Adaptive graph-constrained multi-view linear discriminant analysis method, system and storage medium

Abstract

The application discloses a self-adaptive graph constraint multi-view linear discriminant analysis method, system and storage medium, and the method comprises the following steps: acquiring a common low-dimensional representation of multi-view and a projection matrix of each view; learning a graph capable of reflecting the internal distribution of data by using the common low-dimensional representation to constrain the learning process; learning an optimal projection matrix by using a linear discriminant method; and performing feature extraction on multi-view data of a test set by using the optimal projection matrix, and inputting the feature extraction result into a KNN classification system to complete a classification task. The application combines multi-view canonical correlation analysis and linear discriminant analysis and performs unified expression, and the feature extraction method of multi-view learning is more suitable for a classification task than a single-view feature extraction method. Linear discriminant analysis utilizes label information of unknown label data, simultaneously considers common source knowledge induced by a graph, minimizes the distance between expected canonical variables, and realizes fusion extraction and dimension reduction of multi-view data features.

Description

Technical Field

[0001] This invention belongs to the field of multi-view data classification technology, specifically relating to an adaptive graph-constrained multi-view linear discriminant analysis method, system, and storage medium. Background Technology

[0002] In many practical applications, multi-view learning is generally more robust than single-view learning. A key challenge in multi-view learning is how to effectively utilize information from different feature sets. One effective approach is to fuse information by obtaining a common subspace for these feature sets, typically achieved through feature extraction. Canonical correlation analysis (CCAD) is a classic tool in multi-view learning; it learns a linear projection matrix for each view by maximizing the cross-correlation between two views. Multi-view CCAD is an extension of CCAD for multi-view data, capable of handling data with more than two views.

[0003] Linear discriminant analysis (LDA) is one of the most classic supervised dimensionality reduction algorithms. During dimensionality reduction, it fully utilizes prior label information from large datasets, making data within each class similar to each other and data in different classes dissipate. Combining multi-view canonical correlation analysis (MCA) with LDA can balance linear extraction of features from different views with supervised classification learning using label information. However, current multi-view data classification methods still have some shortcomings, which reduce the performance of multi-view data feature extraction and dimensionality reduction, and consequently, the classification performance.

[0004] (1) For classification problems of multi-view data, it is crucial to make full use of the label information of the data and to discover the discriminative information in the data. From this perspective, many existing multi-view feature extraction methods are unsupervised, do not utilize the labels of the data, and the learned features do not maintain the internal geometric topology information of the original data, resulting in data waste.

[0005] (2) Existing supervised methods divide feature extraction into two unrelated parts. These methods first obtain a common subspace in an unsupervised manner, and then use supervised methods to further extract features from this common subspace. Such methods do not utilize the label information of the data in the first step of solving the common subspace, which may result in the learned common subspace being a suboptimal solution.

[0006] (3) Many existing multi-view feature extraction algorithms only work well on datasets with a small number of views and a small data size. When there are a large number of views or a large data size, the computational complexity will be too high due to too many hyperparameters or other reasons, making it very difficult to process these large datasets. Summary of the Invention

[0007] The purpose of this invention is to address the problems in the prior art by providing an adaptive graph-constrained multi-view linear discriminant analysis method, system, and storage medium that fully utilizes discriminative information such as data labels to improve feature extraction performance.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] Firstly, an adaptive graph-constrained multi-view linear discriminant analysis method is provided, including the following steps:

[0010] Obtain the common low-dimensional representation of multiple views and the projection matrix of each view;

[0011] The learning process is constrained by adaptively learning a graph that reflects the intrinsic distribution of the data using a common low-dimensional representation.

[0012] The optimal projection matrix is ​​learned using a linear discriminant method.

[0013] Feature extraction is performed on the multi-view data of the test set using the optimal projection matrix, and the results of feature extraction are input into the KNN classification system to complete the classification task.

[0014] As a preferred embodiment of the adaptive graph-constrained multi-view linear discriminant analysis method of the present invention, the common low-dimensional representation of the multi-view and the projection matrix of each view are obtained by maximizing the canonical correlation coefficients among the multi-view data in the training set.

[0015] Furthermore, as a preferred embodiment of the adaptive graph-constrained multi-view linear discriminant analysis method of the present invention, the step of obtaining the common low-dimensional representation of the multiple views and the projection matrix of each view includes:

[0016] The features of all views of the input data are standardized to a mean of 0 and normalized by standard deviation to eliminate the influence of differences in units and scales between features;

[0017] The input multi-view data is mapped to a common subspace shared by all views using random linear features, where If the data is for the m-th view, then the expression for the transformation matrix of the m-th view is:

[0018]

[0019] In the formula, D represents a common subspace shared by all views; m d represents the number of dimensions in the m-th view, and d represents the dimension of S.

[0020] As a preferred embodiment of the adaptive graph-constrained multi-view linear discriminant analysis method of the present invention, the step of learning the optimal projection matrix using the linear discriminant method includes:

[0021] Linear discriminant analysis based on least squares utilizes prior label information from a large amount of data to find a function that minimizes the projection matrix W, making the data in each class close to each other and the data in different classes far apart.

[0022] Furthermore, as a preferred embodiment of the adaptive graph-constrained multi-view linear discriminant analysis method of the present invention, the calculation expression of the projection matrix W minimization function is as follows:

[0023] W = (SHS) T +γD) -1 SHY

[0024] In the formula, S is the bias matrix; D is the identity matrix; Y is the data label, and the objective function is applied to S. T The differential is J. By performing SVD decomposition on J and continuously updating S and J until convergence, the common subspace S is obtained.

[0025] Furthermore, as a preferred embodiment of the adaptive graph-constrained multi-view linear discriminant analysis method of the present invention, the step of adaptively learning a graph that can reflect the inherent distribution of the data to constrain the learning process using a common low-dimensional representation includes:

[0026] Construct the following loss function expression:

[0027]

[0028] In the formula, Y represents the data label, α and γ are used to balance the influence of MCCA and LDA in the model algorithm, and L S Let A be the graph Laplacian matrix, and A be the matrix corresponding to the Laplacian matrix L. S Affinity matrix;

[0029] The steps for extracting features from the multi-view data of the test set using the optimal projection matrix include: finding the local optimum for each variable based on the loss function, and then performing iterative optimization to complete the feature extraction.

[0030] Furthermore, as a preferred embodiment of the adaptive graph-constrained multi-view linear discriminant analysis method of the present invention, the loss function is simplified to the following expression:

[0031]

[0032] In the formula,

[0033] Let J = 2ZST +2HS T A+2B, then simplify the above equation to:

[0034]

[0035] When the bias term b and the common subspace S are fixed, the loss function with respect to the projection matrix W is:

[0036]

[0037] When the projection matrix W and the common subspace S are fixed, the loss function with respect to the bias term b is:

[0038]

[0039] When the projection matrix W, the bias term b, and the common subspace S are fixed, the transformation matrix U is... m The loss function is:

[0040]

[0041] When the transformation matrix U m When the bias term b, the common subspace S, and the projection matrix W are fixed, the loss function with respect to the affinity matrix A is:

[0042]

[0043] Secondly, an adaptive graph-constrained multi-view linear discriminant analysis system is provided, including:

[0044] The data acquisition module is used to acquire the common low-dimensional representation of multiple views and the projection matrix of each view;

[0045] The learning constraint module is used to constrain the learning process by adaptively learning a graph that reflects the inherent distribution of the data using a common low-dimensional representation.

[0046] The optimal projection matrix learning module is used to learn the optimal projection matrix using a linear discriminant method.

[0047] The feature extraction and classification module is used to extract features from the multi-view data of the test set using the optimal projection matrix, and input the results of feature extraction into the KNN classification system to complete the classification task.

[0048] Thirdly, a computer-readable storage medium is provided, wherein at least one instruction is stored therein, the at least one instruction being executed by a processor in an electronic device to implement the adaptive graph-constrained multi-view linear discriminant analysis method as described in the first aspect.

[0049] Compared with the prior art, the present invention has at least the following beneficial effects:

[0050] The adaptive graph-constrained multi-view linear discriminant analysis method proposed in this invention utilizes the correlation between the similarity matrix and label information through multi-view canonical correlation analysis, while simultaneously leveraging the label information of unknown label data through linear discriminant analysis. This approach better uncovers discriminative information within the data, making the extraction method supervised. Furthermore, it constructs a data similarity matrix by assigning an optimal neighborhood to each data point based on local distance, ensuring that the learned features retain the internal geometric topology of the original data and avoiding feature waste. This invention combines multi-view canonical correlation analysis and linear discriminant analysis with a unified expression. The multi-view feature extraction method is more suitable for classification tasks than single-view feature extraction methods, while linear discriminant analysis utilizes the label information of unknown label data and, considering graph-induced common source knowledge, minimizes the distance between expected canonical variables, achieving fusion extraction and dimensionality reduction of multi-view data features.

[0051] Furthermore, in feature extraction, this invention iteratively updates the transformation matrix, projection matrix, and affinity matrix based on local optima, thereby improving the stability and performance of the algorithm. This invention jointly optimizes the feature extraction process, the adaptive graph constraint optimization process, and introduces the KNN method for classification, thus enhancing the performance of the processing method. Simultaneously, the method of this invention can also predict new data. This invention improves the stability and feature extraction performance of multi-view data classification methods. Attached Figure Description

[0052] To more clearly illustrate the technical solutions of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. The accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 Flowchart of the adaptive graph-constrained multi-view linear discriminant analysis method according to an embodiment of the present invention;

[0054] Figure 2 The structural block diagram of the adaptive graph constraint multi-view linear discriminant analysis system according to an embodiment of the present invention. Detailed Implementation

[0055] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. The described embodiments are only some embodiments of the present invention, and not all embodiments.

[0056] Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are also within the scope of protection of this invention.

[0057] Example 1

[0058] Please see Figure 1 The adaptive graph-constrained multi-view linear discriminant analysis method of the present invention includes the following steps:

[0059] S1. Obtain the common low-dimensional representation of the multiple views and the projection matrix of each view;

[0060] S2. Adaptively learn a graph that reflects the inherent distribution of the data using a common low-dimensional representation to constrain the learning process;

[0061] S3. Learn the optimal projection matrix using linear discriminant methods;

[0062] S4. Extract features from the multi-view data of the test set using the optimal projection matrix, and input the results of feature extraction into the KNN classification system to complete the classification task.

[0063] In one alternative implementation, step S1 obtains the common low-dimensional representation of the multiple views and the projection matrix of each view by maximizing the canonical correlation coefficients among the multi-view data in the training set.

[0064] Furthermore, step S1, obtaining the common low-dimensional representation of the multiple views and the projection matrix of each view, specifically includes:

[0065] The features of all views of the input data are standardized to a mean of 0 and normalized by standard deviation to eliminate the influence of differences in units and scales between features;

[0066] The input multi-view data is mapped to a common subspace shared by all views using random linear features, where If the data is for the m-th view, then the expression for the transformation matrix of the m-th view is:

[0067]

[0068] In the formula, D represents a common subspace shared by all views; m d represents the number of dimensions in the m-th view, and d represents the dimension of S.

[0069] In one alternative implementation, step S3, which uses a linear discriminant method to learn the optimal projection matrix, includes:

[0070] Linear discriminant analysis based on least squares utilizes prior label information from a large amount of data to find a function that minimizes the projection matrix W, making the data in each class close to each other and the data in different classes far apart.

[0071] Furthermore, the calculation expression for the projection matrix W minimization function is as follows:

[0072] W = (SHS) T +γD) -1 SHY

[0073] In the formula, S is the bias matrix; D is the identity matrix; Y is the data label, and the objective function is applied to S. T The differential is J. By performing SVD decomposition on J and continuously updating S and J until convergence, the common subspace S is obtained.

[0074] In one alternative implementation, step S2, which uses a common low-dimensional representation to adaptively learn a graph that reflects the inherent distribution of the data to constrain the learning process, specifically includes:

[0075] Construct the following loss function expression:

[0076]

[0077] In the formula, Y represents the data label, α and γ are used to balance the influence of MCCA and LDA in the model algorithm, and L S Let A be the graph Laplacian matrix, and A be the matrix corresponding to the Laplacian matrix L. S Affinity matrix;

[0078] Furthermore, the loss function can be simplified to the following expression:

[0079]

[0080] In the formula, B=α(HYW T ) T ;

[0081] Let J = 2ZS T +2HS T A+2B, then simplify the above equation to:

[0082]

[0083] When the bias term b and the common subspace S are fixed, the loss function with respect to the projection matrix W is:

[0084]

[0085] When the projection matrix W and the common subspace S are fixed, the loss function with respect to the bias term b is:

[0086]

[0087] When the projection matrix W, the bias term b, and the common subspace S are fixed, the transformation matrix U is... m The loss function is:

[0088]

[0089] When the transformation matrix U m When the bias term b, the common subspace S, and the projection matrix W are fixed, the loss function with respect to the affinity matrix A is:

[0090]

[0091] Step S4, which describes the process of extracting features from the multi-view data of the test set using the optimal projection matrix, includes: finding the local optimum for each variable based on the loss function, and then performing iterative optimization to complete the feature extraction.

[0092] Example 2

[0093] An adaptive graph-constrained multi-view linear discriminant analysis method according to an embodiment of the present invention includes the following steps:

[0094] Given dataset The dataset has M views. This represents the transformation matrix for the m-th view. This represents the data of the m-th view. D represents the common subspace shared by all views. m Let d represent the number of dimensions in the m-th view, and let L represent the dimensions of S. S Let A be the graph Laplacian matrix, and let A be the affinity matrix corresponding to the Laplacian matrix LS.

[0095] It can be proven that linear discriminant analysis and least squares regression are equivalent. That is, expressing LDA in an equivalent LSR form can reduce redundancy in the calculation process, and can be expressed as:

[0096]

[0097] In the adaptive graph-constrained multi-view linear discriminant analysis method, the MAXVAR representation of multi-view canonical correlation analysis and the least squares regression expression are combined. Simultaneously, a similarity matrix is ​​constructed using the feature mapping matrix of the input data. The resulting objective function is:

[0098]

[0099] Where Y represents the data label, α and γ are used to balance the influence of canonical correlation analysis and linear discriminant analysis in the model algorithm, and A is related to the Laplace matrix L. S The corresponding affinity matrix.

[0100] First, solve for W. Differentiate formula (2) with respect to W. Set the derivative to 0, and we can obtain the expression for W:

[0101] W = (SHS) T +γD) -1 SHY (3)

[0102] In the formula: is the bias matrix; D is the identity matrix.

[0103] Differentiating formula (2) with respect to b and setting the derivative to 0, we can obtain b as:

[0104]

[0105] For U m , change b,U m Substitute into formula (2) and let We can obtain:

[0106]

[0107] In the formula: A = αWW T B=α(HYW T ) T The problem represented by formula (5) is an orthogonal Prouk problem, which is addressed in this invention using the generalized power iteration method.

[0108] Let J be the equation (5) with respect to S. T The derivative of J is obtained by taking the derivative of J = 2ZS. T +2HS T A+2B. At this point, the problem of solving formula (5) for S becomes the problem shown below:

[0109]

[0110] The proposed objective function is optimized using an iterative optimization approach. For the proposed loss function, a local optimum is found for each variable, and then iterative optimization is performed. At the same time, an iterative algorithm is designed to efficiently complete feature extraction and classification problems.

[0111] Example 3

[0112] According to the adaptive graph-constrained multi-view linear discriminant analysis method proposed in Example 2, the following steps are performed:

[0113] Step 1: Load the dataset And initialize matrix S.

[0114] Step 2: Fix b and S, and update the projection matrix W.

[0115] Step 3: Fix W and S, and update the bias term b.

[0116] Step 4: Fix W and b, and update the covariance matrix S.

[0117] Step 5: Calculate U using the covariance matrix S. m .

[0118] Step Six: Fix W, b, S, U m The value of is used to optimize the affinity matrix A.

[0119] Step 7: Repeat steps 5 and 6 until W, b, S, U are reached. m A converges.

[0120] Step 8: Utilize W, b, S, U m A performs feature extraction on the original dataset.

[0121] Step 9: Use the KNN algorithm to classify the extracted features and calculate the classification results.

[0122] Step 10: Calculate the classification accuracy (ACC) based on the classification results.

[0123] Tables 1-6 show the experimental results of the adaptive graph-constrained multi-view linear discriminant analysis method of the present invention on public datasets.

[0124] Table 1. Classification accuracy (%) of each method on the WebKB dataset.

[0125]

[0126] Table 2. Classification accuracy (%) of each method on the Handwritten Digit dataset.

[0127]

[0128] Table 3. Classification accuracy (%) of each method on the AWA dataset.

[0129]

[0130] Table 4. Classification accuracy (%) of each method on the Caltech101-7 dataset.

[0131]

[0132] Table 5. Classification accuracy (%) of each method on the Caltech101-20 dataset.

[0133]

[0134] Table 6. Classification accuracy (%) of each method on the RUSWIDEOBJ dataset.

[0135]

[0136] In Table 1, k represents the parameter settings in the KNN algorithm. The last column shows the results of supervised classification of the datasets in this invention, as shown in Tables 1-6. The methods were tested on six public datasets and compared with several other excellent classification algorithms. The results can verify the effectiveness of the adaptive graph-constrained multi-view linear discriminant analysis method of this invention.

[0137] Example 4

[0138] Please see Figure 2 This invention proposes an adaptive graph-constrained multi-view linear discriminant analysis system, comprising:

[0139] Data acquisition module 1 is used to acquire the common low-dimensional representation of multiple views and the projection matrix of each view;

[0140] Learning constraint module 2 is used to constrain the learning process by adaptively learning a graph that reflects the inherent distribution of the data using a common low-dimensional representation;

[0141] Optimal projection matrix learning module 3 is used to learn the optimal projection matrix using a linear discriminant method.

[0142] The feature extraction and classification module 4 is used to extract features from the multi-view data of the test set through the optimal projection matrix, and input the results of feature extraction into the KNN classification system to complete the classification task.

[0143] Example 5

[0144] This invention provides a computer-readable storage medium storing at least one instruction, which is executed by a processor in an electronic device to implement the adaptive graph-constrained multi-view linear discriminant analysis method.

[0145] For example, the instructions stored in the memory can be divided into one or more modules / units. These modules / units are stored in a computer-readable storage medium and executed by the processor to complete the adaptive graph-constrained multi-view linear discriminant analysis method of the present invention. The one or more modules / units can be a series of computer-readable instruction segments capable of performing specific functions, which describe the execution process of the computer program in the server.

[0146] The electronic device may be a smartphone, laptop, PDA, or cloud server, among other computing devices. It may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the electronic device may also include more or fewer components, or combinations of certain components, or different components; for example, it may also include input / output devices, network access devices, buses, etc.

[0147] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0148] The memory can be an internal storage unit of the server, such as a hard drive or RAM. Alternatively, it can be an external storage device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital Card (SD), or Flash Card. Furthermore, the memory can include both internal and external storage units. The memory stores computer-readable instructions and other programs and data required by the server. It can also temporarily store data that has been output or will be output.

[0149] It should be noted that the information interaction and execution process between the above-mentioned module units are based on the same concept as the method embodiment. For details on their specific functions and technical effects, please refer to the method embodiment section. They will not be repeated here.

[0150] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0151] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying the computer program code to a photographing device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0152] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0153] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. An adaptive graph-constrained multi-view linear discriminant analysis method, characterized in that, The method comprises the following steps: acquiring a common low-dimensional representation of multiple views and projection matrices of respective views; learning a graph capable of reflecting an intrinsic distribution of data to constrain a learning process by using the common low-dimensional representation; learning an optimal projection matrix by using a linear discrimination method; extracting features of multiple view data of a test set by using the optimal projection matrix, and inputting a result of the feature extraction into a KNN classification system to complete a classification task; the step of acquiring the common low-dimensional representation of multiple views and the projection matrices of respective views comprises: normalizing features of all views of input data to 0 mean value and through standard deviation to eliminate influences of unit and scale differences between features; The input multi-view data is mapped to a common subspace shared by the views through a random linear feature mapping, wherein For the data of the mth view, the expression of the transformation matrix of the mth view is: In the formula, represents a common subspace shared by each view; D m represents the number of dimensions of the mth view, d represents the dimension of S.

2. The adaptive graph-constrained multi-view linear discriminant analysis method of claim 1, wherein, acquiring the common low-dimensional representation of multiple views and the projection matrices of respective views by maximizing a canonical correlation coefficient between multiple view data of a training set.

3. The adaptive graph-constrained multi-view linear discriminant analysis method of claim 1, wherein, the step of learning the optimal projection matrix by using the linear discrimination method comprises: using prior label information of a large amount of data based on a least square linear discrimination analysis to make data in each class close to each other and data in different classes far from each other, and finding a projection matrix W that minimizes a function.

4. The adaptive graph-constrained multi-view linear discriminant analysis method of claim 3, wherein, a calculation expression of the projection matrix W that minimizes the function is as follows: W = (SHS T + γD) -1 SHY wherein is a bias matrix; D is an identity matrix; Y is the data labels, and the objective function is J, the differential of S T is J, by performing SVD decomposition on J and continuously updating S and J until convergence to obtain the common subspace S.

5. The adaptive graph-constrained multi-view linear discriminant analysis method of claim 4, wherein, the step of learning the graph capable of reflecting the intrinsic distribution of data to constrain the learning process by using the common low-dimensional representation comprises: constructing a loss function expression as follows: where Y represents the data labels, a and g are used to balance the influence of MCCA and LDA in the model algorithm, L S is a graph Laplacian matrix, A is an affinity matrix corresponding to the Laplacian matrix L S ​ the step of extracting features of multiple view data of the test set by using the optimal projection matrix comprises: finding a local optimal solution of each variable according to the loss function, and then performing iterative optimization to complete the feature extraction.

6. The adaptive graph-constrained multi-view linear discriminant analysis method of claim 5, wherein, the loss function is simplified as an expression as follows: In the formula, A = a WW T B = a (H YW T ) T ; Let J = 2ZS T + 2HS T A + 2B, and simplifying the above equation to: when the bias term b and the common subspace S are fixed, the loss function about the projection matrix W is as follows: when the projection matrix W and the common subspace S are fixed, the loss function about the bias term b is as follows: When the projection matrix W, the bias term b, and the common subspace S are fixed, the loss function with respect to the transformation matrix U m is: When the transformation matrix U m The loss function with respect to the affinity matrix A is given by:

7. An adaptive graph-constrained multi-view linear discriminant analysis system, characterized by, comprise: a data acquisition module configured to acquire a common low-dimensional representation of multiple views and projection matrices of respective views; a learning constraint module configured to learn a graph capable of reflecting an intrinsic distribution of data to constrain a learning process by using the common low-dimensional representation; an optimal projection matrix learning module configured to learn an optimal projection matrix by using a linear discrimination method; a feature extraction and classification module configured to extract features of multiple view data of a test set by using the optimal projection matrix, and input a result of the feature extraction into a KNN classification system to complete a classification task; the step of acquiring the common low-dimensional representation of multiple views and the projection matrices of respective views comprises: normalizing features of all views of input data to 0 mean value and through standard deviation to eliminate influences of unit and scale differences between features; The input multi-view data is mapped to a common subspace shared by the views through a random linear feature mapping, wherein For the data of the mth view, the expression of the transformation matrix of the mth view is: wherein represents a common subspace shared by each view; D m represents the number of dimensions of the mth view, d represents the dimension of S.

8. A computer-readable storage medium, characterized in that: the computer readable storage medium stores at least one instruction, and the at least one instruction is executed by a processor in the electronic device to implement the adaptive graph-constrained multiple view linear discrimination analysis method according to any one of claims 1 to 6.

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