Power consumption data processing method oriented to multiple user types

Abstract

The invention provides a multi-user-type-oriented power consumption data processing method, and relates to the technical field of power grids, and the method comprises the steps: constructing a heterogeneous power graph of a target region based on a plurality of node types, node attributes, and a plurality of edge types and edge attributes; applying heterogeneous graph convolution on the heterogeneous power graph, introducing a time dimension on the basis of the heterogeneous graph convolution, constructing a space-time heterogeneous graph convolution model, applying one-dimensional convolution on the time dimension, extracting a multi-scale space-time dependency mode, and obtaining space-time heterogeneous features corresponding to the heterogeneous power graph; using a fuzzy C-means clustering algorithm to perform user clustering on the space-time heterogeneous features, obtaining a membership matrix of the user to each cluster by optimizing an objective function, determining an optimal cluster number according to a cluster validity index, and obtaining a user clustering result; a typical electricity consumption behavior mode is obtained by converting an electricity consumption load curve into a symbol sequence and identifying a behavior cluster in a user group by applying a community discovery algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of power grids, and in particular to a method for processing power consumption data for multiple user types. Background Art

[0002] With the rapid development of smart grids and energy internet, massive multi-source heterogeneous electricity consumption data is continuously generated and accumulated. The electricity consumption behaviors of different user types vary significantly. Mining the valuable information contained in multi-user electricity data is of great significance for improving the quality of power supply services, optimizing energy resource allocation, and innovating power value-added services.

[0003] Traditional electricity consumption data processing methods mainly target a single user type, ignoring the differences and correlations between electricity consumption patterns of different user types. At the same time, existing methods often use a single data source and a single time scale for modeling and analysis, lacking the ability to mine the laws of user electricity consumption behavior from a multi-scale perspective of time and space. In addition, massive multi-source heterogeneous electricity data brings challenges to existing processing methods in terms of storage, calculation, and analysis. Summary of the invention

[0004] The embodiment of the present invention provides a method for processing electricity consumption data for multiple user types, which can solve the problems in the prior art.

[0005] According to a first aspect of the embodiments of the present invention, Provides a method for processing electricity consumption data for multiple user types, including: A heterogeneous power graph of the target area is constructed based on multiple node types, node attributes, and multiple edge types and edge attributes. The node types include user nodes, transformer nodes, and power supply area nodes. The node attributes include user type, power consumption, and load curve. The edge types include user-transformer connection edges and transformer-power supply area connection edges. The edge attributes include power transmission capacity and distance. Applying heterogeneous graph convolution on the heterogeneous power graph, introducing the time dimension on the basis of the heterogeneous graph convolution, constructing a spatiotemporal heterogeneous graph convolution model, regarding each time step as a graph snapshot, constructing a heterogeneous power graph corresponding to the time step, applying the spatiotemporal heterogeneous graph convolution model on the heterogeneous power graph at each time step, applying one-dimensional convolution on the time dimension while applying graph convolution on the heterogeneous power graphs at different time steps, extracting multi-scale spatiotemporal dependency patterns, and obtaining spatiotemporal heterogeneous features corresponding to the heterogeneous power graph; The fuzzy C-means clustering algorithm is used to cluster users based on the spatiotemporal [l11] heterogeneous features. The membership matrix of users to each cluster is obtained by optimizing the objective function. The optimal number of clusters is determined according to the clustering effectiveness index to obtain the user clustering result. Association rule mining is applied to the internal data of each user group. Based on the association rule mining results, a community discovery algorithm is used to identify the behavior clusters within the user group to obtain the typical electricity consumption behavior pattern.

[0006] In an optional embodiment, The spatiotemporal heterogeneous features corresponding to the heterogeneous power graph include: ; in, Indicates l+1 Layer network in t The spatiotemporal heterogeneous features of the time, σ represents the activation function, P.K They represent the size of the convolution kernel in the time dimension and the size of the convolution kernel of the heterogeneous graph convolution respectively. represents the spatiotemporal convolution kernel parameters, express t The adjacency matrix of the heterogeneous power graph at time, represents the heterogeneous graph convolution operation, Represents the spatiotemporal heterogeneous characteristics of the l-th layer network at time t.

[0007] In an optional embodiment, The fuzzy C-means clustering algorithm is used to group users based on spatiotemporal heterogeneous features. The membership matrix of users to each cluster is obtained by optimizing the objective function, including: Initialize the membership matrix, and randomly assign an initial membership value to each data point so that the sum of the memberships is 1, wherein the spatiotemporal heterogeneous features corresponding to the heterogeneous power graph include the spatiotemporal heterogeneous feature vectors of each node in the heterogeneous power graph, and each data point corresponds to the spatiotemporal heterogeneous feature vector of a user node; According to the current membership matrix, calculate the center vector of each cluster [l12], the center vector is the weighted average of the membership of all data points, and update the cluster center according to the center vector; The membership matrix is ​​updated based on the distance between the data point and the cluster center, and the inverse relationship between the membership value and the distance is achieved by optimizing and minimizing the objective function; Among them, the objective function is the sum of the squares of the distances between the data points and their membership-weighted cluster centers; The cluster center calculation and membership matrix update are iteratively performed until the change of the objective function is less than the preset threshold or the maximum number of iterations is reached, and the optimized membership matrix is ​​output to achieve the soft assignment of users to each cluster.

[0008] In an optional embodiment, The optimal number of clusters is determined based on the clustering effectiveness index, and the user grouping results include: Set the search range of candidate cluster numbers [l13], perform fuzzy C-means clustering on each candidate cluster number, and obtain the corresponding membership matrix and cluster center, wherein the candidate cluster number is randomly set and the value is between the minimum cluster number and the maximum cluster number. Calculate the clustering effectiveness index of each candidate cluster number, wherein the clustering effectiveness index includes partition coefficient, partition entropy and Xie-Beni index; Among them, the partition coefficient represents the mean of the sum of squares of elements in the membership matrix; the partition entropy represents the mean of the elements in the membership matrix multiplied by their logarithms; the Xie-Beni index is the ratio of cluster compactness to cluster separation, where cluster compactness represents the sum of squares of distances between data points and their membership-weighted cluster centers, and cluster separation represents the square of the minimum distance between different cluster centers; Select the candidate cluster number with the largest partition coefficient, the smallest partition entropy, or the smallest Xie-Beni index as the optimal cluster number; The membership matrix and cluster centers under the optimal number of clusters are output, and the belonging label of each data point is determined according to the membership matrix under the optimal number of clusters to obtain the user grouping result.

[0009] In an optional embodiment, Association rule mining is applied to the internal data of each user group. Based on the association rule mining results, the community discovery algorithm is used to identify the behavior clusters within the user group. The typical electricity consumption behavior patterns include: Perform Z-score normalization on the power load curve of each user in the user group, divide the normalized sequence into several intervals, calculate the mean of each interval, and map the mean of each interval to a corresponding symbol according to a predefined symbol alphabet to obtain a power load symbol sequence; Apply FP-growth algorithm to mine frequent patterns of electricity consumption behavior, calculate the frequency of occurrence of each power load symbol by scanning the internal data set of the user group and arrange them in descending order of frequency, create FP-tree to insert the symbol sequence in descending order of frequency, recursively construct conditional pattern base and conditional FP-tree to generate frequent patterns, wherein the internal data set of the user group includes the power load symbol sequence of all users; Based on the mined frequent patterns, electricity consumption behavior association rules are generated, frequent item sets are filtered from the frequent pattern set according to the minimum support threshold, all non-empty subsets of each frequent item set are generated, the confidence of the association rules between the non-empty subsets and the frequent item sets is calculated, and the association rules that meet the requirements are output according to the minimum confidence threshold. The significance value of the association rules is evaluated using the Lift indicator, and the electricity consumption behavior corresponding to the association rules whose significance value is greater than the preset significance threshold is defined as a typical electricity consumption behavior pattern, wherein the frequent pattern set includes the frequent pattern of each electricity load symbol.

[0010] In an optional embodiment, The method further comprises: Based on frequent patterns and association rules, the community discovery algorithm is used to identify behavioral clusters associated within user groups. The modularity is dynamically adjusted by optimizing the modularity objective function until the community attributes of all nodes no longer change, thus achieving community division. The process of dynamically adjusting the modularity is as follows: ; in, △Q represents the change in modularity, represents the weight and the weight of the edges within the community, k i，in Representation Node i The sum of the weights of the edges connecting to other nodes in the community, m represents the fuzzification parameter, represents the sum of the weights of the edges connecting nodes inside and outside the community, k i Representation Node i The degree.

[0011] In an optional embodiment, The method further comprises: Count the frequent pattern sets within each community, and define the frequent patterns whose occurrence frequency exceeds the preset threshold as the candidate typical electricity consumption behavior patterns of the community; Calculate the similarity between candidate typical patterns, merge similar patterns by setting a similarity threshold, and obtain a typical electricity consumption behavior pattern set after deduplication; For each typical electricity consumption behavior pattern, traverse the association rule set in the community, filter out high-confidence association rules with the pattern as the antecedent, and use them as constraint rules for the typical pattern. Use the rule consequent [l14]

[15] as the supplementary attribute of the typical pattern. Filter out repeated power consumption behaviors in the supplementary attributes that have been included in the typical power consumption behavior pattern set, and update the typical power consumption behavior pattern set; For each community's set of typical electricity usage behavior patterns, the support of each typical electricity usage behavior pattern is counted, and the top K patterns with the highest support are taken as the community's main electricity usage behavior preferences, and the patterns with support ranging from K to M are taken as the community's secondary electricity usage behavior preferences, forming a set of typical electricity usage behavior patterns that reflect group behavior preferences and habits, where K is the preset main preference threshold and M is the preset secondary preference threshold.

[0012] This application constructs a heterogeneous power graph containing multiple node types, attributes and multiple edge types and attributes, which fully describes the multi-dimensional heterogeneous information such as the topological structure of the power system, user characteristics and power supply equipment parameters, and provides a complete data foundation for subsequent feature learning and association mining. By constructing a heterogeneous power graph and applying deep learning models such as graph convolution, the intrinsic characteristics of multi-source heterogeneous power data such as topological structure information and spatiotemporal dependencies are fully utilized, which improves the comprehensiveness and accuracy of the association mining of power consumption behavior.

[0013] By introducing fuzzy C-means clustering and adaptive clustering evaluation, the soft clustering of users is realized based on the spatiotemporal heterogeneous characteristics, overcoming the limitations of traditional hard clustering methods, and accurately dividing user groups with similar electricity consumption behavior patterns. Through data mining algorithms such as frequent pattern mining, association rule learning, and community discovery, typical electricity consumption habit combinations and significant correlation features within the group are discovered from multiple angles, and a structured electricity consumption behavior pattern knowledge base is formed, laying the foundation for subsequent personalized services, precision marketing and other applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The figure is a flow chart of a method for processing electricity consumption data for multiple user types according to an embodiment of the present invention. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0016] The technical solution of the present invention is described in detail with specific embodiments below. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0017] Figure 1 FIG. 1 is a flow chart of a method for processing power consumption data of multiple user types according to an embodiment of the present invention. Figure 1As shown, the method includes: S101. construct a heterogeneous power graph of the target area based on multiple node types, node attributes, and multiple edge types and edge attributes, wherein the node types include user nodes, transformer nodes, and power supply area nodes, the node attributes include user types, power consumption, and load curves, the edge types include user-transformer connection edges and transformer-power supply area connection edges, and the edge attributes include power transmission capacity and distance; Exemplarily, the detailed steps of constructing a heterogeneous power graph of a target area based on multiple node types, node attributes and multiple edge types and edge attributes are as follows: Collect multi-source heterogeneous data such as users, transformers, and power supply areas in the target area, including user type information, historical power consumption data, load curve data, transformer type parameters, connection relationships with users and power supply areas, geographical location of power supply areas, jurisdiction, etc. Perform pre-processing operations such as cleaning, deduplication, and normalization on the collected heterogeneous data, handle missing values ​​and outliers, and convert the data into a format suitable for graph model representation.

[0018] According to the preprocessed data, the nodes of the heterogeneous power graph are constructed. Three types of node objects are created: user node, transformer node, and power supply area node. The node attributes include: user node attributes: user type, power consumption, load curve, etc.; transformer node attributes: transformer type, capacity, power supply area, etc.; power supply area node attributes: area name, jurisdiction, total regional power consumption, etc.

[0019] According to the connection relationship between nodes, the edges of the heterogeneous power graph are constructed. Two types of edge objects are created: user-transformer connection edge and transformer-power supply area connection edge. The edge attributes include: user-transformer connection edge attributes: power transmission capacity, power transmission distance, etc.; transformer-power supply area connection edge attributes: the power supply area to which the transformer belongs, the number of transformers in the power supply area, etc.

[0020] Combine all node objects and edge objects to form a complete heterogeneous power graph. Use graph data structures such as adjacency matrix and adjacency list to store node and edge information, and record attribute information of different types of nodes and edges. Perform data verification on the constructed heterogeneous power graph to check the integrity and consistency of node and edge attributes to ensure the correctness and availability of the graph model.

[0021] The constructed heterogeneous power graph can be persistently stored in a graph database (such as Neo4j, JanusGraph) or a custom graph data format (such as JSON, XML) for subsequent graph data analysis and application. Through the above steps, a heterogeneous power graph that fully describes the topological structure, user characteristics, and device properties of the target area power system can be constructed based on multi-source heterogeneous data, laying the foundation for subsequent graph data mining and application.

[0022] S102. Applying heterogeneous graph convolution on the heterogeneous power graph, introducing a time dimension on the basis of the heterogeneous graph convolution, constructing a spatiotemporal heterogeneous graph convolution model, treating each time step as a graph snapshot, constructing a heterogeneous power graph corresponding to the time step, applying the spatiotemporal heterogeneous graph convolution model on the heterogeneous power graph of each time step, applying one-dimensional convolution on the time dimension while applying graph convolution on the heterogeneous power graphs of different time steps, extracting multi-scale spatiotemporal dependency patterns, and obtaining spatiotemporal heterogeneous features corresponding to the heterogeneous power graph; In an optional embodiment, The spatiotemporal heterogeneous features corresponding to the heterogeneous power graph include: ; in, Indicates l+1 Layer network in t The spatiotemporal heterogeneous features of the time, σ represents the activation function, P.K They represent the size of the convolution kernel in the time dimension and the size of the convolution kernel of the heterogeneous graph convolution respectively. represents the spatiotemporal convolution kernel parameters, express t The adjacency matrix of the heterogeneous power graph at time, represents the heterogeneous graph convolution operation, Represents the spatiotemporal heterogeneous characteristics of the l-th layer network at time t.

[0023] Exemplarily, heterogeneous graph convolution design: for different types of nodes and edges in heterogeneous power graphs, independent graph convolution kernel functions are designed. For each type of node, a corresponding node convolution kernel function is designed to aggregate the node's own features and the features transmitted by neighboring nodes; for each type of edge, a corresponding edge convolution kernel function is designed to aggregate the relationship features between connected nodes.

[0024] The heterogeneous graph convolution kernel functions (node ​​convolution kernel functions and edge convolution kernel functions) are combined into a complete heterogeneous graph convolution layer. For each node, the corresponding type of node convolution kernel function is applied to aggregate node features and neighbor information; for each edge between nodes, the corresponding type of edge convolution kernel function is applied to aggregate connection relationship features; the results of node convolution and edge convolution are added to obtain the output features of the heterogeneous graph convolution layer.

[0025] On the basis of heterogeneous graph convolution, the time dimension is introduced to construct a spatiotemporal heterogeneous graph convolution model. Each time step is regarded as a graph snapshot, and the heterogeneous power graph corresponding to the time step is constructed; a heterogeneous graph convolution layer is applied to the heterogeneous power graph of each time step to extract spatial dependency features; and one-dimensional convolution is applied to the time dimension to extract the temporal evolution pattern between different time steps.

[0026] Construction of spatiotemporal heterogeneous graph convolution model: Combine heterogeneous graph convolution layer and time dimension convolution to build a complete spatiotemporal heterogeneous graph convolution model. For the heterogeneous power graph of each time step, apply heterogeneous graph convolution layer to extract spatial dependency features; stack the heterogeneous graph convolution outputs of different time steps in the time dimension to form time series data; apply one-dimensional convolution on the time series data to extract the evolution pattern between time steps; add the output of one-dimensional convolution to the output of heterogeneous graph convolution to obtain the final output features of the spatiotemporal heterogeneous graph convolution model.

[0027] By setting convolution kernels of different sizes and stacking multiple layers of spatiotemporal heterogeneous graph convolution models, multi-scale spatiotemporal dependency patterns are extracted. In the spatial dimension, by setting heterogeneous graph convolution kernels of different sizes, node and edge features within different hop counts are extracted; in the temporal dimension, by setting one-dimensional convolution kernels of different sizes, evolution patterns on different time scales are extracted; by stacking multiple spatiotemporal heterogeneous graph convolution layers, the receptive field is gradually expanded to extract more global and high-level spatiotemporal features.

[0028] The output of the last layer of spatiotemporal heterogeneous graph convolution model is used as the spatiotemporal heterogeneous feature representation of the heterogeneous power graph. For each node, the corresponding spatiotemporal heterogeneous feature vector is output; for different types of nodes, the dimensions of their spatiotemporal heterogeneous feature vectors can be different to meet the feature representation requirements of different types of nodes.

[0029] Through the above steps, the spatiotemporal heterogeneous graph convolution model can be applied on the heterogeneous power graph, and the spatial dependency and time evolution pattern can be extracted at the same time to obtain the spatiotemporal heterogeneous feature representation of each node in the heterogeneous power graph, providing more comprehensive and accurate feature input for subsequent tasks such as user grouping and behavior analysis.

[0030] S103. The fuzzy C-means clustering algorithm is used to perform user grouping on the spatiotemporal [l16] heterogeneous features, and the user membership matrix to each cluster is obtained by optimizing the objective function. The optimal number of clusters is determined according to the clustering effectiveness index to obtain the user grouping result. Association rule mining is applied to the internal data of each user group. Based on the association rule mining results, a community discovery algorithm is used to identify the behavior clusters within the user group to obtain the typical electricity consumption behavior pattern.

[0031] Exemplarily, the fuzzy C-means clustering algorithm is used to group users based on spatiotemporal heterogeneous features. The spatiotemporal heterogeneous feature vector of each user node is used as the input data for clustering; the cluster center and membership matrix are initialized, and the cluster number range and fuzzy factor are set; the objective function is iteratively optimized, and the cluster center and membership matrix are updated until the convergence condition is met; the objective function is to minimize the weighted sum of squares of distances between user nodes and cluster centers, and the weight is the fuzzy factor power of the membership.

[0032] Determine the optimal number of clusters based on the clustering effectiveness index. For each candidate cluster number, calculate the corresponding membership matrix and cluster center; calculate commonly used clustering effectiveness indicators, such as partition coefficient, partition entropy, Xie-Beni index, etc.; comprehensively consider multiple indicators and select the number of clusters with the best score as the final number of user groupings. User grouping result output: According to the membership matrix corresponding to the optimal number of clusters, the user grouping result is obtained. For each user node, select the cluster with the largest membership as the group to which it belongs; output the group label of each user node, and the list of user nodes contained in each group. The user grouping result includes multiple user groups obtained after grouping.

[0033] Apply association rule mining to the power load curve data within each user group. Convert each user's power load curve into a symbol sequence, for example, divide it into three intervals of high, medium and low according to the load value, and represent it with different symbols; build a transaction database for the symbol sequences of all users in the group, and each user's symbol sequence is a transaction; apply frequent pattern mining algorithms (such as Apriori, FP-growth, etc.) to extract frequent symbol combination patterns; generate association rules based on frequent patterns, calculate indicators such as rule support and confidence, and screen strong association rules.

[0034] Apply community discovery algorithms to identify behavioral clusters within user groups. Based on the association rule mining results, construct a user behavior association graph, where nodes are users and edges represent behavioral similarities between users; apply community discovery algorithms (such as Louvain, Infomap, etc.) to identify closely connected user subgroups on the behavior association graph; output a list of users included in each community, as well as frequent behavior patterns and association rules within the community.

[0035] Extraction of typical electricity consumption behavior patterns: Combine frequent patterns, association rules and community structure to extract typical electricity consumption behavior patterns. For each community, count the frequent symbol sequence patterns within it, and take the most frequently occurring pattern as the typical electricity consumption behavior; for each typical behavior pattern, dig out other behavior patterns that are strongly associated with it to form a set of association patterns of typical behaviors; compare the typical behavior patterns of different communities, extract common patterns and characteristic differences, and characterize group behavior preferences.

[0036] Through the above steps, we can make full use of spatiotemporal heterogeneous characteristics to accurately segment users, explore typical electricity consumption behavior patterns within the group, identify the behavioral characteristics and association rules of different user subgroups, and provide decision support for subsequent personalized services, precision marketing and other applications.

[0037] In an optional embodiment, The fuzzy C-means clustering algorithm is used to group users based on spatiotemporal heterogeneous features. The membership matrix of users to each cluster is obtained by optimizing the objective function, including: Initialize the membership matrix, and randomly assign an initial membership value to each data point so that the sum of the memberships is 1, wherein the spatiotemporal heterogeneous features corresponding to the heterogeneous power graph include the spatiotemporal heterogeneous feature vectors of each node in the heterogeneous power graph, and each data point corresponds to the spatiotemporal heterogeneous feature vector of a user node; According to the current membership matrix, calculate the center vector of each cluster [l17], the center vector is the weighted average of the membership of all data points, and update the cluster center according to the center vector; The membership matrix is ​​updated based on the distance between the data point and the cluster center, and the inverse relationship between the membership value and the distance is achieved by optimizing and minimizing the objective function; Among them, the objective function is the sum of the squares of the distances between the data points and their membership-weighted cluster centers; The cluster center calculation and membership matrix update are iteratively performed until the change of the objective function is less than the preset threshold or the maximum number of iterations is reached, and the optimized membership matrix is ​​output to achieve the soft assignment of users to each cluster.

[0038] Exemplarily, the detailed steps of using the fuzzy C-means clustering algorithm to group users based on spatiotemporal heterogeneous features are as follows: The spatiotemporal heterogeneous feature vector of each user node is used as the input data point of the clustering algorithm.

[0039] Set the number of clusters C and the dimension of the membership matrix U to N×C, where N is the number of user nodes; randomly generate the initial value of the membership matrix U, randomly assign C membership values ​​to each user node, and normalize to ensure that the sum of the membership of each row is 1. According to the current membership matrix U, calculate the center vector of each cluster; for the i-th cluster, its center vector is the weighted average of the membership of all data points, the weight is the mth power of the membership of the data point belonging to the i-th class, and m is the fuzzy factor (usually 2); update the center vectors of all C clusters.

[0040] Calculate the distance between each data point and all cluster centers, usually using Euclidean distance or Mahalanobis distance; update the membership matrix U based on the distance, and realize the inverse relationship between the membership value and the distance by optimizing and minimizing the objective function; the objective function is the sum of the squares of the distances between all data points and their membership-weighted cluster centers, and the weight of the cluster center is the mth power of the corresponding membership; use the Lagrange multiplier method to solve the minimum value of the objective function and obtain the update formula of the membership matrix U. Alternately calculate the cluster centers and update the membership matrix; calculate the value of the objective function after each iteration, and stop the iteration when the change is less than the preset threshold or the maximum number of iterations is reached; output the final membership matrix U and cluster centers.

[0041] According to the optimized membership matrix U, each user node is softly clustered; for each user node, its membership to each cluster is represented by the corresponding row vector in the matrix U; the cluster with the largest membership is used as the main cluster of the user, and the other clusters are used as the secondary clusters of the user, so as to achieve the soft division of the user into clusters. Calculate the commonly used clustering effectiveness indicators, such as partition coefficient, partition entropy, Xie-Beni index, etc.; compare the index values ​​under different cluster numbers, and select the cluster number with the best comprehensive performance as the final user cluster number.

[0042] Through the above steps, the fuzzy C-means clustering algorithm can be used to soft-cluster the user's spatiotemporal heterogeneous features, obtain the membership of each user to different clusters, and realize the fuzzy division of user behavior characteristics. Compared with the traditional hard clustering method, fuzzy C-means clustering can better characterize the diversity and complexity of user behavior, and provide more refined and comprehensive user clustering information for subsequent user profiling and personalized services.

[0043] In an optional embodiment, The optimal number of clusters is determined based on the clustering effectiveness index, and the user grouping results include: Set the search range of candidate cluster numbers [l18], perform fuzzy C-means clustering on each candidate cluster number, and obtain the corresponding membership matrix and cluster center, wherein the candidate cluster number is randomly set and the value is between the minimum cluster number and the maximum cluster number. Calculate the clustering effectiveness index of each candidate cluster number, wherein the clustering effectiveness index includes partition coefficient, partition entropy and Xie-Beni index; Among them, the partition coefficient represents the mean of the sum of squares of elements in the membership matrix; the partition entropy represents the mean of the elements in the membership matrix multiplied by their logarithms; the Xie-Beni index is the ratio of cluster compactness to cluster separation, where cluster compactness represents the sum of squares of distances between data points and their membership-weighted cluster centers, and cluster separation represents the square of the minimum distance between different cluster centers; Select the candidate cluster number with the largest partition coefficient, the smallest partition entropy, or the smallest Xie-Beni index as the optimal cluster number; The membership matrix and cluster centers under the optimal number of clusters are output, and the belonging label of each data point is determined according to the membership matrix under the optimal number of clusters to obtain the user grouping result.

[0044] Exemplarily, the optimal number of clusters is determined according to the clustering effectiveness index, and the detailed steps for obtaining the user grouping results are as follows: Set the range of candidate cluster numbers: According to the number of user nodes and domain knowledge, set the search range [Cmin, Cmax] of the candidate cluster number; determine the step size of the cluster number search to obtain a discrete value set of the candidate cluster number.

[0045] Execute fuzzy C-means clustering: for each candidate cluster number C, execute the fuzzy C-means clustering algorithm; input the spatiotemporal heterogeneous features of the user nodes, set the fuzzy factor m and the maximum number of iterations; initialize the membership matrix, iteratively calculate the cluster center and update the membership matrix until convergence or the maximum number of iterations is reached; obtain the optimal membership matrix and cluster center under the current cluster number C.

[0046] For each candidate cluster number C, based on the corresponding membership matrix and cluster center, the following clustering effectiveness indicators are calculated: partition coefficient (PC): the mean of the sum of squares of all elements in the membership matrix, ranging from [1 / C, 1]. The larger the value, the better the clustering effect; partition entropy (PE): the mean of the elements in the membership matrix multiplied by their logarithms, ranging from [0, logC]. The smaller the value, the better the clustering effect; Xie-Beni index (XB): the ratio of cluster compactness to cluster separation, where compactness is the sum of the squares of the distances between all data points and their membership-weighted cluster centers, and separation is the square of the minimum distance between different cluster centers. The smaller the XB value, the better the clustering effect.

[0047] For each candidate cluster number C, multiple clustering effectiveness indicators are comprehensively considered, and the cluster number with the best comprehensive performance is selected as the optimal cluster number C*; commonly used selection strategies include: maximum partition coefficient, minimum partition entropy, minimum Xie-Beni index, etc.; if the optimal cluster numbers of multiple indicators are inconsistent, the weighted average or voting method can be used to determine the final optimal cluster number.

[0048] For the optimal number of clusters C*, output the corresponding optimal membership matrix U* and cluster center V*; for each user node, find the cluster with the largest membership in the optimal membership matrix U* and use it as the user's belonging label; divide user nodes with the same belonging label into the same user group to obtain the final user grouping result.

[0049] For the user grouping results under the optimal number of clusters, calculate commonly used external evaluation indicators, such as the Rand Index and mutual information; compare the user grouping results with known user attribute labels to evaluate the degree of consistency between the grouping results and business understanding; compare the user grouping results under different candidate clustering numbers to analyze the rationality and stability of the optimal clustering number selection.

[0050] Through the above steps, we can introduce multiple clustering effectiveness indicators on the basis of fuzzy C-means clustering to evaluate the clustering quality under different cluster numbers, and select the cluster number with the best comprehensive performance as the final user grouping number. This adaptive clustering number selection method can automatically determine the optimal user grouping granularity according to data characteristics and business needs, and improve the accuracy and practicality of user grouping. At the same time, through the quality evaluation of the final user grouping results, we can further verify the effectiveness of the grouping method and provide a reliable basis for user group division for subsequent user profiling and precision marketing.

[0051] In an optional embodiment, Association rule mining is applied to the internal data of each user group. Based on the association rule mining results, the community discovery algorithm is used to identify the behavior clusters within the user group. The typical electricity consumption behavior patterns include: Perform Z-score normalization on the power load curve of each user in the user group, divide the normalized sequence into several intervals, calculate the mean of each interval, and map the mean of each interval to a corresponding symbol according to a predefined symbol alphabet to obtain a power load symbol sequence; Apply FP-growth algorithm to mine frequent patterns of electricity consumption behavior, calculate the frequency of occurrence of each power load symbol by scanning the internal data set of the user group and arrange them in descending order of frequency, create FP-tree to insert the symbol sequence in descending order of frequency, recursively construct conditional pattern base and conditional FP-tree to generate frequent patterns, wherein the internal data set of the user group includes the power load symbol sequence of all users; Based on the mined frequent patterns, electricity consumption behavior association rules are generated, frequent item sets are filtered from the frequent pattern set according to the minimum support threshold, all non-empty subsets of each frequent item set are generated, the confidence of the association rules between the non-empty subsets and the frequent item sets is calculated, and the association rules that meet the requirements are output according to the minimum confidence threshold. The significance value of the association rules is evaluated using the Lift indicator, and the electricity consumption behavior corresponding to the association rules whose significance value is greater than the preset significance threshold is defined as a typical electricity consumption behavior pattern, wherein the frequent pattern set includes the frequent pattern of each electricity load symbol.

[0052] For example, association rule mining is applied to the internal data of each user group. By converting the power load curve into a symbol sequence, the community discovery algorithm is applied to identify the behavior clusters within the user group. The detailed steps of obtaining the typical power consumption behavior pattern are as follows: The power load curve of each user in the group is Z-score normalized, the curve mean is shifted to 0, and the variance is scaled to 1; the normalized load sequence is divided into several intervals (such as 10 intervals), and the mean of the load value in each interval is calculated; a symbol alphabet (such as AJ) is predefined, and each interval is mapped to a corresponding symbol according to the order of the interval mean from small to large; the load sequence of each user is symbolized to obtain the power load symbol sequence.

[0053] The power load symbol sequences of all users in the group are combined into a data set, and the power load symbol sequence of each user is a transaction; the FP-growth algorithm is used to mine frequent patterns: scan the data set, calculate the occurrence frequency of each symbol, and sort the symbol table in descending order of frequency; create an FP-tree, and insert the symbol sequence in each transaction into the FP-tree according to the symbol table in descending order of frequency; recursively construct the conditional pattern base and conditional FP-tree: for each symbol, construct its conditional pattern base, that is, the set of paths with the symbol as suffix; for each conditional pattern base, construct its conditional FP-tree, and mine frequent patterns in the conditional FP-tree; combine the frequent patterns of each symbol to generate a global frequent pattern set.

[0054] According to the preset minimum support threshold, frequent item sets are screened out from the frequent pattern set; for each frequent item set, all its non-empty subsets are generated; for each non-empty subset and the original frequent item set, the confidence of its association rule is calculated, and the confidence is the ratio of the subset support to the frequent item set support; according to the preset minimum confidence threshold, the association rules that meet the requirements are output; for each association rule, its Lift index is calculated, and the Lift index is the ratio of the confidence of the association rule to the support of the consequent symbol; according to the preset Lift significance threshold, the association rules with Lift values ​​greater than the threshold are selected as significant association rules.

[0055] For each significant association rule, its antecedent symbol sequence is defined as a typical electricity consumption behavior pattern; all typical behavior patterns are clustered, and similar behavior patterns are classified into one category, each category representing a typical electricity consumption behavior cluster; for each behavior cluster, the number of users it covers and the characteristics of the load curve are counted to characterize the user group attributes of this type of behavior pattern; the typical electricity consumption behavior cluster and the corresponding association rules of each user group are output as a description of the behavioral characteristics of the group.

[0056] For each typical electricity consumption behavior cluster, the mean and variance of its load curve are extracted, and a load curve example is drawn; for each association rule, the distribution diagram of its antecedent symbol sequence on the time axis is drawn to show the time characteristics of the behavior pattern; the behavior clusters and association rules of different groups are compared and analyzed to reveal the differences and similarities in electricity consumption behaviors among groups.

[0057] Through the above steps, the power load curve within the user group can be converted into a symbol sequence, and the frequent pattern mining and association rule generation algorithm can be used to discover the typical power consumption behavior patterns and behavior clusters within the group. By characterizing the load characteristics and user attributes of each behavior cluster, we can gain insight into the power consumption habits and preferences of different user groups and provide decision support for the power company's precision marketing and personalized services. At the same time, by visually displaying typical behavior patterns and association rules, the interpretability and operability of the analysis results can be enhanced, making it easier for business personnel to understand and apply mining discoveries.

[0058] In an optional embodiment, The method further comprises: Based on frequent patterns and association rules, the community discovery algorithm is used to identify behavioral clusters associated within user groups. The modularity is dynamically adjusted by optimizing the modularity objective function until the community attributes of all nodes no longer change, thus achieving community division. The process of dynamically adjusting the modularity is as follows: ; in, △Q represents the change in modularity, represents the weight and the weight of the edges within the community, k i，in Representation Node i The sum of the weights of the edges connecting to other nodes in the community, m represents the fuzzification parameter, represents the sum of the weights of the edges connecting nodes inside and outside the community, k i Representation Node i The degree.

[0059] For example, through frequent pattern mining and association rule generation, typical electricity consumption behavior patterns within user groups and the correlation between behaviors are discovered; applying the community discovery algorithm, the behavior pattern nodes are divided into several behavior communities according to the correlation strength. The behavior patterns within each community are closely correlated, while the correlation between communities is relatively weak; the community structure reveals the behavioral association hierarchy and organizational form within the user group, which helps to understand the internal logic and influencing mechanism of user behavior.

[0060] Traditional frequent pattern mining and association rule generation can only discover paired behavioral associations, while community discovery algorithms can automatically identify high-order associations between multiple behavioral patterns to form closely related behavioral clusters; each behavioral community corresponds to a user subgroup, and users within the subgroup behave consistently in the behavioral cluster, while different subgroups behave differently in different behavioral clusters; automatic identification of behavioral clusters and user subgroups can discover the behavioral division of labor and role differentiation within the group, tap into the diversity and heterogeneity of users, and provide precise division for personalized services.

[0061] Modularity is an important indicator to measure the quality of community division, which indicates the degree to which the correlation between nodes within the community exceeds that of a random network. By optimizing the modularity objective function, the community division is dynamically adjusted to maximize the actual correlation between nodes within the community and minimize the actual correlation between communities. The optimized community division can maintain the cohesion of behavior clusters and the separation between behavior clusters to the greatest extent, making the community discovery results more accurate and reliable.

[0062] In an optional embodiment, The method further comprises: Count the frequent pattern sets within each community, and define the frequent patterns whose occurrence frequency exceeds the preset threshold as the candidate typical electricity consumption behavior patterns of the community; Calculate the similarity between candidate typical patterns, merge similar patterns by setting a similarity threshold, and obtain a typical electricity consumption behavior pattern set after deduplication; For each typical electricity consumption behavior pattern, traverse the association rule set in the community, filter out high-confidence association rules with the pattern as the antecedent, and use the rule consequence as the supplementary attribute of the typical pattern; Filter out repeated power consumption behaviors in the supplementary attributes that have been included in the typical power consumption behavior pattern set, and update the typical power consumption behavior pattern set; For each community's set of typical electricity usage behavior patterns, the support of each typical electricity usage behavior pattern is counted, and the top K patterns with the highest support are taken as the community's main electricity usage behavior preferences, and the patterns with support ranging from K to M are taken as the community's secondary electricity usage behavior preferences, forming a set of typical electricity usage behavior patterns that reflect group behavior preferences and habits, where K is the preset main preference threshold and M is the preset secondary preference threshold.

[0063] For example, the frequently co-occurring electricity consumption behaviors in each community are defined as typical electricity consumption patterns, and the significant association rules are used to constrain and supplement the typical patterns. Finally, the detailed steps for obtaining a set of typical electricity consumption behavior patterns that reflect group behavior preferences and habits are as follows: For each behavioral community corresponding to a user subgroup, the set of frequent patterns within it is counted; a preset frequency threshold is set, and the frequent patterns whose occurrence frequency exceeds the threshold are defined as candidate typical electricity consumption behavior patterns of the community; the candidate typical patterns reflect the high-frequency co-occurring behavior combinations of users in the community and represent the main electricity consumption preferences of the subgroup.

[0064] To calculate the similarity between candidate typical patterns, indicators such as the Jaccard similarity coefficient can be used; a similarity threshold is set to merge candidate typical patterns whose similarity exceeds the threshold; the merged typical pattern set removes highly similar repeated patterns, thereby improving the diversity and representativeness of typical patterns.

[0065] The association rule sets within each community are traversed to screen out high-confidence association rules with typical electricity consumption behavior patterns as antecedents. A confidence threshold is set, and association rules with confidence exceeding the threshold are defined as constraint rules of the typical pattern. The consequent of the constraint rules is used as a supplementary attribute of the typical pattern, enriching the semantic connotation and contextual association of the typical pattern.

[0066] The set of supplementary attributes of each typical pattern is deduplicated to filter out repeated electricity usage behaviors that are already included in the typical pattern. The updated set of typical electricity usage behavior patterns includes the original pattern and supplementary attributes without repeated behaviors. The deduplicated typical pattern set is more concise and comprehensive, and can accurately express the behavioral preferences and habits of the community.

[0067] For each community's set of typical electricity consumption behavior patterns, the support of each typical electricity consumption behavior pattern within the community is counted; the main preference threshold K and the secondary preference threshold M are set, and the top K typical patterns with the highest support are defined as the main electricity consumption behavior preferences of the community; the typical patterns with support in the top K to M are defined as the secondary electricity consumption behavior preferences of the community; the main preference reflects the most common and significant behavior pattern within the community, and the secondary preference reflects the relatively minor but still somewhat common behavior pattern within the community.

[0068] For example, "rule consequent" is an important concept in association rules, which refers to the "B" part of the association rule "if A then B", that is, the subsequent events or attributes that will inevitably appear when the rule antecedent A appears. The rule consequent represents the inference result or prediction target of the association rule, reflecting the causal relationship or correlation between the antecedent and the consequent. In association rule mining, the support, confidence and lift of the rule consequent are important indicators for evaluating the significance and effectiveness of the rule.

[0069] The following is an example of a specific rule consequence: Electricity consumption behavior association rule: "If a user has a high electricity load in the afternoon (14:00-16:00) in summer, then the user is likely to have a high electricity load at night (20:00-22:00) as well."

[0070] Postcondition of the rule: The user's electricity load is higher at night (20:00-22:00).

[0071] Meaning explanation: When the rule antecedent "the user's electricity load is higher in the summer afternoon" is established, it is inferred that the user also has a higher electricity load at night, reflecting the correlation between the user's electricity consumption behavior in different time periods.

[0072] The main and secondary preferences of all communities are integrated to form a set of typical electricity consumption behavior patterns that reflect the behavioral preferences and habits of the entire user group. For each typical pattern, its support and association rules in different communities and the entire group are counted to characterize the universality and relevance of the pattern. The typical pattern set is clustered and classified to identify different types of behavioral preferences and habits, such as energy-saving, peak, stable, etc. The typical electricity consumption behavior pattern set provides a multi-level and multi-granular analysis perspective for characterizing the group's electricity consumption behavior, which can fully reveal the group's behavioral characteristics and internal laws.

[0073] For each typical electricity consumption behavior pattern, extract its load curve samples in different time periods and environments, and draw a load curve family; for the constraint rules and supplementary attributes of each typical pattern, generate an association network diagram to display the association structure of the typical pattern; for the main and secondary preferences of the group, draw a support ranking bar chart and a community distribution pie chart to intuitively display the universality and distribution characteristics of the preferences; the visual display of typical patterns can visualize abstract behavior patterns into intuitive graphic images, making it easier for business personnel to understand and apply the analysis results.

[0074] Through the above steps, community discovery can be combined with frequent pattern mining and association rule generation to extract typical electricity consumption behavior patterns from frequent co-occurrence behaviors within the community, and use significant association rules to constrain and supplement typical patterns, and finally obtain a set of typical electricity consumption behavior patterns that reflect group behavior preferences and habits. This comprehensive analysis method can fully mine the behavioral pattern information contained in the community structure, improve the representativeness and richness of typical patterns, and provide accurate user insights for power companies to carry out targeted marketing and personalized services. At the same time, through the clustering classification and visualization of typical patterns, the interpretability and operability of the analysis results can be enhanced, and the effective transformation of data mining results into business applications can be promoted.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for processing electricity consumption data for multiple user types, characterized in that: include: A heterogeneous power graph of the target area is constructed based on multiple node types, node attributes, and multiple edge types and edge attributes. The node types include user nodes, transformer nodes, and power supply area nodes. The node attributes include user type, power consumption, and load curve. The edge types include user-transformer connection edges and transformer-power supply area connection edges. The edge attributes include power transmission capacity and distance. Applying heterogeneous graph convolution on the heterogeneous power graph, introducing the time dimension on the basis of the heterogeneous graph convolution, constructing a spatiotemporal heterogeneous graph convolution model, regarding each time step as a graph snapshot, constructing a heterogeneous power graph corresponding to the time step, applying the spatiotemporal heterogeneous graph convolution model on the heterogeneous power graph at each time step, applying one-dimensional convolution on the time dimension while applying graph convolution on the heterogeneous power graphs at different time steps, extracting multi-scale spatiotemporal dependency patterns, and obtaining spatiotemporal heterogeneous features corresponding to the heterogeneous power graph; The fuzzy C-means clustering algorithm is used to cluster users based on the spatiotemporal [l1][2] heterogeneous features. The membership matrix of users to each cluster is obtained by optimizing the objective function. The optimal number of clusters is determined based on the clustering effectiveness index to obtain the user clustering results. Association rule mining is applied to the internal data of each user group. Based on the association rule mining results, a community discovery algorithm is used to identify the behavior clusters within the user group to obtain the typical electricity consumption behavior pattern.

2. The method according to claim 1, characterized in that The spatiotemporal heterogeneous features corresponding to the heterogeneous power graph include: ； in, Indicates l+1 Layer network in t The spatiotemporal heterogeneous features of the time, σ represents the activation function, P.K They represent the size of the convolution kernel in the time dimension and the size of the convolution kernel of the heterogeneous graph convolution respectively. represents the spatiotemporal convolution kernel parameters, express t The adjacency matrix of the heterogeneous power graph at time, represents the heterogeneous graph convolution operation, Indicates l The spatiotemporal heterogeneous characteristics of the layer network at time t.

3. The method according to claim 1, characterized in that The fuzzy C-means clustering algorithm is used to group users based on spatiotemporal heterogeneous features. The membership matrix of users to each cluster is obtained by optimizing the objective function, including: Initialize the membership matrix, and randomly assign an initial membership value to each data point so that the sum of the memberships is 1, wherein the spatiotemporal heterogeneous features corresponding to the heterogeneous power graph include the spatiotemporal heterogeneous feature vectors of each node in the heterogeneous power graph, and each data point corresponds to the spatiotemporal heterogeneous feature vector of a user node; According to the current membership matrix, calculate the center vector of each cluster [l3][4], the center vector is the weighted average of the membership of all data points, and update the cluster center according to the center vector; The membership matrix is ​​updated based on the distance between the data point and the cluster center, and the inverse relationship between the membership value and the distance is achieved by optimizing and minimizing the objective function; Among them, the objective function is the sum of the squares of the distances between the data points and their membership-weighted cluster centers; The cluster center calculation and membership matrix update are iteratively performed until the change of the objective function is less than the preset threshold or the maximum number of iterations is reached, and the optimized membership matrix is ​​output to achieve the soft assignment of users to each cluster.

4. The method according to claim 1, characterized in that The optimal number of clusters is determined based on the clustering effectiveness index, and the user grouping results include: Set the search range of candidate cluster numbers [l5][6], perform fuzzy C-means clustering on each candidate cluster number, and obtain the corresponding membership matrix and cluster center, wherein the candidate cluster number is randomly set and the value is between the minimum cluster number and the maximum cluster number. Calculate the clustering effectiveness index of each candidate cluster number, wherein the clustering effectiveness index includes partition coefficient, partition entropy and Xie-Beni index; Among them, the partition coefficient represents the mean of the sum of squares of elements in the membership matrix; the partition entropy represents the mean of the elements in the membership matrix multiplied by their logarithms; the Xie-Beni index is the ratio of cluster compactness to cluster separation, where cluster compactness represents the sum of squares of distances between data points and their membership-weighted cluster centers, and cluster separation represents the square of the minimum distance between different cluster centers; Select the candidate cluster number with the largest partition coefficient, the smallest partition entropy, or the smallest Xie-Beni index as the optimal cluster number; Output the membership matrix and cluster centers under the optimal number of clusters, determine the attribution label of each data point according to the membership matrix under the optimal number of clusters, and obtain the user grouping result.

5. The method according to claim 1, characterized in that Association rule mining is applied to the internal data of each user group. Based on the association rule mining results, the community discovery algorithm is used to identify the behavior clusters within the user group. The typical electricity consumption behavior patterns include: Perform Z-score normalization on the power load curve of each user in the user group, divide the normalized sequence into several intervals, calculate the mean of each interval, and map the mean of each interval to a corresponding symbol according to a predefined symbol alphabet to obtain a power load symbol sequence; Apply the FP-growth algorithm to mine frequent patterns of electricity consumption behavior, calculate the frequency of occurrence of each power load symbol by scanning the internal data set of the user group and arrange them in descending order of frequency, create an FP-tree to insert the symbol sequence in descending order of frequency, recursively construct the conditional pattern base and the conditional FP-tree to generate frequent patterns, wherein the internal data set of the user group includes the power load symbol sequence of all users; Based on the mined frequent patterns, electricity consumption behavior association rules are generated, and frequent item sets are filtered from the frequent pattern set according to the minimum support threshold [l7][8]. For each frequent item set, all its non-empty subsets are generated, and the confidence of the association rules between the non-empty subsets and the frequent item sets is calculated. The association rules that meet the requirements are output according to the minimum confidence threshold, and the significance value of the association rules is evaluated using the Lift indicator. The electricity consumption behavior corresponding to the association rules with significance values ​​greater than the preset significance threshold is defined as a typical electricity consumption behavior pattern, wherein the frequent pattern set includes the frequent patterns of each electricity load symbol.

6. The method according to claim 5, characterized in that The method further comprises: Based on frequent patterns and association rules, the community discovery algorithm is used to identify behavioral clusters associated within user groups. The modularity is dynamically adjusted by optimizing the modularity objective function until the community attributes of all nodes no longer change, thus achieving community division. The process of dynamically adjusting the modularity is as follows: ； in, △Q represents the change in modularity, represents the weight and the weight of the edges within the community, k i，in Representation Node i The sum of the weights of the edges connecting to other nodes in the community, m represents the fuzzification parameter, represents the sum of the weights of the edges connecting nodes inside and outside the community, k i Representation Node i The degree.

7. The method according to claim 6, characterized in that The method further comprises: Count the frequent pattern sets within each community, and define the frequent patterns whose occurrence frequency exceeds the preset threshold as the candidate typical electricity consumption behavior patterns of the community; Calculate the similarity between candidate typical patterns, merge similar patterns by setting a similarity threshold, and obtain a typical electricity consumption behavior pattern set after deduplication; For each typical electricity consumption behavior pattern, traverse the association rule set in the community, filter out high-confidence association rules with the pattern as the antecedent, and use them as constraint rules for the typical pattern. Use the rule consequent [l9][10] as the supplementary attribute of the typical pattern. Filter out repeated power consumption behaviors in the supplementary attributes that have been included in the typical power consumption behavior pattern set, and update the typical power consumption behavior pattern set; For each community's set of typical electricity usage behavior patterns, the support of each typical electricity usage behavior pattern is counted, and the top K patterns with the highest support are taken as the community's main electricity usage behavior preferences, and the patterns with support ranging from K to M are taken as the community's secondary electricity usage behavior preferences, forming a set of typical electricity usage behavior patterns that reflect group behavior preferences and habits, where K is the preset main preference threshold and M is the preset secondary preference threshold.

Images