A multi-objective heuristic single-cell deep clustering method

Abstract

The application discloses a multi-target heuristic single cell deep clustering method, and the multi-target heuristic single cell deep clustering algorithm is obtained by improving the scDHA algorithm. The multi-target heuristic single cell deep clustering algorithm firstly adopts a stacked Bayesian autoencoder algorithm and an Autoencoder algorithm to jointly perform multiple dimension reductions on single cell transcriptome sequencing data after preprocessing, then adopts a K-means algorithm and an Ultra-Scalable Spectral Clustering algorithm to jointly cluster multiple dimension reduction data to generate multiple clustering results, and finally adopts a dynamic positive and negative sine optimization algorithm to calculate a unique clustering result from the multiple clustering results. The method has the advantages of fast clustering speed, small hardware memory consumption, low hardware cost, high clustering precision and strong robustness.

Description

Technical Field

[0001] This invention relates to single-cell deep clustering methods, and more particularly to a multi-objective heuristic single-cell deep clustering method. Background Technology

[0002] In recent years, the rapid development of single-cell RNA sequencing technology has driven progress in biological research. Traditional RNA sequencing technologies typically obtain gene expression data at the tissue or cell population level, while single-cell RNA sequencing technology can obtain high-resolution gene expression data at the individual cell level. However, due to cellular heterogeneity, gene expression varies significantly even among cells of the same type. Furthermore, the massive data volume and high-dimensionality of single-cell RNA sequencing data make its analysis even more challenging.

[0003] To address these challenges, a recent study proposed the scDHA (single-cell decomposition using hierarchical autoencoder) algorithm. This scDHA algorithm first uses a stacked Bayesian autoencoder to perform multiple dimensionality reductions on preprocessed single-cell transcriptome sequencing data, resulting in multiple dimensionality-reduced datasets. Then, it employs a K-nearest neighbor adaptation of spectral clustering algorithm to cluster these multiple dimensionality-reduced datasets, generating multiple clustering results. Finally, a consensus clustering algorithm (i.e., weighted-based meta-clustering) is used to determine a final clustering result. However, the scDHA algorithm generates a large amount of unnecessary intermediate data during the clustering process, has a long runtime, and requires significant hardware memory overhead, resulting in slow overall clustering speed and high hardware costs. Furthermore, the local diversity of subsets within the generated clustering results is difficult to guarantee, leaving considerable room for improvement in clustering accuracy and robustness. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a multi-objective heuristic single-cell deep clustering method that has fast clustering speed, low hardware memory overhead, low hardware cost, high clustering accuracy, and strong robustness.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a multi-objective heuristic single-cell deep clustering method, which uses a multi-objective heuristic single-cell deep clustering algorithm to cluster preprocessed single-cell transcriptome sequencing data to obtain clustering results; wherein, the multi-objective heuristic single-cell deep clustering algorithm is obtained by making the following three improvements to the scDHA algorithm: First, the stacked Bayesian autoencoder algorithm used in the scDHA algorithm to perform multiple dimensionality reductions on the preprocessed single-cell transcriptome sequencing data is replaced by a combination of the stacked Bayesian autoencoder algorithm and the Autoencoder algorithm to perform multiple dimensionality reductions on the preprocessed single-cell transcriptome sequencing data; Second, the K-nearest neighbor adaptation of spectral clustering algorithm used in the scDHA algorithm to cluster multiple dimensionality-reduced data to generate multiple clustering results is replaced by a K-means algorithm combined with the Ultra-Scalable Spectral Clustering algorithm to cluster multiple dimensionality-reduced data to generate multiple clustering results; Third, the weighted-based... Instead of using the meta-clustering algorithm to calculate a unique clustering result from multiple clustering results, a dynamic sine and cosine optimization algorithm is used to calculate a unique clustering result from multiple clustering results.

[0006] Preprocessed single-cell transcriptome sequencing data were obtained through the following steps:

[0007] Step A1: Let X be the single-cell transcriptome sequencing data that needs to be clustered, let m be the number of rows and n be the number of columns of single-cell transcriptome sequencing data X, that is, single-cell transcriptome sequencing data X is a data matrix of m rows and n columns;

[0008] Step A2: Preprocess each element in the single-cell transcriptome sequencing data X using formula (1) to obtain the preprocessed single-cell transcriptome sequencing data, which is denoted as the preprocessing matrix M:

[0009]

[0010] Among them, X i Let X represent the element in the i-th row of X. i,j M represents the element in the i-th row and j-th column of X. i,j Let M be the element in the i-th row and j-th column, where i = 1, 2, ..., m, j = 1, 2, ..., n; min(X i ) indicates taking X i The minimum value among n elements, max(X) i) indicates taking X i Find the maximum value among n elements.

[0011] The specific process of using a multi-objective heuristic single-cell deep clustering algorithm to cluster preprocessed single-cell transcriptome sequencing data and obtain the clustering results is as follows:

[0012] Step S1: Perform feature selection on the preprocessing matrix M to obtain the feature matrix. The specific steps are as follows:

[0013] Step S1.1: First, randomly generate a weight vector W with 1 row and n columns and a bias vector b with 1 row and n columns within the range of 0 to 1. Then, calculate each element of the preprocessing matrix M using formula (2) to obtain the calculation results. Finally, use the calculation results of all elements of the preprocessing matrix M to construct the encoding matrix, which is denoted as e:

[0014] e i,j =M i,j ·W 1,j +b 1,j (2)

[0015] Among them, W 1,j b represents the element in the first row and j-th column of the weight vector W; 1,j e represents the element in the 1st row and jth column of the bias vector b. i,j This represents the calculation result of the element in the i-th row and j-th column of the preprocessing matrix M, which is also the element in the i-th row and j-th column of the encoding matrix e;

[0016] Step S1.2: First, randomly generate a weight vector W' with 1 row and n columns and a bias vector b' with 1 row and n columns within the range of 0 to 1. Then, calculate each element of the encoding matrix e using formula (3) to obtain the calculation result. Finally, use the calculation results of all elements of the encoding matrix e to construct the decoding matrix, and denote the decoding matrix as M':

[0017] M' i,j =e i,j ·W' 1,j +b' 1,j (3)

[0018] Among them, W' 1,j b' represents the element in the first row and j-th column of the weight vector W'. 1,j M' represents the element in the first row and j-th column of the bias vector b'. i,j This represents the result of calculating the element in the i-th row and j-th column of the encoding matrix e, which is also the element in the i-th row and j-th column of the decoding matrix M'.

[0019] Step S1.3: Use the AdamW algorithm to iteratively optimize each element of the weight vector W, bias vector b, weight vector W', and bias vector b' in the range of 0 to 1, and use the iterative optimization results of the weight vector W, bias vector b, weight vector W', and bias vector b' to update the encoding matrix e and the decoding matrix M' until M' = M;

[0020] Step S1.4: Denote the final iterative optimization result of W' as W”, and make a one-to-one correspondence between the n columns of W” and the n columns of M, that is, the j-th column of W” corresponds to the j-th column of M;

[0021] Step S1.5: Adjust the number of columns of the nth column of W” so that the elements in the first to nth columns of W” are sorted in descending order. If there are two or more columns of elements with the same size during the adjustment process, then these columns of elements are randomly sorted. The adjusted W” is denoted as W”'.

[0022] Step S1.6: Based on the correspondence between the n columns of W” and the n columns of M, adjust the number of columns of M’s n columns according to the adjustment result W”’ of the n columns of W”, and denote the adjusted M as M”.

[0023] Step S1.7: Take the elements from the 1st to the δth column of M” to form an eigenma matrix of size m×δ, and denote this eigenma matrix as A. The g-th column element of M” corresponds to the g-th column element of eigenma matrix A, where g = 1, 2, ..., δ. round() is a function that rounds to the nearest integer.

[0024] Step S2: Use the stacked Bayesian autoencoder algorithm to perform multiple dimensionality reductions on the feature matrix A, resulting in multiple dimensionality-reduced matrices. The specific process is as follows:

[0025] Step S2.1: Define the dimension reduction number variable, denoted as v, and set the dimension reduction number to λ-1, where λ is an integer greater than or equal to 10 and less than or equal to 15; initialize the dimension reduction number variable v by setting v = 1;

[0026] Step S2.2: Perform the v-th dimensionality reduction on the feature matrix A, specifically as follows:

[0027] Step S2.2.1: Randomly initialize the parameters of the encoding conversion function of the stacked Bayesian autoencoder algorithm within the range of 0 to 1, and denote the resulting encoding conversion function as f. E (·);

[0028] Step S2.2.2: Utilize the currently obtained encoding conversion function f E(·) Calculate the characteristic matrix A to obtain a dimension-reduced matrix with m rows and 16 columns. Denote this dimension-reduced matrix as z'. v The specific calculation formula is shown in equation (4):

[0029] z' v =f E (A) (4)

[0030] Step S2.2.3: Randomly initialize the parameters of the decoding conversion function of the stacked Bayesian autoencoder algorithm within the range of 0 to 1, and denote the resulting decoding conversion function as f. D (·);

[0031] Step S2.2.4: Utilize the currently obtained decoding conversion function f D (·) For the currently obtained dimension reduction matrix z' v The calculation yields a reconstruction matrix with m rows and δ columns, denoted as A'. v The specific calculation formula is shown in equation (5):

[0032] A' v =f D (z' v (5)

[0033] Step S2.2.5: Iteratively optimize the encoding transformation function f in the range of 0 to 1 using the AdamW algorithm. E The parameters and decoding conversion function f in (·) D The parameters in (·) are used, and the encoding conversion function f is employed. E (·) and decoding conversion function f D The iterative optimization result of (·) updates the dimensionality reduction matrix z' v And the reconstruction matrix is ​​denoted as A' v until A' v =A;

[0034] Step S2.2.6: Update the dimensionality reduction matrix z' generated in the last iteration. v denoted as z v ;

[0035] Step S2.3: Determine if the current value of v is equal to λ-1. If it is, proceed to step S2.4. If it is not, first update the value of v by adding 1 to the current value of v, and then return to step S2.2 for the next dimensionality reduction.

[0036] Step S2.4: Use z 1 To z λ-1 Construct a set of reduced-dimensional matrices, denoted as Z1, Z1 = {z 1,z 2 ,…,z λ-1};

[0037] Step S3: Use the Autoencoder algorithm to perform one dimensionality reduction on the feature matrix A to obtain a dimensionality-reduced matrix. The specific steps are as follows:

[0038] Step S3.1: Randomly initialize the parameters of the encoding conversion function of the Autoencoder algorithm within the range of 0 to 1, and denote the resulting encoding conversion function as f. E' (·);

[0039] Step S3.2: Utilize the currently obtained encoding conversion function f E' (·) Calculate the characteristic matrix A to obtain a dimension-reduced matrix with m rows and 16 columns, denoted as z'. λ The specific calculation formula is shown in equation (6):

[0040] z' λ =f E' (A) (6)

[0041] Step S3.3: Randomly initialize the parameters of the decoding conversion function of the Autoencoder algorithm within the range of 0 to 1, and denote the resulting decoding conversion function as f. D' (·);

[0042] Step S3.4: Utilize the currently obtained decoding conversion function f D' (·) For the currently obtained dimension reduction matrix z' λ The calculation yields a reconstruction matrix with m rows and δ columns, denoted as A'. λ The specific calculation formula is shown in equation (7):

[0043] A' λ =f D' (z' λ (7)

[0044] Step S3.5: Iteratively optimize the encoding conversion function f using the AdamW algorithm. E' The parameters and decoding conversion function f in (·) D' The parameters in (·) are used, and the encoding conversion function f is employed. E' (·) and decoding conversion function f D' The iterative optimization result of (·) updates the dimensionality reduction matrix z' λ And the reconstruction matrix is ​​denoted as A' λ until A' λ =A;

[0045] Step S3.6: Update the dimensionality reduction matrix z' generated in the last iteration. λ Let z be the dimension-reduced matrix obtained by performing a first-order dimension reduction on the feature matrix A using the Autoencoder algorithm. λ ;

[0046] Step S4: Place z λ Adding these to Z1 results in a set containing λ reduced-dimensional matrices, denoted as Z, where Z = {z...} 1 ,z 2 ,...,z λ};

[0047] Step S5: First, randomly initialize d K-means algorithms, where each K-means algorithm sets the number of cluster centers to K, where d and K are integers, and 10≤d≤20, 2≤K≤20. Then, use each of the obtained K-means algorithms to perform a clustering calculation on each dimensionality-reduced matrix in set Z, obtaining the clustering result of each dimensionality-reduced matrix under each K-means algorithm. Each clustering result of each dimensionality-reduced matrix under each K-means algorithm contains m cluster labels, and the m cluster labels belong to K categories. Then, use all the obtained clustering results to form the first clustering result set, which is denoted as Π1. in, This indicates that the φ-th K-means algorithm reduces the dimensionality of the matrix z. θ The clustering results obtained from performing a single clustering calculation are φ = 1, 2, ..., d, θ = 1, 2, ..., λ;

[0048] Step S6: First, randomly initialize d Ultra-Scalable Spectral Clustering algorithms, where each Ultra-Scalable Spectral Clustering algorithm has K cluster centers. Then, use each of the obtained Ultra-Scalable Spectral Clustering algorithms to perform a clustering calculation on each dimensionality reduction matrix in set Z, obtaining the clustering result of each dimensionality reduction matrix under each Ultra-Scalable Spectral Clustering algorithm. Each clustering result of each dimensionality reduction matrix under each Ultra-Scalable Spectral Clustering algorithm contains m cluster labels, and the m cluster labels have K categories. Then, use all the obtained clustering results to construct a second clustering result set, denoted as Π2. in, This indicates that the φ-th Ultra-Scalable SpectralClustering algorithm applies the dimensionality reduction matrix z. θ The clustering result obtained from performing a single clustering calculation;

[0049] Step S7: Merge the first clustering result set Π1 and the second clustering result set Π2 to form the total clustering result set, denoted as Π3, where Π3 contains 2×d×λ clustering results.

[0050] Step S8: Use the dynamic sine and cosine optimization algorithm to evaluate the total clustering result set Π3 and obtain a unique clustering result.

[0051] The specific process of using the dynamic sine and cosine optimization algorithm to evaluate the total clustering result set Π3 in step S8 to obtain a unique clustering result is as follows:

[0052] Step S8.1: Define a population containing P individuals, where each individual is a set containing Q elements, where P is an integer and 10 ≤ P ≤ 15, and Q = 2 × d × λ;

[0053] Step S8.2: Randomly initialize each element of each individual in the population with discrete values ​​of 0 or 1 to obtain the 0th generation population. Let the p-th individual in the 0th generation population be denoted as... Let the q-th element of the p-th individual in the 0th generation population be denoted as... p=1,2,...,P, q=1,2,...,Q;

[0054] Step S8.3: Randomly initialize an ultra-scalable ensemble clustering algorithm, and set the number of cluster centers of the ultra-scalable ensemble clustering algorithm to K;

[0055] Step S8.4: Construct the multi-objective fitness function as shown in Equation (8):

[0056]

[0057] Where x represents the input of the multi-objective fitness function, F(x) represents the fitness value when the input is x, ln() represents the logarithmic function, f1(x) represents the fitness function Davies-Bouldin Index when the input is x, f2(x) represents the fitness function Dunn's Index when the input is x, f3(x) represents the fitness function Calinski Harabasz Index when the input is x, and η1, η2 and η3 are three weight factors, where 0≤η1≤1, 0≤η2≤1, 0≤η3≤1, and η1+η2+η3=1;

[0058] Step S8.5: First, use the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to calculate the clustering result for each individual in the 0th generation population. Each individual's clustering result contains m clustering labels, and the clustering labels have K categories. Then, use the clustering result of each individual in the 0th generation population as input to the multi-objective fitness function obtained in step S8.4. Substitute this into the multi-objective fitness function to calculate the fitness value of each individual in the 0th generation population. The fitness value of the p-th individual in the 0th generation population is denoted as...

[0059] Step S8.6: Compare the fitness values ​​of all individuals in the 0th generation population, take the maximum fitness value as the global optimal fitness value, denoted as Γ, and take the individual corresponding to the maximum fitness value as the global optimal individual, denoted as B. If multiple maximum fitness values ​​appear, randomly select one as the maximum fitness value.

[0060] Step S8.7: Set the total number of iterations to T, where T is an integer and 100≤T≤200; set the iteration variable to t and initialize t = 1; set the control factor to α, where 0≤α≤1;

[0061] Step S8.8: Perform the t-th iteration, the specific process is as follows:

[0062] Step S8.8.1: Set the influence factor of generation t to ω. t ω is calculated using formula (9). t :

[0063]

[0064] Where exp() represents the exponential function;

[0065] Step S8.8.2: First, randomly generate three t-th generation random numbers that follow a uniform distribution within the range of 0 to 1. and The random parameters of the tth generation are calculated using formula (10). Then, formula (11) is used to obtain the p-th initial individual of the t-th generation.

[0066]

[0067]

[0068] Where sin represents the sine function and cos represents the cosine function;

[0069] Step S8.8.3: For the p-th initial individual in the t-th generation... Each element in the dataset is discretized, resulting in the p-th individual of the t-th generation population. This p-th individual of the t-th generation population is denoted as...

[0070] Step S8.8.4: First, use the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to calculate the clustering result for each individual in the t-th generation population. Each individual's clustering result contains m clustering labels, and the clustering labels have K categories. Then, use the clustering result of each individual in the t-th generation population as input to the multi-objective fitness function obtained in step S8.4. Substitute this into the multi-objective fitness function to calculate the fitness value of each individual in the t-th generation population. The fitness value of the p-th individual in the t-th generation population is denoted as...

[0071] Step S8.8.5: First compare the fitness values ​​of all individuals in the t-th generation population, and take the maximum fitness value as the optimal fitness value of the t-th generation. The individual corresponding to the maximum fitness value is taken as the optimal individual of the t-th generation. If there are multiple maximum fitness values, randomly select one as the maximum fitness value.

[0072] Step S8.8.6: Compare the optimal fitness value of generation t with the current global optimal fitness value Γ. If the optimal fitness value of generation t is greater than the current global optimal fitness value Γ, then update the current global optimal fitness value Γ with the optimal fitness value of generation t, and update the current global optimal individual B with the optimal individual of generation t. If the optimal fitness value of generation t is not greater than the current global optimal fitness value Γ, then the current global optimal fitness value Γ and the current global optimal individual B remain unchanged.

[0073] Step S8.9: Determine if the current value of t is equal to T. If it is equal, proceed to step S8.10. If it is not equal, first update the value of t by adding 1 to the current value of t, and then return to step S8.8 for the next iteration.

[0074] Step S8.10: First, map the Q elements of the current global optimal individual B to the Q clustering results of the total clustering result set Π3, where the q-th element of the current global optimal individual B corresponds to the q-th clustering result in the total clustering result set Π3; then, determine whether each element in the current global optimal individual B is 1. If an element in the current global optimal individual B is 1, the clustering result in the total clustering result set Π3 corresponding to that element is selected; then, use all the selected clustering results in the total clustering result set Π3 to form a clustering result subset, and denote this clustering result subset as Π4;

[0075] Step S8.11: Calculate the clustering result subset Π4 using the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to obtain the final unique clustering result, which contains m cluster labels and K categories of cluster labels.

[0076] Compared with existing technologies, the advantages of this invention lie in its improvement of the scDHA algorithm to obtain a multi-objective heuristic single-cell deep clustering algorithm. This multi-objective heuristic single-cell deep clustering algorithm first uses a stacked Bayesian autoencoder algorithm and an autoencoder algorithm in combination to perform multiple dimensionality reductions on the preprocessed single-cell transcriptome sequencing data. Then, it uses a K-means algorithm combined with an Ultra-Scalable Spectral Clustering algorithm to cluster multiple dimensionality-reduced data to generate multiple clustering results. Finally, a dynamic sine and cosine optimization algorithm is used to calculate a unique clustering result from these multiple clustering results. During the dimensionality reduction process, it can balance the subsequent hybrid approach of Euclidean distance-based clustering and graph theory clustering (i.e., K-means algorithm combined with Ultra-Scalable Spectral Clustering algorithm) for data sampling and batch processing, thereby avoiding the generation of unnecessary large amounts of intermediate data, thus reducing runtime and hardware memory consumption. The use of the K-means algorithm combined with Ultra-Scalable Spectral Clustering algorithm... The clustering algorithm clusters the dimensionality-reduced matrix to improve the local diversity of the clustering results. Then, the dynamic sine and cosine optimization algorithm is used to calculate a unique clustering result with high accuracy and strong robustness from multiple clustering results. Thus, the present invention has fast clustering speed, low hardware memory overhead, low hardware cost, high clustering accuracy, and strong robustness. Attached Figure Description

[0077] Figure 1 This is a flowchart of the multi-objective heuristic single-cell deep clustering method of the present invention. Detailed Implementation

[0078] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0079] Example 1: A multi-objective heuristic single-cell deep clustering method is used to cluster preprocessed single-cell transcriptome sequencing data to obtain clustering results. The multi-objective heuristic single-cell deep clustering algorithm is derived by improving the scDHA algorithm in the following three ways: 1. Instead of using the stacked Bayesian autoencoder algorithm to perform multiple dimensionality reductions on the preprocessed single-cell transcriptome sequencing data, the scDHA algorithm uses a combination of the stacked Bayesian autoencoder and autoencoder algorithms to perform multiple dimensionality reductions on the preprocessed single-cell transcriptome sequencing data. 2. Instead of using the K-nearest neighbor adaptation of spectral clustering algorithm to cluster multiple dimensionality-reduced data to generate multiple clustering results, the scDHA algorithm uses a combination of the K-means algorithm and the Ultra-Scalable Spectral Clustering algorithm to cluster multiple dimensionality-reduced data to generate multiple clustering results. 3. The weighted-based... Instead of using the meta-clustering algorithm to calculate a unique clustering result from multiple clustering results, a dynamic sine and cosine optimization algorithm is used to calculate a unique clustering result from multiple clustering results.

[0080] In this embodiment, the stacked Bayesian autoencoder algorithm and the Autoencoder algorithm are first used together to perform multiple dimensionality reductions on the preprocessed single-cell transcriptome sequencing data. Then, the K-means algorithm combined with the Ultra-Scalable Spectral Clustering algorithm is used to cluster the multiple dimensionality-reduced data to generate multiple clustering results. Finally, the dynamic sine and cosine optimization algorithm is used to calculate a unique clustering result from the multiple clustering results. During the dimensionality reduction process, the hybrid approach of Euclidean distance-based clustering and graph theory clustering (i.e., the K-means algorithm combined with the Ultra-Scalable Spectral Clustering algorithm) can be balanced. Data sampling and batch processing are performed to avoid generating unnecessary large amounts of intermediate data, thereby reducing running time and hardware memory consumption. After using the K-means algorithm combined with the Ultra-Scalable Spectral Clustering algorithm to cluster the dimensionality-reduced matrix and improve the local diversity of the clustering results, the dynamic sine and cosine optimization algorithm is used to calculate a unique clustering result with high accuracy and strong robustness from the multiple clustering results.

[0081] Example 2: This example is basically the same as Example 1, except that the preprocessed single-cell transcriptome sequencing data is obtained through the following steps:

[0082] Step A1: Let X be the single-cell transcriptome sequencing data that needs to be clustered, let m be the number of rows and n be the number of columns of single-cell transcriptome sequencing data X, that is, single-cell transcriptome sequencing data X is a data matrix of m rows and n columns;

[0083] Step A2: Preprocess each element in the single-cell transcriptome sequencing data X using formula (1) to obtain the preprocessed single-cell transcriptome sequencing data, which is denoted as the preprocessing matrix M:

[0084]

[0085] Among them, X i Let X represent the element in the i-th row of X. i,j M represents the element in the i-th row and j-th column of X. i,j Let M be the element in the i-th row and j-th column, where i = 1, 2, ..., m, j = 1, 2, ..., n; min(X i ) indicates taking X i The minimum value among n elements, max(X) i ) indicates taking X i Find the maximum value among n elements.

[0086] Example 3: This example is basically the same as Example 2, except that: In this example, a multi-objective heuristic single-cell deep clustering algorithm is used to cluster the preprocessed single-cell transcriptome sequencing data. The specific process for obtaining the clustering results is as follows:

[0087] Step S1: Perform feature selection on the preprocessing matrix M to obtain the feature matrix. The specific steps are as follows:

[0088] Step S1.1: First, randomly generate a weight vector W with 1 row and n columns and a bias vector b with 1 row and n columns within the range of 0 to 1. Then, calculate each element of the preprocessing matrix M using formula (2) to obtain the calculation results. Finally, use the calculation results of all elements of the preprocessing matrix M to construct the encoding matrix, which is denoted as e:

[0089] e i,j =M i,j ·W 1,j +b 1,j (2)

[0090] Among them, W 1,j b represents the element in the first row and j-th column of the weight vector W; 1,j e represents the element in the 1st row and jth column of the bias vector b. i,j This represents the calculation result of the element in the i-th row and j-th column of the preprocessing matrix M, which is also the element in the i-th row and j-th column of the encoding matrix e;

[0091] Step S1.2: First, randomly generate a weight vector W' with 1 row and n columns and a bias vector b' with 1 row and n columns within the range of 0 to 1. Then, calculate each element of the encoding matrix e using formula (3) to obtain the calculation result. Finally, use the calculation results of all elements of the encoding matrix e to construct the decoding matrix, and denote the decoding matrix as M':

[0092] M' i,j =e i,j ·W' 1,j +b' 1,j (3)

[0093] Among them, W' 1,j b' represents the element in the first row and j-th column of the weight vector W'. 1,j M' represents the element in the first row and j-th column of the bias vector b'. i,j This represents the result of calculating the element in the i-th row and j-th column of the encoding matrix e, which is also the element in the i-th row and j-th column of the decoding matrix M'.

[0094] Step S1.3: Use the AdamW algorithm to iteratively optimize each element of the weight vector W, bias vector b, weight vector W', and bias vector b' in the range of 0 to 1, and use the iterative optimization results of the weight vector W, bias vector b, weight vector W', and bias vector b' to update the encoding matrix e and the decoding matrix M' until M' = M;

[0095] Step S1.4: Denote the final iterative optimization result of W' as W”, and make a one-to-one correspondence between the n columns of W” and the n columns of M, that is, the j-th column of W” corresponds to the j-th column of M;

[0096] Step S1.5: Adjust the number of columns of the nth column of W” so that the elements in the first to nth columns of W” are sorted in descending order. If there are two or more columns of elements with the same size during the adjustment process, then these columns of elements are randomly sorted. The adjusted W” is denoted as W”'.

[0097] Step S1.6: Based on the correspondence between the n columns of W” and the n columns of M, adjust the number of columns of M’s n columns according to the adjustment result W”’ of the n columns of W”, and denote the adjusted M as M”.

[0098] Step S1.7: Take the elements from the 1st to the δth column of M” to form an eigenma matrix of size m×δ, and denote this eigenma matrix as A. The g-th column element of M” corresponds to the g-th column element of eigenma matrix A, where g = 1, 2, ..., δ. round() is a function that rounds to the nearest integer.

[0099] Step S2: Use the stacked Bayesian autoencoder algorithm to perform multiple dimensionality reductions on the feature matrix A, resulting in multiple dimensionality-reduced matrices. The specific process is as follows:

[0100] Step S2.1: Define the dimension reduction number variable, denoted as v, and set the dimension reduction number to λ-1, where λ is an integer greater than or equal to 10 and less than or equal to 15; initialize the dimension reduction number variable v by setting v = 1;

[0101] Step S2.2: Perform the v-th dimensionality reduction on the feature matrix A, specifically as follows:

[0102] Step S2.2.1: Randomly initialize the parameters of the encoding conversion function of the stacked Bayesian autoencoder algorithm within the range of 0 to 1, and denote the resulting encoding conversion function as f. E (·);

[0103] Step S2.2.2: Utilize the currently obtained encoding conversion function f E(·) Calculate the characteristic matrix A to obtain a dimension-reduced matrix with m rows and 16 columns. Denote this dimension-reduced matrix as z'. v The specific calculation formula is shown in equation (4):

[0104] z' v =f E (A) (4)

[0105] Step S2.2.3: Randomly initialize the parameters of the decoding conversion function of the stacked Bayesian autoencoder algorithm within the range of 0 to 1, and denote the resulting decoding conversion function as f. D (·);

[0106] Step S2.2.4: Utilize the currently obtained decoding conversion function f D (·) For the currently obtained dimension reduction matrix z' v The calculation yields a reconstruction matrix with m rows and δ columns, denoted as A. v The specific calculation formula is shown in equation (5):

[0107] A' v =f D (z' v (5)

[0108] Step S2.2.5: Iteratively optimize the encoding transformation function f in the range of 0 to 1 using the AdamW algorithm. E The parameters and decoding conversion function f in (·) D The parameters in (·) are used, and the encoding conversion function f is employed. E (·) and decoding conversion function f D The iterative optimization result of (·) updates the dimensionality reduction matrix z' v And the reconstruction matrix is ​​denoted as A' v until A' v =A;

[0109] Step S2.2.6: Update the dimensionality reduction matrix z' generated in the last iteration. v denoted as z v ;

[0110] Step S2.3: Determine if the current value of v is equal to λ-1. If it is, proceed to step S2.4. If it is not, first update the value of v by adding 1 to the current value of v, and then return to step S2.2 for the next dimensionality reduction.

[0111] Step S2.4: Use z 1 To z λ-1 Construct a set of reduced-dimensional matrices, denoted as Z1, Z1 = {z 1,z 2 ,...,z λ-1};

[0112] Step S3: Use the Autoencoder algorithm to perform one dimensionality reduction on the feature matrix A to obtain a dimensionality-reduced matrix. The specific steps are as follows:

[0113] Step S3.1: Randomly initialize the parameters of the encoding conversion function of the Autoencoder algorithm within the range of 0 to 1, and denote the resulting encoding conversion function as f. E' (·);

[0114] Step S3.2: Utilize the currently obtained encoding conversion function f E' (·) Calculate the characteristic matrix A to obtain a dimension-reduced matrix with m rows and 16 columns, denoted as z'. λ The specific calculation formula is shown in equation (6):

[0115] z' λ =f E' (A) (6)

[0116] Step S3.3: Randomly initialize the parameters of the decoding conversion function of the Autoencoder algorithm within the range of 0 to 1, and denote the resulting decoding conversion function as f. D' (·);

[0117] Step S3.4: Utilize the currently obtained decoding conversion function f D' (·) For the currently obtained dimension reduction matrix z' λ The calculation yields a reconstruction matrix with m rows and δ columns, denoted as A'. λ The specific calculation formula is shown in equation (7):

[0118] A' λ =f D' (z' λ (7)

[0119] Step S3.5: Iteratively optimize the encoding conversion function f using the AdamW algorithm. E' The parameters and decoding conversion function f in (·) D' The parameters in (·) are used, and the encoding conversion function f is employed. E' (·) and decoding conversion function f D' The iterative optimization result of (·) updates the dimensionality reduction matrix z' λ And the reconstruction matrix is ​​denoted as A' λ until A' λ =A;

[0120] Step S3.6: Update the dimensionality reduction matrix z' generated in the last iteration. λ Let z be the dimension-reduced matrix obtained by performing a first-order dimension reduction on the feature matrix A using the Autoencoder algorithm. λ ;

[0121] Step S4: Place z λ Adding these to Z1 results in a set containing λ reduced-dimensional matrices, denoted as Z, where Z = {z...} 1 ,z 2 ,...,z λ};

[0122] Step S5: First, randomly initialize d K-means algorithms, where each K-means algorithm sets the number of cluster centers to K, where d and K are integers, and 10≤d≤20, 2≤K≤20. Then, use each of the obtained K-means algorithms to perform a clustering calculation on each dimensionality-reduced matrix in set Z, obtaining the clustering result of each dimensionality-reduced matrix under each K-means algorithm. Each clustering result of each dimensionality-reduced matrix under each K-means algorithm contains m cluster labels, and the m cluster labels belong to K categories. Then, use all the obtained clustering results to form the first clustering result set, which is denoted as Π1. in, This indicates that the φ-th K-means algorithm reduces the dimensionality of the matrix z. θ The clustering results obtained from performing a single clustering calculation are φ = 1, 2, ..., d, θ = 1, 2, ..., λ;

[0123] Step S6: First, randomly initialize d Ultra-Scalable Spectral Clustering algorithms, where each Ultra-Scalable Spectral Clustering algorithm has K cluster centers. Then, use each of the obtained Ultra-Scalable Spectral Clustering algorithms to perform a clustering calculation on each dimensionality reduction matrix in set Z, obtaining the clustering result of each dimensionality reduction matrix under each Ultra-Scalable Spectral Clustering algorithm. Each clustering result of each dimensionality reduction matrix under each Ultra-Scalable Spectral Clustering algorithm contains m cluster labels, and the m cluster labels have K categories. Then, use all the obtained clustering results to construct a second clustering result set, denoted as Π2. in, This indicates that the φ-th Ultra-Scalable SpectralClustering algorithm applies the dimensionality reduction matrix z. θ The clustering result obtained from performing a single clustering calculation;

[0124] Step S7: Merge the first clustering result set Π1 and the second clustering result set Π2 to form the total clustering result set, denoted as Π3, where Π3 contains 2×d×λ clustering results.

[0125] Step S8: Use the dynamic sine and cosine optimization algorithm to evaluate the total clustering result set Π3 and obtain a unique clustering result; the specific process is as follows:

[0126] Step S8.1: Define a population containing P individuals, where each individual is a set containing Q elements, where P is an integer and 10 ≤ P ≤ 15, and Q = 2 × d × λ;

[0127] Step S8.2: Randomly initialize each element of each individual in the population with discrete values ​​of 0 or 1 to obtain the 0th generation population. Let the p-th individual in the 0th generation population be denoted as... Let the q-th element of the p-th individual in the 0th generation population be denoted as... p=1,2,...,P, q=1,2,...,Q;

[0128] Step S8.3: Randomly initialize an ultra-scalable ensemble clustering algorithm, and set the number of cluster centers of the ultra-scalable ensemble clustering algorithm to K;

[0129] Step S8.4: Construct the multi-objective fitness function as shown in Equation (8):

[0130]

[0131] Where x represents the input of the multi-objective fitness function, F(x) represents the fitness value when the input is x, ln() represents the logarithmic function, f1(x) represents the fitness function Davies-Bouldin Index when the input is x, f2(x) represents the fitness function Dunn's Index when the input is x, f3(x) represents the fitness function Calinski Harabasz Index when the input is x, and η1, η2 and η3 are three weight factors, where 0≤η1≤1, 0≤η2≤1, 0≤η3≤1, and η1+η2+η3=1;

[0132] Step S8.5: First, use the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to calculate the clustering result for each individual in the 0th generation population. Each individual's clustering result contains m clustering labels, and the clustering labels have K categories. Then, use the clustering result of each individual in the 0th generation population as input to the multi-objective fitness function obtained in step S8.4. Substitute this into the multi-objective fitness function to calculate the fitness value of each individual in the 0th generation population. The fitness value of the p-th individual in the 0th generation population is denoted as...

[0133] Step S8.6: Compare the fitness values ​​of all individuals in the 0th generation population, take the maximum fitness value as the global optimal fitness value, denoted as Γ, and take the individual corresponding to the maximum fitness value as the global optimal individual, denoted as B. If multiple maximum fitness values ​​appear, randomly select one as the maximum fitness value.

[0134] Step S8.7: Set the total number of iterations to T, where T is an integer and 100≤T≤200; set the iteration variable to t and initialize t = 1; set the control factor to α, where 0≤α≤1;

[0135] Step S8.8: Perform the t-th iteration, the specific process is as follows:

[0136] Step S8.8.1: Set the influence factor of generation t to ω. t ω is calculated using formula (9). t :

[0137]

[0138] Where exp() represents the exponential function;

[0139] Step S8.8.2: First, randomly generate three t-th generation random numbers that follow a uniform distribution within the range of 0 to 1. and The random parameters of the tth generation are calculated using formula (10). Then, formula (11) is used to obtain the p-th initial individual of the t-th generation.

[0140]

[0141]

[0142] Where sin represents the sine function and cos represents the cosine function;

[0143] Step S8.8.3: For the p-th initial individual in the t-th generation... Each element in the dataset is discretized, resulting in the p-th individual of the t-th generation population. This p-th individual of the t-th generation population is denoted as...

[0144] Step S8.8.4: First, use the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to calculate the clustering result for each individual in the t-th generation population. Each individual's clustering result contains m clustering labels, and the clustering labels have K categories. Then, use the clustering result of each individual in the t-th generation population as input to the multi-objective fitness function obtained in step S8.4. Substitute this into the multi-objective fitness function to calculate the fitness value of each individual in the t-th generation population. The fitness value of the p-th individual in the t-th generation population is denoted as...

[0145] Step S8.8.5: First compare the fitness values ​​of all individuals in the t-th generation population, and take the maximum fitness value as the optimal fitness value of the t-th generation. The individual corresponding to the maximum fitness value is taken as the optimal individual of the t-th generation. If there are multiple maximum fitness values, randomly select one as the maximum fitness value.

[0146] Step S8.8.6: Compare the optimal fitness value of generation t with the current global optimal fitness value Γ. If the optimal fitness value of generation t is greater than the current global optimal fitness value Γ, then update the current global optimal fitness value Γ with the optimal fitness value of generation t, and update the current global optimal individual B with the optimal individual of generation t. If the optimal fitness value of generation t is not greater than the current global optimal fitness value Γ, then the current global optimal fitness value Γ and the current global optimal individual B remain unchanged.

[0147] Step S8.9: Determine if the current value of t is equal to T. If it is equal, proceed to step S8.10. If it is not equal, first update the value of t by adding 1 to the current value of t, and then return to step S8.8 for the next iteration.

[0148] Step S8.10: First, map the Q elements of the current global optimal individual B to the Q clustering results of the total clustering result set Π3, where the q-th element of the current global optimal individual B corresponds to the q-th clustering result in the total clustering result set Π3; then, determine whether each element in the current global optimal individual B is 1. If an element in the current global optimal individual B is 1, the clustering result in the total clustering result set Π3 corresponding to that element is selected; then, use all the selected clustering results in the total clustering result set Π3 to form a clustering result subset, and denote this clustering result subset as Π4;

[0149] Step S8.11: Calculate the clustering result subset Π4 using the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to obtain the final unique clustering result, which contains m cluster labels and K categories of cluster labels.

[0150] The flowchart of the multi-objective heuristic single-cell deep clustering method in this embodiment is as follows: Figure 1 As shown in the figure. In this embodiment, a population is constructed to represent the clustering result set. The ultra-scalable ensemble clustering algorithm is used to calculate each individual in each generation of the population, and a multi-objective fitness function is designed to evaluate the calculation results (i.e., each individual in each generation of the population). During the calculation of each individual in each generation of the population, a control factor is created and a dynamic sine and cosine optimization algorithm is introduced to iteratively update the population, ultimately obtaining a unique clustering result. Throughout the iterative process, the created control factor is used to improve the optimization capability of the dynamic sine and cosine optimization algorithm. At the same time, the multi-objective fitness function is used to evaluate the calculation results to ensure the local diversity of the clustering result subset represented by each individual in the population. Finally, the clustering subset represented by the optimal population is integrated into a single clustering result, improving and ensuring the accuracy and robustness of the final clustering result.

[0151] In summary, the multi-objective heuristic single-cell deep clustering method of this invention improves upon the conventional scDHA algorithm to obtain a multi-objective heuristic single-cell deep clustering algorithm. Even after preprocessing single-cell transcriptome sequencing data, the preprocessed data still suffers from high dimensionality and data redundancy. While the scDHA algorithm, using a stacked Bayesian autoencoder, can extract high-order abstract feature representations from the preprocessed single-cell transcriptome sequencing data, it cannot guarantee the completeness of the extracted data. Therefore, in the multi-objective heuristic single-cell deep clustering algorithm of this invention, after feature selection on the preprocessed single-cell transcriptome sequencing data, it reduces the number of dimensionality reduction steps of the stacked Bayesian autoencoder algorithm while jointly applying the Autoencoder algorithm for dimensionality reduction. This ensures the integrity of the dimensionality reduction matrix set without increasing the algorithm's runtime or hardware memory usage. Furthermore, since the scDHA algorithm's K-nearest neighbor adaptation of spectral clustering algorithm cannot guarantee the diversity of the cluster sets after obtaining the dimensionality-reduced data set, this approach addresses this issue. In the multi-objective heuristic single-cell deep clustering algorithm of this invention, the algorithm employs the K-means algorithm based on Euclidean distance and the Ultra-Scalable Spectral Clustering algorithm based on graph theory to improve the diversity of clustering results. Furthermore, the Ultra-Scalable Spectral Clustering algorithm utilizes sampling and batch processing, resulting in lower overall runtime and hardware memory usage compared to the K-nearest neighbor adaptation of spectral clustering algorithm. Finally, while the scDHA algorithm uses a weighted-based meta-clustering algorithm to calculate unique clustering results, the multi-objective heuristic single-cell deep clustering algorithm of this invention employs a dynamic sine / cosine optimization algorithm that automatically learns the similarity between clustering results and dynamically adjusts the size of the cluster sets, thereby obtaining more accurate and stable unique clustering results.

Claims

1. A multi-objective heuristic single-cell deep clustering method, characterized in that... A multi-objective heuristic single-cell deep clustering algorithm was used to cluster preprocessed single-cell transcriptome sequencing data to obtain clustering results. The multi-objective heuristic single-cell deep clustering algorithm was derived by making the following three improvements to the scDHA algorithm:

1. Instead of using the stacked Bayesian autoencoder algorithm to perform multiple dimensionality reductions on the preprocessed single-cell transcriptome sequencing data, the scDHA algorithm now uses a combination of the stacked Bayesian autoencoder and autoencoder algorithms to perform multiple dimensionality reductions on the preprocessed single-cell transcriptome sequencing data.

2. Instead of using the K-nearest neighbor adaptation of spectral clustering algorithm to cluster multiple dimensionality-reduced data to generate multiple clustering results, the scDHA algorithm now uses a combination of the K-means algorithm and the Ultra-Scalable Spectral Clustering algorithm to cluster multiple dimensionality-reduced data to generate multiple clustering results.

3. The weighted-based... Instead of using the meta-clustering algorithm to calculate a unique clustering result from multiple clustering results, a dynamic sine and cosine optimization algorithm is used to calculate a unique clustering result from multiple clustering results.

2. The multi-objective heuristic single-cell deep clustering method according to claim 1, characterized in that... Preprocessed single-cell transcriptome sequencing data were obtained through the following steps: Step A1: Let X be the single-cell transcriptome sequencing data that needs to be clustered, let m be the number of rows and n be the number of columns of single-cell transcriptome sequencing data X, that is, single-cell transcriptome sequencing data X is a data matrix of m rows and n columns; Step A2: Preprocess each element in the single-cell transcriptome sequencing data X using formula (1) to obtain the preprocessed single-cell transcriptome sequencing data, which is denoted as the preprocessing matrix M: Among them, X i Let X represent the element in the i-th row of X. i,j M represents the element in the i-th row and j-th column of X. i,j Let M be the element in the i-th row and j-th column, where i = 1, 2, ..., m, j = 1, 2, ..., n; min(X i ) indicates taking X i The minimum value among n elements, max(X) i ) indicates taking X i Find the maximum value among n elements.

3. The multi-objective heuristic single-cell deep clustering method according to claim 2, characterized in that... The specific process of using a multi-objective heuristic single-cell deep clustering algorithm to cluster preprocessed single-cell transcriptome sequencing data and obtain the clustering results is as follows: Step S1: Perform feature selection on the preprocessing matrix M to obtain the feature matrix. The specific steps are as follows: Step S1.1: First, randomly generate a weight vector W with 1 row and n columns and a bias vector b with 1 row and n columns within the range of 0 to 1. Then, calculate each element of the preprocessing matrix M using formula (2) to obtain the calculation results. Finally, use the calculation results of all elements of the preprocessing matrix M to construct the encoding matrix, which is denoted as e: have been i,j =M i,j ·W 1,j +b 1,j (2) Among them, W 1,j b represents the element in the first row and j-th column of the weight vector W; 1,j e represents the element in the 1st row and jth column of the bias vector b. i,j This represents the calculation result of the element in the i-th row and j-th column of the preprocessing matrix M, which is also the element in the i-th row and j-th column of the encoding matrix e; Step S1.2: First, randomly generate a weight vector W' with 1 row and n columns and a bias vector b' with 1 row and n columns within the range of 0 to 1. Then, calculate each element of the encoding matrix e using formula (3) to obtain the calculation result. Finally, use the calculation results of all elements of the encoding matrix e to construct the decoding matrix, and denote the decoding matrix as M': m' i,j =e i,j ·W' 1,j +b' 1,j (3) Among them, W' 1,j b' represents the element in the first row and j-th column of the weight vector W'. 1,j M' represents the element in the first row and j-th column of the bias vector b'. i,j This represents the result of calculating the element in the i-th row and j-th column of the encoding matrix e, which is also the element in the i-th row and j-th column of the decoding matrix M'. Step S1.3: Use the AdamW algorithm to iteratively optimize each element of the weight vector W, bias vector b, weight vector W', and bias vector b' in the range of 0 to 1, and use the iterative optimization results of the weight vector W, bias vector b, weight vector W', and bias vector b' to update the encoding matrix e and the decoding matrix M' until M' = M; Step S1.4: Denote the final iterative optimization result of W' as W”, and make a one-to-one correspondence between the n columns of W” and the n columns of M, that is, the j-th column of W” corresponds to the j-th column of M; Step S1.5: Adjust the number of columns of the nth column of W” so that the elements in the first to nth columns of W” are sorted in descending order. If there are two or more columns of elements with the same size during the adjustment process, then these columns of elements are randomly sorted. The adjusted W” is denoted as W”'. Step S1.6: Based on the correspondence between the n columns of W” and the n columns of M, adjust the number of columns of M’s n columns according to the adjustment result W”’ of the n columns of W”, and denote the adjusted M as M”. Step S1.7: Take the elements from the 1st to the δth column of M” to form an eigenma matrix of size m×δ, and denote this eigenma matrix as A. The g-th column element of M” corresponds to the g-th column element of eigenma matrix A, where g = 1, 2, ..., δ. round() is a function that rounds to the nearest integer. Step S2: Use the stacked Bayesian autoencoder algorithm to perform multiple dimensionality reductions on the feature matrix A, resulting in multiple dimensionality-reduced matrices. The specific process is as follows: Step S2.1: Define the dimension reduction number variable, denoted as v, and set the dimension reduction number to λ-1, where λ is an integer greater than or equal to 10 and less than or equal to 15; initialize the dimension reduction number variable v by setting v = 1; Step S2.2: Perform the v-th dimensionality reduction on the feature matrix A, specifically as follows: Step S2.2.1: Randomly initialize the parameters of the encoding conversion function of the stacked Bayesian autoencoder algorithm within the range of 0 to 1, and denote the resulting encoding conversion function as f. E (·); Step S2.2.2: Utilize the currently obtained encoding conversion function f E (·) Calculate the characteristic matrix A to obtain a dimension-reduced matrix with m rows and 16 columns. Denote this dimension-reduced matrix as z'. v The specific calculation formula is shown in equation (4): z' v =f E (A) (4) Step S2.2.3: Randomly initialize the parameters of the decoding conversion function of the stacked Bayesian autoencoder algorithm within the range of 0 to 1, and denote the resulting decoding conversion function as f. D (·); Step S2.2.4: Utilize the currently obtained decoding conversion function f D (·) For the currently obtained dimension reduction matrix z' v The calculation yields a reconstruction matrix with m rows and δ columns, denoted as A'. v The specific calculation formula is shown in equation (5): A' v =f D (z' v ) (5) Step S2.2.5: Iteratively optimize the encoding transformation function f in the range of 0 to 1 using the AdamW algorithm. E The parameters and decoding conversion function f in (·) D The parameters in (·) are used, and the encoding conversion function f is employed. E (·) and decoding conversion function f D The iterative optimization result of (·) updates the dimensionality reduction matrix z' v And the reconstruction matrix is ​​denoted as A' v until A' v =A; Step S2.2.6: Update the dimensionality reduction matrix z' generated in the last iteration. v denoted as z v ; Step S2.3: Determine if the current value of v is equal to λ-1. If it is, proceed to step S2.

4. If it is not, first update the value of v by adding 1 to the current value of v, and then return to step S2.2 for the next dimensionality reduction. Step S2.4: Use z 1 To z λ-1 Construct a set of reduced-dimensional matrices, denoted as Z1, Z1 = {z 1 ,z 2 ,…,z λ-1 }; Step S3: Use the Autoencoder algorithm to perform one dimensionality reduction on the feature matrix A to obtain a dimensionality-reduced matrix. The specific steps are as follows: Step S3.1: Randomly initialize the parameters of the encoding conversion function of the Autoencoder algorithm within the range of 0 to 1, and denote the resulting encoding conversion function as f. E' (·); Step S3.2: Utilize the currently obtained encoding conversion function f E' (·) Calculate the characteristic matrix A to obtain a dimension-reduced matrix with m rows and 16 columns, denoted as z'. λ The specific calculation formula is shown in equation (6): z' λ =f E' (A) (6) Step S3.3: Randomly initialize the parameters of the decoding conversion function of the Autoencoder algorithm within the range of 0 to 1, and denote the resulting decoding conversion function as f. D' (·); Step S3.4: Utilize the currently obtained decoding conversion function f D' (·) For the currently obtained dimension reduction matrix z' λ The calculation yields a reconstruction matrix with m rows and δ columns, denoted as A'. λ The specific calculation formula is shown in equation (7): A' λ =f D' (z' λ ) (7) Step S3.5: Iteratively optimize the encoding conversion function f using the AdamW algorithm. E' The parameters and decoding conversion function f in (·) D' The parameters in (·) are used, and the encoding conversion function f is employed. E' (·) and decoding conversion function f D' The iterative optimization result of (·) updates the dimensionality reduction matrix z' λ And the reconstruction matrix is ​​denoted as A' λ until A' λ =A; Step S3.6: Update the dimensionality reduction matrix z' generated in the last iteration. λ Let z be the dimension-reduced matrix obtained by performing a first-order dimension reduction on the feature matrix A using the Autoencoder algorithm. λ ; Step S4: Place z λ Adding these to Z1 results in a set containing λ reduced-dimensional matrices, denoted as Z, where Z = {z...} 1 ,z 2 ,…,z λ }; Step S5: First, randomly initialize d K-means algorithms, where each K-means algorithm sets the number of cluster centers to K, where d and K are integers, and 10≤d≤20, 2≤K≤20. Then, use each of the obtained K-means algorithms to perform a clustering calculation on each dimensionality-reduced matrix in set Z, obtaining the clustering result of each dimensionality-reduced matrix under each K-means algorithm. Each clustering result of each dimensionality-reduced matrix under each K-means algorithm contains m cluster labels, and the m cluster labels belong to K categories. Then, use all the obtained clustering results to form the first clustering result set, which is denoted as Π1. in, This indicates that the φ-th K-means algorithm reduces the dimensionality of the matrix z. θ The clustering results obtained from performing a single clustering calculation are φ = 1, 2, ..., d, θ = 1, 2, ..., λ; Step S6: First, randomly initialize d Ultra-Scalable Spectral Clustering algorithms, where each Ultra-Scalable Spectral Clustering algorithm has K cluster centers. Then, use each of the obtained Ultra-Scalable Spectral Clustering algorithms to perform a clustering calculation on each dimensionality reduction matrix in set Z, obtaining the clustering result of each dimensionality reduction matrix under each Ultra-Scalable Spectral Clustering algorithm. Each clustering result of each dimensionality reduction matrix under each Ultra-Scalable Spectral Clustering algorithm contains m cluster labels, and the m cluster labels have K categories. Then, use all the obtained clustering results to construct a second clustering result set, denoted as Π2. in, This indicates that the φ-th Ultra-Scalable SpectralClustering algorithm applies the dimensionality reduction matrix z. θ The clustering result obtained from performing a single clustering calculation; Step S7: Merge the first clustering result set ∏1 and the second clustering result set Π2 to form the total clustering result set, denoted as Π3, where Π3 contains 2×d×λ clustering results. Step S8: Use the dynamic sine and cosine optimization algorithm to evaluate the total clustering result set Π3 and obtain a unique clustering result.

4. The multi-objective heuristic single-cell deep clustering method according to claim 3, characterized in that... The specific process of using the dynamic sine and cosine optimization algorithm to evaluate the total clustering result set Π3 in step S8 to obtain a unique clustering result is as follows: Step S8.1: Define a population containing P individuals, where each individual is a set containing Q elements, where P is an integer and 10 ≤ P ≤ 15, and Q = 2 × d × λ; Step S8.2: Randomly initialize each element of each individual in the population with discrete values ​​of 0 or 1 to obtain the 0th generation population. Let the p-th individual in the 0th generation population be denoted as... Let the q-th element of the p-th individual in the 0th generation population be denoted as... Step S8.3: Randomly initialize an ultra-scalable ensemble clustering algorithm, and set the number of cluster centers of the ultra-scalable ensemble clustering algorithm to K; Step S8.4: Construct the multi-objective fitness function as shown in Equation (8): Where x represents the input of the multi-objective fitness function, F(x) represents the fitness value when the input is x, ln() represents the logarithmic function, f1(x) represents the fitness function Davies-Bouldin Index when the input is x, f2(x) represents the fitness function Dunn's Index when the input is x, f3(x) represents the fitness function Calinski Harabasz Index when the input is x, and η1, η2 and η3 are three weight factors, where 0≤η1≤1, 0≤η2≤1, 0≤η3≤1, and η1+η2+η3=1; Step S8.5: First, use the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to calculate the clustering result for each individual in the 0th generation population. Each individual's clustering result contains m clustering labels, and the clustering labels have K categories. Then, use the clustering result of each individual in the 0th generation population as input to the multi-objective fitness function obtained in step S8.

4. Substitute this into the multi-objective fitness function to calculate the fitness value of each individual in the 0th generation population. The fitness value of the p-th individual in the 0th generation population is denoted as... Step S8.6: Compare the fitness values ​​of all individuals in the 0th generation population, take the maximum fitness value as the global optimal fitness value, denoted as Γ, and take the individual corresponding to the maximum fitness value as the global optimal individual, denoted as B. If multiple maximum fitness values ​​appear, randomly select one as the maximum fitness value. Step S8.7: Set the total number of iterations to T, where T is an integer and 100≤T≤200; set the iteration variable to t and initialize t = 1; set the control factor to α, where 0≤α≤1; Step S8.8: Perform the t-th iteration, the specific process is as follows: Step S8.8.1: Set the influence factor of generation t to ω. t ω is calculated using formula (9). t : Where exp() represents the exponential function; Step S8.8.2: First, randomly generate three random numbers r1 of generation t that follow a uniform distribution within the range of 0 to 1. t , and The random parameter r3 of the t-th generation is calculated using formula (10). t Then, formula (11) is used to obtain the p-th initial individual of the t-th generation. Where sin represents the sine function and cos represents the cosine function; Step S8.8.3: For the p-th initial individual in the t-th generation... Each element in the dataset is discretized, resulting in the p-th individual of the t-th generation population. This p-th individual of the t-th generation population is denoted as... Step S8.8.4: First, use the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to calculate the clustering result for each individual in the t-th generation population. Each individual's clustering result contains m clustering labels, and the clustering labels have K categories. Then, use the clustering result of each individual in the t-th generation population as input to the multi-objective fitness function obtained in step S8.

4. Substitute this into the multi-objective fitness function to calculate the fitness value of each individual in the t-th generation population. The fitness value of the p-th individual in the t-th generation population is denoted as... Step S8.8.5: First compare the fitness values ​​of all individuals in the t-th generation population, and take the maximum fitness value as the optimal fitness value of the t-th generation. The individual corresponding to the maximum fitness value is taken as the optimal individual of the t-th generation. If there are multiple maximum fitness values, randomly select one as the maximum fitness value. Step S8.8.6: Compare the optimal fitness value of generation t with the current global optimal fitness value Γ. If the optimal fitness value of generation t is greater than the current global optimal fitness value Γ, then update the current global optimal fitness value Γ with the optimal fitness value of generation t, and update the current global optimal individual B with the optimal individual of generation t. If the optimal fitness value of generation t is not greater than the current global optimal fitness value Γ, then the current global optimal fitness value Γ and the current global optimal individual B remain unchanged. Step S8.9: Determine if the current value of t is equal to T. If it is equal, proceed to step S8.

10. If it is not equal, first update the value of t by adding 1 to the current value of t, and then return to step S8.8 for the next iteration. Step S8.10: First, map the Q elements of the current global optimal individual B to the Q clustering results of the total clustering result set ∏3, where the q-th element of the current global optimal individual B corresponds to the q-th clustering result in the total clustering result set ∏3; then, determine whether each element in the current global optimal individual B is 1. If an element in the current global optimal individual B is 1, the clustering result in the total clustering result set ∏3 corresponding to that element is selected; then, use all the selected clustering results in the total clustering result set ∏3 to form a clustering result subset, and denote this clustering result subset as Π4; Step S8.11: Calculate the clustering result subset Π4 using the ultra-scalable ensemble clustering algorithm obtained in step S8.3 to obtain the final unique clustering result, which contains m cluster labels and K categories of cluster labels.

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