral trends and the differences in their business value.

[0017] In yet another embodiment, ,in It is a distance calculated based on the cosine of the included angle, such as , The distance is calculated based on differences in value levels. This is the initial mixing distance.

[0018] In an optional embodiment, calculating a behavioral drift vector for each customer based on the direction and magnitude of changes in data characteristics of the same customer between two time points includes: For any customer, extract their multidimensional feature vector V1 at the first preset time point and their multidimensional feature vector V2 at the second preset time point; After aligning and normalizing the feature vectors V1 and V2, the vector difference is calculated. To obtain the customer's behavior drift vector, such as Figure 2 As shown.

[0019] Assume a customer has three behavioral dimensions: average monthly login frequency, average monthly spending, and average monthly active days. For customer A, at a first preset time point, such as January, their behavioral data corresponds to a multi-dimensional feature vector V1 of 10 logins, 800 yuan, and 15 days. At a second preset time point, such as March, their behavioral data changes, and the corresponding multi-dimensional feature vector V2 becomes 15 logins, 700 yuan, and 20 days. These two vectors are snapshots of customer A's behavior at the two time points. To eliminate the influence of different dimensional units, the feature vectors are normalized, for example, by scaling all their components to between 0 and 1. After normalization, suppose V1 becomes 0.2, 0.8, 0.5, and V2 becomes 0.3, 0.7, 0.7. Behavioral drift vector. The values ​​are obtained by subtracting V1 from V2, i.e., 0.1, -0.1, and 0.2. The new vector represents the changing trend of customer behavior, with the sign and magnitude of each component representing the degree of enhancement or weakening of the corresponding behavioral dimension. For example, the number of logins and active days may increase, while the amount spent may decrease.

[0020] In an optional embodiment, the process of determining the neighborhood cardinality k is as follows: The feature space is divided into grids of a preset size, and the local density within each grid is calculated. Calculate the quantiles of the local density values ​​for all non-empty grids; Based on the quantile interval of the local density of the grid where each data point is located, a k value is mapped to the data point from a preset candidate set. The higher the quantile interval of the density, the larger the mapped k value.

[0021] Assume the customer feature space consists of two dimensions: recent spending amount and login frequency. Divide this two-dimensional space into a 10×10 grid. By counting the number of customers falling into each grid cell, the local density of each grid can be obtained. For example, a grid located in a high-spending, high-frequency area may have 200 customer points, with a local density of 200; while a grid located in a low-spending, low-frequency area may have only 10 customer points, with a density of 10. After calculating the local density of all grids, these density values ​​are sorted and quantiles are calculated. For example, grids with a density value greater than 150 are defined as high-density quantiles above the 90th percentile, those between 50 and 150 are medium-density, and those below 50 are low-density. A candidate set of k values ​​is preset, such as 5, 15, and 30. For customer points falling into high-density grids, a larger k value, such as 30, is assigned to them to discover more robust clustering structures in dense areas. Conversely, for customer points falling in sparse areas, a smaller k value, such as 5, is assigned to avoid incorrectly connecting them to distant, unrelated points.

[0022] In an optional embodiment, the correction of the mutually reachable distance specifically refers to: For data points p and q, calculate the standard reachability distance between them; If there exists a normalized intensity between data points p and q The relationships between customers, among which Then, a decay function that depends on the correlation strength is used. The standard reachable distance is reduced to obtain the corrected reachable distance, wherein the attenuation function is... Regarding the strength of the association It is a monotonically decreasing function with a range in (0,1].

[0023] In customer clustering analysis, data points p and q represent two customers. Based on their characteristics, a standard mutual reachability distance can first be calculated, representing their proximity in the feature space, assumed to be 15 units. It's possible that we learn from an external business system that customer p registered through a referral link from customer q; this referral relationship constitutes an association between customers. This association can be quantified as a normalized strength. For example, setting it to 0.8 indicates a very strong association. To incorporate association information into distance calculations, a decay function is introduced, such as... When the association strength S_assoc is 0.8, the attenuation factor β is 0.28. Multiplying the attenuation factor by the previously calculated standard reachable distance yields a corrected distance of 4.2. Thus, although two customers may have some distance in their original features, the strong association shortens their effective distance, making them more likely to be grouped into the same cluster during the clustering process. If there is no association, The value is 0, the attenuation factor is 1, and the distance remains unchanged.

[0024] In an optional embodiment, the step of calculating the cluster's lifecycle durability using the cluster's structural information in the clustering hierarchy tree, and then fusing the lifecycle durability with the aggregated value of all customers within the cluster to calculate a business stability score, specifically involves: For any potential cluster C in the clustering hierarchy tree, calculate the stability. ,in When point p within a cluster leaves cluster C value, When cluster C dies value; Calculate the median of all customer value levels within cluster C as the aggregated value of cluster C; After normalizing the aggregated values ​​of stability and value levels of all potential clusters, the business stability score is obtained by weighted summation.

[0025] A potential customer cluster C is identified in a hierarchical tree generated by a hierarchical clustering algorithm. This cluster C has a distance parameter... It is formed when it equals 0.5. When it grows to 1.2, it dies out due to merging into a larger cluster, hence its death value. The value is 1.2. There is a core client point p1 within the cluster, which continues until... It will only leave the cluster when it equals 3.0. There is also an edge client point p2, which is... A value equal to 1.5 indicates the cluster will detach. Therefore, p1 contributes 1.8 to cluster stability, and p2 contributes 0.3. Summing the contributions of all points within the cluster yields the cluster's initial stability score. After calculating the stability of cluster C, business value is evaluated. Assume cluster C contains five customers with value levels of five stars, four stars, four stars, and three stars. The median of these value levels, four stars, is taken as the cluster's aggregated value. Then, the stability and aggregated value of all potential clusters are normalized to fall within the range of 0 to 1. A weighted formula, such as 0.7 × normalized stability + 0.3 × normalized value, is used to calculate the final business stability score. The cluster with the highest score is the most worthwhile customer segment to focus on and operate within.

[0026] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0027] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to method embodiments, the description is relatively simple, and relevant parts can be referred to the descriptions in the method embodiments. The systems and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0028] The method and electronic device for providing product object information provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A customer data analysis method, characterized in that, Includes the following steps: Acquire raw customer data collected at at least two preset time points; calculate a behavioral drift vector for each customer based on the direction and magnitude of changes in data characteristics of the same customer between the two time points; The customer distance is obtained using the original customer data and the drift vector. Based on the customer distance and the determined neighborhood cardinality k, the core distance of each data point is calculated. The mutual reachability distance between any two data points is calculated based on the core distance and customer distance. If there is a customer relationship between the two data points, the mutual reachability distance is adjusted. Construct a minimum spanning tree of customer data based on the corrected mutual reachability distance, and generate a clustering hierarchy tree; For each potential cluster in the clustering hierarchy tree, the cluster's lifecycle durability is calculated using the cluster's structural information in the clustering hierarchy tree, and the lifecycle durability is combined with the aggregated value of the value levels of all customers within the cluster to calculate the business stability score. Based on the business stability score and the preset minimum cluster size threshold, customer grouping results are extracted from the clustering hierarchy tree, and data points that do not belong to any group are identified as noise points.

2. The method according to claim 1, characterized in that, The process of obtaining the customer distance using the original customer data and the drift vector specifically involves: For any two customers i and j, calculate the Gower distance based on numerical and categorical features as the initial mixture distance; Calculate the cosine of the angle between the behavior drift vectors and obtain the directional consistency coefficient; Obtain their customer value level and calculate the value modulation factor; The customer distance is obtained based on the initial mixing distance, the adjustment term based on the directional consistency coefficient, and the value modulation factor.

3. The method according to claim 1, characterized in that, The method calculates a behavioral drift vector for each customer based on the direction and magnitude of changes in data characteristics of the same customer between two time points, including: For any customer, extract their multidimensional feature vector V1 at the first preset time point and their multidimensional feature vector V2 at the second preset time point; After aligning and normalizing the feature vectors V1 and V2, the vector difference is calculated. This yields the customer's behavior drift vector.

4. The method according to claim 1, characterized in that, The process of determining the neighborhood cardinality k is as follows: The feature space is divided into grids of a preset size, and the local density within each grid is calculated. Calculate the quantiles of the local density values ​​for all non-empty grids; Based on the quantile interval of the local density of the grid where each data point is located, a k value is mapped to the data point from a preset candidate set. The higher the quantile interval of the density, the larger the mapped k value.

5. The method according to claim 1, characterized in that, The corrected mutual reachability distance is specifically as follows: For data points p and q, calculate the standard reachability distance between them; If there exists a normalized intensity between data points p and q The relationships between customers, among which Then, a decay function that depends on the correlation strength is used. The standard reachable distance is reduced to obtain the corrected reachable distance, wherein the attenuation function is... Regarding the strength of the association It is a monotonically decreasing function with a range in (0,1].

6. The method according to claim 1, characterized in that, The process involves calculating the cluster's lifecycle durability using the cluster's structural information within the clustering hierarchy tree, and then combining this lifecycle durability with the aggregated value of all customers within the cluster to calculate a business stability score. Specifically: For any potential cluster C in the clustering hierarchy tree, calculate the stability. ,in When point p within a cluster leaves cluster C value, When cluster C dies value; Calculate the median of all customer value levels within cluster C as the aggregated value of cluster C; After normalizing the aggregated values ​​of stability and value levels of all potential clusters, the business stability score is obtained by weighted summation.

7. A customer data analysis system, characterized in that, Includes the following modules: The data acquisition module is used to acquire raw customer data collected at at least two preset time points; and to calculate a behavioral drift vector for each customer based on the direction and magnitude of the data feature changes of the same customer between the two time points. The distance calculation module is used to obtain the customer distance using the original customer data and the drift vector, and to calculate the core distance of each data point based on the customer distance and the determined neighborhood cardinality k value. The reachability calculation module is used to calculate the mutual reachability distance between any two data points based on the core distance and the customer distance. If there is a customer relationship between the two data points, the mutual reachability distance is corrected. The cluster partitioning module is used to construct the minimum spanning tree of customer data based on the corrected mutual reachability distance, and to generate the clustering hierarchy tree; For each potential cluster in the clustering hierarchy tree, the cluster's lifecycle durability is calculated using the cluster's structural information in the clustering hierarchy tree, and the lifecycle durability is combined with the aggregated value of the value levels of all customers within the cluster to calculate the business stability score. The result output module is used to extract customer clustering results from the clustering hierarchy tree based on the business stability score and the preset minimum cluster size threshold, and to identify data points that do not belong to any cluster as noise points.

8. The system according to claim 7, characterized in that, The process of obtaining the customer distance using the original customer data and the drift vector specifically involves: For any two customers i and j, calculate the Gower distance based on numerical and categorical features as the initial mixture distance; Calculate the cosine of the angle between the behavior drift vectors and obtain the directional consistency coefficient; Obtain their customer value level and calculate the value modulation factor; The customer distance is obtained based on the initial mixing distance, the adjustment term based on the directional consistency coefficient, and the value modulation factor.

9. The system according to claim 7, characterized in that, The method calculates a behavioral drift vector for each customer based on the direction and magnitude of changes in data characteristics of the same customer between two time points, including: For any customer, extract their multidimensional feature vector V1 at the first preset time point and their multidimensional feature vector V2 at the second preset time point; After aligning and normalizing the feature vectors V1 and V2, the vector difference is calculated. This yields the customer's behavior drift vector.

10. The system according to claim 7, characterized in that, The process of determining the neighborhood cardinality k is as follows: The feature space is divided into grids of a preset size, and the local density within each grid is calculated. Calculate the quantiles of the local density values ​​for all non-empty grids; Based on the quantile interval of the local density of the grid where each data point is located, a k value is mapped to the data point from a preset candidate set. The higher the quantile interval of the density, the larger the mapped k value.

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