An incremental clustering method, system, terminal and storage medium for atmospheric aerosol particle mass spectrum data set

Abstract

The present invention relates to the field of data processing technology, and discloses an incremental clustering method, system, terminal, and storage medium for an atmospheric aerosol particle mass spectrum dataset. The method comprises: obtaining an atmospheric aerosol particle mass spectrum dataset and performing cluster initialization processing to obtain multiple cluster initialization parameters; determining a target cluster selection strategy, and performing a first similarity calculation and cluster assignment processing on the multiple cluster initialization parameters to obtain multiple cluster center matrices; merging and denoising the multiple cluster center matrices to obtain initial clustering results, and performing a second similarity calculation to obtain iterative similarity; performing cluster convergence judgment and iterative cyclic clustering processing on the initial clustering results, and outputting the clustering results of the atmospheric aerosol particle mass spectrum dataset. The present invention can significantly reduce inter-cluster mixing during the cluster analysis of the atmospheric aerosol particle mass spectrum dataset, thereby ensuring the accuracy of the clustering result output.

Description

Technical Field

[0001] The present invention relates to the field of data processing technology, and in particular to a method, system, terminal and computer-readable storage medium for incremental clustering of atmospheric aerosol particle mass spectrum data sets. Background Art

[0002] Clustering is an unsupervised learning technique that automatically identifies the inherent structure of data using metrics such as distance or density. It divides data points into clusters without prior labels, minimizing intra-cluster variance and maximizing inter-cluster variance. Cluster analysis techniques can reveal the inherent structural patterns of datasets and have broad applications in fields such as computer vision (e.g., image segmentation), bioinformatics (e.g., gene expression analysis), and complex network analysis (e.g., community detection).

[0003] Cluster analysis of large datasets of atmospheric aerosol particle mass spectra is a key focus of current atmospheric research and protection. However, traditional cluster analysis methods for atmospheric aerosol particle mass spectra datasets suffer from inter-cluster confusion, resulting in inaccurate cluster analysis results and low analysis efficiency.

[0004] Therefore, the existing technology still needs to be improved and developed. Summary of the Invention

[0005] The main purpose of the present invention is to provide an incremental clustering method, system, terminal and computer-readable storage medium for atmospheric aerosol particle mass spectrum datasets, aiming to solve the problem that the clustering analysis method of atmospheric aerosol particle mass spectrum datasets in the prior art has inter-cluster confusion, resulting in low accuracy and low analysis efficiency of the clustering analysis results of atmospheric aerosol particle mass spectrum datasets.

[0006] To achieve the above object, the present invention provides an incremental clustering method for an atmospheric aerosol particle mass spectrum dataset, the incremental clustering method for an atmospheric aerosol particle mass spectrum dataset comprising the following steps:

[0007] Acquiring an atmospheric aerosol particle mass spectrum dataset, and performing cluster initialization processing on the atmospheric aerosol particle mass spectrum dataset to obtain a plurality of cluster initialization parameters;

[0008] Determining a target cluster selection strategy, and performing a first similarity calculation and cluster assignment process on a plurality of cluster initialization parameters using the target cluster selection strategy to obtain a plurality of cluster center matrices;

[0009] Performing merging and denoising on the plurality of cluster center matrices to obtain an initial clustering result, and performing a second similarity calculation on the initial clustering result to obtain an iterative similarity;

[0010] Cluster convergence determination and iterative cyclic clustering processing are performed on the initial clustering result according to the iterative similarity, and a clustering result of the atmospheric aerosol particle mass spectrum data set is output.

[0011] Optionally, in the incremental clustering method for atmospheric aerosol particle mass spectrum data set, the cluster initialization parameters include a target cluster, a cluster center of each target cluster, the number of data points in each target cluster, and a cluster number;

[0012] The method of obtaining an atmospheric aerosol particle mass spectrum dataset and performing cluster initialization processing on the atmospheric aerosol particle mass spectrum dataset to obtain a plurality of cluster initialization parameters specifically includes:

[0013] Acquiring an atmospheric aerosol particle mass spectrum dataset, and converting the atmospheric aerosol particle mass spectrum dataset into a target data matrix;

[0014] Obtaining a vector for each row in the target data matrix, and performing L2 norm normalization on the vector to obtain a normalized data vector;

[0015] Determining a plurality of random sample vectors in the normalized data vector, wherein the random sample vector is a vector randomly extracted from the normalized data vector, and setting each of the random sample vectors as a cluster center to obtain a plurality of cluster centers and a plurality of the target clusters;

[0016] Initialization processing is performed on each of the target clusters to obtain the number of data points in each of the target clusters and the cluster number.

[0017] Optionally, in the incremental clustering method for atmospheric aerosol particle mass spectrum dataset, the target cluster selection strategy includes a similarity priority strategy and a density priority strategy;

[0018] The determining of the target cluster selection strategy and performing a first similarity calculation and cluster assignment process on the plurality of cluster initialization parameters using the target cluster selection strategy to obtain a plurality of cluster center matrices specifically includes:

[0019] Using any random number generation algorithm to construct an integer array according to the number of data points in each target cluster and the cluster number, and extracting each data point in the integer array in sequence;

[0020] If the target cluster selection strategy is the similarity priority strategy, similarity calculation is performed on each of the data points, and cluster allocation processing is performed according to the similarity priority strategy to obtain multiple cluster center matrices;

[0021] If the target cluster selection strategy is the density priority strategy, similarity calculation is performed on each of the data points, and cluster allocation processing is performed according to the density priority strategy to obtain multiple cluster center matrices.

[0022] Optionally, the incremental clustering method for the atmospheric aerosol particle mass spectrum dataset, wherein the similarity calculation is performed on each of the data points, and cluster assignment processing is performed according to the similarity priority strategy to obtain multiple cluster center matrices, specifically includes:

[0023] Calculating the similarity between each data point and the plurality of target clusters, and determining a first allocation target cluster corresponding to each data point when the similarity is maximum, wherein the first allocation target cluster is the target cluster with the greatest similarity to the data point among the plurality of target clusters;

[0024] Each of the data points is added to the corresponding first allocation target cluster to obtain multiple cluster center matrices.

[0025] Optionally, the incremental clustering method for the atmospheric aerosol particle mass spectrum dataset, wherein the similarity calculation is performed on each of the data points, and cluster assignment processing is performed according to the density priority strategy to obtain multiple cluster center matrices, specifically includes:

[0026] Calculating the similarity between each of the data points and the plurality of target clusters;

[0027] Determining a preset intra-cluster similarity, and extracting a plurality of second allocation target clusters whose similarity is greater than or equal to the preset intra-cluster similarity;

[0028] Calculating the cluster density of each of the second allocation target clusters, and obtaining a third allocation target cluster with the largest cluster density among the second allocation target clusters, wherein the third allocation target cluster is the target cluster with the largest cluster density among the plurality of second allocation target clusters;

[0029] Each of the data points is added to the corresponding third allocation target cluster to obtain a plurality of cluster center matrices.

[0030] Optionally, the incremental clustering method for the atmospheric aerosol particle mass spectrum dataset, wherein the merging and denoising of the multiple cluster center matrices to obtain an initial clustering result, and performing a second similarity calculation on the initial clustering result to obtain an iterative similarity, specifically includes:

[0031] Calculating the inter-cluster similarity between the plurality of cluster center matrices, and extracting the cluster center matrices whose inter-cluster similarity is greater than a preset inter-cluster similarity, to obtain a cluster index set;

[0032] Merging the cluster index set to obtain a de-redundant cluster set;

[0033] Deleting clusters with a data vector count of 0 in the de-redundant cluster set, and performing cluster sorting and cluster numbering to obtain an initial clustering result;

[0034] An inter-iteration similarity calculation is performed on the initial clustering result to obtain an iterative similarity, wherein the inter-iteration similarity calculation includes an inter-iteration similarity calculation based on cluster distribution and an inter-iteration similarity calculation based on cluster numbers.

[0035] Optionally, the incremental clustering method for the atmospheric aerosol particle mass spectrum dataset, wherein the performing clustering convergence determination and iterative cyclic clustering processing on the initial clustering result according to the iterative similarity, and outputting the clustering result of the atmospheric aerosol particle mass spectrum dataset, specifically includes:

[0036] Determining a preset convergence value, and judging whether the iterative similarity is less than the preset convergence value;

[0037] If so, the initial clustering result is subjected to iterative cyclic clustering processing, wherein the input of each iteration is the clustering result output by the previous iteration, until the iterative similarity is greater than or equal to the preset convergence value or the number of iterations is greater than the preset iteration number threshold, and the clustering result of the atmospheric aerosol particle mass spectrum data set is output.

[0038] In addition, to achieve the above-mentioned object, the present invention further provides an incremental clustering system for atmospheric aerosol particle mass spectrum datasets, wherein the incremental clustering system for atmospheric aerosol particle mass spectrum datasets comprises:

[0039] A clustering initialization module is used to obtain an atmospheric aerosol particle mass spectrum data set and perform clustering initialization processing on the atmospheric aerosol particle mass spectrum data set to obtain a plurality of clustering initialization parameters;

[0040] a cluster selection strategy determination module, configured to determine a target cluster selection strategy, and perform a first similarity calculation and cluster allocation process on a plurality of cluster initialization parameters using the target cluster selection strategy to obtain a plurality of cluster center matrices;

[0041] an inter-iteration similarity calculation module, configured to perform a merging process and a denoising process on the plurality of cluster center matrices to obtain an initial clustering result, and perform a second similarity calculation on the initial clustering result to obtain an iterative similarity;

[0042] A clustering result output module is used to perform clustering convergence judgment and iterative cyclic clustering processing on the initial clustering result according to the iterative similarity, and output the clustering result of the atmospheric aerosol particle mass spectrum data set.

[0043] In the present invention, an atmospheric aerosol particle mass spectrum data set is obtained, and cluster initialization processing is performed on the atmospheric aerosol particle mass spectrum data set to obtain multiple cluster initialization parameters; a target cluster selection strategy is determined, and the target cluster selection strategy is used to perform a first similarity calculation and cluster assignment processing on the multiple cluster initialization parameters to obtain multiple cluster center matrices; the multiple cluster center matrices are merged and denoised to obtain an initial clustering result, and a second similarity calculation is performed on the initial clustering result to obtain an iterative similarity; cluster convergence judgment and iterative cyclic clustering processing are performed on the initial clustering result based on the iterative similarity, and the clustering result of the atmospheric aerosol particle mass spectrum data set is output. The present invention uses a target cluster selection strategy to perform similarity calculation and cluster assignment processing on the cluster initialization parameters corresponding to the atmospheric aerosol particle mass spectrum data set, so that the cluster to which each data point belongs can be flexibly and dynamically selected by two strategies, including a traditional similarity priority strategy and a specially designed density priority strategy, and can generate a cluster set that meets the inter-cluster similarity and intra-cluster similarity constraints. Furthermore, by merging and denoising the cluster center matrices and performing iterative cyclic clustering according to the similarity between iterations, the inter-cluster confusion can be significantly reduced, effectively improving the clustering analysis efficiency of atmospheric aerosol particle mass spectrometry datasets under high-dimensional big data conditions and the accuracy of clustering result output. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of a preferred embodiment of the incremental clustering method of atmospheric aerosol particle mass spectrum data set of the present invention;

[0045] Figure 2 Schematic diagram of the relationship between clusters of the similarity priority strategy and the density priority strategy of the preferred embodiment of the incremental clustering method for atmospheric aerosol particle mass spectrum data set of the present invention;

[0046] Figure 3 Schematic diagram of the ratio of data contained in each cluster to the total data volume and its mixing situation in a preferred embodiment of the incremental clustering method for atmospheric aerosol particle mass spectrum data set of the present invention;

[0047] Figure 4 Schematic diagram of cluster average mass spectra of main clusters of a preferred embodiment of the incremental clustering method for atmospheric aerosol particle mass spectrum data set of the present invention;

[0048] Figure 5 1 is a structural diagram of a preferred embodiment of an incremental clustering system for atmospheric aerosol particle mass spectrum data sets according to the present invention;

[0049] Figure 6 It is a structural diagram of a preferred embodiment of the terminal of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the present invention more clear and distinct, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0051] Clustering is an unsupervised learning technique that automatically identifies the inherent structure of data through metrics such as distance or density. It then divides data points into clusters without prior labels, minimizing intra-cluster variance and maximizing inter-cluster variance. This technique can reveal inherent structural patterns in data and has broad applications in fields such as computer vision (e.g., image segmentation), bioinformatics (e.g., gene expression analysis), and complex network analysis (e.g., community detection). However, modern data science faces two core challenges: the exponential growth of data dimensionality and the massive scale of sample sizes. These challenges place demands on clustering algorithms for computational efficiency, parameter adaptability, noise robustness, and the ability to handle large amounts of data.

[0052] Various clustering algorithms achieve data partitioning through different similarity metrics and optimization strategies. The traditional clustering method system mainly includes the following: prototype-based K-means, density-based DBSCAN (Density-Based Spatial Clustering of Applications with Noise), hierarchical clustering, spectral clustering, and clustering based on adaptive resonance theory (ART).

[0053] The K-means algorithm uses the number of clusters preset by the user. As a parameter, first randomly initialize The centroid position of each cluster is optimized by iteratively minimizing the sum of squared Euclidean distances between the data points in the cluster and the centroid. The output contains clusters and their corresponding centroid vectors. The overall time complexity of the algorithm is , which has high computational efficiency but cannot handle non-convex clusters. Its improved K-means++ improves algorithm stability by using a probabilistic centroid initialization strategy, and its time complexity is maintained at Another improved K-medoids algorithm (i.e., k-center clustering algorithm) uses actual data points as cluster centers, which enhances the robustness to outliers, but the computational complexity increases to However, the clustering results of the K-means algorithm are significantly affected by the number of clusters, the initial centroid selection and noise, and because the distance metric fails in high dimensions, this type of algorithm is not suitable for clustering large-scale high-dimensional data.

[0054] DBSCAN divides clusters into core points, boundary points, and noise points based on density connectivity. It does not require a preset number of clusters and has strong noise resistance, but it requires a pre-specified neighborhood radius. and minimum points The algorithm expands the cluster by connecting the neighborhood of the core point, which contains at least The data points of points, the boundary points belong to the neighborhood of a core point but do not meet the core point conditions themselves, and are not covered by any clusters are noise points. DBSCAN needs to calculate the distance between all pairs of data points, and the complexity is After optimizing neighborhood queries using spatial indexes such as R-tree (a multidimensional data structure for spatial data indexing), the complexity can be reduced to Variants of DBSCAN include HDBSCAN (Hierarchical Density-Based Spatial Clustering of Applications with Noise) and OPTICS (Ordering Points To Identify the Clustering Structure). The clustering results require empirical artificial division, and since the distance metric fails in high-dimensional data, the DBSCAN algorithm is not suitable for high-dimensional big data.

[0055] Hierarchical clustering is divided into two types: divisive and agglomerative. Divisive hierarchical clustering recursively divides data from top to bottom based on the maximum distance criterion, and has extremely high computational complexity. Agglomerative hierarchical clustering merges the nearest neighbor clusters from bottom to top, and finally generates a dendrogram. In the initial stage, the distance between all data points is calculated, and then the closest clusters are merged iteratively and the distance matrix is ​​updated until all points are clustered. The complexity of the agglomerative method is , after optimizing the distance update using the priority queue, it can be reduced to The space complexity of storing the distance matrix is , with high memory overhead. Although hierarchical clustering provides an intuitive cluster hierarchy, its high computational and storage costs limit its application to large-scale, high-dimensional data. A variant of this algorithm, the BIRCH algorithm (Balanced Iterative Reducing and Clustering using Hierarchies), compresses data by constructing a clustering feature tree to accommodate big data needs. However, when the data dimension exceeds 20, the statistical information provided by the CF tree becomes invalid, resulting in a significant decrease in clustering quality. Furthermore, BIRCH's clustering results are significantly affected by the order in which data is inserted. Points in the same cluster may be assigned to different subtrees depending on the insertion order, resulting in significant deviations from the true clustering distribution. Furthermore, the construction of the CF tree (Clustering Feature Tree) requires adjusting the branching factor, leaf node capacity, and radius threshold. This complex parameter selection can easily lead to an unbalanced tree structure or illogical clustering. Therefore, the practical application of the BIRCH algorithm in big data is quite limited.

[0056] Spectral Clustering requires selecting a similarity matrix construction method (such as Gaussian kernel) and the number of clusters, and outputs clusters based on graph partitioning. The algorithm first constructs a similarity matrix, calculates the normalized Laplace matrix and performs eigendecomposition, and selects the first The feature vectors form a low-dimensional embedding space, and finally K-means clustering is applied to obtain the result. Spectral clustering can identify complex non-convex clusters, but its time complexity is high, and the complexity of constructing the similarity matrix is , the complexity of the eigendecomposition is , the total complexity is , and the calculation requires a lot of space, the space complexity of storing the similarity matrix is , making it difficult to scale to big data.

[0057] Clustering based on ART theory is a type of incremental learning that can adaptively generate clusters without specifying the number of clusters. The principle is as follows: a new data point is compared with an existing cluster. If the similarity (such as cosine similarity) exceeds a preset threshold, it is included in the cluster and the cluster center is updated. Otherwise, a new cluster is created. The time complexity of this method is . Although ART can cluster large amounts of high-dimensional data after fixing the number of clusters, the choice of learning rate requires empirical attempts to make the clustering process converge. In addition, once the clusters are generated in this method, they will not be annihilated. A large number of fragmented redundant clusters will be generated, and there will be a lot of overlap between them. In addition, the iteration based on the learning rate causes the cluster center and the cluster average to not coincide. Subsequent manual empirical merging is still required, which is difficult to achieve when processing large amounts of data. Therefore, when clustering based on ART theory is applied, the results are not intuitive and difficult to quantify, making it difficult to effectively apply to the clustering of big data.

[0058] To address these issues, the present invention proposes a Flexible Adaptive Similarity Clustering (FASC) algorithm that combines similarity and density. This algorithm generates clusters that satisfy both inter-cluster and intra-cluster similarity constraints. The clustering results are intuitive and quantitative, with simple input parameters and easy deployment and use. The cluster to which each data point belongs is dynamically selected using two flexible strategies: a traditional similarity-first strategy and a specially designed density-first strategy. The latter, in principle, significantly reduces inter-cluster confusion. The number of clusters is optimized using an innovative cluster allocation mechanism, similarity-based dynamic cluster merging, and cluster sorting methods. The algorithm adaptively generates and eliminates clusters online to an optimal value, while also automatically identifying noisy data. The FASC algorithm supports real-time data stream processing and uses an incremental update method to avoid global recalculation when updating clusters. Therefore, in terms of efficiency, the FASC algorithm significantly outperforms traditional clustering methods in both time and space complexity, making it particularly suitable for mining high-dimensional big data.

[0059] The incremental clustering method for atmospheric aerosol particle mass spectrum data set described in the preferred embodiment of the present invention is as follows: Figure 1 As shown, the incremental clustering method for atmospheric aerosol particle mass spectrum dataset includes the following steps:

[0060] Step S10: Acquire an atmospheric aerosol particle mass spectrum dataset, and perform cluster initialization processing on the atmospheric aerosol particle mass spectrum dataset to obtain a plurality of cluster initialization parameters. The cluster initialization parameters include a target cluster, a cluster center of each target cluster, the number of data points in each target cluster, and a cluster number.

[0061] The FASC algorithm set in the present invention can cluster any data set without any prior information (the FASC clustering algorithm in the present invention is applicable to any data set, but in this embodiment it is mainly applied to the atmospheric aerosol particle mass spectrum data set) into clusters, and these clusters meet the inter-cluster similarity less than the threshold (i.e. the inter-cluster similarity is preset in the present invention) and the intra-cluster similarity is greater than the threshold The condition (i.e., the preset intra-cluster similarity in the present invention) makes the similarity between data points within each cluster higher, while the similarity between different clusters is lower, and these similarities are quantitative and controllable.

[0062] For the convenience of description, the present invention specifies that the symbol for the logical operation "equality" is "==", and the assignment symbol is "="; the operation for obtaining the size of a set X is X.size, the operation for obtaining the length of an array data structure Y is Y.length, the center of a cluster is vector, and the count of a cluster is count (this meaning is used in the following text, for example, represents a cluster count, represents the center of a cluster, which will not be explained in detail in the following text).

[0063] The input parameters are as follows: This paper introduces the atmospheric aerosol particle mass spectrum dataset. The data matrix of the atmospheric aerosol particle mass spectrum dataset is ,in, is the number of samples, is the number of feature dimensions. Each row is a data vector, and each column is a feature dimension. The method to convert a data set of samples into a data matrix is ​​as follows: The value in For the The first sample The value of the dimension. If there is no value or the value is 0, then The following parameters are user-defined according to the application scenario and requirements: Inter-cluster similarity threshold (i.e., the preset inter-cluster similarity in the present invention): ; Intra-cluster similarity threshold (i.e., the preset intra-cluster similarity in the present invention): ; Initial maximum number of clusters: If there is no restriction, ; Maximum number of loop clusters: If there is no restriction, ; Maximum number of iteration cycles: If there is no restriction, ; Inter-iteration similarity convergence threshold: , if we want absolute convergence, let ;Similarity algorithm: , input value and is a vector or matrix with the same feature dimension, and the output is a similarity value or matrix; the cluster selection strategy is: ,in, Density priority, The similarity is prioritized; the similarity between clusters is calculated as follows: ,in, is the cluster distribution, Number the cluster.

[0064] Specifically, an atmospheric aerosol particle mass spectrum dataset is obtained and converted into a target data matrix; a vector of each row in the target data matrix is ​​obtained, and the vector is normalized based on the L2 norm to obtain a normalized data vector.

[0065] Determine multiple random sample vectors in the normalized data vector, wherein the random sample vector is a vector randomly extracted from the normalized data vector, and set each of the random sample vectors as a cluster center to obtain multiple cluster centers and multiple target clusters; initialize each of the target clusters to obtain the number of data points in each target cluster and the cluster number.

[0066] The clustering process of the FASC algorithm in the present invention consists of three stages:

[0067] Phase 1: Cluster initialization. Let ,in, is the number of iterations; Each row of is normalized based on the L2 norm (for a vector, the L2 norm is its modulus, and the L2 normalization here is Divide the vector represented by each row in by its modulus to make its modulus 1). A random number between ,exist Select row index as A random sample vector of , let it be the center of the first cluster: ; and let the cluster count ( ) is 1: ,in, is the vector of the first cluster center, is the vector corresponding to the cluster center, is the count corresponding to the cluster center, and so on. Then initialize the cluster count array ( ):make , the array stores the number of data points assigned to each cluster; initialize the array that stores the cluster number to which each data point belongs ( ): .

[0068] Step S20: Determine a target cluster selection strategy, and use the target cluster selection strategy to perform a first similarity calculation and cluster allocation process on the plurality of cluster initialization parameters to obtain a plurality of cluster center matrices. The target cluster selection strategy includes a similarity priority strategy and a density priority strategy.

[0069] Specifically, an integer array is constructed according to the number of data points in each target cluster and the cluster number using any random number generation algorithm, and each data point in the integer array is extracted in sequence.

[0070] Phase 2: Perform similarity calculation, cluster selection and data allocation. Update the number of iterations , record the cluster count array of the previous cycle , and the number array of the previous cycle Use any random number generation algorithm (such as a pseudo-random number generation algorithm based on modular arithmetic) to obtain a length of And the range is 1 to Integer array of , in order from Select , for Randomly select the array from , and select the row index in turn without duplication Data vector , such random selection of data vectors can prevent the optimization process from falling into local optimum. , then calculate Similarity with all cluster centers at this time: , is the transpose of the matrix consisting of all cluster center vectors arranged in rows. The similarity algorithm can be selected according to the application scenario and requirements. Here, cosine similarity is used as an example, and so on. ,in, for The L2 norm of , directly precompute the similarity matrix between all data points and all cluster centers , Right now , For the The cluster center of the cluster, In particular, when using the cosine similarity metric, In engineering implementation, this matrix operation process can significantly reduce the computational complexity. Subsequently, cluster allocation and update are performed. The clusters to be assigned are selected using one of the following two strategies: For general data, the density-first strategy is preferred; if the data is known to be clearly divided into spherical clusters with distinct boundaries, or if cluster blending is not a concern, the similarity-first strategy can be used.

[0071] If the target cluster selection strategy is the similarity priority strategy, the similarity between each data point and the multiple target clusters is calculated, and the first allocation target cluster corresponding to each data point when the similarity is maximum is determined, wherein the first allocation target cluster is the target cluster with the greatest similarity to the data point among the multiple target clusters; each data point is added to the corresponding first allocation target cluster to obtain multiple cluster center matrices.

[0072] A. Similarity priority strategy: select ( is the number of clusters) The cluster with the highest similarity ,in, (represents input), the corresponding similarity is (Indicates output).

[0073] If the target cluster selection strategy is the density priority strategy, then calculate the similarity between each of the data points and the multiple target clusters; determine the preset intra-cluster similarity, and extract multiple second allocation target clusters whose similarity is greater than or equal to the preset intra-cluster similarity; calculate the cluster density of each of the second allocation target clusters, and obtain the third allocation target cluster with the largest cluster density among the second allocation target clusters, wherein the third allocation target cluster is the target cluster with the largest cluster density among the multiple second allocation target clusters; add each of the data points to the corresponding third allocation target cluster to obtain multiple cluster center matrices.

[0074] B. Density priority strategy: take the strategy that satisfies Index , is a data point with a similarity greater than or equal to the preset cluster similarity. To calculate the data points The similarity with each cluster and index Classify into collection .like , then in Select the cluster with the largest density , if multiple clusters have the same density, the one with the highest similarity is selected first, i.e. , , the corresponding similarity is .like ,make , .

[0075] like Figure 2 As shown ( Figure 2 Different colors represent different clusters). According to theoretical analysis, the similarity-first selection strategy will cause cluster mixing when the distance between cluster centers is less than the inter-cluster similarity, while the density-first strategy will only cause inter-cluster mixing when the distance between cluster centers is less than the inter-cluster similarity. Figure 2 Therefore, the density-first strategy theoretically significantly reduces the mixing frequency of clusters.

[0076] The pseudo code for cluster selection is as follows:

[0077]

[0078] Then the cluster allocation process is carried out: if (i.e. the similarity is less than the preset intra-cluster similarity), when the current number of clusters does not exceed the preset threshold ( hour, , indicating that the current number of clusters is less than the maximum number of clusters in the loop ; hour, , indicating that the current number of clusters is less than or equal to the initial maximum number of clusters ), follow these steps:

[0079] , which means adding 1 to the length of the current cluster;

[0080] , which means that the updated cluster center of the current cluster is assigned to ;

[0081] Generate a new cluster, which means assigning the updated cluster count of the current cluster to 1. Specifically, first increase the total number of clusters by 1, then create a new cluster numbered with the number of current clusters and set its count to 1. Classified into this cluster ( ). exist and When, or and When , the outlier processing is triggered, that is, the point is regarded as an outlier: the cluster number of the point is set to -1 ( ). On the contrary, if ,exist Perform the following steps to perform an incremental cluster update:

[0082] ,in, Cluster Cluster count of ;

[0083] ,in, Cluster The cluster center of

[0084] .

[0085] Then assign a cluster number to the current vector ( ),exist When the cluster number is directly assigned, the cluster number is not updated. The operation in this stage is Until all numbers in have been selected.

[0086] Step S30: performing a merging process and a denoising process on the plurality of cluster center matrices to obtain an initial clustering result, and performing a second similarity calculation on the initial clustering result to obtain an iterative similarity.

[0087] Specifically, the inter-cluster similarity between the plurality of cluster center matrices is calculated, and the cluster center matrices whose inter-cluster similarity is greater than the preset inter-cluster similarity are extracted to obtain a cluster index set; and the cluster index set is merged to obtain a de-redundant cluster set.

[0088] Phase 3: Dynamic merging and sorting of redundant clusters: The first part of this phase, namely the dynamic merging of redundant clusters, is only The cluster center matrix generated in stage 2 is Dynamic merging can reduce redundant clusters and speed up convergence.

[0089] The method is as follows: Start from the first cluster (let ), enter dynamic cluster merging and execute the following loop: calculate the inter-cluster similarity between each cluster and other clusters (cosine similarity is used as an example here) , For the The cluster center of each cluster. Get the cluster index set that needs to be merged , is the cluster to be merged. , indicating that there are no redundant clusters to be merged, then let ,return , repeat the dynamic cluster merging cycle. On the contrary, if , then it is proved that there are non-redundant clusters that can be merged and updated. The cluster count expression is:

[0090] ;

[0091] Will Perform weighted average merging into new clusters and replace , the expression after substitution is: .

[0092] Accordingly Update to match the merged clusters, the expression is:

[0093] , that is, until the size of the cluster index set is less than 2, indicating that there are no redundant clusters to be merged.

[0094] Then order , reset the index and delete redundant clusters, the expression is:

[0095] .

[0096] Dynamic cluster merging loop until there are no more clusters to merge ( ) or stops when the number of clusters has reached a threshold ( ).

[0097] The pseudo code of the redundant cluster dynamic merging algorithm is as follows:

[0098]

[0099] The clusters with 0 data vectors in the de-redundant cluster set are deleted, and cluster sorting and cluster numbering are performed to obtain an initial clustering result.

[0100] The second part of this phase is cluster arrangement, which needs to be performed after any iteration cycle. The main task is to delete clusters that occupy 0 data vectors during the iteration process and calculate the similarity between iterations.

[0101] The steps of cluster arrangement after iteration are:

[0102] , The cluster number is The cluster count of is the size of the row index set of the data vector;

[0103] ;

[0104] Take integers without repetition , , the assigned cluster number is The row index set of the data vector ,like , then delete , otherwise update .

[0105] Then use any sorting algorithm (including quick sort, merge sort and heap sort, etc.) from large to small according to Value sorting The order of the clusters in The cluster numbers in are updated to match the sorted There are many ways to implement the update. One intuitive way is to sort the The transposition operation is performed accordingly. The permutation cluster number.

[0106] The pseudo code for cluster arrangement is as follows:

[0107]

[0108] An inter-iteration similarity calculation is performed on the initial clustering result to obtain an iterative similarity, wherein the inter-iteration similarity calculation includes an inter-iteration similarity calculation based on cluster distribution and an inter-iteration similarity calculation based on cluster numbers.

[0109] There are two ways to calculate the similarity between iterations:

[0110] 1. Based on cluster distribution ( ) Iteration similarity calculation: first get the cluster count array , the expression is:

[0111] ;

[0112] Then calculate and The similarity between iterations of , The expression is:

[0113] ;

[0114] This method can quickly reach convergence at a higher inter-iteration similarity threshold, and is more suitable for situations where the distribution of cluster counts is relatively uniform.

[0115] 2. Based on cluster number ( ) is calculated by the iteration similarity, the expression is:

[0116] ;

[0117] ;

[0118] Calculate the difference between this iteration and the previous iteration The repetition ratio at each index is , this method is strictly convergent and applicable in any case.

[0119] The pseudo code for calculating the similarity between iterations is as follows:

[0120]

[0121] Step S40: performing cluster convergence determination and iterative cyclic clustering processing on the initial clustering result according to the iterative similarity, and outputting the clustering result of the atmospheric aerosol particle mass spectrum dataset.

[0122] Specifically, a preset convergence value is determined, and it is judged whether the iterative similarity is less than the preset convergence value; if so, the initial clustering result is subjected to iterative cyclic clustering processing, wherein the input of each iteration is the clustering result output by the previous iteration, until the iterative similarity is greater than or equal to the preset convergence value or the number of iterations is greater than a preset iteration number threshold, and the clustering result of the atmospheric aerosol particle mass spectrum data set is output.

[0123] After the end of stage 3, clustering enters the next round of iteration and starts again from stage 1 to continuously update the cluster division until convergence ( ) or exceeds the iteration threshold ( ). When performing incremental learning, for streaming input data, you can use , continuously clustering the input data. The main pseudo code of the FASC algorithm is as follows:

[0124]

[0125]

[0126]

[0127]

[0128] Complexity analysis of FASC algorithm: The time complexity of FASC is mainly composed of the following parts. 1. In data preprocessing: The time complexity of L2 normalization operation is 2. Cluster allocation and update: Each round of iteration needs to calculate the similarity between each sample and all cluster centers, and the time complexity is ( is the number of dynamic clusters, i.e. ). 3. Dynamic cluster merging: Filter and merge cluster pairs by similarity threshold, the complexity is 4. The comprehensive time complexity is FASC reduces redundant clusters by dynamically merging them. , can be regarded as a constant, and the total algorithm time complexity can be approximated as , which is better than traditional algorithms. In terms of space complexity, FASC only needs to store the cluster center matrix (complexity is ) and the inter-cluster similarity matrix (complexity is ), the total space complexity is Compared with traditional methods, such as spectral clustering, the complexity is And the complexity of K-means is ,FASC occupies less memory space during calculation and is suitable for high-dimensional big data scenarios.

[0129] For example, the application of the FASC algorithm provided in the present invention is as follows:

[0130] For example, we use a large dataset of atmospheric aerosol particle mass spectra. This dataset contains 10 million 600-dimensional data points: each data point is a single-particle laser desorption ionization mass spectrum of a real ambient atmospheric aerosol particle. Each dimension represents a specific mass-to-charge ratio, ranging from -300 to +300, with integer precision. We implement the FASC algorithm described above using MATLAB, using a single CPU core. The default parameters are as follows: , ; ; ; ; Because the mass spectrometry dataset is a sparse matrix, cosine similarity was used as the similarity metric. The algorithm converged after three iterations, taking 12,867 seconds. Fifty clusters meeting the predefined criteria were obtained. There were 1.33 million outliers, accounting for 13.3% of the total. This number of outliers is expected given the complex conditions in the real atmosphere and the high heterogeneity of particulate matter composition.

[0131] like Figure 3 As shown in the figure, it is the ratio of the data contained in each cluster to the total data volume. There are no mixed pairs, indicating that there is no mixing between the clusters, proving that FASC effectively solves the inter-cluster mixing problem of traditional algorithms. In addition, according to the previous theoretical description of the FASC algorithm, it is easy to know that in the clustering results of FASC, the cluster center and the cluster average coincide. Therefore, the cluster center can be used as a representative of the data contained in the cluster. The center vectors of the five main clusters are displayed in the form of mass spectrum as follows (as shown in the figure). Figure 4 Clusters 1 to 5 represent common types of particulate matter in the atmosphere, consistent with previous conventional observations. These results confirm the correctness of the FASC clustering.

[0132] The key points of innovation of the present invention mainly include:

[0133] 1. The specially designed clustering process can produce quantitative and intuitive clustering results under simple custom parameters. Regarding the data cluster allocation mechanism, an online dynamic cluster generation and annihilation mechanism is proposed, which can achieve the optimal number of clusters without pre-specifying the number of clusters. Regarding the selection of data clusters and cluster merging, an innovative density-first cluster selection strategy and a method for dynamic merging and organizing clusters are proposed, which simultaneously considers cluster density and similarity, significantly reducing inter-cluster contamination. Regarding cluster generation, the algorithm supports the specification of inter-cluster similarity and intra-cluster similarity. The clustering results are controllable and quantitative, and the interpretability and ease of use are superior to traditional methods.

[0134] 2. The constraints, operational steps, and convergence determination methods of deep optimization make this algorithm particularly suitable for high-dimensional big data. Limiting the number of initial and loop clusters and precalculating similarities within loops significantly reduces the algorithm's time complexity. The efficient clustering process only requires storing information about cluster and data attribution, resulting in low space complexity, significantly outperforming traditional algorithms. Flexible options for calculating similarities between iterations enable rapid convergence under varying data conditions.

[0135] In addition, the present invention innovatively uses online generation and merging to dynamically adjust and optimize the number of clusters, which is superior to traditional incremental learning algorithms. After clustering, a sorting process based on cluster count is performed. In actual engineering implementation, sorting can be omitted and the calculation process of the similarity between iterations can be modified accordingly. Furthermore, the merging of redundant clusters can be achieved through other methods, and the present invention only demonstrates the most intuitive method. Convergence conditions can be determined in other ways, such as the number of clusters, the number of data points contained in a cluster, or the proportion of the total number of data points.

[0136] In addition, the present invention is arranged When similarity pre-calculation is used to speed up the calculation, a possible variation is to No pre-calculation of similarity between data and clusters is performed, and the The dynamic cluster generation method of the same data point-by-data point detection is used. This method has a higher computational complexity but may converge faster.

[0137] Further, if Figure 5 As shown, based on the above-mentioned incremental clustering method of atmospheric aerosol particle mass spectrum dataset, the present invention also provides an incremental clustering system of atmospheric aerosol particle mass spectrum dataset, wherein the incremental clustering system of atmospheric aerosol particle mass spectrum dataset includes:

[0138] A clustering initialization module 51 is used to obtain an atmospheric aerosol particle mass spectrum dataset and perform clustering initialization processing on the atmospheric aerosol particle mass spectrum dataset to obtain a plurality of clustering initialization parameters;

[0139] a cluster selection strategy determination module 52 for determining a target cluster selection strategy, and performing a first similarity calculation and cluster assignment process on a plurality of cluster initialization parameters using the target cluster selection strategy to obtain a plurality of cluster center matrices;

[0140] An inter-iteration similarity calculation module 53 is configured to merge and denoise the plurality of cluster center matrices to obtain an initial clustering result, and perform a second similarity calculation on the initial clustering result to obtain an iterative similarity;

[0141] The clustering result output module 54 is configured to perform clustering convergence determination and iterative cyclic clustering processing on the initial clustering result according to the iterative similarity, and output the clustering result of the atmospheric aerosol particle mass spectrum dataset.

[0142] Further, if Figure 6 As shown, based on the above-mentioned incremental clustering method and system for atmospheric aerosol particle mass spectrum data set, the present invention also provides a terminal, which includes a processor 10, a memory 20 and a display 30. Figure 6 Only some of the components of the terminal are shown, but it should be understood that implementation of all of the shown components is not required, and more or fewer components may be implemented instead.

[0143] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard drive or memory of the terminal. In other embodiments, the memory 20 may also be an external storage device of the terminal, such as a plug-in hard drive, a Smart Media Card (SMC), a Secure Digital (SD) card, a flash memory card, etc. equipped with the terminal. Furthermore, the memory 20 may include both the internal storage unit of the terminal and an external storage device. The memory 20 is used to store application software installed on the terminal and various types of data, such as program code of the terminal. The memory 20 may also be used to temporarily store data that has been output or is about to be output. In one embodiment, the memory 20 stores an incremental clustering program 40 for an atmospheric aerosol particle mass spectrum dataset. The incremental clustering program 40 for an atmospheric aerosol particle mass spectrum dataset can be executed by the processor 10, thereby implementing the incremental clustering method for an atmospheric aerosol particle mass spectrum dataset of the present application.

[0144] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, configured to execute program code or process data stored in the memory 20, such as executing an incremental clustering method for the atmospheric aerosol particle mass spectrum dataset.

[0145] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch screen, etc. The display 30 is used to display information on the terminal and to display a visual user interface.

[0146] In one embodiment, when the processor 10 executes the incremental clustering program 40 for the atmospheric aerosol particle mass spectrum dataset in the memory 20 , the steps of the incremental clustering method for the atmospheric aerosol particle mass spectrum dataset are implemented.

[0147] In summary, the present invention provides an incremental clustering method, system and terminal for an atmospheric aerosol particle mass spectrum data set. The method includes: obtaining an atmospheric aerosol particle mass spectrum data set, and performing cluster initialization processing on the atmospheric aerosol particle mass spectrum data set to obtain multiple cluster initialization parameters; determining a target cluster selection strategy, and using the target cluster selection strategy to perform a first similarity calculation and cluster assignment processing on the multiple cluster initialization parameters to obtain multiple cluster center matrices; merging and denoising the multiple cluster center matrices to obtain an initial clustering result, and performing a second similarity calculation on the initial clustering result to obtain iterative similarity; performing cluster convergence judgment and iterative cyclic clustering processing on the initial clustering result according to the iterative similarity, and outputting the clustering result of the atmospheric aerosol particle mass spectrum data set. This paper employs a target cluster selection strategy to perform similarity calculation and cluster assignment on the cluster initialization parameters corresponding to an atmospheric aerosol particle mass spectrometry dataset. This allows each data point to be assigned a cluster using two flexible and dynamic strategies: a traditional similarity-first strategy and a specially designed density-first strategy. This strategy generates clusters that satisfy both inter-cluster and intra-cluster similarity constraints. Furthermore, by merging and denoising the cluster center matrix and performing iterative clustering based on inter-iteration similarity, inter-cluster confusion is significantly reduced, effectively improving the efficiency of cluster analysis and the accuracy of clustering output for atmospheric aerosol particle mass spectrometry datasets under high-dimensional data conditions.

[0148] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or terminal comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or terminal. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or terminal comprising the element.

[0149] Of course, those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing related hardware (such as a processor, controller, etc.) through a computer program. The program can be stored in a computer-readable storage medium that can be read by a computer. When executed, the program can include the processes in the above-described method embodiments. The computer-readable storage medium can be a memory, a magnetic disk, an optical disk, etc.

[0150] It should be understood that the application of the present invention is not limited to the above examples. For those skilled in the art, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. An incremental clustering method for atmospheric aerosol particle mass spectrum dataset, characterized by: The incremental clustering method for the atmospheric aerosol particle mass spectrum dataset includes: Acquiring an atmospheric aerosol particle mass spectrum dataset, and performing cluster initialization processing on the atmospheric aerosol particle mass spectrum dataset to obtain a plurality of cluster initialization parameters; Determining a target cluster selection strategy, and performing a first similarity calculation and cluster assignment process on a plurality of cluster initialization parameters using the target cluster selection strategy to obtain a plurality of cluster center matrices; The target cluster selection strategy includes a similarity priority strategy and a density priority strategy; The determining of the target cluster selection strategy and performing a first similarity calculation and cluster assignment process on the plurality of cluster initialization parameters using the target cluster selection strategy to obtain a plurality of cluster center matrices specifically includes: Using any random number generation algorithm to construct an integer array according to the number of data points in each target cluster and the cluster number, and extracting each data point in the integer array in sequence; If the target cluster selection strategy is the similarity priority strategy, similarity calculation is performed on each of the data points, and cluster allocation processing is performed according to the similarity priority strategy to obtain multiple cluster center matrices; If the target cluster selection strategy is the density priority strategy, similarity calculation is performed on each of the data points, and cluster allocation processing is performed according to the density priority strategy to obtain multiple cluster center matrices; Performing merging and denoising on the plurality of cluster center matrices to obtain an initial clustering result, and performing a second similarity calculation on the initial clustering result to obtain an iterative similarity; Cluster convergence determination and iterative cyclic clustering processing are performed on the initial clustering result according to the iterative similarity, and a clustering result of the atmospheric aerosol particle mass spectrum data set is output.

2. The incremental clustering method for atmospheric aerosol particle mass spectrum dataset according to claim 1, characterized in that: The cluster initialization parameters include the target cluster, the cluster center of each target cluster, the number of data points in each target cluster, and the cluster number; The method of obtaining an atmospheric aerosol particle mass spectrum dataset and performing cluster initialization processing on the atmospheric aerosol particle mass spectrum dataset to obtain a plurality of cluster initialization parameters specifically includes: Acquiring an atmospheric aerosol particle mass spectrum dataset, and converting the atmospheric aerosol particle mass spectrum dataset into a target data matrix; Obtaining a vector for each row in the target data matrix, and performing L2 norm normalization on the vector to obtain a normalized data vector; Determining a plurality of random sample vectors in the normalized data vector, wherein the random sample vector is a vector randomly extracted from the normalized data vector, and setting each of the random sample vectors as a cluster center to obtain a plurality of cluster centers and a plurality of the target clusters; Initialization processing is performed on each of the target clusters to obtain the number of data points in each of the target clusters and the cluster number.

3. The incremental clustering method for atmospheric aerosol particle mass spectrum dataset according to claim 1, characterized in that: The similarity calculation is performed on each of the data points, and cluster allocation is performed according to the similarity priority strategy to obtain multiple cluster center matrices, specifically including: Calculating the similarity between each data point and the plurality of target clusters, and determining a first allocation target cluster corresponding to each data point when the similarity is maximum, wherein the first allocation target cluster is the target cluster with the greatest similarity to the data point among the plurality of target clusters; Each of the data points is added to the corresponding first allocation target cluster to obtain multiple cluster center matrices.

4. The incremental clustering method for atmospheric aerosol particle mass spectrum dataset according to claim 1, characterized in that: The similarity calculation is performed on each of the data points, and cluster allocation is performed according to the density priority strategy to obtain multiple cluster center matrices, specifically including: Calculating the similarity between each of the data points and the plurality of target clusters; Determining a preset intra-cluster similarity, and extracting a plurality of second allocation target clusters whose similarity is greater than or equal to the preset intra-cluster similarity; Calculating the cluster density of each of the second allocation target clusters, and obtaining a third allocation target cluster with the largest cluster density among the second allocation target clusters, wherein the third allocation target cluster is the target cluster with the largest cluster density among the plurality of second allocation target clusters; Each of the data points is added to the corresponding third allocation target cluster to obtain a plurality of cluster center matrices.

5. The incremental clustering method for atmospheric aerosol particle mass spectrum dataset according to claim 1, characterized in that: The merging and denoising of the plurality of cluster center matrices to obtain an initial clustering result, and performing a second similarity calculation on the initial clustering result to obtain an iterative similarity specifically includes: Calculating the inter-cluster similarity between the plurality of cluster center matrices, and extracting the cluster center matrices whose inter-cluster similarity is greater than a preset inter-cluster similarity, to obtain a cluster index set; Merging the cluster index set to obtain a de-redundant cluster set; Deleting clusters with a data vector count of 0 in the de-redundant cluster set, and performing cluster sorting and cluster numbering to obtain an initial clustering result; An inter-iteration similarity calculation is performed on the initial clustering result to obtain an iterative similarity, wherein the inter-iteration similarity calculation includes an inter-iteration similarity calculation based on cluster distribution and an inter-iteration similarity calculation based on cluster numbers.

6. The incremental clustering method for atmospheric aerosol particle mass spectrum dataset according to claim 1, characterized in that: The performing clustering convergence determination and iterative cyclic clustering processing on the initial clustering result according to the iterative similarity, and outputting the clustering result of the atmospheric aerosol particle mass spectrum dataset, specifically includes: Determining a preset convergence value, and judging whether the iterative similarity is less than the preset convergence value; If so, the initial clustering result is subjected to iterative cyclic clustering processing, wherein the input of each iteration is the clustering result output by the previous iteration, until the iterative similarity is greater than or equal to the preset convergence value or the number of iterations is greater than the preset iteration number threshold, and the clustering result of the atmospheric aerosol particle mass spectrum data set is output.

7. An incremental clustering system for atmospheric aerosol particle mass spectrum datasets, characterized by: The incremental clustering system for atmospheric aerosol particle mass spectrum dataset is applied to the incremental clustering method for atmospheric aerosol particle mass spectrum dataset according to any one of claims 1 to 6, and the incremental clustering system for atmospheric aerosol particle mass spectrum dataset comprises: A clustering initialization module is used to obtain an atmospheric aerosol particle mass spectrum data set and perform clustering initialization processing on the atmospheric aerosol particle mass spectrum data set to obtain a plurality of clustering initialization parameters; a cluster selection strategy determination module, configured to determine a target cluster selection strategy, and perform a first similarity calculation and cluster allocation process on a plurality of cluster initialization parameters using the target cluster selection strategy to obtain a plurality of cluster center matrices; an inter-iteration similarity calculation module, configured to perform a merging process and a denoising process on the plurality of cluster center matrices to obtain an initial clustering result, and perform a second similarity calculation on the initial clustering result to obtain an iterative similarity; A clustering result output module is used to perform clustering convergence judgment and iterative cyclic clustering processing on the initial clustering result according to the iterative similarity, and output the clustering result of the atmospheric aerosol particle mass spectrum data set.

8. A terminal, characterized in that: The terminal includes: a memory, a processor, and an incremental clustering program for an atmospheric aerosol particle mass spectrum dataset stored in the memory and executable on the processor. When the incremental clustering program for an atmospheric aerosol particle mass spectrum dataset is executed by the processor, the steps of the incremental clustering method for an atmospheric aerosol particle mass spectrum dataset according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores an incremental clustering program for an atmospheric aerosol particle mass spectrum dataset. When the incremental clustering program for an atmospheric aerosol particle mass spectrum dataset is executed by a processor, the steps of the incremental clustering method for an atmospheric aerosol particle mass spectrum dataset according to any one of claims 1 to 6 are implemented.

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