Unsupervised feature selection method based on multi-stage learning optimization

Abstract

The invention relates to an unsupervised feature selection method based on multi-stage learning optimization, and belongs to the technical field of high-dimensional data preprocessing. Performing standardization preprocessing on the obtained original high-dimensional data set, initializing a feature state vector for the high-dimensional data set after standardization preprocessing, and setting a feature state of a preset proportion as a selection state and the rest as an elimination state; setting the state of a preset number of features in the selected state as an elimination state, generating a candidate feature subset, carrying out multi-stage optimization learning, changing the feature state through iteration, and calculating the score of the candidate feature subset by using an unsupervised evaluation index to obtain an optimal feature subset; and performing clustering based on the optimal feature subset to obtain a clustering label, and performing a subsequent classification task based on the clustering label. The method aims at screening out a most representative low-dimensional feature subset from high-dimensional data, and the performance of an unsupervised learning task is improved while the data dimension is reduced.

Description

Technical Field

[0001] This invention relates to an unsupervised feature selection method based on multi-stage learning optimization, belonging to the field of high-dimensional data preprocessing technology. Background Technology

[0002] Feature selection, as a core preprocessing technique in machine learning and data mining, plays a crucial role in high-dimensional data analysis, pattern recognition, and knowledge discovery tasks. With the rapid development of the Internet of Things, high-throughput sequencing technology, and multimedia applications, high-dimensional data is experiencing explosive growth, widely present in fields such as gene expression profiling, medical image diagnosis, financial risk modeling, social network mining, and e-commerce recommendation systems. This type of data typically contains a large number of features, including not only numerous redundant and irrelevant features but also potential noise, leading to the well-known curse of dimensionality. The curse of dimensionality not only significantly increases computational and storage costs but, more seriously, causes model overfitting, decreased generalization performance, and reduced interpretability of results.

[0003] To address this challenge, feature selection techniques aim to sift out a low-dimensional, compact, and information-rich optimal subset of features from the original high-dimensional feature space, thereby reducing computational complexity while improving the performance and robustness of subsequent machine learning models. Among numerous feature selection methods, unsupervised feature selection has wider applicability due to the lack of sample labels, especially demonstrating significant value in real-world scenarios where labeling costs are high or difficult to obtain (such as bioinformatics, anomaly detection, and market segmentation). Unsupervised feature selection methods can be mainly divided into three categories: filter, wrapper, and embedded. Filter methods (such as variance selection and correlation coefficient methods) are computationally efficient, but their evaluation criteria are independent of subsequent learners, often ignoring the interactions between features and their correlation with downstream tasks such as clusterers, which may lead to poor performance of the selected feature subset in practical applications. Wrapper methods (such as feature selection based on genetic algorithms) treat feature selection as a search problem, directly using clustering performance as the evaluation criterion. Although they usually achieve high performance, their computational cost is extremely high, and they are prone to getting trapped in local optima, making them difficult to handle ultra-high-dimensional data. Embedded methods (such as L1 regularization-based feature selection) embed the feature selection process into the training of a specific model, balancing efficiency and effectiveness, but their results are usually tied to a specific model and lack generality.

[0004] In the course of in-depth research in this field, scholars have been committed to improving the search efficiency and solution quality of feature selection algorithms. For example, Zhang et al. ("A hybrid genetic algorithm for feature selection", 2020) attempted to combine global search strategies with local search strategies to enhance the algorithm's search capability and avoid premature convergence. Wang et al. ("Unsupervised feature selection via adaptive graph learning and constraint", 2018) introduced an adaptive graph learning mechanism to better preserve the manifold structure of the data. Chen et al. ("Unsupervised feature selection with structured graph optimization", 2020) used structured graph optimization to simultaneously consider feature relevance and sample relevance. These methods have improved the performance of feature selection through different strategies. However, blindly combining global and local search strategies may increase the complexity of the algorithm, and the over-reliance on the manifold structure assumption of the data may fail on truly complex data. In unsupervised feature selection algorithms based on optimization strategies, the quality of the final feature subset heavily depends on the efficiency and effectiveness of the optimization process. Therefore, designing an optimization mechanism that can efficiently perform global search and avoid getting trapped in local optima is key to improving the performance of unsupervised feature selection. Summary of the Invention

[0005] The purpose of this invention is to provide an unsupervised feature selection method based on multi-stage learning optimization, which aims to select the most representative low-dimensional feature subset from high-dimensional data, thereby reducing the data dimensionality and improving the performance of unsupervised learning tasks.

[0006] To achieve the above objectives, the technical solution of this invention is: an unsupervised feature selection method based on multi-stage learning optimization. This method, through iterative optimization in two stages—elimination and selection—can efficiently and accurately select the optimal feature subset from high-dimensional data, significantly improving the performance of subsequent unsupervised learning tasks. It includes the following steps: S1: Perform standardization preprocessing on the acquired original high-dimensional dataset, initialize the feature state vector on the standardized high-dimensional dataset, and set a preset proportion of feature states as selected states and the rest as eliminated states. S2: Set the state of a preset number of features in the selection state to the elimination state, generate a candidate feature subset and perform multi-stage optimization learning, iteratively change the feature state and use unsupervised evaluation index to calculate the score of the candidate feature subset to obtain the optimal feature subset; wherein, the multi-stage optimization learning includes a feature elimination stage and a feature selection stage. S3: Perform clustering based on the optimal feature subset to obtain cluster labels, and then perform subsequent classification tasks based on the cluster labels.

[0007] Optionally, the feature elimination stage specifically includes: S210: Determine the number of features whose state needs to be changed from the currently selected features based on the elimination rule; S211: Change the feature state of the number of features from the selection state to the elimination state to generate a subset of candidate features; S212: Calculate the score of the candidate feature subset using an unsupervised evaluation metric; S213: If the current iteration is the first round, save the score of the current candidate feature subset. If it is not the first round, compare the score of the candidate feature subset in the current round with the highest score of the candidate feature subset in the previous round, save the score of the candidate feature subset with the highest score, eliminate another candidate feature subset, and thus update the preliminary optimized optimal feature subset and the eliminated feature set. S214: Iterate through S210 to S213 until the iteration termination condition is met, and output the current preliminary optimal feature subset and the eliminated feature set. The iteration termination condition is reaching the maximum number of iterations or completing all features.

[0008] Optionally, the expression for determining the number of features to be changed based on the elimination rule is: N_remove = floor(β * N_total) Where N_remove is the number of features to be changed, floor is the floor function, β is the dynamically decreasing elimination rate, and N_total is the total number of features in the original high-dimensional dataset.

[0009] Optionally, the feature selection stage specifically includes: S220: The selection phase is triggered when all features are marked as eliminated. S221: Determine the number of features whose state needs to be changed from the elimination feature set based on the selection rules; S222: Change the feature state of the number of features from the elimination state to the selection state to generate a subset of candidate features; S223: Calculate the score of the candidate feature subset using an unsupervised evaluation metric; S224: If the current iteration is the first round, save the score of the current candidate feature subset. If it is not the first round, compare the score of the candidate feature subset in the current round with the highest score of the candidate feature subset in the previous round, save the score of the candidate feature subset with the highest score, and thus update the final optimal feature subset. S225: Iterate through S221 to S224 until the iteration termination condition is met, and output the current optimal feature subset. The iteration termination condition is reaching the maximum number of iterations or completing all features.

[0010] Optionally, the number of features to be changed based on the selection rules is fixed at 1.

[0011] Optionally, the unsupervised evaluation metric is the silhouette coefficient.

[0012] The beneficial effects of this invention are: 1. This invention, through a multi-stage collaborative optimization mechanism, can effectively eliminate redundant and irrelevant features in high-dimensional data, significantly reducing the feature dimensionality while improving the accuracy and efficiency of subsequent clustering algorithms.

[0013] 2. This invention combines elimination and selection tasks with a dynamically adjusted operation strategy, which can adaptively transition from coarse-grained global search to fine-grained local optimization, effectively avoiding local optima and ensuring the quality of feature subsets.

[0014] 3. The entire feature selection process of this invention relies solely on the contour coefficient for internal evaluation and does not depend on any sample label information, making it suitable for unlabeled data scenarios that are widespread in the real world.

[0015] 4. This invention can be used as an independent feature selection module and can be flexibly combined with various unsupervised clustering algorithms (such as K-Means, DBSCAN, CPDD-ID, etc.), with a wide range of applications. Attached Figure Description

[0016] Figure 1 This is the overall flowchart of the present invention; Figure 2 This is a graph showing the average number of features in the feature subsets of the six algorithms of this invention. Detailed Implementation

[0017] The present invention will be further described below with reference to specific embodiments.

[0018] Example 1: As Figure 1As shown, an unsupervised feature selection method based on Multi-Stage Learning Optimization (MSLO) is presented. This method first initializes the original high-dimensional dataset and constructs a feature state vector. Second, a global search is performed through a elimination task stage, iteratively setting some feature states to elimination states and using silhouette coefficients to evaluate the quality of the feature subset, thus eliminating redundant and irrelevant features. Next, a local fine-grained search is performed through a selection task stage, re-evaluating and restoring the states of the eliminated features to avoid getting trapped in local optima. Finally, the feature subset with the highest silhouette coefficient is output. Finally, this optimal feature subset is used as input to a clustering algorithm to achieve efficient and accurate clustering of high-dimensional data, including the following steps: S1: Perform standardization preprocessing on the acquired original high-dimensional dataset, initialize the feature state vector on the standardized high-dimensional dataset, and set a preset proportion of feature states as selected states and the rest as eliminated states. It should be understood that this embodiment has broad applicability, and the original high-dimensional dataset can be high-dimensional datasets of various types such as audio, text, and images; Optionally, S1 specifically involves: inputting the original high-dimensional dataset Feature = [f1, f2, ..., f d ], where d is the dimension, and the original high-dimensional dataset is subjected to standardized preprocessing. Specifically, the standardized preprocessing includes data cleaning, data transformation and data standardization.

[0019] Furthermore, a binary feature state vector X ∈ {0,1}^d is randomly initialized, where 1 represents a feature in the selection state and 0 represents a feature in the elimination state. Next, parameters are set: the initial and final values ​​of the initial operation ratio for the elimination phase, and the maximum number of iterations.

[0020] Understandably, traditional feature selection methods typically start by gradually eliminating features from the entire feature set. However, this embodiment employs a random initialization strategy, designed based on the following principles: First, it breaks local optima by randomly generating an initial feature subset, preventing the algorithm from starting the search from the same point and increasing exploration diversity. Second, it leverages the characteristics of high-dimensional data, allowing random initialization to quickly skip obviously redundant regions. Third, it improves computational efficiency by starting the search from a compact subset, thus increasing convergence speed. Through this embodiment S1, random initialization enables the algorithm to converge within an average of 15 generations, while traditional full feature initialization requires more than 45 generations, reducing computation time by approximately 67%.

[0021] S2: Set the state of a preset number of features in the selection state to the elimination state, generate a candidate feature subset and perform multi-stage optimization learning, iteratively change the feature state and use unsupervised evaluation index to calculate the score of the candidate feature subset to obtain the optimal feature subset; wherein, the multi-stage optimization learning includes a feature elimination stage and a feature selection stage. Optionally, the feature elimination stage specifically includes: S210: Determine the number of features whose state needs to be changed from the currently selected features based on the elimination rule; Optionally, the expression for determining the number of features to be changed based on the elimination rule is: N_remove = floor(β * N_total) Where N_remove is the number of features to be changed, floor is the floor function, β is the dynamically decreasing elimination rate, and N_total is the total number of features in the original high-dimensional dataset.

[0022] S211: Change the feature state of the number of features from the selection state to the elimination state to generate a subset of candidate features; S212: Calculate the score of the candidate feature subset using an unsupervised evaluation metric; S213: If the current iteration is the first round, save the score of the current candidate feature subset. If it is not the first round, compare the score of the candidate feature subset in the current round with the highest score of the candidate feature subset in the previous round, save the score of the candidate feature subset with the highest score, eliminate another candidate feature subset, and thus update the preliminary optimized optimal feature subset and the eliminated feature set. S214: Iterate through S210 to S213 until the iteration termination condition is met, and output the current preliminary optimal feature subset and the eliminated feature set. The iteration termination condition is reaching the maximum number of iterations or completing all features.

[0023] It is understood that S210-S214 of this embodiment is the execution flow of the elimination task, which identifies and eliminates redundant features through a global search. Specifically, the elimination task adopts a linearly decreasing elimination rate strategy, the technical principles of which include: first, the idea of ​​simulated annealing, which achieves coarse-grained search through large-scale elimination in the early stage and fine adjustment with small steps in the later stage; second, using the silhouette coefficient as the evaluation standard to ensure that the clustering quality is improved with each elimination; and third, the elimination rate β decreases linearly with the number of iterations to achieve adaptive adjustment. Optionally, the feature selection stage specifically includes: S220: The selection phase is triggered when all features are marked as eliminated. S221: Determine the number of features whose state needs to be changed from the elimination feature set based on the selection rules; Optionally, the number of features to be changed based on the selection rules is fixed at 1.

[0024] S222: Change the feature state of the number of features from the elimination state to the selection state to generate a subset of candidate features; S223: Calculate the score of the candidate feature subset using an unsupervised evaluation metric; S224: If the current iteration is the first round, save the score of the current candidate feature subset. If it is not the first round, compare the score of the candidate feature subset in the current round with the highest score of the candidate feature subset in the previous round, save the score of the candidate feature subset with the highest score, and thus update the final optimal feature subset. S225: Iterate through S221 to S224 until the iteration termination condition is met, and output the current optimal feature subset. The iteration termination condition is reaching the maximum number of iterations or completing all features.

[0025] It is understood that S220-S225 of this embodiment is the task selection execution flow, which optimizes the feature subset through local search. Specifically, the above-mentioned full elimination state is a fault-tolerant mechanism and an unconventional path. If the elimination stage results in the elimination of all features, the selection task is triggered. In this stage, the number of features whose states need to be changed is fixed at 1, and a local fine search is performed: a single feature is selected from the elimination set in turn, its state is restored to selection, a new candidate subset is generated, and its silhouette coefficient is evaluated. All eliminated features are iteratively evaluated, and finally, the feature subset with the largest silhouette coefficient value is output, which is the optimal feature subset selected by the MSLO algorithm in this embodiment.

[0026] It is understandable that the selection task in this embodiment serves as a supplement to the elimination task, and its necessity is based on the following findings: First, the phenomenon of false elimination, that is, important features may be initially eliminated in high-dimensional data; second, avoiding local optima, because a single elimination strategy may lead to the permanent removal of high-quality features, and the selection task provides a chance to correct this; third, refining the operation by fixing the number of operands to 1 to avoid oscillations in the search process. Optionally, the unsupervised evaluation metric mentioned above is the silhouette coefficient. Specifically, the silhouette coefficient is used to measure intra-cluster compactness and inter-cluster separation, which helps to preserve the original characteristics of the data and plays a key role in enhancing model interpretability. For any sample point in the dataset, its silhouette coefficient s(i) is expressed as:

[0027] Where a(i) is the average distance between sample i and other samples in the same cluster (i.e., intra-cluster dissimilarity), expressed as:

[0028] In the formula, C i It is the cluster to which sample i belongs, |C i | represents the number of samples in the cluster, and d(i,j) represents the distance between samples i and j; Where b(i) is the average distance between sample i and all samples in the nearest neighbor cluster, expressed as:

[0029] The silhouette coefficient S of the entire feature subset is the average silhouette coefficient of all samples, expressed as:

[0030] Where N is the total number of samples; S3: Perform clustering based on the optimal feature subset to obtain cluster labels, and then perform subsequent classification tasks based on the cluster labels.

[0031] Optionally, in this embodiment, the clustering can be performed using the CPDD-ID clustering algorithm. It is understood that the collaborative design of feature selection and CPDD-ID clustering algorithm in this embodiment is based on the following three aspects: First, the principle of complementarity, where feature selection removes redundancy and clustering algorithm mines structure, forming a complete analysis process; second, adaptive matching, where silhouette coefficients simultaneously evaluate the quality of feature subsets and clustering effect, forming a closed-loop optimization; and third, efficiency optimization, which can significantly reduce running time and memory usage. Based on the detailed implementation description, the effectiveness of the technical solution of the present invention will be illustrated below through a specific implementation example and experiment.

[0032] Implementation example: Step 1: Input the original high-dimensional dataset and perform standardized preprocessing. Initialize the feature state vector X. Randomly set a preset proportion of feature states to "1" (selected state) and the rest to "0" (elimination state). Calculate the silhouette coefficient of the initial feature subset X, denoted as original_S. Step 2: Begin the iterative loop. First, check if the current iteration count is less than the maximum iteration count. If yes, continue checking if all features have been traversed; otherwise, end the elimination task. Randomly select k features from the untraversed features, change their states, generate a subset of candidate features, and calculate the new silhouette coefficient new_S. Compare new_S with original_S. If the new value is larger, confirm the change and update the parameters; otherwise, revert the change. After completing the operation, increment the iteration counter and return to the loop's starting point.

[0033] Step 3: Check if the feature subset is empty. If yes, trigger the selection task, set the operand to 1, and perform a local search; otherwise, proceed to the next step. Select individual feature restoration states sequentially from the elimination set, and calculate the silhouette coefficient Se_new_S for each candidate subset. After iterating through all options, select the feature subset with the largest silhouette coefficient value as the output.

[0034] Step 4: Input the optimized feature subset into the clustering algorithm. First, sub-clusters are created, and the data is initially grouped using methods such as kernel density estimation. Then, the similarity (Sim) between each sub-cluster is calculated, and similar sub-clusters are merged according to a preset strategy. Finally, the clustering results are output, and a clustering label (Label) is assigned to each sample.

[0035] Furthermore, this embodiment conducts experimental comparisons with five advanced feature selection algorithms on a high-dimensional dataset, selecting accuracy (Acc) and normalized mutual information (NMI) as clustering metrics. Clustering accuracy, as a key quantitative indicator for verifying the effectiveness of feature selection, provides direct evidence for evaluating algorithm performance by accurately comparing the degree of matching between clustering results and true class labels. Specifically: Let the true class labels of the samples be L = {l1,l2,...,l n The clustering result after processing by the technical solution of this embodiment is C={c1, c2, ..., c}. n}, then the expression for accuracy ACC is:

[0036] in, This is a mapping function that maps cluster labels to real labels, and the Hungarian algorithm can be used for label matching. N is the total number of samples. It has the following expression:

[0037] Understandably, unlike traditional classification tasks, this embodiment innovatively applies the ACC metric to evaluate the effectiveness of unsupervised feature selection. By using the Hungarian algorithm to solve for the optimal label mapping relationship, it effectively eliminates the interference of order differences between cluster labels and true categories. This application ensures a quantitative evaluation of the feature selection algorithm's ability to improve clustering accuracy.

[0038] In this embodiment, NMI plays a crucial role in evaluating the consistency of clustering results before and after feature selection. Based on information theory principles, this metric quantifies the degree of information sharing between the clustering results and the actual partitions from an entropy perspective. Its expression is:

[0039] in, It is mutual information, expressed as:

[0040] in, It is the total number of samples. The representative sample labels are obtained after clustering. This indicates that the sample belongs to the true category. The probability, This indicates that the sample belongs to a cluster category. The probability, This represents the probability that a sample belongs to both.

[0041] Information entropy is expressed as:

[0042] Understandably, compared to traditional clustering evaluation, this embodiment focuses specifically on the ability of the feature selection algorithm to preserve the intrinsic structure of the data through the NMI index. The closer the index value is to 1, the higher the consistency between the clustering results after feature selection and the actual data distribution, thus verifying that this embodiment effectively preserves key clustering information while removing redundant features.

[0043] Furthermore, this experiment prepared nine high-dimensional datasets to verify the effectiveness of the MSLO algorithm in this embodiment on high-dimensional datasets. Detailed information on the nine high-dimensional datasets is shown in Table 1.

[0044] Table 1. Detailed information on high-dimensional datasets

[0045] Furthermore, the experiment compared the accuracy of the MSLO algorithm with five other advanced feature selection algorithms. All feature selection algorithms used the DBSCAN algorithm to cluster the output feature subsets and were evaluated using the external clustering metrics ACC and NMI. The specific results are shown in Tables 2 and 3.

[0046] Table 2. Evaluation of MSLO and five comparative algorithms' ACC results on high-dimensional datasets using DBSCAN.

[0047] Table 3. Evaluation of NMI results of MSLO and five comparative algorithms on high-dimensional datasets using DBSCAN.

[0048] As shown in Table 2, the MSLO feature selection algorithm outperforms the other five comparative algorithms in ACC results on six high-dimensional datasets, including Colon and CML_treatment. It is slightly inferior on the ALL_AML_4, CNS, and Isolet datasets. Table 3 shows the comparative results of the MSLO algorithm on the NMI evaluation metric. Although it is not as good as the optimal feature selection algorithm on three datasets, it still demonstrates that the present invention can adapt to most high-dimensional datasets. Furthermore, the feature subset output by the MSLO feature selection algorithm contains the fewest number of features, which greatly reduces the computational cost of the algorithm.

[0049] Furthermore, Figure 2 The paper presents the average number of features in the feature subsets output by six feature selection algorithms across nine high-dimensional datasets. It can be seen that MSLO has fewer average features than the other five algorithms across all nine high-dimensional datasets. Therefore, the MSLO algorithm achieves higher accuracy with fewer features.

[0050] In summary, this invention first constructs an initial feature subset by initializing the feature states. Second, it employs a two-stage optimization strategy involving elimination and selection: in the elimination stage, some features are marked as eliminated using a global search, and the quality of the feature subset is evaluated using silhouette coefficients, iteratively eliminating redundant and irrelevant features; in the selection stage, a local search is performed on the elimination results to re-evaluate and recover the key features that were mistakenly eliminated, thereby optimizing the final feature subset. Finally, the feature subset with the best evaluation metric is output. This invention can efficiently select the most representative low-dimensional feature subset from high-dimensional data, effectively reducing data dimensionality while significantly improving the performance and efficiency of subsequent clustering or classification models.

[0051] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. An unsupervised feature selection method based on multi-stage learning optimization, characterized in that, The method comprises the following steps: S1: standardizing the obtained original high-dimensional data set, initializing a feature state vector of the standardized high-dimensional data set, and setting a preset proportion of feature states as selected states and the rest as eliminated states; S2: setting a preset number of features in the selected state as the eliminated state, generating a candidate feature subset and performing multi-stage optimization learning, changing the feature state through iteration, and calculating the score of the candidate feature subset using an unsupervised evaluation index to obtain an optimal feature subset; wherein the multi-stage optimization learning comprises a feature elimination stage and a feature selection stage; S3: clustering based on the optimal feature subset to obtain a clustering label, and performing subsequent classification tasks based on the clustering label.

2. The method of unsupervised feature selection based on multi-stage learning optimization according to claim 1, characterized in that, The feature elimination stage specifically comprises: S210: determining the number of features to be changed in state from the currently selected features based on an elimination rule; S211: changing the state of the number of features from the selected state to the eliminated state to generate a candidate feature subset; S212: calculating the score of the candidate feature subset using an unsupervised evaluation index; S213: if it is the first iteration round, saving the score of the current candidate feature subset, if it is not the first iteration round, comparing the score of the candidate feature subset of the current round with the highest score of the candidate feature subset of the previous round, saving the score of the candidate feature subset with the highest score, eliminating another candidate feature subset, and updating the preliminary optimal feature subset and the eliminated feature set; S214: iteratively performing S210 to S213 until the iteration termination condition is met, and outputting the current preliminary optimal feature subset and the eliminated feature set, wherein the iteration termination condition is to reach the maximum number of iterations or to iterate through all features.

3. The method of claim 2, wherein, The expression for determining the number of features to be changed in state based on the elimination rule is: N_remove = floor ( β * N_total )； wherein, N_remove is the number of features to be changed state, floor is the floor function, β is the dynamic decreasing elimination rate, N_total is the total number of features of the original high-dimensional dataset.

4. The method of claim 2, wherein, The feature selection stage specifically comprises: S220: triggering the selection stage when all features are marked as eliminated states; S221: determining the number of features to be changed in state from the eliminated feature set based on a selection rule; S222: changing the state of the number of features from the eliminated state to the selected state to generate a candidate feature subset; S223: calculating the score of the candidate feature subset using an unsupervised evaluation index; S224: if it is the first iteration round, saving the score of the current candidate feature subset, if it is not the first iteration round, comparing the score of the candidate feature subset of the current round with the highest score of the candidate feature subset of the previous round, saving the score of the candidate feature subset with the highest score, and updating the final optimal feature subset; S225: iteratively performing S221 to S224 until the iteration termination condition is met, and outputting the current optimal feature subset, wherein the iteration termination condition is to reach the maximum number of iterations or to iterate through all features.

5. The method of unsupervised feature selection based on multi-stage learning optimization according to claim 4, characterized in that, The number of features to be changed in state based on the selection rule is fixed at 1.

6. The method of claim 1, wherein, The unsupervised evaluation index is the silhouette coefficient.

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