A clustering method for specifying class capacity and system thereof

Abstract

The present application relates to the technical field of artificial intelligence and algorithm development, solves the technical problem that the traditional clustering method cannot identify the obstacle area in the space, relates to a clustering method with specified category capacity, comprising the following processes: a connected graph is established according to the spatial coordinate information of a discrete point set to be clustered; the connected relationship between any two discrete point sets in the connected graph is determined and the cost is calculated; the initial points of two nodes connected with a virtual source point in 2-category specified capacity clustering are selected according to a two-point selection algorithm; and further relates to a system applied to the clustering method with specified category capacity, comprising: a connected graph establishment module used for establishing a connected graph according to the spatial coordinate information of a discrete point set to be clustered. The present application converts the clustering problem with specified capacity into a network flow model and obtains an optimal solution, and the solution of the model can perfectly process the clustering problem with specified category capacity and effectively avoid the problems of spatial interlacing and containing between categories.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence and algorithm development technology, and in particular to a clustering method and system with specified category capacity. Background Technology

[0002] Clustering is a method for grouping objects into groups such that objects in one group are more similar to objects in other groups. It is a primary task in exploratory data analysis and a commonly used technique in statistical data analysis, applied in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics, and machine learning.

[0003] In specific scenarios, general clustering algorithms cannot meet the requirements of special clustering tasks. In the open-pit mine spoil transportation scenario, the spoil blocks transported to a spoil heap often come from multiple mining sites. Simultaneously, it is required that spoil blocks from the same mining site be spatially clustered together, and that the volume occupied by these spoil blocks in the spoil heap is equal to the transported volume. This problem is non-trivial when the spoil heap consists of several spoil blocks with a certain capacity. While performing spatial clustering, it is necessary to handle potential conflicts in spoil block volume for each spoil source. Traditional clustering algorithms only cluster based on the spatial distribution of discrete points and cannot handle specific clustering constraints.

[0004] Meanwhile, when clustering discrete points in non-convex regions or regions with obstructed spaces, traditional clustering methods cannot identify the obstructed regions, resulting in disconnected branches in the clustering results. In the open-pit mine spoil disposal scenario, spoil heaps are distributed as discrete points, but the transport volume from the mining area may be continuous. That is, there are complete spoil heaps that cannot fully accommodate the transport volume from a single mining area. To achieve accurate spoil disposal, post-processing operations such as cutting the spoil heaps are required. Traditional clustering algorithms are practically helpless in addressing this requirement. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a clustering method and system with specified category capacity, which solves the technical problem that traditional clustering methods cannot identify obstacle regions in space. This invention transforms the clustering problem with specified capacity into a network flow model and finds the optimal solution. The solution obtained by the model can perfectly handle the clustering problem with specified category capacity and effectively avoid problems such as spatial overlap and inclusion between categories.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a clustering method with specified category capacity, comprising the following processes:

[0007] Establish a connected graph based on the spatial coordinate information of the discrete point set to be clustered;

[0008] determining the connectivity between any two discrete point sets in the connected graph and calculating the cost;

[0009] selecting the initial points of the two nodes connected with the virtual source point in the 2-class specified capacity clustering according to the two-point selection algorithm;

[0010] establishing the network flow model of the 2-class specified capacity clustering according to the connected graph and the initial points;

[0011] iteratively solving the k-class specified capacity clustering problem from the network flow model of the 2-class specified capacity clustering.

[0012] Further, the discrete point set is a discrete point set with capacity attributes, which is composed of a plurality of discrete points containing coordinate information and corresponding capacity sizes.

[0013] Further, the virtual source point for ensuring the flow conservation of the discrete point set is introduced in the connected graph.

[0014] Further, the connected graph includes a node set, an edge set, and a cost on the edge set.

[0015] The node set is composed of coordinate points of block centers of the mining or dumping site.

[0016] The edge set is composed of lines with adjacent relationship between nodes as endpoints.

[0017] The cost on the edge set is calculated by the Euclidean distance between the two endpoints.

[0018] Further, after the step of establishing the connected graph according to the spatial coordinate information of the discrete point set to be clustered, the step further includes accessing each connected branch between the discrete points in the connected graph one by one, and individually constructing edges between the discrete points and other connected branches.

[0019] Further, the step of determining the connectivity between any two discrete point sets in the connected graph and calculating the cost includes:

[0020] establishing edges between any two discrete points in the discrete point set;

[0021] calculating the cost function of the edges between any two discrete points in the discrete point set.

[0022] Further, the two-point selection algorithm is to select the two points with the maximum Euclidean distance based on the discrete points.

[0023] Further, the two-point selection algorithm is to select the two points with the maximum distance on the connected graph.

[0024] The present invention also provides a system for clustering methods applied to the above-mentioned specified category capacity, comprising:

[0025] A connected graph building module is used to build a connected graph based on the spatial coordinate information of the discrete point set to be clustered.

[0026] A connectivity determination module is used to determine the connectivity relationship between any two discrete point sets in a connected graph and calculate the cost.

[0027] An initial point selection module is used to select the initial points of two nodes connected to the virtual source point in a 2-class specified capacity cluster according to a two-point selection algorithm.

[0028] A network flow model building module is used to build a 2-class specified capacity clustered network flow model based on the connected graph and initial points;

[0029] An iterative solution module is used to iteratively solve a k-class clustering problem with a network flow model that uses 2-class clustering with specified capacity.

[0030] Furthermore, the clustering system also includes:

[0031] The access and construction module is used to access the connected branches between discrete points in the connected graph one by one and construct the edges between discrete points and other connected branches separately.

[0032] By employing the above technical solution, the present invention provides a clustering method and system for specifying category capacity, which has at least the following beneficial effects:

[0033] 1. This invention transforms the clustering problem with a specified cluster capacity into a multi-step network flow model problem, enabling the solution of clustering schemes that meet the cluster capacity requirements. Furthermore, thanks to the superiority of the connected graph structure, using distances on the connected graph instead of Euclidean distance can handle cases of non-convex or obstacle-containing spaces that traditional clustering methods cannot address. Moreover, the multi-step network flow model ensures that the number of points requiring segmentation is less than or equal to k-1 when dealing with cases where the specified capacity is not completely separable at discrete points—a feat also impossible with traditional clustering algorithms.

[0034] 2. This invention transforms the clustering problem of a specified capacity into a network flow problem by establishing a connected graph of discrete point sets. An optimized model for accurate solution is established, achieving a precise solution to the problem. Furthermore, an iterative algorithm for k-class clustering of a specified capacity is designed to solve the multi-class case. The model's solution can perfectly handle clustering problems of a specified capacity and effectively avoids problems such as spatial overlap and inclusion between classes.

[0035] 3. This invention transforms the 2-class specified capacity clustering problem into a network flow problem based on virtual source nodes, selected connection nodes, and a connected graph. A mature solution algorithm is then used to calculate the optimal solution. The optimal solution derived from the network flow model ensures that when the specified capacity cannot be perfectly partitioned by the node capacity, only one node needs to be partitioned. Attached Figure Description

[0036] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0037] Figure 1 This is a flowchart of the clustering method for specifying category capacity in Embodiment 1 of the present invention;

[0038] Figure 2 This is a schematic diagram of the pseudocode for the iterative solution algorithm in Embodiment 1 of the present invention;

[0039] Figure 3 This is a schematic diagram illustrating an example of establishing a discrete point connected graph in Embodiment 1 of the present invention;

[0040] Figure 4 This is a schematic diagram illustrating the principle of solving a clustering case with a specified capacity of 5-classes in Embodiment 1 of the present invention;

[0041] Figure 5 This is a clustering result diagram of the convex closure region case in Embodiment 1 of the present invention;

[0042] Figure 6 This is a clustering result diagram of the non-convex closure region case in Embodiment 1 of the present invention;

[0043] Figure 7 This is a schematic diagram of a connected graph in Embodiment 1 of the present invention;

[0044] Figure 8 This is a schematic diagram of the clustering system with specified category capacity in Embodiment 1 of the present invention;

[0045] Figure 9 This is a flowchart of the clustering method for specifying category capacity in Embodiment 2 of the present invention;

[0046] Figure 10 This is a schematic diagram of the clustering system with specified category capacity in Embodiment 2 of the present invention.

[0047] In the diagram: 100, Connectivity Graph Establishment Module; 101, Access and Construction Module; 200, Connectivity Relationship Determination Module; 300, Initial Point Selection Module; 400, Network Flow Model Establishment Module; 500, Iterative Solution Module. DETAILED DESCRIPTION

[0048] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments. By this, the implementation process of how to apply technical means to solve technical problems and achieve technical effects of the present application can be fully understood and implemented.

[0049] Those of ordinary skill in the art can understand that all or part of the steps in the above-mentioned embodiment methods can be completed by programs instructing related hardware, therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment in the form of combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer usable program codes.

[0050] Embodiment one

[0051] Please refer to Figure 1 and Figure 7 , which show a clustering method of specifying category capacity of the embodiment one of the present application, including the following steps:

[0052] S1, a connected graph is established according to the spatial coordinate information of the discrete point set to be clustered, and it is required that there is a connected path between any two discrete points. The discrete point set is a discrete point set with capacity attribute, which is composed of a plurality of discrete points containing coordinate information and corresponding capacity size. At the same time, as a clustering hyperparameter, the clustering task will specify the number of categories to be clustered and the capacity corresponding to the category. This clustering method of specifying category capacity can divide the discrete points into a specified number of categories according to the capacity requirement of each category, and ensure that each category corresponds to a specified category capacity value.

[0053] The connected graph includes a node set, an edge set, and a cost on the edge set. The node set is composed of coordinate points of block centroids of mining fields or waste dumps. The edge set is composed of adjacent relationships in line segments with nodes as endpoints. The cost on the edge set is calculated by the Euclidean distance between the two endpoints. A virtual source point is introduced in the connected graph to ensure the flow conservation of the discrete point set.

[0054] In this embodiment, the discrete point set is X, each point in the set is denoted as x i , and the capacity of each point is denoted as v i . The specified number of categories is k, and the capacity of each specified category is t i , i = 1, 2, …, k. In order to establish a connected graph on the discrete point set X, it is necessary to establish the connection relationship between points in the discrete point set.

[0055] Generally, it is assumed that the distribution of discrete points is relatively uniform in a local area, so when determining the connectivity between a point i and the remaining discrete points, the m points with the smallest Euclidean distance between them are selected, and edges between these m points and point i are added, and there are no edges between the remaining points and i. Thus, a connected graph G(X, E) on the discrete point set X is established.

[0056] In order to make the results of the next stage of the network flow model completely separate the two parts of the region in space, the cost function of the edges in the constructed connected graph is relied on. For each edge (x i ,x j ) in the connected graph, x i ,x j are two points on the edge, such as the starting point and the ending point, or the starting point to any point on the edge, and the length of the edge is the Euclidean distance between the two endpoints: ||x i -x j ||2, which is used as the cost function c ij of the edge (i, j), which can ensure that when solving the subsequent model, the flow value from the source point will preferentially go to the nearest adjacent node, thereby ensuring the connectivity of the region as a whole.

[0057] Exemplarily, Figure 3 A connected graph example is provided, which is established on 2500 discrete points. As can be seen from the graph, the directly constructed connected graph has obvious local connectivity, that is, when a node i is connected to a set S i of m other nodes, the node j in S i is also likely to be connected to the set S i \{j}∪{i}.

[0058] S2, determining the connectivity between any two discrete point sets in the connected graph and calculating the cost, comprising:

[0059] S21, establishing an edge between any two discrete points in the discrete point set;

[0060] S22, calculating the cost function of the edge between any two discrete points in the discrete point set;

[0061] S3, selecting the initial points of the two nodes connected to the virtual source point in the 2-class specified capacity clustering according to the two-point selection algorithm, and the 2-class specified capacity clustering initial point selection algorithm selects two nodes connected to the virtual source point according to the maximum Euclidean distance between the nodes in the connected graph or the maximum distance in the connected graph, thereby ensuring that there is no category interlacing in the subsequent algorithm.

[0062] The two-point selection algorithm is to select the two points with the maximum Euclidean distance based on the Euclidean distance of the discrete points.

[0063] Arbitrarily selecting initial points for 2-class clustering with a specified capacity can lead to overlapping or region containment in the clustering results. To avoid overlapping, the initial points should be as far apart as possible, while to avoid region containment, the initial points should be located as close as possible to the boundaries of the discrete point closure.

[0064] Therefore, two selection algorithms are given for the initial points of 2-class clustering with specified capacity:

[0065] Method 1: Select the two points with the largest distance based on the Euclidean distance between discrete points;

[0066] Method 2: Select the two points with the largest distance on the connected graph.

[0067] Both methods have their advantages and disadvantages when dealing with practical problems. Method 1 is computationally simple, requiring only the identification of the index corresponding to the maximum value in the Euclidean distance matrix of discrete points; while Method 2 requires calculating the shortest path for all pairs of points in the connected graph and finding the longest shortest path (i.e., the diameter of the graph) to determine these two initial points. The time complexity of the algorithm for finding the graph diameter is O(n^2). 3 The solution time is too long. However, Method 1 is only applicable to the case where the closure is a convex region, while Method 2 can be applied to the case where the closure is a convex region as well as some non-convex regions. For the case of some non-convex regions, the initial point selected by Method 1 will still result in the case where the spatial region of a certain class with a specified capacity is multi-connected, but Method 2 can completely avoid the occurrence of this case.

[0068] S4. Based on the connected graph and initial points, establish a network flow model for 2-class clustering with specified capacity. This transforms the 2-class clustering task into a network flow problem with two source points. The capacity corresponding to each class flows out from the source points, and the capacity is allocated to different points in the space through the connected graph. Simultaneously, the cost of the network flow model ensures that the capacity allocation results in two connected regions in the space.

[0069] Assuming the selected initial points are i0, j0, we will continue to use the notation given in steps 1 and 2, where k = 2, and the specified capacities for the two categories are t1 and t2, respectively. Based on the connected graph constructed in step S1, we add two virtual source points s1 and s2, and add two virtual edges (s1, i0) and (s2, j0) connecting the source points to the initial points of the connected graph. For node i, its out-degree set is denoted as:

[0070] V + (i)={j∈V|(i,j)∈E}

[0071] Its in-degree set is denoted as:

[0072] V - (i)={j∈V|(j,i)∈E}

[0073] Two specified capacities can be viewed as two streams flowing out from two source points. 2-class specified capacity clustering can be seen as a process of gradually filling all discrete points within the region through two selected initial points. Each time a new discrete point i flows into the current stream, the current stream will preferentially use the capacity v of that discrete point. i Once filled, it flows to the next point closest to the source.

[0074] Let the size of the k-th flow on edge (i,j) be:

[0075]

[0076] Therefore, the model needs to satisfy the following constraints:

[0077]

[0078]

[0079] Condition (1) restricts the flow value remaining at each discrete point to not exceed its capacity limit; condition (2) ensures that the inflow of each category of flow value at all points except the source point is greater than the outflow, which is a necessary condition to ensure that there is no overlap in the results. Meanwhile, it is assumed that the flow values ​​flowing from the virtual source point s1 into i0 through edge (s1, i0) are all of the first type and have a size of t1; the flow values ​​flowing from the virtual source point s2 into j0 through edge (s2, j0) are all of the second type and have a size of t2. Therefore, it can be guaranteed that the optimal solution obtained by the model satisfies the requirements of the 2-category specified capacity clustering problem.

[0080] The network flow model for 2-category capacity clustering is expressed as follows:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] S5. Solve the k-class clustering problem with a specified capacity by iteratively using a network flow model of 2-class clustering with specified capacity. Design an iterative algorithm for k-class clustering with specified capacity, transforming the k-class clustering task into a k-1-time 2-class clustering task. Through the iterative algorithm, the clustering scheme with specified capacity can be solved.

[0087] The iterative algorithm of k-class specified-capacity clustering can be converted into a network flow model implementation of 2-class specified-capacity clustering with k-1 iterations, and the optimal solution of the calculation problem is obtained.

[0088] The k-class specified-capacity clustering problem can be solved by designing an iterative 2-class specified-capacity clustering algorithm. In each iteration step, the k specified capacities t1,..., tk are divided into two parts, and the two parts are connected to the virtual source point and the two selected nodes, respectively. k The sum is two:

[0089]

[0090] The clustering results of class 1 are given by using the network flow model of 2-class specified-capacity clustering given in step S4. Repeat the above iteration to solve classes 2 to k. The pseudo code of the iterative solution algorithm is shown in Figure 2 .

[0091] Figure 4 The principle diagram of the iterative algorithm in solving a 5-class specified-capacity clustering case implementation is shown, Figure 5 The clustering effect diagram of the case. Figure 6 The solution result diagram of the iterative algorithm using method 2 to select the initial point for a closed non-convex case.

[0092] The network flow model of 2-class specified-capacity clustering converts the 2-class specified-capacity clustering problem into a network flow problem according to the virtual source point, the selected connection point and the connected graph, and solves it through a mature solution algorithm to obtain the optimal solution of the problem. The optimal solution obtained based on the network flow model ensures that when the specified capacity cannot be perfectly divided by the node capacity, only one node needs to be split.

[0093] Please refer to Figure 8 The embodiment also provides a system applied to the clustering method with specified class capacity, which comprises:

[0094] The connected graph establishing module 100 is used to establish a connected graph according to the spatial coordinate information of the discrete point set to be clustered;

[0095] The connected relationship determining module 200 is used to determine the connected relationship between any two discrete point sets in the connected graph and calculate the cost;

[0096] The initial point selecting module 300 is used to select the initial point of the two nodes connected to the virtual source point in the 2-class specified-capacity clustering according to the two-point selection algorithm;

[0097] The network flow model establishing module 400 is used to establish a network flow model of 2-class specified-capacity clustering according to the connected graph and the initial point.

[0098] The iterative solution module 500 is used for iteratively solving a k-class specified capacity clustering problem from a 2-class specified capacity clustering network flow model.

[0099] The embodiment establishes a topological structure of a discrete point set, i.e., a network graph of a connected graph, according to spatial coordinate information of the discrete points. The graph distance is used to replace the Euclidean distance for clustering, and an iterative algorithm is designed to realize the clustering of a special clustering task with a specified class capacity.

[0100] By converting the clustering problem with a specified class capacity into a multi-step network flow model problem, a clustering scheme meeting the class capacity requirement can be solved. At the same time, thanks to the superiority of the connected graph structure, the use of the distance on the connected graph instead of the Euclidean distance can solve the non-convex or obstacle space containing situation that cannot be handled by the traditional clustering method. Moreover, the multi-step network flow model ensures that the number of points that need to be cut is less than or equal to k-1 when dealing with the case that the specified capacity is not completely divisible on the discrete points, which is also not achieved by the traditional clustering algorithm.

[0101] Embodiment two

[0102] Please refer to Figure 9 , a specified class capacity clustering method of the embodiment two of the present application is shown, which comprises the following steps:

[0103] S1, a connected graph is established according to the spatial coordinate information of the discrete point set to be clustered, the discrete point set is a discrete point set with a capacity attribute, and the discrete point set is composed of a plurality of discrete points containing coordinate information and corresponding capacity sizes.

[0104] S11, each connected branch between the discrete points in the connected graph is accessed one by one, and an edge between the discrete point and other connected branches is individually constructed. The edge is still constructed by connecting any two discrete points in the discrete point set, which ensures that the finally generated connected graph is single-connected, can avoid the situation that the directly generated connected graph has multiple connected branches, and improves the accuracy of the connected graph.

[0105] The connected graph includes a node set, an edge set, and a cost on the edge set; the node set is composed of coordinate points of block centers of the mining or dump sites; the edge set is composed of lines with adjacent relationships between the nodes as end points; the cost on the edge set is calculated by the Euclidean distance between the two end points; and a virtual source point is introduced in the connected graph to ensure the flow conservation of the discrete point set.

[0106] S2, the connected relationship and the cost between any two discrete point sets in the connected graph are determined, which includes:

[0107] S21, establish edges formed by connecting any two discrete points in the discrete point set;

[0108] S22, calculate a cost function of the edges formed by any two discrete points in the discrete point set;

[0109] S3, select initial points of two nodes connected with the virtual source point in the 2-class specified capacity clustering according to a two-point selection algorithm.

[0110] The two-point selection algorithm is to select two points with the largest distance based on the Euclidean distance of the discrete points.

[0111] S4, establish a network flow model of the 2-class specified capacity clustering according to the connected graph and the initial points;

[0112] S5, iteratively solve the k-class specified capacity clustering problem from the network flow model of the 2-class specified capacity clustering.

[0113] Please refer to Figure 10 The embodiment also provides a system applied to the clustering method with the specified class capacity, which comprises:

[0114] The connected graph establishing module 100 is configured to establish a connected graph according to spatial coordinate information of the discrete point set to be clustered;

[0115] The access and construction module 101 is configured to access each connected branch between the discrete points in the connected graph one by one, and construct edges between the discrete points and other connected branches separately;

[0116] The connected relationship determining module 200 is configured to determine the connected relationship between any two discrete point sets in the connected graph and calculate a cost;

[0117] The initial point selecting module 300 is configured to select initial points of two nodes connected with the virtual source point in the 2-class specified capacity clustering according to a two-point selection algorithm.

[0118] The network flow model establishing module 400 is configured to establish a network flow model of the 2-class specified capacity clustering according to the connected graph and the initial points;

[0119] The iterative solving module 500 is configured to iteratively solve the k-class specified capacity clustering problem from the network flow model of the 2-class specified capacity clustering.

[0120] In the embodiment, exemplary, Figure 2An example of a connected graph built on 2500 discrete points is provided. As can be seen from the graph, the directly constructed connected graph has obvious local connectivity, i.e. a node i is connected to a set S i of m other nodes, and the node j in S i is also connected to the set S i \{j}∪{i} with a high probability. Therefore, for the directly generated connected graph, there may be a situation of multi-connected branches. In order to deal with this situation, after the connected graph is generated, each connected branch in the connected graph is accessed one by one, and edges between the remaining other connected branches are constructed separately to ensure that the finally generated connected graph is single-connected.

[0121] Embodiment Three

[0122] Please refer to Figure 1 , which shows a clustering method for specifying the capacity of a category according to an embodiment of the present application, including the following steps:

[0123] S1, a connected graph is established according to the spatial coordinate information of a discrete point set to be clustered, the discrete point set being a discrete point set having a capacity attribute, the discrete point set being composed of a plurality of discrete points including coordinate information and corresponding capacity sizes;

[0124] The connected graph includes a node set, an edge set, and a cost on the edge set; the node set is composed of coordinate points of block centers of a mining site or a dump site; the edge set is composed of lines with adjacent relationships between nodes as end points; the cost on the edge set is calculated by the Euclidean distance between the two end points; a virtual source point is introduced in the connected graph to ensure the flow conservation of the discrete point set.

[0125] S2, the connected relationship and the cost between any two discrete point sets in the connected graph are determined, including:

[0126] S21, an edge formed by connecting any two discrete points in the discrete point set is established;

[0127] S22, a cost function of the edge formed by any two discrete points in the discrete point set is calculated;

[0128] S3, two initial points of two nodes connected to the virtual source point in the 2-category specified capacity clustering are selected according to a two-point selection algorithm.

[0129] The two-point selection algorithm is: selecting the two points with the largest distance based on the connected graph.

[0130] Randomly selecting the initial points of the 2-category specified capacity clustering may cause the clustering results to be interleaved or the regions to be included. To avoid the interleaving situation, the initial points need to be as far apart as possible, and to avoid the region inclusion situation, the initial points need to be located as close to the boundary of the discrete point closure as possible.

[0131] Therefore, two selection algorithms are given for the initial points of 2-class clustering with specified capacity:

[0132] Method 1: Select the two points with the largest distance based on the Euclidean distance between discrete points;

[0133] Method 2: Select the two points with the largest distance on the connected graph.

[0134] Both methods have their advantages and disadvantages when dealing with practical problems. Method 1 is computationally simple, requiring only the identification of the index corresponding to the maximum value in the Euclidean distance matrix of discrete points; while Method 2 requires calculating the shortest path for all pairs of points in the connected graph and finding the longest shortest path (i.e., the diameter of the graph) to determine these two initial points. The time complexity of the algorithm for finding the graph diameter is O(n^2). 3 The solution time is too long. However, Method 1 is only applicable to the case where the closure is a convex region, while Method 2 is applicable to the case where the closure is a convex region and some non-convex regions. For the case of some non-convex regions, the initial point selected by Method 1 will still result in the case where the spatial region of a certain class with a specified capacity is multi-connected, but Method 2 can completely avoid the occurrence of this case.

[0135] S4. Based on the connected graph and initial points, establish a network flow model with 2-class clustering of specified capacity;

[0136] S5. Iteratively solve the k-class clustering problem using a network flow model with 2-class specified capacity clustering.

[0137] In this embodiment, the two-point selection algorithm is as follows: select the two points with the largest distance on the connected graph. This method can be applied to the case where the closure is a convex region and a partially non-convex region. For the case of a partially non-convex region, the initial point selected by method 1 will still result in the case where the spatial region of a certain category with a specified capacity is multi-connected. However, method 2 can completely avoid the occurrence of this situation.

[0138] This invention transforms a clustering problem of specified capacity into a network flow problem by constructing a connected graph of discrete point sets. An optimized model for accurate solution is established, achieving a precise solution to the problem. Furthermore, an iterative algorithm for k-class clustering of specified capacity is designed to solve the multi-class case. The solution scheme perfectly handles clustering problems of specified capacity and effectively avoids problems such as spatial overlap and inclusion between classes.

[0139] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0140] The above embodiments have been described in detail, and the principles and embodiments of the present application have been described by applying specific examples. The above examples are only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, according to the idea of the present application, the specific embodiments and application scope will be changed, and the above description should not be understood as a limitation of the present application.

Claims

1. A clustering method with a specified class capacity, characterized in that, The clustering method described is applied to the open-pit mine spoil transportation scenario. The process includes the following: A connected graph is constructed based on the spatial coordinate information of the discrete point set to be clustered; the connected graph includes a node set, an edge set, and the cost on the edge set; the node set consists of the coordinate points of the centroid of the block in the mining area or spoil heap; the edge set consists of line segments with nodes as endpoints that have adjacency relationships; the cost on the edge set is calculated by the Euclidean distance between the two endpoints. Determine the connectivity between any two discrete point sets in a connected graph and calculate the cost; The initial points of two nodes connected to the virtual source point in a 2-category cluster of specified capacity are selected according to the two-point selection algorithm. The two-point selection algorithm is: selecting the two points with the largest distance on the connected graph. Based on the connected graph and initial points, construct a network flow model with 2-class clustering of specified capacity, including: Assuming the selected initial points are i0 and j0, and the specified capacities for the two categories are t1 and t2 respectively, two virtual source points s1 and s2 are added to the connected graph, and two virtual edges (s1, i0) and (s2, j0) are added connecting the source points to the initial points of the connected graph. The out-degree set of the discrete point i is denoted as: V + (i)={j∈V|(i,j)∈E} The in-degree set is denoted as: V − (i)={j∈V|(j,i)∈E} The two specified capacities are viewed as two streams flowing out from two virtual source points s1 and s2, respectively. 2-class specified capacity clustering is seen as a process of gradually filling all discrete points within the region through two selected initial points i0 and j0. Each time a new discrete point i is inflowed, the current stream will preferentially fill that discrete point's capacity v. i The flow fills the edge and then flows to the next point closest to the source. Let the size of the k-th flow on edge (i,j) be denoted as . Then the constraints of the network flow model are: （1） Among them, condition (1) restricts the size of the flow value left at each discrete point from exceeding its capacity limit; condition (2) ensures that the inflow of each type of flow value at all points except the source point is greater than the outflow, which is a necessary condition to ensure that there is no overlap in the results. Assume that the flow values ​​from virtual source node s1 into i0 via edge (s1, i0) are all of type 1 and have a size of t1; and the flow values ​​from virtual source node s2 into j0 via edge (s2, j0) are all of type 2 and have a size of t2. Then the network flow model of 2-class specified capacity clustering is expressed as follows: In the formula, c ij Let (i,j) be the cost function of edge (i,j); v is the size of the k-th flow on edge (j,i); i Let i be the capacity of the discrete point i; The flow values ​​from virtual source node s1 into i0 through edge (s1, i0) are all of the first type. The flow values ​​from the virtual source node s1 into i0 through the edge (s1, i0) are all of the second type. The flow values ​​from the virtual source node s2 into j0 through the edge (s2,j0) are all of the second type. The flow values ​​from the virtual source node s2 into j0 through the edge (s2,j0) are all of the first type. The k-class specified capacity clustering problem is solved iteratively using a network flow model with 2-class specified capacity clustering.

2. The clustering method according to claim 1, characterized in that: The discrete point set is a set of discrete points with capacity attributes. The discrete point set consists of several discrete points that contain coordinate information and their corresponding capacity size.

3. The clustering method according to claim 1, characterized in that: The virtual source point is introduced into the connected graph to ensure the conservation of flow for the set of discrete points.

4. The clustering method according to claim 1, characterized in that: The step of establishing a connected graph based on the spatial coordinate information of the discrete point set to be clustered also includes visiting the connected branches between each discrete point in the connected graph one by one, and constructing the edges between the discrete point and other connected branches separately.

5. The clustering method according to claim 1, characterized in that: The process of determining the connectivity between any two discrete point sets in a connected graph and calculating the cost includes: Establish the edge formed by connecting any two discrete points in the set of discrete points; Calculate the cost function of the edge formed between any two discrete points in a set of discrete points.

6. The clustering method according to claim 1, characterized in that: The two-point selection algorithm is as follows: select the two points with the largest distance based on the Euclidean distance between discrete points.

7. A system for clustering a specified category capacity according to any one of claims 1-6, characterized in that, include: A connected graph establishment module (100) is used to establish a connected graph based on the spatial coordinate information of the discrete point set to be clustered. A connectivity determination module (200) is used to determine the connectivity relationship between any two discrete point sets in a connected graph and calculate the cost. An initial point selection module (300) is used to select the initial points of two nodes connected to the virtual source point in a 2-category specified capacity cluster according to a two-point selection algorithm; A network flow model building module (400) is used to build a network flow model with 2-class specified capacity clustering based on the connected graph and the initial point; An iterative solution module (500) is used to iteratively solve a k-category specified capacity clustering problem using a network flow model with 2-category specified capacity clustering.

8. The system according to claim 7, characterized in that, The system further includes an access and construction module (101), which is used to access the connected branches between discrete points in the connected graph one by one and construct the edges between discrete points and other connected branches separately.

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