Method for multi-view sample clustering and feature selection based on non-negative matrix factorization

Abstract

The application relates to a multi-view sample clustering and feature selection method based on non-negative matrix decomposition, comprising the following steps: acquiring unlabeled multi-view query samples, which comprise original feature data of multiple views; inputting the unlabeled multi-view query samples into a trained multi-view unsupervised feature selection model to perform the following steps on each view: performing descending order sorting on the original feature data of each view to obtain an original feature sequence arranged in descending order of feature importance; selecting part of the features from the sorted feature sequence to form a feature subset of the view; and outputting the feature subset of the view or a low-dimensional embedding representation obtained after dimension reduction by a projection matrix; wherein the multi-view unsupervised feature selection model is obtained by decoupling common and private representations and introducing k-nearest neighbor tolerance redundancy penalty through alternating iterative optimization training based on a non-negative matrix decomposition framework. The method can obtain better downstream clustering or classification performance in an unsupervised scene.

Description

Technical Field

[0001] This invention belongs to the field of multi-view data processing and machine learning technology, specifically relating to a multi-view sample clustering and feature selection method based on non-negative matrix factorization. Background Technology

[0002] Multi-view data is widely used in computer vision, bioinformatics, social network analysis, and other fields. Unlike single-view data, multi-view data describes the same instance from different perspectives through multiple heterogeneous feature sets, providing more comprehensive and complementary information. Feature selection aims to extract the most discriminative subset of features from the original feature set. Because it preserves the physical meaning of features and has strong interpretability, it has become an important technique for processing multi-view data. In practical applications, obtaining labeled data is costly. Unsupervised feature selection evaluates feature importance by mining the inherent geometric structure and statistical properties of the data, and has significant practical value.

[0003] However, existing unsupervised feature selection methods have the following limitations: First, most methods only focus on feature importance while ignoring the correlation between features, resulting in a large amount of redundant information in the selected feature subset; second, traditional methods usually pre-compute a fixed similarity matrix (such as based on cosine similarity or Gaussian kernel), which is static and cannot adapt to changes in the training process and is susceptible to noise interference; third, most multi-view methods force all views to share a unified latent representation, ignoring the fact that each view contains both shared and unique information, and forced fusion can easily cause the common representation to be contaminated by view-specific noise; fourth, existing methods mostly only maintain the local structure of the sample space and ignore the geometric structure of the feature space.

[0004] In summary, existing unsupervised feature selection methods suffer from feature redundancy and noise interference. This invention aims to solve these problems. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention provides a multi-view sample clustering and feature selection method based on nonnegative matrix factorization. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a multi-view sample clustering and feature selection method based on nonnegative matrix factorization, including: The unlabeled multi-view query samples are preprocessed by mean normalization to obtain preprocessed feature data. The multi-view query samples include the original feature data of multiple views of the same object obtained from different angles or by different extraction methods. The unlabeled multi-view query samples are input into the trained multi-view unsupervised feature selection model to perform the following steps for each view: Based on the feature weights learned during the training phase, the number of preprocessed features corresponding to each view is sorted in descending order to obtain a feature sequence arranged in descending order of feature importance. Select a specified number or proportion of features that rank highly from the feature sequence arranged in descending order of feature importance to form a feature subset of the view; Output the feature subset of the view or obtain a low-dimensional embedding representation by reducing the dimensionality of the projection matrix learned during the training phase from the feature subset of the view; The multi-view unsupervised feature selection model is based on a non-negative matrix factorization framework and is obtained through alternating iterative optimization training by decoupling public and private representations and introducing k-nearest neighbor tolerating redundancy penalties.

[0006] Compared with the prior art, the beneficial effects of the present invention are as follows: To address the issues of feature redundancy and noise interference in existing unsupervised feature selection methods, this invention provides a multi-view sample clustering and feature selection method based on nonnegative matrix factorization. By decoupling the low-dimensional representation of multi-view data into global common semantics and view-specific representations and applying orthogonal constraints, it effectively prevents view-specific noise from contaminating the common semantics, thus improving the robustness of feature selection. Furthermore, by introducing feature self-representation learning to dynamically construct a feature similarity matrix and combining it with a local k-nearest neighbor indicator matrix to form a redundancy penalty term, it penalizes high-similarity features outside the neighborhood while tolerating features that are neighbors, thus eliminating feature redundancy while preserving key information for maintaining local geometric structure. It significantly improves the information density and complementarity of the selected feature subsets; by constructing the anchor bipartite graph Laplacian matrix to maintain the global geometric structure of the sample space, and by constructing the feature graph Laplacian matrix to constrain the smoothness of the projection matrix, it achieves manifold preservation at both the sample and feature levels and reduces the computational complexity of graph construction; by iteratively optimizing the joint objective function, it can simultaneously learn the feature weights and projection matrices of each view, so that in the inference stage, only weighted sorting and feature selection of unlabeled multi-view query samples are needed to quickly output high-discrimination, low-redundancy feature subsets or low-dimensional embedding representations, thereby achieving better downstream clustering or classification performance with lower computational overhead in unsupervised scenarios. Attached Figure Description

[0007] Figure 1 This is a flowchart illustrating the multi-view sample clustering and feature selection method based on nonnegative matrix factorization provided in this embodiment of the invention. Figure 2 This is a flowchart of the training method for the multi-view unsupervised feature selection model provided in this embodiment of the invention; Figure 3 This is a schematic diagram illustrating the training process of the multi-view unsupervised feature selection model provided in this embodiment of the invention. Figure 4 This refers to the method proposed in this invention and several comparative methods provided in the embodiments of this invention. Detailed Implementation The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0008] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0009] The present invention will now be described in detail with reference to the accompanying drawings, a method for multi-view sample clustering and feature selection based on nonnegative matrix factorization.

[0010] Figure 1 This is a flowchart illustrating the multi-view sample clustering and feature selection method based on nonnegative matrix factorization provided in an embodiment of the present invention. Figure 1 As shown, the method includes: S100: Perform mean normalization preprocessing on the acquired unlabeled multi-view query samples to obtain preprocessed feature data. The multi-view query samples include the original feature data of multiple views of the same object obtained from different angles or with different extraction methods.

[0011] Here, the unlabeled multi-view query samples have data sources including, but not limited to: real-time acquired images, biometric features output by gene sequencers, text data provided by social network platforms, or pre-extracted feature files read from local / cloud storage. The data type is digitized feature vectors, with each view corresponding to a set of feature vectors, and none of the view data contains category labels.

[0012] Furthermore, "different perspectives" refers to describing the object from different physical or semantic levels. For example, for the same image, features can be extracted from three perspectives: color distribution, texture structure, and shape contour; for the same patient, data can be collected from three biological levels: gene expression, methylation, and proteomic profiles.

[0013] "Different extraction methods" refers to using different algorithms or computational methods to generate feature vectors from the original data. For example, for the same document, three different text feature extraction methods can be used: bag-of-words model, TF-IDF method, and Word2Vec word embedding, to obtain three sets of feature vectors respectively.

[0014] It should be noted that this method can complete feature selection without any label information, and belongs to the category of unsupervised learning.

[0015] S200: Input the unlabeled multi-view query samples into the trained multi-view unsupervised feature selection model to perform the following steps for each view: S201: Based on the feature weights learned during the training phase, sort the preprocessed feature data corresponding to each view in descending order to obtain a feature sequence arranged in descending order of feature importance.

[0016] Specifically, it rearranges the feature dimensions within each view according to their corresponding weight values ​​from largest to smallest, rather than sorting the feature values ​​of the samples.

[0017] It should be noted that the view mentioned in the actual inference phase is different from the training view used in the model training phase. Figure 1 A one-to-one correspondence. That is, the total number of views processed in the inference phase is the same as the total number of views used in the training phase. For example, if the training phase uses three views—color, texture, and shape—then the unlabeled query samples input in the inference phase must also contain the original feature data of these three views. Furthermore, the semantic meaning and feature dimensions of each view remain consistent with those in the training phase. Finally, the first view learned in the training phase... Feature weights of each view This is only used for the reasoning stage. The raw feature data of each view is sorted. Feature weights are not used interchangeably between different views.

[0018] Here, the feature weights learned during the training phase can be understood as: a scalar value of importance calculated for each feature dimension of each view during the training process. The larger the weight value, the stronger the discriminative power or information contribution of the corresponding feature in distinguishing different sample categories or maintaining data structure. Therefore, sorting the features in descending order according to their weights during the inference phase ensures that the most discriminative features are placed at the top of the sequence, thus prioritizing the retention of these high-value features and discarding low-weight features when selecting a feature subset later.

[0019] It should be understood that, for the sake of brevity, the process of obtaining the feature weights and projection matrices learned during the training phase will be described in detail below, and will not be repeated here.

[0020] S202: Select a specified number or proportion of features from the feature sequence arranged in descending order of feature importance to form a feature subset of the view.

[0021] For example, the top 100-500 features can be selected, or the top 10%-50% of features can be used to form a feature subset of the view. Furthermore, according to experimental verification based on the present invention, when the preset number of local nearest neighbors k is 2 or 3, the information density of the feature subset is the highest. In this case, selecting the top 10%-20% of features yields the optimal clustering performance.

[0022] Those skilled in the art can flexibly adjust this ratio or quantity according to specific application scenarios (such as clustering accuracy, classifier performance, real-time requirements, etc.).

[0023] S203: Output the feature subset of the view or obtain a low-dimensional embedding representation by reducing the dimensionality of the projection matrix learned during the training phase for the feature subset of the view.

[0024] It should be understood that obtaining the feature subset or low-dimensional embedding representation of the view means completing the unsupervised feature selection and dimensionality reduction processing of unlabeled multi-view query samples. The output feature subset or low-dimensional embedding representation is the final result of the method of this invention, which can be directly used for downstream machine learning tasks such as clustering, classification, retrieval, or visualization without further data cleaning or feature transformation.

[0025] The training process of the multi-view unsupervised feature selection model in the above data processing is described in detail below. The multi-view unsupervised feature selection model is based on the nonnegative matrix factorization framework and is obtained through alternating iterative optimization training by decoupling public and private representations and introducing k-nearest neighbor tolerating redundancy penalties.

[0026] Figure 2 This is a flowchart of the training method for the multi-view unsupervised feature selection model provided in this embodiment of the invention. Figure 3 This is a schematic diagram illustrating the training process of the multi-view unsupervised feature selection model provided in this embodiment of the invention. For example... Figure 2-3 As shown, the multi-view unsupervised feature selection model is trained in the following manner (S1-S5), specifically: S1: Obtain the multi-view training dataset Obtain a dataset containing multiple unlabeled multi-view training samples. Each multi-view training sample includes raw feature data from multiple training views. Perform mean normalization preprocessing on the raw feature data to obtain preprocessed training data.

[0027] It should be noted that when performing the same mean normalization on unlabeled query samples during the inference phase, the mean and standard deviation parameters saved during the training phase should be used to ensure the consistency of the data distribution.

[0028] S2: Construct the anchor bipartite graph and the Laplacian matrix of the feature map. For each training view, k-means clustering is performed on the samples, and multiple anchor points are selected. Based on the similarity matrix between the training samples and the anchor points, a bipartite graph Laplacian matrix is ​​generated to maintain the global geometric structure of the sample space. At the same time, based on the preprocessed training data, the similarity between features within each training view is calculated, and a feature map Laplacian matrix is ​​constructed to constrain the smoothness of the subsequent projection matrix.

[0029] Specifically, S2 includes: S2.1: Constructing the Laplace matrix of a bipartite graph

[0030] For each view, perform k-means clustering on n training samples, select m anchor points (n > m), calculate the similarity between each training sample and each anchor point, and construct a sample-anchor point similarity matrix using the calculated similarity values. ; Calculate the degree matrix of anchor points based on the sample-anchor point similarity matrix Using the degree matrix Sample-anchor similarity matrix Construct the bipartite graph Laplace matrix Among them, the bipartite Laplace matrix The calculation expression is: In the formula, It is an identity matrix.

[0031] For example, in one embodiment of the present invention, the number of anchor points m is taken as 10% of the total number of training samples n, which can achieve a good balance between maintaining computational efficiency and structural fidelity.

[0032] Bipartite graph Laplacian matrices are used to preserve the global geometric structure of the sample space. Traditional graph Laplacian matrices require calculating the similarity between all sample pairs, resulting in a computational complexity of O(n log n). This invention constructs a bipartite graph between samples and anchor points by selecting a small number of anchor points. The resulting bipartite graph Laplace matrix reduces the computational complexity to a minimum. While n is much larger than m, it can still effectively constrain the smoothness of the low-dimensional representation of the samples on the manifold, so that similar samples in the original space remain similar after low-dimensional embedding.

[0033] S2.2: Constructing the Laplacian matrix of the feature map In the Within the view, based on the first The original input feature matrix of each view Calculate the first The similarity between features within each view is used to construct a corresponding static feature similarity map; based on the static feature similarity map, the degree matrix and adjacency matrix are obtained to construct the first view. Laplacian matrix of feature map corresponding to each view .

[0034] The Laplacian matrix of a feature map is used to preserve the local geometry of the feature space. Within each view, the similarity between features is pre-calculated based on the preprocessed training data to construct a feature map, from which the Laplacian matrix of the feature map is derived. This Laplacian matrix of the feature map imposes a smoothing constraint on the projection matrix, ensuring that similar features in the original feature space still have similar mapping weights after projection, thus avoiding the loss of geometric information in the feature space.

[0035] S3: Construct the local k-nearest neighbor indicator matrix In the initial feature space of each training view, the distance between each feature is calculated based on the preprocessed training data. For each feature, its predefined k nearest neighbor features are found, and a binarized local k nearest neighbor indicator matrix is ​​constructed.

[0036] Specifically, S3 includes: in the first In the initial feature space of each view, calculate the pairwise distances between all features to obtain multiple distance values; based on these multiple distance values, find the k nearest neighbors of each feature, where k is a preset positive integer (2 or 3); based on the k nearest neighbors of each feature, construct the first... Local k-nearest neighbor indicator matrix corresponding to each view .

[0037] Here, the local k-nearest neighbor indicator matrix The elements in the formula satisfy the following formula: ; in Representation and Features Most similar A set of features.

[0038] S4: Establish the objective function for joint optimization The objective function is constructed based on the data reconstruction error term of nonnegative matrix factorization, the orthogonal decoupling constraint term of public and private representations, the feature self-representation learning term, the redundancy penalty term formed by combining the local k-nearest neighbor indicator matrix, and the dual geometric structure preservation term constructed based on the bipartite graph Laplacian matrix and the feature graph Laplacian matrix.

[0039] To enable the model to learn discriminative and low-redundancy feature subsets from multi-view data, this invention introduces five constraints into the objective function simultaneously, addressing different levels of the problem: (1) Error term of data reconstruction based on nonnegative matrix factorization Based on the nonnegative matrix factorization assumption, the error between the weighted original data and the low-dimensional reconstructed representation must be minimized. In other words, the data reconstruction error term needs to ensure that the learned projection matrix and low-dimensional embedding representation faithfully preserve the main information of the original data.

[0040] (2) Orthogonal decoupling constraint terms To separate the global semantics shared by all views from the private information specific to each view, the low-dimensional representation is explicitly decomposed into a global common semantic matrix and a private representation matrix. By minimizing the trace inner product of the global common semantic matrix and the private representation matrix, they can be forced to tend to orthogonal in space, thereby preventing view-specific noise from contaminating the common semantics.

[0041] (3) Feature self-representation learning term A self-representation constraint is imposed on the projection matrix, assuming that each feature can be represented by a linear combination of other features. This learning term dynamically constructs the feature similarity matrix, avoiding noise interference from static similarity. A regularization term is also added to control the complexity of the self-representation matrix.

[0042] (4) Redundancy penalty term based on k-nearest neighbor tolerance To preserve local geometric structure while eliminating redundant features, the similarity matrix obtained from self-representation learning is multiplied element-wise by the local k-nearest neighbor indicator matrix to obtain a redundancy penalty matrix. This term penalizes feature pairs that are not neighbors but have high similarity (i.e., The feature self-representation learning term dynamically learns the similarity between features, while the redundancy penalty term selectively applies constraints using the k-nearest neighbor indicator matrix. Together, they ensure that redundant features are suppressed while locally necessary features are preserved.

[0043] (5) Dual geometry preservation term On the one hand, using the bipartite Laplace matrix For the global common semantic matrix Constraints are applied to preserve the global manifold structure in the sample space; on the other hand, the Laplacian matrix of the feature map is used to constrain the projection matrix, ensuring that similar features in the original feature space still have similar weights after projection. These two methods work together to ensure that the inherent geometric structure of the data is preserved at both the sample and feature levels.

[0044] Based on the above five constraints, a joint objective function is constructed, and its calculation expression is as follows: ; In the formula, It is the total number of views. It is the first The feature weight diagonal matrix of each view It is the first Projection matrix of each view, It is a global common semantic matrix. yes transpose, It is the first Private representation matrix of each view It is the first The feature self-representation similarity matrix of each view It is the first The original input feature matrix of each view. It is the first Redundancy penalty for each view It is the first The diagonal elements of the feature weight diagonal matrix for each view represent the importance weights of each feature. It is the first Laplacian matrix of feature maps for each view It is a bipartite Laplace matrix. Represents the trace of a matrix. It refers to the square of the Frobenius norm of the matrix; , , and These are preset regularization tradeoff parameters; It is the first Data reconstruction error term for each view; It is the first Orthogonal decoupling constraint terms for each view; It is the first Each view's feature self-representation learning term; It is the first Redundancy penalty for each view; It is the first Dual geometry preservation item for each view.

[0045] S5: Alternating Iterative Optimization The alternating iterative algorithm is used to update multiple sets of variables in the objective function step by step until the preset maximum number of iterations is reached, or the difference between the objective function values ​​of two adjacent iterations is less than the preset convergence threshold. This yields the feature weights and projection matrices learned by each training view during the training phase. These feature weights and projection matrices are then used to perform weighted sorting and dimensionality reduction on unlabeled multi-view query samples during the inference phase.

[0046] It should be understood that since the objective function contains multiple coupled variables, the global optimal solution cannot be directly obtained. Therefore, an alternating iteration strategy is adopted, in which the remaining variables are fixed in each iteration and only the current variable is updated, thereby decomposing the complex optimization problem into several subproblems to be solved sequentially.

[0047] Specifically, S5 includes: using an alternating iterative algorithm to update the variable matrices in the objective function step by step. The variable matrices include a global common semantic matrix, private representation matrices for each view, projection matrices for each view, feature self-representation similarity matrices for each view, feature weight vectors for each view, and redundancy penalty matrices for each view; when updating one variable matrix, the remaining variable matrices remain unchanged; wherein: S5.1: Update the global common semantic matrix using the multiplier update rule The mathematical expression for the updated global common semantic matrix is:

[0048] In the formula, This indicates element-wise multiplication; S5.2: Update the private representation matrix of each view using the multiplier update rule. Among them, the The mathematical expression for the updated private representation matrix of each view is:

[0049] S5.3: Update the projection matrix of each view Among them, the The mathematical expression for the updated projection matrix of each view is: ; ; ; In the formula, , , For the first The feature matrix of each view For the first The characteristic adjacency matrix of each view; S5.4: Update the feature self-representation similarity matrix for each view Among them, the The mathematical expression for the updated feature self-representation similarity matrix of each view is: ; No. The diagonal elements of the updated feature self-representation similarity matrix of each view are zero; S5.5: Update the feature weight vectors for each view Among them, the The mathematical expression for the updated feature weight vector of each view is:

[0050] ; In the formula, It is a vector composed of the squares of the original norms of each feature. It is the learning rate. In one embodiment of the present invention, the learning rate... Set it to 0.001; S5.6: Update the redundancy penalty matrix for each view The updated feature self-representation similarity matrix is ​​multiplied element-wise with the local k-nearest neighbor indicator matrix constructed in step S3 to obtain the updated redundancy penalty matrix for each view; wherein the local k-nearest neighbor indicator matrix remains unchanged during the update process; S7: Convergence Judgment and Parameter Output Repeat steps S5.1 to S5.6 until the maximum number of iterations is reached, or the difference in the objective function values ​​is less than the convergence threshold (in one embodiment of the invention, the convergence threshold is...). 10 -5 After training, the final feature weight vector and projection matrix of each view are output, which are used as the feature weights and projection matrices learned by each training view during the training phase.

[0051] To verify the effectiveness and advancement of the proposed multi-view sample clustering and feature selection method based on nonnegative matrix factorization (hereinafter referred to as "this method"), the inventors conducted simulation experiments and compared the experimental results with existing mainstream unsupervised feature selection methods. The experiments used three standard multi-view datasets: the Wiki_fea dataset, the WebKB dataset, and the 20newsgroups dataset. Three existing unsupervised feature selection methods, LSAG, OMVFS, and InfFS_U, were selected for comparison. Clustering accuracy (ACC) was used as the performance evaluation metric. In this method, the low-dimensional subspace dimension is set to the number of true classes in the dataset, the number of anchor points is 10% of the total number of samples, the number of local nearest neighbors k is 2 or 3, and the self-representation matrix constrains the weights. =10, hyperparameters such as orthogonal separation, redundancy penalty, and structural consistency are at 10. -3 Up to 10 3 Grid search optimization was performed within the interval; the comparison methods all adopted the parameter settings recommended in the original literature. The experiment extracted 5%, 10%, 15%, 20%, 25%, 30%, 35%, and 40% of the original features from each dataset, respectively. These extracted feature subsets were then input into the K-means clustering algorithm to calculate the corresponding ACC and NMI values. Figure 4 As shown, experimental results demonstrate that on all three datasets, the proposed method significantly outperforms the three comparative methods in both ACC and NMI at different feature extraction ratios. The performance advantage of the proposed method is particularly pronounced when the feature extraction ratio is low (e.g., 5%–15%), indicating that it can achieve higher clustering accuracy with fewer features. As the feature extraction ratio increases, the performance of the proposed method continuously improves and remains stable, while the performance improvement of the comparative methods is smaller or fluctuates. These experimental results demonstrate that the multi-view unsupervised feature selection method based on k-nearest neighbor-tolerant redundancy penalty proposed in this invention can effectively remove redundant features, suppress view-specific noise, and achieve better clustering performance with a lower-dimensional feature subset.

[0052] To address the issues of feature redundancy and noise interference in existing unsupervised feature selection methods, this invention provides a multi-view sample clustering and feature selection method based on nonnegative matrix factorization. By decoupling the low-dimensional representation of multi-view data into global common semantics and view-specific representations and applying orthogonal constraints, it effectively prevents view-specific noise from contaminating the common semantics, thus improving the robustness of feature selection. Furthermore, by introducing feature self-representation learning to dynamically construct a feature similarity matrix and combining it with a local k-nearest neighbor indicator matrix to form a redundancy penalty term, it penalizes high-similarity features outside the neighborhood while tolerating features that are neighbors, thus eliminating feature redundancy while preserving key information for maintaining local geometric structure. It significantly improves the information density and complementarity of the selected feature subsets; by constructing the anchor bipartite graph Laplacian matrix to maintain the global geometric structure of the sample space, and by constructing the feature graph Laplacian matrix to constrain the smoothness of the projection matrix, it achieves manifold preservation at both the sample and feature levels and reduces the computational complexity of graph construction; by iteratively optimizing the joint objective function, it can simultaneously learn the feature weights and projection matrices of each view, so that in the inference stage, only weighted sorting and feature selection of unlabeled multi-view query samples are needed to quickly output high-discrimination, low-redundancy feature subsets or low-dimensional embedding representations, thereby achieving better downstream clustering or classification performance with lower computational overhead in unsupervised scenarios.

[0053] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for clustering and feature selection of multi-view samples based on nonnegative matrix factorization, characterized in that, include: The unlabeled multi-view query samples are preprocessed by mean normalization to obtain preprocessed feature data. The multi-view query samples include the original feature data of multiple views of the same object obtained from different angles or by different extraction methods. The unlabeled multi-view query samples are input into the trained multi-view unsupervised feature selection model to perform the following steps for each view: Based on the feature weights learned during the training phase, the preprocessed feature data corresponding to each view is sorted in descending order to obtain a feature sequence arranged in descending order of feature importance. Select a specified number or proportion of features that rank highly from the feature sequence arranged in descending order of feature importance to form a feature subset of the view; Output the feature subset of the view or obtain a low-dimensional embedding representation by reducing the dimensionality of the projection matrix learned during the training phase from the feature subset of the view; The multi-view unsupervised feature selection model is based on a non-negative matrix factorization framework and is obtained through alternating iterative optimization training by decoupling public and private representations and introducing k-nearest neighbor tolerating redundancy penalties.

2. The multi-view sample clustering and feature selection method based on nonnegative matrix factorization according to claim 1, characterized in that, The multi-view unsupervised feature selection model was trained in the following way: S1: Obtain the multi-view training dataset Obtain a dataset containing multiple unlabeled multi-view training samples, each multi-view training sample including raw feature data from multiple training views; perform mean normalization preprocessing on the raw feature data to obtain preprocessed training data; S2: Construct the anchor point bipartite graph and the Laplacian matrix of the feature map. For each training view, k-means clustering is performed on the samples, multiple anchor points are selected, and a bipartite graph Laplacian matrix is ​​generated based on the similarity matrix between the training samples and the anchor points to maintain the global geometric structure of the sample space. Simultaneously, based on the preprocessed training data, the similarity between features within each training view is calculated, and the feature map Laplacian matrix is ​​constructed to constrain the smoothness of the subsequent projection matrix. S3: Construct the local k-nearest neighbor indicator matrix In the initial feature space of each training view, the distance between each feature is calculated based on the preprocessed training data, and the k nearest neighbor features of each feature are found to construct a binarized local k nearest neighbor indicator matrix. S4: Establish the objective function for joint optimization The objective function is constructed based on the data reconstruction error term of nonnegative matrix factorization, the orthogonal decoupling constraint term of public and private representations, the feature self-representation learning term, the redundancy penalty term formed by combining the local k-nearest neighbor indicator matrix, and the dual geometric structure preservation term constructed based on the bipartite graph Laplacian matrix and the feature graph Laplacian matrix. S5: Alternating Iterative Optimization The alternating iterative algorithm is used to update multiple sets of variables in the objective function step by step until the preset maximum number of iterations is reached, or the difference between the objective function values ​​of two adjacent iterations is less than the preset convergence threshold, to obtain the feature weights and projection matrices learned by each training view during the training phase. The feature weights and projection matrices learned by each training view during the training phase are used to perform weighted sorting and dimensionality reduction processing on the unlabeled multi-view query samples during the inference phase.

3. The multi-view sample clustering and feature selection method based on nonnegative matrix factorization according to claim 2, characterized in that, S2 include: S2.1: Construct the Laplace matrix of the bipartite graph Perform k-means clustering on n training samples for each view, and select m anchor points, where n is greater than m; Calculate the similarity between each training sample and each anchor point, obtain multiple similarity values, and construct a sample-anchor point similarity matrix. ; Calculate the degree matrix of the anchor points based on the sample-anchor point similarity matrix. ; Using the degree matrix and the sample-anchor similarity matrix Construct the bipartite graph Laplace matrix ; Wherein, the bipartite Laplace matrix The calculation expression is: ； In the formula, It is the identity matrix; S2.2: Construct the Laplacian matrix of the feature map In the Within the view, based on the first The original input feature matrix of each view Calculate the first The similarity between features within each view is used to construct a corresponding static feature similarity map; Based on the static feature similarity map, the degree matrix and adjacency matrix are obtained to construct the first... Laplacian matrix of feature map corresponding to each view .

4. The multi-view sample clustering and feature selection method based on nonnegative matrix factorization according to claim 2, characterized in that, S3 includes: In the In the initial feature space of each view, calculate the distance between all pairs of features to obtain multiple distance values; Based on the multiple distance values, find the k nearest features to each feature, which are the k nearest neighbors of that feature, where k is a preset positive integer; Based on the k nearest neighbors of each feature, construct the first... Local k-nearest neighbor indicator matrix corresponding to each view .

5. The multi-view sample clustering and feature selection method based on nonnegative matrix factorization according to claim 2, characterized in that, The objective function is calculated as follows: ； In the formula, It is the total number of views. It is the first The feature weight diagonal matrix of each view The first one is the one mentioned Projection matrix of each view, It is a global common semantic matrix. yes transpose, The first one is the one mentioned Private representation matrix of each view The first one is the one mentioned The feature self-representation similarity matrix of each view The first one is the one mentioned The original input feature matrix of each view. The first one is the one mentioned Redundancy penalty for each view The first one is the one mentioned The diagonal elements of the feature weight diagonal matrix for each view represent the importance weights of each feature. The first one is the one mentioned Laplacian matrix of feature maps for each view It is the bipartite Laplace matrix. Represents the trace of a matrix. It refers to the square of the Frobenius norm of the matrix; , , and These are preset regularization tradeoff parameters; The first one is the one mentioned Data reconstruction error term for each view; The first one is the one mentioned Orthogonal decoupling constraint terms for each view; The first one is the one mentioned Each view's feature self-representation learning term; The first one is the one mentioned Redundancy penalty for each view; The first one is the one mentioned Dual geometry preservation item for each view.

6. The multi-view sample clustering and feature selection method based on nonnegative matrix factorization according to claim 5, characterized in that, S5 includes: An alternating iterative algorithm is used to update the variable matrices in the objective function step by step. These variable matrices include a global common semantic matrix, a view-specific private representation matrix, a view-specific projection matrix, a view-specific feature self-representation similarity matrix, a view-specific feature weight vector, and a view-specific redundancy penalty matrix. When updating one variable matrix, the remaining variable matrices remain unchanged. Wherein: S5.1: Update the global common semantic matrix using the multiplier update rule. The mathematical expression for the updated global common semantic matrix is: In the formula, This indicates element-wise multiplication; S5.2: Update the private representation matrices of each view using the multiplier update rule. Among them, the first The mathematical expression for the updated private representation matrix of each view is: S5.3: Update the projection matrices of each view. Among them, the first The mathematical expression for the updated projection matrix of each view is: ； ； ； In the formula, , , For the first The feature matrix of each view For the first The characteristic adjacency matrix of each view; S5.4: Update the self-representation similarity matrix of each view feature. Among them, the first The mathematical expression for the updated feature self-representation similarity matrix of each view is: ； The first The diagonal elements of the updated feature self-representation similarity matrix of each view are zero; S5.5: Update the feature weight vectors of each view. Among them, the first The mathematical expression for the updated feature weight vector of each view is: ； In the formula, It is a vector composed of the squares of the original norms of each feature. It is the learning rate; S5.6: Update the redundancy penalty matrix for each view. The updated feature self-representation similarity matrix is ​​multiplied element-wise with the local k-nearest neighbor indicator matrix constructed in step S3 to obtain the updated redundancy penalty matrix for each view; wherein the local k-nearest neighbor indicator matrix remains unchanged during the update process; S7: Convergence Judgment and Parameter Output Repeat steps S5.1 to S5.6 until the maximum number of iterations is reached, or the difference in the objective function values ​​is less than the convergence threshold; after training is completed, output the final feature weight vector and projection matrix of each view, which are respectively used as the feature weights and projection matrices learned by each training view during the training phase.

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