High-dimensional data feature extraction and dimension reduction processing system and method based on matrix decomposition

Abstract

The invention relates to the technical field of data feature extraction, in particular to a high-dimensional data feature extraction and dimension reduction processing system and method based on matrix factorization, and the system comprises a data acquisition module which is used for reading an original high-dimensional matrix; the preprocessing module is used for receiving the original high-dimensional matrix and outputting a preprocessed matrix; the noise pattern recognition module is used for receiving the preprocessed matrix and outputting a noise category label vector and a confidence coefficient vector; the weight matrix generation module is used for receiving the noise category label vector and the confidence coefficient vector and outputting a diagonal weight matrix; the matrix decomposition module is used for receiving the preprocessed matrix and the diagonal weight matrix and outputting a low-dimensional feature matrix and a basis matrix; and the post-processing module is used for receiving the low-dimensional feature matrix and outputting a normalized feature matrix. According to the method, the discrimination and decomposition precision of low-dimensional features are remarkably improved through self-adaptive optimization of emphatically reserving effective samples and suppressing noise sample interference.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data feature extraction, in particular to a high-dimensional data feature extraction and dimension reduction processing system and method based on matrix decomposition. BACKGROUND

[0002] Under the background of rapid development of big data and artificial intelligence technology, high-dimensional data such as images, texts, and sensor data are increasingly widely used in scientific research, industry, medical treatment, and other fields. High-dimensional data usually contains a large number of feature dimensions and sample information, but it has problems such as redundant features, noise interference, and data missing, which directly affect the efficiency and accuracy of subsequent data analysis. Therefore, feature extraction and dimension reduction processing of high-dimensional data have become the core link of data preprocessing.

[0003] Existing high-dimensional data dimension reduction methods, such as principal component analysis and non-negative matrix factorization, have obvious limitations in practical application. On the one hand, for the problem of data missing, traditional missing value imputation methods rely on empirical assumptions and are difficult to accurately restore missing information, which can easily lead to subsequent analysis bias. On the other hand, the types of noise in high-dimensional data are complex, and existing methods mostly use a unified denoising strategy, lacking precise identification and targeted processing of noise patterns, which leads to effective features being masked by noise, and the robustness of the data after dimension reduction is insufficient.

[0004] Traditional matrix decomposition methods do not fully consider the quality difference of samples, and give the same weight to all samples, which leads to excessive interference of noise samples or low confidence samples on the decomposition result, making it difficult to extract truly discriminative low-dimensional features. In addition, existing processes often ignore the cooperative optimization of preprocessing and decomposition process, making the data quality preprocessing, noise processing, and matrix decomposition link disjointed, further limiting the dimension reduction accuracy and feature expression ability. SUMMARY

[0005] In view of the above shortcomings of the prior art, the present application provides a high-dimensional data feature extraction and dimension reduction processing system and method based on matrix decomposition, which can effectively solve the problems mentioned in the prior art.

[0006] To achieve the above purpose, the present application is realized by the following technical scheme:

[0007] The present application provides a high-dimensional data feature extraction and dimension reduction processing system based on matrix decomposition, comprising:

[0008] A data acquisition module for reading an original high-dimensional matrix , wherein m is the feature dimension and n is the sample number;

[0009] A preprocessing module for receiving the original high-dimensional matrix and outputting a preprocessed matrix The preprocessing module comprises:

[0010] The missing value imputation unit is configured to perform missing value imputation on the original high-dimensional matrix X to obtain a high-dimensional matrix X

[0011] The normalization unit is configured to perform column-wise zero-mean-unit-variance transformation on the completed matrix X to obtain a preprocessed matrix X

[0012] The noise pattern recognition module is configured to receive the preprocessed matrix X and output a noise class label vector l and a confidence vector c The noise pattern recognition module comprises:

[0013] The residual calculation unit is configured to perform baseline low-rank decomposition on the preprocessed matrix X to obtain a baseline residual matrix E

[0014] The variational autoencoder unit is configured to encode and decode each column of the baseline residual matrix E and output the noise class label vector l and the confidence vector c

[0015] The weight matrix generation module is configured to receive the noise class label vector l and the confidence vector c and output a diagonal weight matrix W

[0016] The parameter storage unit is configured to store a set of learnable scalar parameters where k is the noise class number, and is a learnable scalar corresponding to the noise class k

[0017] The matrix decomposition module is configured to receive the preprocessed matrix X and the diagonal weight matrix W and output a low-dimensional feature matrix U and a basis matrix V The matrix decomposition module comprises:

[0018] The objective function construction unit is configured to construct an objective function, as shown in the following formula:

[0019]

[0020] where is the total loss to be minimized, is the element-wise square root of the diagonal weight matrix, is the Frobenius norm, is a regularization coefficient

[0021] ​​​​​a multiplication update unit, configured to iteratively solve the low-dimensional feature matrix V and the basis matrix U by alternately updating the formula until convergence is reached;

[0022] a post-processing module, configured to receive the low-dimensional feature matrix V and output a normalized feature matrix .

[0023] Further, the missing value supplement unit performs kernel norm minimization completion on the original high-dimensional matrix X by using a singular value threshold algorithm, and the specific execution steps include:

[0024] S101, constructing an observation mask matrix M, and traversing each element in the original high-dimensional matrix X element by element If the element is missing, the corresponding position of the observation mask matrix M is set to If the element is not missing, is set to Finally, an observation mask matrix M with the same shape as the original high-dimensional matrix X is obtained.

[0025] S102, setting an initial threshold , the initial threshold is the average value of the absolute values of all observed elements in the original matrix X, and initializing a loop counter k=0, the formula is:

[0026] ;

[0027] Wherein, is the number of observed elements, is the absolute value of the element ;

[0028] S103, in the kth iteration, singular value decomposition is performed on the current estimated complete matrix to obtain , wherein and are the left singular vector matrix and the right singular vector matrix respectively, is the transpose of the right singular vector matrix, is a diagonal matrix, the diagonal elements are singular values, and represent the main components of the diagonal matrix ; calculate the adaptive threshold , the formula is:

[0029] ;

[0030] Wherein, is a decay coefficient and , is the adaptive threshold value for the kth iteration, k is the current iteration number, and is for each singular value The soft threshold operator is applied to obtain a new singular value matrix , the formula is:

[0031]

[0032] , wherein is a soft threshold operator, is to set the singular values less than the threshold to 0 and retain the singular values greater than the threshold ;

[0033] The updated singular value matrix is used to reconstruct a low-rank estimation matrix , the low-rank estimation matrix is fused with the original observation value to obtain a new estimation matrix , wherein is an element-wise multiplication, and 1 is an all-1 matrix;

[0034] S104, calculate the relative difference between the results of two consecutive iterations , the formula is:

[0035]

[0036] , wherein is the Frobenius norm of the calculation matrix, is the Frobenius norm difference between the current iteration and the last iteration result; set the relative difference threshold , if the relative difference is less than the threshold or the iteration number reaches the maximum iteration number , stop iteration and output the final complete matrix as the completion matrix.

[0037] Further, the column zero-mean-unit-variance transformation specifically calculates the mean and the standard deviation of each column of the completion matrix , and performs transformation on each element of the column to obtain the preprocessed matrix .

[0038] Further, the residual calculation unit performs baseline low-rank decomposition, which includes performing baseline low-rank decomposition on the preprocessed matrix using singular value decomposition to obtain a baseline estimate , and calculating a baseline residual matrix . ​​

[0039] Further, the variational autoencoder unit comprises an encoder network and a decoder network ;

[0040] For each column of the baseline residual matrix , the residual vector is encoded into latent variable z using the encoder network , and then the latent variable z is used to reconstruct the residual vector using the decoder network ;

[0041] The reconstruction error and the KL divergence are calculated, and the joint loss function is optimized to train the variational autoencoder, which is formulated as:

[0042] ;

[0043] wherein, is the balance coefficient of the KL divergence;

[0044] After the joint loss is optimized, the noise class label and the confidence are output, forming the noise class label vector I and the confidence vector c.

[0045] Further, the method steps of the mapping unit for constructing the diagonal weight matrix comprise:

[0046] S201, reading the noise class label and the confidence for each sample j.

[0047] S202, calculating the weight , and the calculation formula is:

[0048] ;

[0049] wherein, is the Sigmoid function, is the bias parameter of the noise class label , and is the coefficient parameter of the confidence ;

[0050] S203, constructing the diagonal weight matrix W = diag( ).

[0051] Further, the method of the multiplication update unit for iterative solution is alternating minimization, and the following formula is iteratively executed:

[0052] ;

[0053] ;

[0054] wherein, is a regularization coefficient;

[0055] setting a minimization threshold when the relative change rate of the total loss to be minimized is less than the minimization threshold , output the low-dimensional feature matrix V and the basis matrix U.

[0056] Further, the method steps of the post-processing module performing row-wise normalization include:

[0057] S301, calculating the norm of each row of the low-dimensional feature matrix V ;

[0058] S302, dividing each row by the norm to obtain a normalized row vector ;

[0059] S303, combining all normalized row vectors to output a normalized feature matrix .

[0060] The high-dimensional data feature extraction and dimension reduction processing method based on matrix decomposition includes the following steps:

[0061] S1, data acquisition step, the data acquisition module reads the original high-dimensional matrix X;

[0062] S2, preprocessing step, the preprocessing module receives the original high-dimensional matrix X and performs missing value imputation and standardization to obtain the preprocessed matrix ;

[0063] S3, noise pattern recognition step, the noise pattern recognition module receives the preprocessed matrix and outputs the noise class label vector l and the confidence vector c;

[0064] S4, weight matrix generation step, the weight matrix generation module receives the noise class label vector l and the confidence vector c and outputs the diagonal weight matrix W;

[0065] S5, decomposition step, the weighted non-negative matrix factorization module receives the preprocessed matrix and the diagonal weight matrix W, performs weighted non-negative matrix factorization, and outputs the low-dimensional feature matrix V and the basis matrix U;

[0066] S6, a post-processing step, the post-processing module receives the low-dimensional feature matrix V and outputs the normalized feature matrix after normalization .

[0067] The technical scheme provided by the application has the following beneficial effects compared with the known prior art:

[0068] 1. The application generates a diagonal weight matrix by combining the noise category label and confidence level output by the noise pattern recognition module with learnable parameters, and incorporates sample quality differences into the matrix decomposition objective function. High weight is given to samples with low noise and high confidence, and low weight is given to samples with high noise and low confidence, achieving adaptive optimization of "focusing on retaining effective samples and suppressing noise sample interference", significantly improving the discriminability and decomposition accuracy of low-dimensional features.

[0069] 2. The application uses kernel norm minimization completion and singular value threshold algorithm to achieve accurate recovery of missing values and avoid empirical bias of traditional filling methods; through the noise pattern recognition and confidence evaluation of the residual matrix by the variational autoencoder, accurate classification and quantitative representation of noise types are achieved. The collaborative processing of missing value imputation and noise recognition provides a high-quality data basis for subsequent matrix decomposition, greatly enhancing the robustness of the system to complex data scenarios

[0070] 3. The application constructs a complete processing flow of "missing value imputation-standardization-noise recognition-weighted decomposition-normalization": in the preprocessing stage, the dimension influence is eliminated by standardization, in the matrix decomposition stage, overfitting is avoided by regularization constraint, and in the post-processing stage, the feature scale is unified by row-wise normalization. The whole process is closely linked to ensure that during the conversion process from original high-dimensional data to low-dimensional features, effective features are not lost and noise interference is suppressed, providing reliable low-dimensional feature support for subsequent data analysis. BRIEF DESCRIPTION OF DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0072] Figure 1 is a schematic diagram of the system structure of the present application;

[0073] Figure 2 is a schematic diagram of the method flow of the present application. DETAILED DESCRIPTION

[0074] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0075] The present application will be further described in connection with the embodiments.

[0076] Embodiment 1

[0077] With reference to Figure 1 , the matrix decomposition-based high-dimensional data feature extraction and dimension reduction processing system comprises:

[0078] a data acquisition module configured to read an original high-dimensional matrix X , wherein m is the feature dimension, and n is the sample number;

[0079] a preprocessing module configured to receive the original high-dimensional matrix X and output a preprocessed matrix X , the preprocessing module comprising:

[0080] a missing value imputation unit configured to perform kernel norm minimization completion on the original high-dimensional matrix X to obtain a completed matrix X

[0081] a normalization unit configured to perform column-wise zero-mean-unit-variance transformation on the completed matrix X to output the preprocessed matrix X

[0082] a noise pattern recognition module configured to receive the preprocessed matrix X and output a noise category label vector l and a confidence vector c, the noise pattern recognition module comprising: a residual calculation unit configured to perform baseline low-rank decomposition on the preprocessed matrix X to obtain a baseline residual matrix E;

[0083] a variational autoencoder unit configured to encode and decode each column of the baseline residual matrix E and output the noise category label vector l and the confidence vector c;

[0084] a weight matrix generation module configured to receive the noise category label vector l and the confidence vector c and output a diagonal weight matrix W, the weight matrix generation module comprising:

[0085] a parameter storage unit configured to store a set of learnable scalar parameters

[0086] a parameter storage unit configured to store a set of learnable scalar parameters ​where k corresponds to the noise class number, and is a learnable scalar corresponding to the noise class k;

[0087] a matrix decomposition module configured to receive the preprocessed matrix X and the diagonal weight matrix W and output a low-dimensional feature matrix V and a basis matrix U The matrix decomposition module comprises:

[0088] a target function construction unit configured to construct a target function, the formula being as follows:

[0089] ;

[0090] where, is a total loss to be minimized, is an element-wise square root of the diagonal weight matrix, is a Frobenius norm, is a regularization coefficient;

[0091] a multiplication updating unit configured to iteratively solve until convergence by alternately updating the formula, and output the low-dimensional feature matrix V and the basis matrix U;

[0092] a post-processing module configured to receive the low-dimensional feature matrix V and output a normalized feature matrix V .

[0093] Specifically, the system constructs a complete processing framework from reading of original high-dimensional data to output of normalized low-dimensional features, covering the whole process of data acquisition, preprocessing, noise identification, weighted decomposition and post-processing. The technical effect is to realize end-to-end processing of high-dimensional data feature extraction and dimension reduction, and the advantage is that the missing value processing, noise identification and matrix decomposition are deeply cooperated through modular design, solving the problem of insufficient dimension reduction precision caused by disconnection of each link in traditional methods, and providing a systematic solution for high-dimensional data processing.

[0094] Further, the missing value imputation unit performs core norm minimization completion on the original high-dimensional matrix X by using a singular value threshold algorithm, and the specific execution steps include:

[0095] S101, constructing an observation mask matrix M, and element-wise traversing each element in the original high-dimensional matrix X If the element is missing, set in the corresponding position of the observation mask matrix M; if the element is not missing, set , and finally obtain an observation mask matrix M which has the same shape as the original high-dimensional matrix X;

[0096] ​​S102, set an initial threshold value , the initial threshold value is the average of the absolute values of all observed elements in the original matrix X, and a loop counter k = 0 is initialized, the formula is:

[0097] ;

[0098] wherein, is the number of observed elements, is the absolute value of the element ;

[0099] S103, in the kth iteration, singular value decomposition is performed on the complete matrix of the current estimate, to obtain , wherein and are left singular vector matrix and right singular vector matrix respectively, is the transpose of the right singular vector matrix, is a diagonal matrix, the diagonal elements are singular values, indicating the main components of the diagonal matrix ; calculate the adaptive threshold value , the formula is:

[0100] ;

[0101] wherein, is a decay coefficient and , is the adaptive threshold value of the kth iteration, k is the current iteration number, and the soft threshold operator is applied to each singular value to obtain a new singular value matrix , the formula is:

[0102] ;

[0103] wherein, is a soft threshold operator, sets the singular values less than the threshold value to 0 and retains the singular values greater than the threshold value ;

[0104] Using the updated singular value matrix , the low-rank estimated matrix is reconstructed, the low-rank estimated matrix is fused with the original observation value to obtain a new estimated matrix , wherein is element-wise multiplication, and 1 is an all-one matrix;

[0105] S104, calculate the relative difference of the results of two consecutive iterations , the formula is:

[0106] ;

[0107] wherein, is the Frobenius norm of the calculation matrix, is the Frobenius norm difference between the current iteration and the last iteration result; set the relative difference threshold , if the relative difference is less than the threshold or the number of iterations reaches the maximum number of iterations , stop iteration and output the final complete matrix as the completion matrix.

[0108] Specifically, the missing value supplement unit performs kernel norm minimization completion by using the singular value threshold algorithm, accurately restores the missing elements based on the low rank characteristics of the matrix, and avoids the empirical bias of traditional mean or interpolation filling; through iterative optimization of the adaptive decay threshold, the convergence speed and completion accuracy are balanced, the internal structure of the data can be preserved, and it is especially suitable for missing value restoration scenarios of large-scale high-dimensional data.

[0109] Further, the column-wise zero-mean-unit-variance transformation is specifically to calculate the mean and the standard deviation of each column of the complete matrix , and perform transformation on each element of the column to obtain the preprocessed matrix ; the normalization unit processes the complete matrix through the column-wise zero-mean-unit-variance transformation, eliminates the dimensional differences of different feature dimensions, and makes each feature participate in subsequent analysis under a unified scale; avoids the problem that strong features dominate the results caused by dimensional differences, provides a stable data basis for noise identification and matrix decomposition, and improves the robustness of the entire system.

[0110] Further, the residual calculation unit performs baseline low-rank decomposition, which includes performing baseline low-rank decomposition on the preprocessed matrix using singular value decomposition to obtain a baseline estimate , and calculating a baseline residual matrix ; the residual calculation unit obtains the baseline residual matrix through the baseline low-rank decomposition, separates the preprocessed matrix into an effective signal baseline estimate and a noise residual, and realizes the preliminary separation of the effective signal and the noise; makes the subsequent noise pattern identification focus on the residual matrix, reduces the interference of the effective signal on the noise judgment, and improves the pertinence and accuracy of the noise identification.

[0111] Further, the variational autoencoder unit includes an encoder network and a decoder network ;

[0112] For each column of the baseline residual matrix , the residual vector is encoded into latent variable z using an encoder network , and then the latent variable z is used to reconstruct the residual vector using a decoder network ; ;

[0113] The reconstruction error and the KL divergence are calculated, and the joint loss function is optimized to train the variational autoencoder, which is formulated as:

[0114] ;

[0115] wherein is the balance coefficient of the KL divergence;

[0116] After the joint loss is optimized, the noise class label and the confidence are output, forming the noise class label vector I and the confidence vector c.

[0117] The variational autoencoder unit encodes and decodes the residual matrix array vector, realizes accurate classification of the noise class and quantitative evaluation of the confidence; through joint optimization of the reconstruction error and the KL divergence, the noise recognition accuracy is improved, and the output noise class label and confidence vector provide a quantitative basis for subsequent weighted processing, supporting fine regulation and control of noise processing.

[0118] Further, the method steps for constructing the diagonal weight matrix by the mapping unit include:

[0119] S201, reading the noise class label and the confidence for each sample j.

[0120] S202, calculating the weight , and the calculation formula is:

[0121] ;

[0122] wherein is a Sigmoid function, is a bias parameter of the noise class label , and is a coefficient parameter of the confidence ;

[0123] S203, constructing the diagonal weight matrix W = diag( ).

[0124] The weight matrix generation module constructs a diagonal weight matrix based on noise category labels and confidence levels, dynamically generating sample weights so that samples with low noise and high confidence levels receive higher weights, and vice versa. Through learnable parameters and the Sigmoid function, the weights are adaptively adjusted to noise characteristics, suppressing the interference of noise samples on the matrix decomposition results from the data level.

[0125] Furthermore, the method for iteratively solving the multiplicative update unit is alternating minimization, iteratively executing the following formula:

[0126] ;

[0127] ;

[0128] in, The regularization coefficient is used.

[0129] Set minimum threshold When the total loss to be minimized relative rate of change Less than the minimum threshold When the function is in operation, the low-dimensional feature matrix V and the basis matrix U are output. The multiplicative update unit solves the objective function iteratively through the alternating update formula, efficiently converges to the optimal solution, and outputs the low-dimensional feature matrix and the basis matrix. The element-wise multiplicative update rule reduces the computational complexity and is suitable for high-dimensional data scenarios. At the same time, the regularization term constraint effectively suppresses overfitting and improves the generalization ability of low-dimensional features.

[0130] Furthermore, the post-processing module performs row-wise normalization using the following steps:

[0131] S301. For each row of the low-dimensional feature matrix V Calculate norm ;

[0132] S302. Divide each row by the norm. This yields the normalized row vectors. ;

[0133] S303. Combine all normalized row vectors and output the normalized feature matrix. .

[0134] Specifically, the post-processing module performs row-wise normalization on the low-dimensional feature matrix to unify the scale of sample features with a modulus of 1. This eliminates the impact of differences in feature intensity between samples on subsequent analysis, making low-dimensional features more stable in scenarios such as similarity calculation and classifier input, and improving the interpretability and practicality of the features.

[0135] In a specific embodiment, medical image diagnosis CT or MRI image is often formed into a high-dimensional feature matrix after feature extraction, including texture, gray scale, shape and other features, but there are generally missing features in the data, such as image blur in some areas, which leads to failure to extract features and noise interference such as device imaging noise and artifacts, which directly affects the accuracy of subsequent lesion identification. The present application can reduce the dimension of the high-dimensional feature matrix and extract low-dimensional features with strong robustness to assist doctors in accurate diagnosis.

[0136] Data acquisition step: the data acquisition module reads the high-dimensional feature matrix of 50 lung CT images of a hospital , where m=800 is the feature dimension, including 800 image features, n=50 is the sample number, 50 patients, and about 15% of the elements in the matrix have missing values due to image blur.

[0137] Preprocessing step: the missing value interpolation unit uses the singular value threshold algorithm to complete the missing values, first constructs an observation mask matrix M, the missing elements correspond to , and the non-missing elements correspond to ; calculate the initial threshold , set the attenuation coefficient , and the maximum number of iterations ; when the iteration is 120 times, the relative difference , stop iteration, and output the completed matrix Z. The missing value recovery error is 0.03, which is significantly better than the traditional mean filling of 0.12; the standardization unit calculates the mean and standard deviation of each column of the completed matrix Z, performs transformation to output the preprocessed matrix , and eliminates the dimensional differences of different features.

[0138] Noise pattern recognition step: the residual calculation unit performs baseline low-rank decomposition on , takes the first 60 singular values using singular value decomposition to obtain the baseline estimate , calculates the residual matrix , and separates out residual signals such as image artifacts and device noise. The variational autoencoder unit trains the variational autoencoder, and the encoder includes 2 layers of fully connected network with hidden layer dimensions of 64 to 32; the decoder has a symmetric structure, and the residual vector of each column of E is encoded-decoded to optimize the joint loss , ; after training, the noise category label , represents artifact noise, represents device noise, and the confidence vector , the average confidence is 0.89, and the noise type recognition accuracy reaches 93%.

[0139] Weight matrix generation step: read pre-trained learnable parameters: artifact noise Corresponding , ; device noise Corresponding , ; Calculate sample weights: samples of noise categories , ; samples of categories , ; Construct diagonal weight matrix W = diag( ), realize weight enhancement for high confidence and low noise samples.

[0140] Decomposition step: matrix decomposition module constructs objective function , regularization coefficient , dimension reduction dimension r = 30; Multiplication update unit alternately iterates:

[0141] ;

[0142] ;

[0143] After 80 iterations, the total loss J converges, and the base matrix and the low-dimensional feature matrix are output.

[0144] Post-processing step: the post-processing module calculates the norm of each row of V , executes normalization , and outputs the normalized feature matrix .

[0145] Implementation effect: after missing value completion, the data integrity is improved from 85% to 100%, providing high-quality data for subsequent processing; noise recognition and weighted decomposition make the signal-to-noise ratio of lesion-related features in low-dimensional feature increase by 40%; input into the lung lesion classification model, the accuracy is improved by 18% compared with the traditional PCA method, effectively assisting the accurate diagnosis of medical images.

[0146] Embodiment 2

[0147] Referring to Figure 2 , the high-dimensional data feature extraction and dimension reduction processing method based on matrix decomposition, the steps include:

[0148] S1, data acquisition step, the data acquisition module reads the original high-dimensional matrix X;

[0149] S2, preprocessing step, the preprocessing module receives the original high-dimensional matrix X and performs missing value imputation and standardization to obtain the preprocessed matrix ;

[0150] S3, a noise pattern recognition step, a noise pattern recognition module receives the pre-processed matrix and outputs a noise class label vector I and a confidence vector c;

[0151] S4, a weight matrix generation step, a weight matrix generation module receives the noise class label vector I and the confidence vector c and outputs a diagonal weight matrix W;

[0152] S5, a decomposition step, a weighted non-negative matrix decomposition module receives the pre-processed matrix and the diagonal weight matrix W, performs weighted non-negative matrix decomposition, and outputs a low-dimensional feature matrix V and a basis matrix U;

[0153] S6, a post-processing step, a post-processing module receives the low-dimensional feature matrix V and outputs a normalized feature matrix .

[0154] The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit it; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for part of the technical features; and these modifications or replacements will not make the essence of the corresponding technical solutions deviate from the protection scope of the technical solutions of the embodiments of the present application.

Claims

1. A high-dimensional data feature extraction and dimensionality reduction processing system based on matrix factorization, characterized by, Comprise: a data acquisition module, configured to read an original high-dimensional matrix wherein m is a feature dimension, and n is a sample number. a pre-processing module for receiving the original high-dimensional matrix and outputting a pre-processed matrix the pre-processing module comprising: a missing value imputation unit, for imputing missing values in the original high-dimensional matrix to obtain an imputed matrix performing nuclear norm minimization completion on the imputed matrix to obtain a completed matrix a standardization unit for column-wise zero-mean unit-variance transformation of the completion matrix, outputting the pre-processed matrix ; a noise pattern recognition module that receives the pre-processed matrix and outputs a noise class label vector and a confidence vector , the noise pattern recognition module comprising: a residual calculation unit configured to perform a baseline low-rank decomposition on the pre-processed matrix to obtain a baseline residual matrix E; Variational autoencoder unit for encoding-decoding each column of the baseline residual matrix E and outputting the noise category label vector l and the confidence vector c; Weight matrix generation module for receiving the noise category label vector l and the confidence vector c and outputting the diagonal weight matrix W, the weight matrix generation module comprising: a parameter storage unit for storing a set of learnable scalar parameters where k corresponds to a noise class number, and is a learnable scalar corresponding to the noise class k. a matrix factorization module configured to receive the pre-processed matrix and the diagonal weight matrix W and output a low-dimensional feature matrix and a basis matrix The matrix factorization module comprises: Objective function construction unit for constructing the objective function, the formula is as follows: ； wherein, is a total loss to be minimized, is an element-wise square root of the diagonal weight matrix, is a Frobenius norm, is a regularization coefficient; Multiplication update unit, by alternating update formula iteration until convergence, output the low-dimensional feature matrix V and the base matrix U; a post-processing module for receiving the low-dimensional feature matrix V and outputting a normalized feature matrix . 2.The high-dimensional data feature extraction and dimension reduction processing system based on matrix factorization of claim 1, wherein, The missing value interpolation unit adopts singular value threshold algorithm to perform kernel norm minimization completion on the original high-dimensional matrix X, and the specific execution steps include: S101. Construct the observation mask matrix M, and iterate through each element of the original high-dimensional matrix X. If the element If missing, set the corresponding position in the observation mask matrix M. If the element If not missing, then set. Finally, we obtain the observation mask matrix M, which has the same shape as the original high-dimensional matrix X; S102、Set initial threshold , the initial threshold is the average of the absolute values of all observed elements in the original matrix X, and initialize the loop counter k = 0, the formula is: ； wherein, is the absolute value of the difference between the observed element number, is the element taken . S103、In the kth iteration, singular value decomposition is performed on the complete matrix of the current estimation to obtain , where and are left and right singular vector matrices respectively, is the transpose of the right singular vector matrix, is a diagonal matrix, and the diagonal elements are are singular values, representing the main components of the diagonal matrix ; an adaptive threshold is calculated , and the formula is: ； wherein is a decay coefficient and , is the adaptive threshold of the kth iteration, k is the current iteration number, and is applied to each singular value a soft threshold operator is applied to obtain a new singular value matrix The formula is: ； wherein, is a soft threshold operator, is a function that sets singular values smaller than a threshold to 0 and preserves singular values larger than a threshold to 0 and preserves singular values larger than a threshold with the updated singular value matrix , reconstructing the low-rank estimation matrix , fusing the low-rank estimation matrix with the original observation value to obtain a new estimation matrix , wherein is element-wise multiplication, and 1 is an all-one matrix S104、calculating the relative difference of the results of two successive iterations with the formula: ； wherein, is the Frobenius norm of the matrix, is the Frobenius norm difference between the current iteration and the result of the last iteration; a relative difference threshold is set , if the relative difference is less than the threshold or the number of iterations reaches the maximum number of iterations , the iteration is stopped and the final complete matrix is output as the completion matrix. 3.The high-dimensional data feature extraction and dimension reduction processing system based on matrix factorization of claim 1, wherein, The column-wise zero-mean-unit-variance transformation is specifically a computation of the mean and standard deviation for each column of the completed matrix and performing a transformation on each element of the column to obtain a pre-processed matrix . 4.The high-dimensional data feature extraction and dimension reduction processing system based on matrix factorization of claim 1, wherein, The residual computation unit performs baseline low-rank decomposition including pre-processing the matrix Baseline low-rank decomposition is performed using singular value decomposition to obtain baseline estimates and computes a baseline residual matrix . 5.The high-dimensional data feature extraction and dimension reduction processing system based on matrix factorization of claim 1, wherein, The variational autoencoder unit comprises an encoder network and a decoder network ; For the baseline residual matrix Each column Using encoder network The residual vector Encode it as a latent variable z, and then use a decoder network. Reconstruct the residual direction of the latent variable z ; Compute reconstruction error and KL divergence and optimize joint loss function Train variational autoencoder, formula: ； wherein, is the balancing coefficient for the KL divergence; Optimized joint loss output noise class labels with confidence , forming a noise class label vector I and a confidence vector c. 6.The high-dimensional data feature extraction and dimension reduction processing system based on matrix factorization of claim 1, wherein, The mapping unit constructs the method steps of the diagonal weight matrix, which includes: S201, read the noise class label for each sample j and confidence S202, calculating the weight The calculation formula is: ； wherein, is a Sigmoid function, is a noise class label is a bias parameter, is a confidence is a coefficient parameter; S203, construct a diagonal weight matrix W = diag( ). 7.The high-dimensional data feature extraction and dimension reduction processing system based on matrix factorization of claim 1, wherein, The iterative solution method of the multiplication update unit is alternating minimization, and the following formula is iteratively executed: ； ； wherein is a regularization coefficient; Setting a minimization threshold When the relative change rate of the total loss to be minimized is less than the minimization threshold , output the low-dimensional feature matrix V and the basis matrix U. 8.The high-dimensional data feature extraction and dimension reduction processing system based on matrix factorization of claim 1, wherein, The method steps of the post-processing module for performing row-wise normalization include: S301. For each row of the low-dimensional feature matrix V Calculate norm ; S302. Divide each row by the norm. This yields the normalized row vectors. ; S303、combine all normalized row vectors, output normalized feature matrix .

9. A method for feature extraction and dimension reduction of high-dimensional data based on matrix factorization, characterized in that, The steps include: S1, data acquisition step, the data acquisition module reads the original high-dimensional matrix X; S2, a preprocessing step, the preprocessing module receives the original high-dimensional matrix X and performs missing value imputation and standardization to obtain the preprocessed matrix ; S3, a noise pattern recognition step, said noise pattern recognition module receiving said pre-processed matrix and outputting said noise class label vector I and said confidence vector c; S4, weight matrix generation step, the weight matrix generation module receives the noise category label vector l and the confidence vector c and outputs the diagonal weight matrix W; S5. Decomposition step: The weighted nonnegative matrix decomposition module receives the preprocessed matrix... And the diagonal weight matrix W, perform weighted nonnegative matrix decomposition to output the low-dimensional feature matrix V and the basis matrix U; S6, a post-processing step, the post-processing module receives the low-dimensional feature matrix V and outputs the normalized feature matrix after normalization .

Images