Spatial aggregation detection method for large-scale disease data

Abstract

The invention discloses a spatial aggregation detection method for large-scale disease data, and the method comprises the following specific steps: A, dividing a to-be-detected region into a plurality of geographic units, carrying out the modeling of the to-be-detected region into an undirected graph structure based on the geographic units, and creating an adjacent matrix; b, constructing a candidate scanning window set of each geographic unit based on an adjacent constraint control mechanism and a low-risk region elimination mechanism; c, searching a maximum likelihood cluster in the scanning window set based on a spatial search mechanism of the scanning window and taking the maximum likelihood cluster as a candidate result; and D, carrying out Monte Carlo simulation test and statistical significance analysis on the maximum likelihood cluster in the candidate results obtained in the step C, and selecting the aggregation region conforming to a set significance threshold as the aggregation region. According to the method, the accuracy and the detection efficiency of disease space aggregation detection under large-scale geographic data and fine scale can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of spatial clustering detection of diseases, and specifically to a spatial clustering detection method for large-scale disease data based on an improved FleXScan algorithm, which is used to efficiently identify abnormal disease clustering patterns in large-scale geographical areas and assist in epidemic early warning and prevention and control. Background Art

[0002] The purpose of detecting the spatial clustering of diseases is to identify whether there is a clustering phenomenon of the disease and to locate the areas where these clusters occur. This technology is of great significance for further identifying clues to the cause of the disease and effectively formulating disease prevention and control strategies. In recent years, spatial scanning statistics methods have been widely used in the field of epidemiology to detect disease clustering and have played an important role in public health research. Spatial scanning statistics methods mainly include the SaTScan method based on a circular scanning window and the FleXScan method based on a free-form scanning window, depending on the shape of the scanning window. The SaTScan method uses a circular scanning window to detect clustered areas and is suitable for more regular disease clustering patterns. However, when the disease cluster area presents a complex shape, the circular scanning window may lead to missed detections. The FleXScan method uses a free-form scanning window and can detect clustered areas of any shape, thus overcoming the limitations of the traditional circular window and having more advantages in the accuracy of clustering results.

[0003] The basic principle of the FleXScan algorithm is to dynamically generate a free-form scanning window. By analyzing the number of cases within the scanning window, it can identify unusual spatial clusters (such as infectious disease outbreak hotspots or cancer hotspots). This method has the advantage of being able to adapt to irregular disease distribution patterns, such as disease clusters along rivers or transportation routes, avoiding the under-detection problem of traditional circular window methods. Although the FleXScan method can effectively identify complex disease clusters, it faces certain challenges when processing large-scale geographic data. The traditional FleXScan algorithm uses an exhaustive search strategy to search subsets, which leads to an exponential increase in computational complexity. In particular, as the core parameter K (representing the maximum number of basic geographic units that the scanning window can contain) increases, the number of scanning windows required for calculation increases dramatically, resulting in low computational efficiency when processing large-scale data and becoming a performance bottleneck. Therefore, the FleXScan algorithm is difficult to scale to large-scale data. Improved algorithms are urgently needed to optimize computational efficiency and achieve spatial cluster detection in large-scale disease data. Summary of the Invention

[0004] The purpose of the present invention is to provide a spatial clustering detection method for large-scale disease data, which can effectively improve the accuracy and efficiency of disease spatial clustering detection under large-scale geographic data and fine scale.

[0005] The present invention adopts the following technical solutions:

[0006] A spatial clustering detection method for large-scale disease data includes the following specific steps:

[0007] A: Divide the area to be detected into several geographical units, model the area to be detected as an undirected graph structure based on the geographical units, and create an adjacency matrix;

[0008] B: Based on the proximity constraint control mechanism and the low-risk area elimination mechanism, a set of candidate scanning windows is constructed for each geographic unit;

[0009] C: A spatial search mechanism based on the scanning window, which searches for the maximum likelihood cluster in the scanning window set and takes it as the candidate result;

[0010] D: Perform Monte Carlo simulation test and statistical significance analysis on the maximum likelihood clusters in the candidate results obtained in step C, and select the clustering area that meets the set significance threshold as the clustering area.

[0011] In step B, based on the proximity constraint control mechanism, the members in each scanning window are limited to several adjacent geographical units with the shortest distance from the central unit, and low-risk areas are eliminated from the candidate scanning windows based on the risk threshold, thus obtaining a set of candidate scanning windows for each geographical unit.

[0012] Step B includes the following specific steps:

[0013] B1: Design a method for constructing local scanning window sets based on adjacency graph;

[0014] For each geographic unit, according to the connection relationship of the geographic unit in the adjacency graph, a set of scanning windows that meet the set window size constraints are constructed with the geographic unit as the central unit.

[0015] B2: Constructing proximity constraint control of scanning window based on Euclidean distance;

[0016] Each scanning window is limited to the geographical unit and the k-1 geographical units closest to it in the adjacency graph, forming a subgraph containing k nodes, which is recorded as the scanning window Z i ,k;

[0017] B3: Establish a mechanism to eliminate low-risk areas based on risk thresholds;

[0018] For each geographic unit, the ratio of the number of observed cases to the expected number of cases is used as the risk ratio. If the risk ratio of a geographic unit is less than the threshold, the geographic unit is considered a low-risk area; otherwise, it is considered a high-risk area. Low-risk areas are not included in the construction of the scanning window as central units and are not included as adjacent geographic units in other scanning windows.

[0019] B4: Using the proximity constraint control mechanism and the low-risk area elimination mechanism, a local scanning window set construction method based on the adjacency graph is used to merge the local scanning window sets generated by all geographic units to form a candidate scanning window set.

[0020] In step C, all possible connected region subsets are searched within each candidate scanning window, and the scores corresponding to the connected region subsets are calculated using the set scoring function; and among all scanning windows and their corresponding connected region subsets, the connected region subset with the largest score is selected as the globally optimal abnormal region, that is, the maximum likelihood cluster as the candidate result.

[0021] Step C includes the following steps:

[0022] C1: Construct a likelihood function based on the Poisson model and combine it with the log-likelihood ratio to construct a likelihood ratio score function;

[0023] C2: Combining the seed node selection mechanism, linear time subset scanning properties and connectivity screening, the maximum likelihood cluster is screened within the scan window in the candidate scan window set, and the maximum likelihood cluster is used as the candidate result.

[0024] Step C2 includes the following steps:

[0025] C21: Seed node selection based on priority function;

[0026] If the priority value of a node, i.e., the risk ratio, is greater than the priority values ​​of all its adjacent nodes, then the node is used as a seed node, and all seed nodes in each candidate scan window are obtained;

[0027] C22: Based on the obtained seed nodes, a local subgraph of all seed nodes is constructed through priority elimination and connectivity screening;

[0028] That is, remove all nodes in the scan window whose priority values ​​are higher than the priority value of the seed node and their first-order adjacent nodes, and construct the local subgraph corresponding to the seed node based on the set of all nodes connected to the seed node among the remaining nodes;

[0029] C23: Using the linear time optimal subset identification method based on LTSS, the optimal subset of linear complexity, i.e. maximum likelihood cluster identification, is performed in each local subgraph, and the maximum likelihood cluster is used as the candidate result.

[0030] In step C2, during the search process of the maximum likelihood cluster in the local search and global optimization phases, the connectivity of the subsets is determined based on the union-find set.

[0031] In step C23, identifying the optimal subset of linear complexity includes the following steps:

[0032] First, sort the nodes and sort all nodes in descending order according to their priority values;

[0033] Then, prefix subset evaluation is performed. Starting from the empty set, nodes are added to the current subset in sequence, and the LLR (log-likelihood ratio) score of the corresponding subset is calculated.

[0034] Finally, the maximum scoring subset is determined, and the subset with the largest LLR value among all prefix subsets is selected as the maximum likelihood cluster in the current local subgraph and as the candidate result.

[0035] The connectivity judgment of subsets based on union-find set judgment includes the following steps:

[0036] (1) Perform subset initialization; each node in the candidate subset is considered as an independent set for initialization;

[0037] (2) Constructing adjacency relationships and performing set merging; traversing all nodes in the candidate subset, and judging the adjacent nodes of each node: if the node and its adjacent nodes also belong to the current subset, then performing a merge operation on the node and its adjacent nodes in the union-check set;

[0038] (3) Perform connectivity judgment; perform a root node search operation on all nodes in the subset. If all nodes have the same root node, it means that the subset is connected; otherwise, it is a non-connected subgraph.

[0039] The structure of the union-find set is optimized through path compression and rank-merge optimization strategies.

[0040] The present invention effectively avoids the computational overhead caused by exponential subset enumeration through a specially designed and combined seed node selection mechanism, linear time subset scanning property (LTSS) and union-find structure, reducing the complexity of the entire maximum likelihood cluster (MLC) search process to a near-linear level. Compared with the traditional FleXScan algorithm that uses an exhaustive approach to search for connected subsets, the computational efficiency is significantly improved, and it is particularly suitable for practical application scenarios with a wide geographical range and a large number of nodes.

[0041] The present invention also ensures the spatial coherence of the constructed scanning window through proximity constraint control and risk threshold mechanism; and introduces connectivity judgment in the identification of maximum likelihood clusters to avoid the generation of disconnected abnormal clustering areas, thereby enhancing the spatial explanatory power and reliability of the recognition results and ensuring spatial connectivity and recognition accuracy.

[0042] The present invention also designs and optimizes the risk area identification strategy, based on the risk ratio evaluation mechanism of the number of cases / expected number of cases, and combines the threshold to eliminate low-risk areas, so that the identification of clustered areas is more focused on high-risk areas, avoiding noise interference and improving the accuracy of abnormality identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the process of the present invention;

[0044] Figure 2 Schematic diagram of a node of an area to be detected including 18 geographical units in an embodiment;

[0045] Figure 3 This is a schematic diagram of a scanning window created with node 1 as the central unit in the embodiment;

[0046] Figure 4 Schematic diagram of the traditional FleXScan algorithm processing the scanning window;

[0047] Figure 5 Schematic diagram of the optimized FleXScan algorithm of the present invention using seed nodes to process the scan window. DETAILED DESCRIPTION

[0048] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. In the following description, when referring to the drawings, identical numerals in different figures represent identical or similar elements, unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all possible embodiments consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present disclosure, as detailed in the appended claims.

[0049] The present invention is described in detail below with reference to the accompanying drawings and embodiments:

[0050] like Figure 1 As shown, the spatial clustering detection method for large-scale disease data of the present invention includes the following specific steps in sequence:

[0051] A: Divide the area to be inspected into N geographic units, model the area to be inspected as an undirected graph structure G = (V, E) based on the geographic units, and create an adjacency matrix;

[0052] Where V represents the node set, E represents the edge set; each node corresponds to a geographical unit; the edges between nodes represent the spatial adjacency relationship between geographical units;

[0053] In this paper, adjacency is determined using the "shared vertex (Queen adjacency rule)" rule. This means that two geographic units are considered adjacent when they share at least one vertex in geographic space, and an undirected edge is established between the two corresponding nodes. By traversing the boundary vertices of all geographic units, a complete edge set E is generated to support subsequent connectivity determination and cluster area detection.

[0054] To accurately describe the spatial location of nodes, this method uses the spatial coordinates of the center point of each geographic unit as a spatial reference, and uses an undirected graph structure to map the graph structure to the geographic space. This process transforms the problem of spatial cluster analysis into a graph problem, facilitating the use of graph algorithms in subsequent steps.

[0055] In this embodiment, after studying the area to be detected, the entire area to be detected can be divided into N geographical units (such as counties, towns, and villages). For each geographical unit, c i Represents the geographic unit r i The number of observed cases, p i Represents the population; the entire area to be detected is abstracted into a graph structure G, each geographic unit is abstracted as a node in the graph structure G, and each geographic unit is identified by the coordinates of the centroid of the geographic unit, where i = 1, 2, ..., N, where N is the total number of geographic units.

[0056] B: Based on the proximity constraint control mechanism and the low-risk area elimination mechanism, a set of candidate scanning windows is constructed for each geographic unit;

[0057] In the present invention, based on the proximity constraint control mechanism, the members in each scanning window are limited to several adjacent geographical units with the shortest distance from the central unit, and low-risk areas are eliminated from the candidate scanning windows based on the risk threshold, and finally a set of candidate scanning windows for each geographical unit is obtained; the above operation can effectively improve the effectiveness and computational efficiency of the candidate windows and ensure the spatial coherence between the geographical units in the scanning window.

[0058] Specifically, the step B includes the following specific steps:

[0059] B1: Design a method for constructing local scanning window sets based on adjacency graph;

[0060] In the present invention, for each geographical unit, according to the geographical unit r i The connection relationship in the adjacency graph is based on the geographical unit r iA set of scanning windows is constructed for the central unit (i.e., center) expansion;

[0061] In this embodiment, the geographical unit r i The scanning window centered on is when constructing the scanning window, the geographic unit r i The unit contained in the corresponding window and used as the starting unit for window construction; the subsequent window space expansion construction process is based on this geographic unit r i Taking the window as the starting point, the window is gradually expanded to its spatially adjacent geographic units until the set window size constraint (i.e., proximity constraint) is met.

[0062] For the sake of convenience, the present invention will start with the geographical unit r i It is called the central unit. The size of the scanning window k represents the number of geographic units contained in the scanning window. The value of k ranges from 1 to the maximum window size K, that is, k = 1, 2, ..., K. The value of the maximum window value K is user input or preset. In the FleXScan algorithm, the upper limit of K is 30.

[0063] B2: Constructing proximity constraint control of scanning window based on Euclidean distance;

[0064] Each scanning window is defined by the geographic unit r i and the k-1 geographical units closest to it in the adjacency graph, forming a subgraph containing k nodes, which is recorded as the scanning window Z i ,k;

[0065] In the process of window construction, in order to ensure the compactness and spatial interpretation ability of the spatial clustering area, each scanning window Z is limited to i , the members in k must be within the distance r from the center unit i The k-1 adjacent geographical units with the smallest distance are controlled by proximity constraints. The minimum distance is measured based on the Euclidean distance, that is, according to the spatial distance between the centroids (or representative points) of the geographical units, all the reachable geographical units are sorted in ascending order and the first k-1 geographical units are selected to join the window. i Together they form the scanning window Z i ,k; the adjacent geographic unit is the unit that is adjacent to the central unit r in the adjacency graph. i Geographic units that are connected by paths are those that can be reached through a series of adjacency relationships. The Euclidean distance d(ij) can be determined by calculating the spatial coordinate difference between the centroids (or representative points) of two geographic units. The calculation method is:

[0066]

[0067] Among them, (x i ,y i ) and (x j,y j ) represent geographic units r i and geographic unit r j The coordinates of the center of mass of

[0068] Through proximity constraint control, not only can the computational efficiency be effectively improved, but the spatial coherence between geographic units within the scanning window can also be ensured, which helps to improve the spatial explanatory power of the final recognition results.

[0069] B3: Establish a mechanism to eliminate low-risk areas based on risk thresholds;

[0070] In order to further improve the effectiveness and computational efficiency of the candidate windows, the present invention designs a low-risk area elimination mechanism based on a risk threshold, which is used to eliminate low-risk areas during the scanning window construction process.

[0071] For each geographical unit, according to its number of observed cases c i and the expected number of cases E i Calculate the risk ratio R i =c i / E i , E i =C*p i / P, C represents the total number of observed cases in the area to be detected, p i Represents geographic unit r i The population of the area to be detected, P represents the total population in the area to be detected; E i It can also be expressed as the product of the overall incidence rate and the population in the detection area.

[0072] Set the risk threshold δ (set to 0.2 in this embodiment) and set the risk ratio R i Compared with the set risk threshold δ, if the geographical unit y i The risk ratio R i If it is less than the threshold δ, then the geographic unit r i is a low-risk area, otherwise it is a high-risk area; for the geographical unit r corresponding to the low-risk area i ,During the scan window construction process, the following two culling rules are executed:

[0073] (1) No longer use this geographical unit r i Participates in the construction of the scanning window as a central unit;

[0074] (2) No longer use this geographical unit r i A geographical unit that serves as an adjacency to other scanning windows;

[0075] B4: Using the proximity constraint control mechanism constructed in step B2 and the low-risk area elimination mechanism constructed in step B3, the local scanning window sets generated by all geographic units are merged according to the local scanning window set construction method based on the adjacency graph in step B1 to finally form a candidate scanning window set, which is recorded as

[0076] C: A spatial search mechanism based on the scanning window, which searches for the maximum likelihood cluster in the scanning window set and takes it as the candidate result;

[0077] The present invention uses a spatial search mechanism based on a scanning window to identify the most significant abnormal clustering area in the space, namely the Maximum Likelihood Cluster (MLC), as follows:

[0078] First, a scoring function (such as the Log-Likelihood Ratio (LLR) function) is defined; this scoring function maps any subset of regions that meet the conditions to a real value to measure the clustering strength of any spatial region subset;

[0079] Then, multiple scanning window sets that satisfy the spatial adjacency constraints are constructed, and all possible connected region subsets are searched within each scanning window (i.e., local search). The score values ​​corresponding to the connected region subsets are calculated through the scoring function. Among all scanning windows and their corresponding connected region subsets, the connected region subset with the largest score value is selected (i.e., global optimization) as the globally optimal abnormal region, i.e., the maximum likelihood cluster is used as the candidate result.

[0080] For example, the FleXScan algorithm can be used to perform the above-mentioned spatial clustering detection. The FleXScan algorithm is widely used in the identification of complex shape clustering areas. Its basic process is as follows:

[0081] First, the scoring function is set: the log-likelihood ratio (LLR) is used as the objective function to evaluate the abnormal clustering intensity of the candidate region;

[0082] Then, a set of scanning windows is constructed and connected subsets are exhaustively enumerated: a scanning window of the adjacent area is constructed for each geographic unit; then, within each scanning window, all possible geographic unit subsets are enumerated, and connectivity is determined recursively, with scores calculated for all legal subsets; then, the subset with the highest score is selected as the maximum likelihood cluster for each window, and then the one with the highest score is selected globally as the abnormal cluster area.

[0083] Although the FleXScan algorithm can identify irregularly shaped clusters, its processing efficiency is heavily dependent on the number of subsets and the connectivity determination algorithm. In large-scale geographic data, the following problems exist:

[0084] 1. Subset exhaustion causes exponential computational overhead;

[0085] 2. Connectivity judgment relies on recursive methods, which is inefficient;

[0086] 3. The lack of effective subset screening strategy leads to serious redundant calculations.

[0087] To overcome the shortcomings of the above-mentioned FleXScan algorithm, the present invention makes the following improvements based on the traditional FleXScan algorithm framework:

[0088] (1) To address the defect of the traditional FleXScan algorithm that requires exhaustive enumeration of all subsets, the present invention adopts a seed node selection mechanism to screen the subset search starting point based on risk ratio priority, which can greatly reduce the search space and avoid invalid enumeration;

[0089] (2) Aiming at the defect of inefficient recursive connectivity judgment in the traditional FleXScan algorithm, the present invention introduces a union-find structure for fast connectivity judgment, which can reduce the complexity of connectivity judgment and improve the stability of the algorithm;

[0090] (3) To address the drawback of the traditional FleXScan algorithm that all subsets need to be scored during the subset screening process, the present invention applies the linear time subset scanning property (LTSS) to evaluate only the priority prefix subsets, which can reduce the search process from exponential to linear.

[0091] (4) Aiming at the defect of the traditional FleXScan algorithm in the rough identification of risk areas during the subset screening process, the present invention introduces a risk threshold mechanism for risk area identification, which can focus on high-risk areas and improve detection accuracy;

[0092] (5) In order to address the defect of large spatial window redundancy in the subset screening process of the traditional FleXScan algorithm, the present invention can effectively control the window size and improve the efficiency of local cluster detection by limiting the set of adjacent areas and eliminating low-risk nodes;

[0093] Based on the above improvements, the present invention can significantly improve the computational efficiency and recognition effect of the entire spatial clustering detection process by optimizing the subset search logic, connectivity judgment method and priority screening strategy without changing the basic framework of FleXScan. It is particularly suitable for spatial pattern recognition tasks of large-scale geographic data.

[0094] Specifically, in this embodiment, step C includes the following specific steps:

[0095] C1: construct likelihood ratio score function;

[0096] To measure whether a geographic unit has significant abnormal clustering, it is necessary to quantitatively evaluate the difference in case distribution between the geographic unit and its external geographic units. To this end, the present invention constructs a corresponding likelihood function based on the Poisson model and introduces the log-likelihood ratio (LLR) as a scoring function.

[0097] First, assume that the area to be detected is divided into N geographical units, and the i-th geographical unit r i The number of observed cases within c i and population p i The parameter is λ i The Poisson distribution of , then the probability density function of the Poisson distribution is:

[0098] Among them, λ i is the incidence rate, and the symbol ! represents factorial;

[0099] Then, hypothesis testing framework;

[0100] In this embodiment:

[0101] Null hypothesis H0: For all scanning windows Z, the incidence rates inside and outside the window are equal;

[0102] Alternative hypothesis H1: There exists at least one scanning window Z, where the incidence intensity inside the window is higher than that outside the window.

[0103] Finally, the likelihood function is constructed and the log-likelihood ratio is derived;

[0104] In this embodiment, under the null hypothesis, the incidence rate inside and outside the scanning window is the same, denoted as λ G ;

[0105] The global likelihood function is:

[0106] Perform logarithmic processing on the global likelihood function and obtain

[0107]

[0108] Under the alternative hypothesis H1, the incidence rates inside and outside the scanning window are different, denoted as λ Z and λ o ; then the likelihood function within the window is:

[0109] (i∈Z means that geographic unit i is within window Z)

[0110] The likelihood function outside the window is:

[0111] ( Indicates that geographic unit j is not within window Z)

[0112] Then the overall likelihood function is:

[0113]

[0114] Then perform logarithmic processing on the overall likelihood function and obtain

[0115]

[0116] Then the log-likelihood ratio formula, i.e. the likelihood ratio score function, is:

[0117] LLR=log L1-log L0

[0118] Right now:

[0119]

[0120] From the likelihood ratio score function above, it can be seen that the larger the LLR value, the more obvious the difference between inside and outside the window, that is, there is significant clustering within the window, and the subset with the largest LLR value is defined as the maximum likelihood cluster (MLC).

[0121] Based on the above derivation and judgment, the present invention adopts the log-likelihood ratio (LLR) as the aggregation scoring function, which has the following advantages:

[0122] (1) It can effectively measure the difference in case distribution inside and outside the window and reflect the intensity of abnormal clustering;

[0123] (2) The results have a statistically significant basis, which is convenient for subsequent significance testing;

[0124] (3) Supports combination with subset sorting and linear scanning methods to improve search efficiency.

[0125] Therefore, LLR is selected as the core scoring metric as the basic support for maximum likelihood cluster (MLC) identification.

[0126] C2: Combining the seed node selection mechanism, the linear time subset scanning property (LTSS) and connectivity screening, the maximum likelihood cluster is screened within the scan window in the candidate scan window set, and the maximum likelihood cluster is used as the candidate result;

[0127] In the scanning statistics method based on the FleXScan algorithm, in order to identify the most significant abnormal area (i.e., the maximum likelihood cluster MLC), it is usually necessary to exhaustively enumerate all possible connected subsets within a given scanning window and calculate the log-likelihood ratio (LLR) value for each subset.

[0128] As shown above, due to the exponential growth in the number of connected subsets, traditional methods have huge computational overhead in determining subset connectivity and calculating scoring functions, resulting in extremely low efficiency and difficulty adapting to the processing needs of large-scale spatial data. Therefore, this paper proposes an efficient maximum likelihood cluster (MLC) search method that combines a seed node selection mechanism, a linear time subset scanning property (LTSS), and an efficient connectivity determination structure (union-find set) to overcome the high computational cost of exhaustively enumerating all subsets in traditional methods, thereby efficiently and quickly screening maximum likelihood clusters (MLCs) as candidate results.

[0129] In this embodiment, step C2 includes the following specific steps:

[0130] C21: Seed node selection based on priority function;

[0131] In order to improve the search efficiency of Maximum Likelihood Clustering (MLC), the present invention introduces a seed node selection mechanism based on a priority function to identify representative starting nodes in the candidate window and avoid the computational cost caused by exhaustively enumerating all subsets.

[0132] Assume that the area to be detected is constructed as an undirected graph G = (V, E), V = {v1, v2, ..., v N} represents the node set corresponding to all geographic units, E represents the set of spatial adjacent edges between nodes; for each node v i ∈V; with node V i The number of observed cases c i and expected number of cases E i The ratio of the corresponding node V i The priority value (i.e., the risk ratio mentioned above) Pr(r i ), Pr(r i )=c i / E i ;

[0133] Among them, Pr(r i ) is larger, which means the number of cases in the unit population of the node is higher and the abnormality is greater;

[0134] If a node v i The priority value Pr(r i ) is greater than all its adjacent nodes N(v i ) priority value, then the node v i Mark as a seed node:

[0135]

[0136] Among them, N(v i ) represents node v i The set of adjacent nodes of ;

[0137] According to the above method, a number of seed nodes that meet the above conditions are obtained in each candidate scanning window, and in subsequent steps, the above seed nodes are used as starting points to construct its local search area.

[0138] C22: Based on the obtained seed nodes, a local subgraph of all seed nodes is constructed through priority elimination and connectivity screening;

[0139] That is: for each seed node v s , remove all nodes with a higher priority than the seed node v in the scan window s The node with the priority value and its first-order adjacent nodes, and remove all the remaining nodes that cannot be connected to the seed node v s The set of all connected nodes is based on the final set of retained nodes and the seed node V s Constitute the seed node v s The corresponding local subgraph G sub (v s )=(V sub (v s ),E sub );

[0140] After completing the selection of seed nodes, for each seed node v s , construct its local subgraph G sub (v s ), the steps are as follows:

[0141] C221: Based on the priority exclusion mechanism, remove all nodes with a priority value higher than the seed node v from the scan window. s Nodes with priority values ​​and their first-order adjacent nodes;

[0142] Specifically, let the current seed node be v s , its priority value is Priority(r s ), the exclusion set is:

[0143]

[0144] Step C221: using a priority elimination method to avoid multiple seed nodes from repeatedly covering the same area;

[0145] C222: Construct local subgraph of seed nodes;

[0146] In the elimination set V rm After that, we get the remaining node set V′=V\V rm ; In the remaining node set V′, keep the node with the same s The set of all connected nodes:

[0147] V sub (v s )={v i ∈V′|v i With the seed node v s The remaining nodes in the graph are connected};

[0148] The local subgraph of the seed node is finally obtained:

[0149] G sub (v s )=(V sub (v s ),E sub ); the subscript sub indicates local;

[0150] In step C222, the local subgraph G is obtained by using the connectivity screening method. sub (v s ) contains only the seed node v s Connected and non-excluded nodes ensure that the search process is carried out within the connected area dominated by the seed node;

[0151] Through the above steps, for each seed node v s Generate a corresponding local subgraph G sub , and all the local subgraphs obtained do not overlap with each other. The search process is only performed in the obtained local subgraphs, thus avoiding the exhaustive search of all possible connected subsets in the entire candidate window.

[0152] Compared with the traditional FleXScan algorithm that exhaustively enumerates all possible connected subsets in the candidate window, the present invention can effectively reduce the number of subsets that need to be evaluated by introducing priority functions and subgraph partitioning mechanisms, retaining only sub-regions with high epidemiological abnormalities, greatly reducing the number of subsets to be searched, thereby significantly improving search efficiency and reducing computing resource consumption.

[0153] C23: Using the LTSS-based linear time optimal subset identification method, the optimal subset of linear complexity, i.e., maximum likelihood cluster identification, is performed within each local subgraph, and the maximum likelihood cluster is used as the candidate result;

[0154] In C21 and C22, by identifying seed nodes and constructing corresponding local subgraphs, the spatial scope required for the Maximum Likelihood Clustering (MLC) search has been significantly reduced. To further improve search efficiency, this method introduces the Linear-Time Subset Scanning (LTSS) property to identify the optimal subset within each local subgraph with linear complexity, i.e., the subset with the highest likelihood ratio score.

[0155] According to the linear time subset scanning property, for a specific class of additive score functions (such as the log-likelihood ratio (LLR) function), under the premise of satisfying monotonicity and subset additivity, the subset with the largest score must be contained in a prefix set composed of the high-priority nodes accumulated in sequence.

[0156] In the present invention, the priority function is the node V in step C21 i The priority value Pr(r i ), Pr(r i )=c i / E i ; Based on the priority function, in each local subgraph G sub =(V sub ,E sub ) and perform the following operations:

[0157] First, sort the nodes and sort all nodes v in descending order according to the priority Pr(v). The sorted sequence [v1, v2, ..., v n ], where Pr(v1)≥Pr(v2)≥…≥,Pr(v n ); v∈V sub ;

[0158] Then perform prefix subset evaluation, starting from the empty set, and sequentially add nodes v i Add to the current subset and calculate the log-likelihood ratio (LLR) score of the corresponding subset, which is recorded as:

[0159]

[0160] Among them, L(H1(S k )) represents the subset S under the alternative hypothesis k The likelihood function of , L(H0) represents the likelihood function under the global hypothesis;

[0161] Finally, determine the maximum scoring subset, that is, select the subset S with the largest LLR value among all prefix subsets * , subset S * That is the maximum likelihood cluster (MLC) in the current local subgraph and is used as the candidate result;

[0162] S * =arg max k LLR(S k );

[0163] The traditional FleXScan algorithm requires enumerating all possible connected subsets in a connected graph, which has an exponential time complexity. However, in this invention, since each local subgraph only requires sorting the nodes once (O(nlogn)) and linearly scanning all prefix subsets (O(n)), the overall complexity is reduced to a near-linear level.

[0164] In summary, the introduction of LTSS simplifies the MLC search from an exponential subset enumeration problem to a linear subset construction process, greatly improving the computational efficiency of spatial clustering detection under large-scale data.

[0165] In step C2, during the search for the maximum likelihood cluster in the local search and global optimization phases, the connectivity of the subsets is determined based on the union-find set.

[0166] In spatial scanning statistics, the algorithm identifies the subset with the highest score (e.g., log-likelihood ratio, LLR) within the scanning window as a candidate anomalous cluster. To ensure the rationality of the spatial results, the identified subset must be a connected subgraph. Only connected subgraphs meet the actual definition of a spatial anomalous cluster. Even if the score is high, disconnected subsets are not considered valid clusters (usually containing one or more geographic units).

[0167] Therefore, connectivity assessment is a necessary condition for determining the effectiveness and legitimacy of cluster areas, and it is crucial in the following two stages:

[0168] Local search stage: only calculate the score for the connected subset;

[0169] Global optimization stage: During screening, ensure that the optimal clusters selected are also connected.

[0170] The accuracy of connectivity judgment directly affects the spatial rationality of the clustering area, the stability of the maximum likelihood estimation results, and the computational efficiency of the algorithm.

[0171] Traditional methods (such as FleXScan) use recursion to determine connectivity, which is inefficient and becomes a performance bottleneck, especially in large-scale data.

[0172] To this end, the present invention proposes a method for quickly judging the connectivity of subsets based on a union-find data structure, replacing the existing recursive judgment strategy, which specifically includes the following steps:

[0173] (1) Initialize the subset;

[0174] Number all nodes in the scan window and initialize each node in the candidate subset as an independent set, that is, the parent node of each node points to itself;

[0175] (2) Constructing adjacency relationships and performing set merging;

[0176] Traverse all nodes in the subset and judge the adjacent nodes of each node: if the node and its adjacent nodes also belong to the current subset, then perform a "merge" operation on the node and its adjacent nodes in the union-check set, indicating that the two nodes belong to the same connected component;

[0177] (3) Perform connectivity determination;

[0178] Perform the "find root node" operation on all nodes in the subset. If all nodes have the same root node, it means that the subset is connected; otherwise, it is a disconnected subgraph.

[0179] To improve efficiency, the union-find structure adopted introduces path compression and rank-merge optimization strategies to ensure that in the worst case the time complexity of the "merge-find" operation is an approximate constant O(α(N)), where α(N) is the inverse Ackermann function and grows very slowly.

[0180] By introducing a union-find structure, this paper optimizes the traditional connectivity judgment method at the algorithm level, effectively solving the problems of low recursive efficiency and poor scalability in the existing technology, and providing key support for the efficient operation of spatial scanning statistical algorithms in the context of big data.

[0181] D: Perform Monte Carlo simulation test and statistical significance analysis on the maximum likelihood clusters (MLCs) in the candidate results obtained in step C, and select the clustering areas that meet the set significance threshold as the clustering areas;

[0182] In spatial scanning statistical methods, clusters identified using the maximum likelihood ratio statistic may be caused by random fluctuations in the number of cases or by the failure of the null hypothesis. To determine whether a cluster is significant, statistical inference is necessary. Because the statistical distribution function under the null hypothesis cannot be theoretically derived, the present invention employs a Monte Carlo simulation method to perform significance testing and determine the statistical significance of the identified clusters.

[0183] Described step D comprises the following specific steps:

[0184] D1: Set the null hypothesis and model;

[0185] In this paper, the null hypothesis model is a nonparametric model in which the centroid locations of each subregion and their measured values ​​(used to determine case intensity) are known a priori. The null hypothesis assumes that the number of cases is randomly distributed across the subregions, and the probability of assigning a case to each subregion is proportional to its measured value.

[0186] D2: Conduct Monte Carlo simulation test;

[0187] (1) Randomly assign cases: In each simulation, the total number of observed cases is randomly assigned among all sub-regions according to the null hypothesis; the probability of assigning a case to each sub-region is proportional to its measured value.

[0188] (2) Calculate the maximum likelihood ratio statistic: After each allocation, calculate the maximum likelihood ratio (LLR) statistic value as a measure of the clustering area.

[0189] (3) Repeat the simulation:

[0190] Repeat the above steps M1 times to obtain M1 maximum likelihood ratio statistics. In this embodiment, the value of M1 is 4999.

[0191] (4) Conduct significance assessment:

[0192] The statistical values ​​obtained from the M1 simulations are ranked together with the maximum likelihood ratio statistical value of the real data. If the statistical value calculated from the real data ranks in the top M2, it is considered that the null hypothesis can be rejected under the significance threshold M3 significance level, and the identified cluster area is judged to be statistically significant. The corresponding geographical unit is regarded as the cluster area.

[0193] Among them, the value of M2 can be 250, The value of M3 can be 5%;

[0194] Monte Carlo simulation tests and significance analysis are conventional techniques in this field and will not be described in detail here. However, the present invention is based on Monte Carlo simulation tests and significance analysis. Through the above-mentioned improvements, the present invention can provide a more flexible, efficient, and robust abnormal clustering significance assessment capability while ensuring detection accuracy, further enhancing the credibility and decision-making reference value of the disease spatial clustering detection results.

[0195] In the present invention, a scanning window is applied to each divided geographic unit so that all windows to be scanned are included in the corresponding set A1. Subsequently, the maximum likelihood cluster is searched in the above scanning window, that is, the connected subgraph with the largest LLR value is found as the candidate result. When searching in each scanning window, the seed node in the scanning window is first found, and then a local subgraph is created for each seed node. The maximum likelihood cluster is searched only in each local subgraph. The nodes in the local subgraph are then sorted in descending order of priority. Each time, the node with the highest priority is selected to form a set, and the LLR value is calculated. The connected subgraph with the largest LLR value in these local subgraphs is selected as the likelihood cluster of the current scanning window. A likelihood cluster is selected for each scanning window, and the likelihood cluster with the largest LLR value is finally used as the maximum likelihood cluster (MLC) of the entire study area as a candidate result. Finally, all the maximum likelihood clusters in the candidate results are subjected to Monte Carlo testing for statistical significance, and the corresponding geographic unit is obtained as the cluster area.

[0196] The present invention will be further described below with reference to specific embodiments:

[0197] A: Divide the area to be inspected into several geographic units, model the area to be inspected as an undirected graph structure G = (V, E) based on the geographic units, and create an adjacency matrix;

[0198] like Figure 2 As shown, assuming that the area to be detected is an 18-node graph, the entire area to be detected is divided into 18 geographical units. For each geographical unit, use c i Represents the geographic unit r i The number of observed cases, p i Represents the population; each geographic unit is identified by the coordinates of the centroid of the geographic unit.

[0199] B: Based on the proximity constraint control mechanism and the low-risk area elimination mechanism, a set of candidate scanning windows is constructed for each geographic unit;

[0200] Construct proximity constraint control of scanning window based on Euclidean distance;

[0201] Each scanning window is defined by the geographic unit r i and the k-1 geographical units with the smallest distance in its adjacency graph together to form a subgraph containing k nodes, which is recorded as the scanning window Z i ,k;

[0202] In the process of window construction, in order to ensure the compactness and spatial interpretation ability of the spatial clustering area, each scanning window Z is limited to i , the members in k must be within the distance r from the center unit iThe k-1 adjacent geographical units with the smallest distance are controlled by proximity constraints. The minimum distance is measured based on the Euclidean distance, that is, according to the spatial distance between the centroids (or representative points) of the geographical units, all the reachable geographical units are sorted in ascending order and the first k-1 geographical units are selected to join the window. i Together they form the scanning window Z i ,k; the adjacent geographic unit is the unit that is adjacent to the central unit r in the adjacency graph. i Geographic units that are connected by paths are those that can be reached through a series of adjacency relationships. The Euclidean distance d(ij) can be determined by calculating the spatial coordinate difference between the centroids (or representative points) of two geographic units. The calculation method is:

[0203]

[0204] Among them, (x i ,y i ) and (x j ,y j ) represent geographic units r i and geographic unit r j The coordinates of the center of mass of

[0205] This proximity constraint control can not only effectively improve the computational efficiency, but also ensure the spatial coherence between geographic units within the scanning window, which helps to improve the spatial interpretation of the final recognition results.

[0206] Construct a low-risk area elimination mechanism based on risk thresholds

[0207] In order to further improve the effectiveness and computational efficiency of the candidate windows, the present invention designs a low-risk area elimination mechanism based on a risk threshold, which is used to eliminate low-risk areas during the scanning window construction process.

[0208] For each geographical unit, according to its number of observed cases c i and the expected number of cases E i Calculate the risk ratio R i =c i / E i , E i =C*p i / P,p i Represents geographic unit r i The population of the area to be tested, P represents the total population in the area to be tested, C represents the total number of observed cases in the area to be tested, E i It can also be expressed as the product of the overall incidence rate and the population in the detection area.

[0209] Set the risk threshold δ to 0.2 and the risk ratio R i Compared with the set risk threshold δ, if the geographical unit ri The risk ratio R i If it is less than the threshold δ, then the geographic unit r i is a low-risk area, otherwise it is a high-risk area; for the geographical unit r corresponding to the low-risk area i ,During the scan window construction process, the following two culling rules are executed:

[0210] (1) No longer use this geographical unit r i Participates in the construction of the scanning window as a central unit;

[0211] (2) No longer use this geographical unit r i A geographical unit that serves as an adjacency to other scanning windows;

[0212] By using the constructed proximity constraint control mechanism and low-risk area elimination mechanism, and following the local scanning window set construction method based on the adjacency graph, the local scanning window sets generated by all geographic units are merged to form a candidate scanning window set, which is denoted as

[0213] In this embodiment, each geographical unit r i As the center, select k-1 units r from the center i The nearest neighbor nodes form the scanning window and discard low-risk areas;

[0214] like Figure 3 As shown, Figure 3 The figure represents one of the scan windows, centered around node 1. The scan window size, K = 8, covers the following geographic units: {1, 2, 3, 4, 5, 6, 7, 8}. Since the risk threshold is 0.2, nodes 6, 7, and 8 have calculated probabilities greater than 0.2, indicating low risk areas. Therefore, they are excluded from the scan window. Therefore, the set of nodes included in the candidate scan window is: {1, 2, 3, 4, 5}. The MLC search is performed only within these scan windows, and the algorithm creates a total of 18 such scan windows.

[0215] C: A spatial search mechanism based on the scanning window, which searches for the maximum likelihood cluster in the scanning window set and takes it as the candidate result.

[0216] C1: construct likelihood ratio score function;

[0217] C2: Combining the seed node selection mechanism, the linear time subset scanning property (LTSS) and connectivity screening, the maximum likelihood cluster is screened within the scan window in the candidate scan window set, and the maximum likelihood cluster is used as the candidate result;

[0218] Based on the likelihood ratio score function constructed in step C1:

[0219] C21: First, seed nodes are selected in each scanning window based on the priority function;

[0220] C22: Based on the obtained seed nodes, a local subgraph of all seed nodes is constructed through priority elimination and connectivity screening;

[0221] like Figure 4 As shown in the figure, to find the connected subset with the highest score in the current scanning window, the traditional FleXScan algorithm generates all possible subsets of the set consisting of 5 nodes in the window, and then finds the connected subset with the highest score. The number of sets that the algorithm needs to consider is 2^5.

[0222] like Figure 5 The figure shows the optimization algorithm based on priority elimination and connectivity screening in the present invention. The present invention will first find the seed nodes in the scanning window, and use the seed nodes to eliminate a large number of candidate subsets. Figure 5 As shown, the seed nodes in the scan window are nodes 2 and 3, and the priorities of these nodes are higher than the priorities of all neighboring nodes around them; then, the present invention creates a local subgraph for each seed node, and the rule is to exclude nodes in the neighborhood with a higher priority than the current seed node and its neighboring nodes, as well as nodes that are unreachable from the seed node. For example, the process of creating a local subgraph for node 3 is as follows: exclude nodes with a higher priority than node 3 and its neighboring nodes, as well as nodes that are unreachable from node 3. No node meets this condition, so no node is excluded from the local subgraph of node 3, as shown in FIG. Figure 5 As shown in G1. The present invention only searches for the subset with the highest score in the local subgraph. The number of subsets that need to be considered in G1 is 2^4. For node 2, node 3 has a higher priority than node 2, so node 3 is excluded. Nodes 1, 4, and 5 are neighbors of node 3, so nodes 1, 4, and 5 are excluded. Finally, the local subgraph created for node 2 only contains node 2, as shown in Figure 5 As shown in G2. The present invention only searches for the subset with the highest score in this local subgraph. The number of subsets that need to be considered in G2 is 2^0. Finally, the present invention finds the subset with the highest score in the current scan window in the two local subgraphs G1 and G2. The total number of subsets that need to be considered is 2^4+2^0=17, which is 15 fewer than the 32 subsets considered by the traditional FleXScan algorithm. These 15 excluded subsets are proven to be suboptimal subsets.

[0223] C23: Using the LTSS-based linear time optimal subset identification method, the optimal subset of linear complexity, i.e., maximum likelihood cluster identification, is performed within each local subgraph, and the maximum likelihood cluster is used as the candidate result;

[0224] To find the subset with the highest score, the traditional FleXScan algorithm considers all possible subsets, excludes disconnected subsets, calculates the scores of the remaining subsets, and then finds the subset with the highest score. The traditional FleXScan algorithm finds the subset with the highest score: {3, 2, 5, 1}, with a score of 41.6310.

[0225] The present invention searches in each local subgraph created by the seed node. When searching in each local subgraph, by introducing the linear time subset scanning property (LTSS), it is not necessary to consider all possible subsets, but only a linear number of subsets. The principle of the LTSS property is: calculate the priority of all nodes, where the calculation formula of the priority function is also the number of cases / expected number of cases, and then sort the nodes according to the priority. The subset with the highest score is in the connected subset composed of the top k nodes of priority. Specifically, the nodes with the highest priority are added in sequence to form a set. If the subset is not connected, the node with the highest priority is temporarily discarded, and the next node with the highest priority is selected until all nodes are selected. In this process, the connected subset with the highest score is the connected cluster with the highest score in the current scanning window. The specific steps are as follows:

[0226] (1) First, sort the nodes and sort all nodes in descending order according to their priority;

[0227] (1.1) Calculate the priority of each node:

[0228] Id 1 2 3 4 5 Priority 1.28498 1.50508 1.52347 1.11003 1.37416

[0229] (1.2) Sort the nodes in descending order of priority: {3, 2, 5, 1, 4}

[0230] (2) Select the nodes with the highest priority to form a set, that is, perform prefix subset evaluation. Starting from the empty set, add the nodes to the current subset in sequence and calculate the log-likelihood ratio (LLR) score of the corresponding subset:

[0231] Local subgraph G1:

[0232] Subset: {3}, score: 8.2212;

[0233] Subset: {3, 2}, score: 21.1435;

[0234] Subset: {3, 2, 5}, score: 30.5370;

[0235] Subset: {3, 2, 5, 1}, score: 41.6310;

[0236] Subset: {3, 2, 5, 1, 4}, score: 37.8382;

[0237] Local subgraph G2:

[0238] Subset: {2}, score: 12.8683;

[0239] (3) Determine the maximum scoring subset, that is, select the subset with the largest LLR value among all prefix subsets as the maximum likelihood cluster (MLC) in the current local subgraph and use it as the candidate result;

[0240] In this embodiment, the subset with the highest score in the entire process is {3, 2, 5, 1}.

[0241] The connection cluster with the highest score found by the traditional FleXScan algorithm is {3, 2, 5, 1}.

[0242] From the above structure, it can be seen that the results of the present invention and the traditional FleXScan algorithm are consistent, but the number of subsets that our optimization algorithm needs to consider is linear, while the number of subsets considered by the traditional FleXScan algorithm is exponential.

[0243] D: Perform Monte Carlo simulation test and statistical significance analysis on the maximum likelihood cluster among the candidate results;

[0244] Through the above-mentioned maximum likelihood ratio statistic, a clustering area with the greatest probability can be found in any observed case distribution. The generation of this clustering area may come from the normal fluctuation of the random variable of the number of cases, or it may come from the failure of the null hypothesis. This needs to be determined through statistical inference. The null hypothesis model set here is a non-parametric model. The position of the centroid points of each sub-region and the measured values ​​of each sub-region (used to determine the intensity of the number of cases in each sub-region) are all observed prior values. For this non-parametric statistical inference, it is impossible to obtain the theoretical form of the distribution function of the statistic under the null hypothesis, but it can be made using Monte Carlo simulation.

[0245] Since the distribution function of the statistic under the null hypothesis cannot be theoretically derived, the total number of observed cases is randomly distributed across all subregions according to the null hypothesis, with the probability of a case in each subregion being proportional to its measured value. Each time the distribution is completed, a Monte Carlo simulation value is obtained, and the maximum likelihood ratio statistic is calculated. For example, if this is repeated 4999 times, 4999 observed maximum likelihood ratio statistics are obtained. These are then combined with the maximum likelihood ratio statistics obtained from the actual case distribution data and ranked together. If the statistic obtained from the actual data ranks in the top 250, the null hypothesis is considered to be rejected at a confidence level of 5% (250 / (4999 + 1)), indicating that clustering does exist in the identified possible clusters. It is important to note that the spatial scanning statistic method assumes that the total number of cases in the entire study area remains constant, meaning that the total number of cases assigned must remain consistent in each Monte Carlo simulation.

[0246] It should be noted that those skilled in the art can also understand that the various illustrative logical blocks and steps listed in the embodiments of the present application can be implemented by electronic hardware, computer software, or a combination of the two. Whether such functions are implemented by hardware or software depends on the specific application and the design requirements of the entire system. Those skilled in the art can use various methods to implement the described functions for each specific application, but such implementation should not be understood as exceeding the scope of protection of the embodiments of the present application.

[0247] Likewise, although the present disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art after reading and understanding the specification and drawings. The present disclosure includes all such modifications and variations and is limited only by the scope of the claims. In particular, with respect to the various functions performed by the components described above (e.g., elements, resources, etc.), unless otherwise indicated, the terms used to describe such components are intended to correspond to any component (functionally equivalent) that performs the specific functions of the described components, even if structurally not equivalent to the disclosed structures. In addition, although specific features of the present disclosure may have been disclosed with respect to only one of several implementations, such features may be combined with one or more other features of other implementations as may be desired and beneficial for any given or specific application. In addition, with respect to the terms "including," "having," "having," "having," or variations thereof used in the specific embodiments or claims, such terms are intended to be inclusive in a manner similar to the term "comprising."

[0248] Other embodiments of the present disclosure will readily occur to those skilled in the art after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the present disclosure being indicated by the following claims.

[0249] It should be understood that the present disclosure is not limited to the exact structures that have been described above and shown in the drawings, and that various modifications and changes can be made without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.

Claims

1. A spatial clustering detection method for large-scale disease data, characterized by: The specific steps include: A: Divide the area to be detected into several geographical units, model the area to be detected as an undirected graph structure based on the geographical units, and create an adjacency matrix; B: Based on the proximity constraint control mechanism and the low-risk area elimination mechanism, a set of candidate scanning windows is constructed for each geographic unit; C: A spatial search mechanism based on the scanning window, which searches for the maximum likelihood cluster in the scanning window set and takes it as the candidate result; D: Perform Monte Carlo simulation test and statistical significance analysis on the maximum likelihood clusters in the candidate results obtained in step C, and select the clustering area that meets the set significance threshold as the clustering area.

2. The spatial aggregation detection method according to claim 1, wherein: In step B, based on the proximity constraint control mechanism, the members in each scanning window are limited to several adjacent geographical units with the shortest distance from the central unit, and low-risk areas are eliminated from the candidate scanning windows based on the risk threshold, thus obtaining a set of candidate scanning windows for each geographical unit.

3. The spatial aggregation detection method according to claim 1, wherein: Step B includes the following specific steps: B1: Design a method for constructing local scanning window sets based on adjacency graph; For each geographic unit, according to the connection relationship of the geographic unit in the adjacency graph, a set of scanning windows that meet the set window size constraints are constructed with the geographic unit as the central unit. B2: Constructing proximity constraint control of scanning window based on Euclidean distance; Each scanning window is limited to the geographical unit and the k-1 geographical units closest to it in the adjacency graph, forming a subgraph containing k nodes, which is recorded as the scanning window Z i ,k; B3: Establish a mechanism to eliminate low-risk areas based on risk thresholds; For each geographic unit, the ratio of the number of observed cases to the expected number of cases is used as the risk ratio. If the risk ratio of a geographic unit is less than the threshold, the geographic unit is considered a low-risk area; otherwise, it is considered a high-risk area. Low-risk areas are not included in the construction of the scanning window as central units and are not included as adjacent geographic units in other scanning windows. B4: Using the proximity constraint control mechanism and the low-risk area elimination mechanism, a local scanning window set construction method based on the adjacency graph is used to merge the local scanning window sets generated by all geographic units to form a candidate scanning window set.

4. The spatial aggregation detection method according to claim 1, wherein: In step C, all possible connected region subsets are searched within each candidate scanning window, and the scores corresponding to the connected region subsets are calculated using the set scoring function; and among all scanning windows and their corresponding connected region subsets, the connected region subset with the largest score is selected as the globally optimal abnormal region, that is, the maximum likelihood cluster as the candidate result.

5. The spatial aggregation detection method according to claim 4, wherein: Step C includes the following steps: C1: Construct a likelihood function based on the Poisson model and combine it with the log-likelihood ratio to construct a likelihood ratio score function; C2: Combining the seed node selection mechanism, linear time subset scanning properties and connectivity screening, the maximum likelihood cluster is screened within the scan window in the candidate scan window set, and the maximum likelihood cluster is used as the candidate result.

6. The method for detecting spatial aggregation according to claim 5, wherein: Step C2 includes the following steps: C21: Seed node selection based on priority function; If the priority value of a node, i.e., the risk ratio, is greater than the priority values ​​of all its adjacent nodes, then the node is used as a seed node, and all seed nodes in each candidate scan window are obtained; C22: Based on the obtained seed nodes, a local subgraph of all seed nodes is constructed through priority elimination and connectivity screening; That is, remove all nodes in the scan window whose priority values ​​are higher than the priority value of the seed node and their first-order adjacent nodes, and construct the local subgraph corresponding to the seed node based on the set of all nodes connected to the seed node among the remaining nodes; C23: Using the linear time optimal subset identification method based on LTSS, the optimal subset of linear complexity, i.e. maximum likelihood cluster identification, is performed in each local subgraph, and the maximum likelihood cluster is used as the candidate result.

7. The spatial aggregation detection method according to claim 1, wherein: In step C2, during the search process of the maximum likelihood cluster in the local search and global optimization phases, the connectivity of the subsets is determined based on the union-find set.

8. The method for detecting spatial aggregation according to claim 6, wherein: In step C23, identifying the optimal subset of linear complexity includes the following steps: First, sort the nodes and sort all nodes in descending order according to their priority values; Then, the prefix subset evaluation is performed, starting from the empty set, adding nodes to the current subset in sequence, and calculating the LLR score of the corresponding subset; Finally, the maximum scoring subset is determined, and the subset with the largest LLR value among all prefix subsets is selected as the maximum likelihood cluster in the current local subgraph and as the candidate result.

9. The method for detecting spatial aggregation according to claim 7, wherein: The connectivity judgment of subsets based on union-find set judgment includes the following steps: (1) Perform subset initialization; each node in the candidate subset is considered as an independent set for initialization; (2) Constructing adjacency relationships and performing set merging; traversing all nodes in the candidate subset, and judging the adjacent nodes of each node: if the node and its adjacent nodes also belong to the current subset, then performing a merge operation on the node and its adjacent nodes in the union-check set; (3) Perform connectivity judgment; perform a root node search operation on all nodes in the subset. If all nodes have the same root node, it means that the subset is connected; otherwise, it is a non-connected subgraph.

10. The spatial aggregation detection method according to claim 9, characterized in that: The structure of the union-find set is optimized through path compression and rank-merge optimization strategies.

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