Self-adaptive graph learning fuzzy clustering method based on low-rank matrix decomposition in medical field

Abstract

The invention discloses an adaptive graph learning fuzzy clustering method based on low-rank matrix decomposition in the medical field, and the method comprises the following steps: carrying out the preprocessing of collected original medical image data, and forming an image feature matrix X; establishing an LAGFC objective function f which is transformed by utilizing a Feychel conjugate technology; iteratively optimizing and updating parameters in the loss function of the LAGFC objective function f in sequence until convergence or reaching the maximum iteration number; and reading the position of the maximum value of the clustering indication matrix F to obtain a clustering label. Through an adaptive graph learning mechanism and a matrix decomposition-fuzzy clustering unified framework, and through low-rank matrix decomposition guided graph learning and fuzzy clustering joint optimization, the data representation discrimination and clustering robustness are synchronously improved, so that more stable, efficient and interpretable semi-supervised clustering is realized, the clustering precision and generalization ability are improved, and the clustering efficiency is improved. The method is especially suitable for medical image data analysis tasks of high-dimensional and complex structures.

Description

Technical Field

[0001] This invention relates to an adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field. Background Technology

[0002] Facial images serve as a source and supplement to medical data. Facial features (including color, texture, symmetry, and proportion) are strongly correlated with many genetic diseases, endocrine disorders, and cardiovascular diseases. For example, many genetic syndromes (such as Down syndrome, Marfan syndrome, and Williams syndrome) have unique facial features, known as "facial phenotypes." When AI models are trained on thousands of facial images with clear diagnoses (such as "hypertension" or "diabetes"), they may discover subtle, disease-related facial patterns that are difficult for the human eye to detect. These patterns may not be a single feature but a complex combination. Therefore, clustering can be used to identify facial images.

[0003] Clustering technology is fundamental to classification data. Clustering is a core tool for analyzing data distribution and is widely used in data mining, image processing and recommendation systems. Existing clustering methods can be divided into two categories: (1) Hard clustering (such as K-Means, spectral clustering): Each sample belongs to only a single cluster. Defects: The discrete constraints of spectral clustering make the optimization problem NP-hard, requiring relaxation and discretization, and relying on post-processing to generate hard assignments; at the same time, hard assignment is difficult to handle samples with fuzzy boundaries. (2) Fuzzy clustering (such as FCM): Samples are assigned to multiple clusters based on membership degree, which is more suitable for fuzzy boundary data. Considering the challenges of hard clustering, in recent years, some researchers have introduced fuzzy logic into the traditional hard assignment-based spectral clustering and proposed some fuzzy spectral clustering methods. For example, FGC replaces the discrete indicator matrix with a fuzzy membership degree matrix, GBFC introduces a balanced regularization term to ensure uniform cluster size in direct acquisition, and LGFCA adds a graph divergence term to enhance cluster discrimination. These methods can directly output fuzzy assignments and improve the local structure recognition ability. These methods present two challenges: (1) They mainly rely on a fixed similarity graph to learn fuzzy assignments. The static structure of the pre-constructed graph is difficult to adapt to the data distribution, and the process is prone to information loss (such as LGFCA) due to artificial parameters (such as the number of nearest neighbors k) and noise interference. (2) They cannot effectively utilize label information in semi-supervised application scenarios.

[0004] The graph clustering methods mentioned aim to learn a low-dimensional representation of each sample from the manifold structure of the data, which is mainly constructed from the local structure of the data. Matrix factorization, on the other hand, aims to learn a low-dimensional representation of each sample from the global structure of the data, reducing data dimensionality redundancy and enabling more efficient clustering (e.g., NMF, CF). Combining these two low-dimensional representation learning methods is highly efficient (e.g., GNMF, LCCF).

[0005] Considering the application scenarios of semi-supervised learning, in recent years, researchers have proposed several efficient clustering models that utilize label information based on the manifold structure of the data and global reconstruction information. SODNMF adds a bigraph regularization term; CSNMF uses correlation entropy for noise mitigation; DCNMF fuses point pairs / paired constraints; ABNMTF optimizes the similarity graph during the learning process using label information; and HCSSMF uses hypergraphs to handle non-convex problems. However, current matrix factorization methods for manifold constraints still require dimensionality reduction before clustering (a two-step separation), leading to a mismatch between feature representation and clustering objectives.

[0006] In summary, existing methods suffer from the following fundamental defects: (1) Existing fuzzy graph clustering methods have a predefined similarity graph defect and cannot effectively utilize known label information in semi-supervised application scenarios. (2) Existing clustering methods that integrate manifold constraints and matrix factorization ideas suffer from performance limitations due to the separation of dimensionality reduction and clustering processes. To address these issues, it is urgent to construct a unified framework to achieve collaborative optimization of adaptive graph learning and fuzzy clustering. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide an adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field.

[0008] The objective of this invention is achieved through the following technical solution: A first aspect of the present invention provides an adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field, comprising the following steps: The acquired raw medical image data is preprocessed to form an image feature matrix X; A LAGFC objective function f is established using Fenchel conjugate transformation. The loss function of the LAGFC objective function f is to maximize the objective function f which includes the data matrix X, the basis matrix W, the Laplacian matrix L, the discretization regularization matrix G, the clustering indicator matrix F, the label constraint matrix A, the similarity graph matrix S, the first dynamic weight p, and the second dynamic weight b. The parameters in the loss function of the LAGFC objective function f are iteratively optimized and updated until convergence or the maximum number of iterations is reached. Read the position of the maximum value in the clustering indicator matrix F to obtain the cluster label.

[0009] Furthermore, the acquired raw medical image data is preprocessed to form an image feature matrix X, including: Image data from medical imaging equipment is collected, uniformly adjusted to a fixed resolution, and the images are flattened into column vector form to form an image feature matrix X. The parameters include the image feature dimension and the number of image samples. The image feature matrix X is normalized using a standardization process.

[0010] Furthermore, the LAGFC objective function f transformed using the Fenchel conjugation technique is specifically as follows: In the formula, W is the basis matrix, initialized with all zeros; F is the clustering indicator matrix, initialized with one-hot encoding for labeled samples and with uniform distribution for unlabeled samples; S is the similarity graph matrix, initialized with all zeros. p represents the first dynamic weight, b represents the second dynamic weight; A is the label constraint matrix, with 1 for labeled sample positions and 0 for the rest. A and L are Laplace matrices. =diag(sum( + ) / 2))-( + ) / 2); G is the discretization regularization matrix, = - , It is the identity matrix. α is a vector with all elements equal to 1; α is the noise resistance strength, and γ is the label constraint strength. , , The Gaussian kernel bandwidth represents the matrix factorization terms. The Gaussian kernel bandwidth represents the self-expression term, and n represents the number of samples; The loss function of the LAGFC objective function f is specifically as follows: In the formula, β is the graph learning intensity. Represents the sparse constraints on the learned graph / 2 is the strength value of the sparsity constraint; the larger the value, the sparser the learned S.

[0011] Further, the step of iteratively optimizing and updating the parameters in the loss function of the LAGFC objective function f until convergence or the maximum number of iterations is reached includes: Calculate the first dynamic weight p and the second dynamic weight b; Update the similarity graph and clustering indicator matrix; Update the base matrix.

[0012] Further, the calculation of the first dynamic weight p and the second dynamic weight b includes: In the formula, t represents the current iteration number.

[0013] Further, the updating of the similarity graph and clustering indicator matrix includes: Calculate the Lagrange daily number and extrapolation weights: (1) Calculate Lipschitz from the variable values ​​in the current iteration to form the variable similarity graph for the next iteration. and clustering indicator matrix Prepare for the update: Where B = diag(b), P = diag(p), and Lg represents Lg = A(L − γG)A⊤; (2) Take the maximum value between the calculated Lipschitz constant and the set constant value to prevent the Lipschitz constant from being too small, which would result in a large gradient: (3) Update the extrapolated weights using the calculated Lipschitz constant to accelerate variable updates: In the formula, This represents the maximum value of the extrapolated weights in the current iteration. Indicates a by The sequence determined by =1, This represents the extrapolation weight of the current iteration S. Indicates the extrapolation weights of the current iteration F; This indicates the strength of the learning effect of extrapolation weights. <1; Calculate similar graphs and clustering indicator matrix The median value: Update similar images and clustering indicator matrix : Update the similarity graph using gradient descent. : Update the clustering indicator matrix using gradient descent. : ; Test whether the gradient descent occurs with the extrapolation weights applied: If the intermediate values ​​of the similarity graph S and clustering indicator matrix F, calculated more quickly through extrapolation weights, result in no overall improvement in the transformed loss function of the objective function f, then let: And return to update similar images and clustering indicator matrix The steps.

[0014] Further, the updated basis matrix includes: Singular Value Decomposition: Where P = diag(p); and They are respectively for The left and right singular matrices for singular value decomposition. It is a singular value matrix; Update the base matrix : .

[0015] The beneficial effects of this invention are: In an exemplary embodiment of the present invention, by using an adaptive graph learning mechanism and a matrix factorization-fuzzy clustering unified framework, and by jointly optimizing graph learning and fuzzy clustering guided by low-rank matrix factorization, the discriminative power of data representation and the robustness of clustering are improved simultaneously, thereby achieving more stable, efficient, and interpretable semi-supervised clustering, improving clustering accuracy and generalization ability, and is particularly suitable for high-dimensional and complex medical image data analysis tasks. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating an adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field, provided in an exemplary embodiment of the present invention. Figure 2 This is a schematic diagram of a basis matrix generated in multiple ways according to an exemplary embodiment of the present invention; Figure 3 This is a schematic diagram of the clustering indicator matrix generated by SemiGNMF and SemiLCCF provided in an exemplary embodiment of the present invention; Figure 4 This is a schematic diagram of the clustering indicator matrix generated by SemiMMF and SODNMF provided in an exemplary embodiment of the present invention; Figure 5This is a schematic diagram of the clustering indicator matrix generated by CSNMF and ABNMTF in an exemplary embodiment of the present invention; Figure 6 This is a schematic diagram of the clustering indicator matrix generated by LGFCA and SSFM-FWCW in an exemplary embodiment of the present invention; Figure 7 This is a schematic diagram of the clustering indicator matrix generated by LAGFC and LAGFC without divergence regularization terms provided in an exemplary embodiment of the present invention. Figure 8 This is a schematic diagram of Gaussian distribution data points provided in an exemplary embodiment of the present invention; Figure 9 This is a schematic diagram of the membership values ​​of data points to various categories after 0, 13, and 30 iterations, provided in an exemplary embodiment of the present invention. Figure 10 This is a schematic diagram of the data after 30 iterations without a divergence regularization term, provided in an exemplary embodiment of the present invention. Figure 11 This is a schematic diagram of the data after 0, 13, and 30 iterations, provided in an exemplary embodiment of the present invention. Detailed Implementation

[0017] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] In the description of this invention, it should be noted that the directions or positional relationships indicated by terms such as "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer" are based on the directions or positional relationships shown in the accompanying drawings and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0019] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0020] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0021] First, it should be noted that the specific objectives of the following exemplary embodiments include: (1) designing an adaptive graph learning mechanism to dynamically generate similar graphs to alleviate the parameter sensitivity and information loss of predefined graphs; (2) in semi-supervised scenarios, deeply integrating label information into the graph construction and clustering process to enhance the model's discriminative power; and (3) constructing a unified optimization framework to achieve collaborative optimization of matrix factorization, graph learning, and fuzzy clustering, avoiding process fragmentation. Specifically: (A) Adaptive semi-supervised fuzzy graph learning model: It is a data matrix. It's a similarity graph; the first term of the model learns an adaptive similarity graph. The second term of the model is... A sparse constraint is typically a 1-norm, such that... The non-zero elements in the graph represent the local structure of the data. The third term is the graph learning term, which uses a constructed similarity graph to learn the low-dimensional representation of the samples, where... It is a Laplace diagram (construction method: =diag(sum( + ) / 2))-( + ) / 2), It is a low-dimensional representation of the samples (and also the fuzzy membership assignment matrix of these samples), while It is a constraint matrix, the purpose of which is to ensure that labeled samples have the same low-dimensional representation. The following is... An example, where p is the number of labeled samples: The fourth term is a discretization regularization term, which promotes... The discretized clustering results are obtained directly, where = - ( It is the identity matrix. (A vector whose elements are all 1).

[0022] (B) Unifying adaptive graph learning, matrix factorization, and fuzzy clustering into a single-stage optimization framework (LAGFC): in The basis matrix is ​​equivalent to the orthogonalized centroids between samples, and alpha is the regularization parameter. This framework is based on the adaptive semi-supervised fuzzy graph learning model proposed in (1), and the first term added is a matrix factorization term, which minimizes the maximum correlation entropy criterion. The error describes the global reconstruction information between samples. Furthermore, the maximum correlation entropy criterion is used in the first and second terms to replace the Euclidean distance metric (to mitigate the impact of large error terms on the loss function), thus enhancing the robustness of the model.

[0023] See Figure 1 , Figure 1 The flowchart shown is a process for an adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field, provided in an exemplary embodiment of the present invention, including the following steps: The acquired raw medical image data is preprocessed to form an image feature matrix X; A LAGFC objective function f is established using Fenchel conjugate transformation. The loss function of the LAGFC objective function f is to maximize the objective function f which includes the data matrix X, the basis matrix W, the Laplacian matrix L, the discretization regularization matrix G, the clustering indicator matrix F, the label constraint matrix A, the similarity graph matrix S, the first dynamic weight p, and the second dynamic weight b. The parameters in the loss function of the LAGFC objective function f are iteratively optimized and updated until convergence or the maximum number of iterations is reached. Read the position of the maximum value in the clustering indicator matrix F to obtain the cluster label.

[0024] Specifically, in this exemplary embodiment, the LAGFC method proposed in this exemplary embodiment improves the discriminativeness of data representation and the robustness of clustering through the joint optimization of graph learning guided by low-rank matrix factorization and fuzzy clustering, thereby achieving more stable, efficient and interpretable semi-supervised clustering, improving clustering accuracy and generalization ability, and is particularly suitable for medical image data analysis tasks with high-dimensional and complex structures.

[0025] The following content will explain the specific implementation method: More preferably, in an exemplary embodiment, the acquired raw medical image data is preprocessed to form an image feature matrix X, including: Image data from medical imaging equipment (such as CT, MRI, ultrasound, etc.) is collected, uniformly adjusted to a fixed resolution, and the images are flattened into column vector form to form an image feature matrix X. The parameters include the image feature dimension and the number of image samples. The image feature matrix X is normalized using standardization operations (such as Z-score normalization or min-max normalization).

[0026] Specifically, in this exemplary embodiment, the data preparation stage includes: (1) input data: data matrix X (dimension: number of features × number of samples), label constraint matrix A (fill in 1 for labeled sample positions, and 0 for the rest); (2) parameter initialization: setting noise resistance strength α, graph learning strength β, and label constraint strength γ. For example: Input: Data matrix Label constraint matrix The regularization parameters are alpha, beta, lambda, and gamma.

[0027] More preferably, in an exemplary embodiment, the loss function of the LAGFC model is transformed by combining block coordinate update (BCU) and Fenchel conjugate (FC) techniques. The LAGFC objective function f transformed using the Fenchel conjugate technique is specifically as follows: In the formula, W is the basis matrix, initialized with all zeros; F is the clustering indicator matrix, initialized with one-hot encoding for labeled samples and with uniform distribution for unlabeled samples; S is the similarity graph matrix, initialized with all zeros. p represents the first dynamic weight, b represents the second dynamic weight; A is the label constraint matrix, with 1 for labeled sample positions and 0 for the rest. A and L are Laplace matrices. =diag(sum( + ) / 2))-( + ) / 2); G is the discretization regularization matrix, = - , It is the identity matrix. α is a vector with all elements equal to 1; α is the noise resistance strength, and γ is the label constraint strength. , , The Gaussian kernel bandwidth represents the matrix factorization terms. The Gaussian kernel bandwidth represents the self-expression term, and n represents the number of samples; The loss function of the LAGFC objective function f is specifically as follows: In the formula, β is the graph learning intensity. Represents the sparse constraints on the learned graph / 2 is the strength value of the sparsity constraint; the larger the value, the sparser the learned S.

[0028] Specifically, in this exemplary embodiment, during the model initialization phase, three types of core matrices need to be created: a base matrix W (initialized with all zeros), a clustering indicator matrix F (labeled samples are initialized with one-hot encoding, and unlabeled samples are uniformly distributed), and a similarity graph matrix S (initialized with all zeros). For example: =zeros(c,d); =(eye(c,c),(1 / n)*ones(np)); =zeros(n,n).

[0029] More preferably, in an exemplary embodiment, the step of iteratively optimizing and updating the parameters in the loss function of the LAGFC objective function f until convergence or the maximum number of iterations is reached includes: S1: Calculate the first dynamic weight p and the second dynamic weight b; S2: Update the similarity graph and clustering indicator matrix; S3: Update the basis matrix.

[0030] Specifically, in this exemplary embodiment, the iterative optimization process includes: (1) calculating dynamic weights (first dynamic weight p, second dynamic weight b): calculating noise resistance weights for each sample and calculating representation similarity between samples; (2) updating similarity graph: dynamically constructing graph structure based on sample similarity; (3) updating clustering indicator matrix: fusing graph structure, label constraints and global reconstruction information, and labeling samples to always maintain 0 / 1 discrete values; (4) updating base matrix: extracting global features through matrix decomposition.

[0031] Repeat the above steps until convergence (approximately 50-300 times).

[0032] More preferably, in an exemplary embodiment, step S1, calculating the first dynamic weight p and the second dynamic weight b, includes: In the formula, t represents the current iteration number.

[0033] Specifically, in this exemplary embodiment, the update and This is equivalent to weighting the loss for each sample, thus reducing the impact of outliers.

[0034] More preferably, in an exemplary embodiment, step S2, updating the similarity graph and clustering indicator matrix, includes: S21: Calculate the Lagrange daily number and extrapolation weights: (1) Calculate Lipschitz from the variable values ​​in the current iteration to form the variable similarity graph for the next iteration. and clustering indicator matrix Prepare for the update: Where B = diag(b), P = diag(p), and Lg represents Lg = A(L − γG)A⊤; (2) Take the maximum value between the calculated Lipschitz constant and the set constant value to prevent the Lipschitz constant from being too small, which would result in a large gradient: (3) Update the extrapolated weights using the calculated Lipschitz constant to accelerate variable updates: In the formula, This represents the maximum value of the extrapolated weights in the current iteration. Indicates a by The sequence determined by =1, This represents the extrapolation weight of the current iteration S. Indicates the extrapolation weights of the current iteration F; This indicates the strength of the learning effect of extrapolation weights. <1; S22: Calculate the similarity graph and clustering indicator matrix The median value: S23: Update similar images and clustering indicator matrix : Update the similarity graph using gradient descent. : Update the clustering indicator matrix using gradient descent. : ; S24: Check if the gradient descent occurs with the extrapolation weights applied. If the intermediate values ​​of the similarity graph S and clustering indicator matrix F, calculated more quickly through extrapolation weights, result in no overall improvement in the transformed loss function of the objective function f, then let: And return to update similar images and clustering indicator matrix The steps.

[0035] More preferably, in an exemplary embodiment, step S3, the updating of the base matrix includes: Singular Value Decomposition: Where P = diag(p); and They are respectively for The left and right singular matrices for singular value decomposition. It is a singular value matrix; Update the base matrix : .

[0036] In the final output stage, the cluster label is obtained by directly reading the position of the maximum value of the indicator matrix, and the membership degree of the boundary samples is obtained by gradient (e.g., [0.6, 0.4, 0]).

[0037] Another exemplary embodiment of the present invention provides an electronic device including a memory and a processor, wherein the memory stores computer instructions executable on the processor, and the processor executes the computer instructions as follows: Figure 1 The steps of the method are described.

[0038] Another exemplary embodiment of the present invention provides a computer storage medium having computer instructions stored thereon, wherein the computer instructions, when executed, perform actions such as... Figure 1 The steps of the method are described.

[0039] The LAGFC method proposed in this exemplary embodiment achieves significant technical improvements in multiple aspects through an adaptive graph learning mechanism and a unified framework of matrix factorization-fuzzy clustering (the experiment is repeated 10 times on each dataset, randomly selecting c classes, and the mean results and standard deviations are reported): Table 1. Clustering results of the COIL dataset Table 2. Clustering results of the ORL dataset Table 3. Clustering results of the WarpPIE dataset Table 4. Clustering results of the MNIST dataset Table 5. Clustering results of the USPS dataset (1) Superior noise resistance: In tests on five datasets including COIL20, ORL, warpPIE, MNIST, and USPS, with 20% synthetic outliers (noisy images with random pixels 0 / 255), and with 30% of the samples being labeled, LAGFC outperformed all other datasets in terms of clustering accuracy (ACC) and normalized mutual information (NMI). On the WarpPIE dataset, ACC improved by 8.12% and NMI by 11.17%; on the MNIST dataset, ACC improved by 9.58% and NMI by 6.7%; and on the USPS dataset, ACC improved by 7.67% and NMI by 10.44%. Its noise resistance stems from the introduction of maximum correlation entropy (MCC) in global reconstruction and graph learning, effectively suppressing outlier interference (such as...). Figure 2 As shown in the visualization experiment, the basis matrix of the traditional MF method is contaminated by noise, while LAGFC remains pure. Figure 2 The diagram shows the basis matrices generated by the SemiGNMF, SemiLCCF, SemiMMF, SODNMF, CSNMF, ABNMTF, and LAGFC methods, from top to bottom, when the dataset contains 20% synthetic anomalous images. This data comes from WarpPIE, a publicly available face image clustering dataset.

[0040] (2) End-to-end optimization to eliminate information loss: Traditional matrix factorization methods require post-processing to transform into low-dimensional representations, resulting in information loss. Figure 3 Its output cannot directly indicate cluster labels; while LAGFC directly generates a fuzzy indicator matrix with significant 0-1 properties (This shows that its output cannot directly indicate cluster labels); Figure 7 (i) Clearly distinguish cluster labels and eliminate post-processing steps. Figures 3-7 Figures (a) to (j) respectively show the indicator matrices generated by the SemiGNMF, SemiLCCF, SemiMMF, SODNMF, CSNMF, ABNMTF, LGFCA, SSFM-FWCW, LAGFC, and LAGFC without divergence regularization.

[0041] (3) Semi-supervised label propagation: By constraining the divergent regularization term through label, the membership degree of labeled samples is promoted to approach 0 / 1. Figure 7 (i) enables label propagation for unlabeled samples. A variant of this regularization term is removed. Figure 7 (j) The 0-1 property is lost in the labeled samples.

[0042] (4) Strong stability and high efficiency: In repeated experiments with cluster numbers c=2~10, LAGFC achieved the best average results across all datasets compared to other methods. The unified framework enables synchronous convergence of graph construction, representation learning, and clustering, verifying the model's efficiency and stability.

[0043] Although the experimental portion of this invention uses publicly available general datasets (such as COIL20, ORL, etc.) for validation, this aims to demonstrate, at the algorithmic level, the general superiority of the method described in this invention in processing high-dimensional data, overcoming noise interference, and discovering complex intrinsic structures. These capabilities are precisely the core challenges in medical image analysis. Specifically: (1) The general technical problem solved by this method is highly isomorphic to the specific challenges in medical image analysis.

[0044] (2) The publicly available dataset used has data characteristics that have a clear mapping and analogy relationship with various medical images.

[0045] The relevant application scenarios are shown in the table below: The successful application of this invention on the ORL and warpPIE face datasets validates its ability to accurately identify individuals despite variations in lighting and facial expressions. This feature can be directly applied to the task of staging Alzheimer's disease using brain MRI images: different identities in the dataset can be analogized to different stages of the disease (e.g., healthy controls, mild cognitive impairment, Alzheimer's disease), and variations in lighting and facial expressions within an individual can be analogized to individual differences in brain structure among different patients at the same disease stage. Through adaptive graph learning, this invention can effectively capture atrophy patterns in key brain regions (such as the hippocampus) associated with disease progression, thereby enabling precise and automated staging of the disease and assisting in clinical diagnosis.

[0046] In summary, experiments on multiple standard datasets have fully demonstrated the robustness of the core technical features of this invention—the robustness brought by low-rank matrix factorization and the high discriminative power brought by adaptive graph learning. These features are precisely what is needed to solve key challenges in medical image analysis, such as noise interference, high-dimensional complexity, and the identification of subtle lesions. Therefore, there is sufficient reason to believe that the method described in this invention will exhibit equal or even more significant performance improvements in specific applications such as medical image segmentation, classification, and disease typing. Furthermore, as a general clustering analysis framework, the application scope of this invention is not limited to medical images, but can also be widely applied to other fields that require the discovery of intrinsic structure from complex high-dimensional data.

[0047] Summary of core effects: (1) Noise resistance: ACC improved by up to 9.58% under outlier interference; (2) Efficiency: End-to-end output avoids information loss; (3) Discriminability: Semi-supervised label propagation enhances the processing of samples with blurred boundaries; (4) Robustness: Stability is maintained in experiments with 5 datasets and multiple clusters.

[0048] in addition, Figures 8-11 A visualization of the synthetic dataset experiment is shown: Figure 8 This is a schematic diagram of a three-dimensional Gaussian distribution of data points: it contains 3 clusters, each with 50 samples, showing the spatial distribution of the original data. Figure 9 The three figures illustrate the cluster label indication perspective: the evolution of the fuzzy indicator matrix FA in iterations 0 (a), 13 (b), and 30 (c), reflecting the characteristic that the sample membership converges to near 0 / 1. Figure 10 The ablation experiment results are shown: the data representation after 30 iterations without a divergence regularization term shows that the labeled samples lose their one-hot encoding characteristics; while Figure 11 The three figures illustrate the data representation perspective: the spatial distribution of FA at iterations 0 (a), 13 (b), and 30 (c), showing the process of unlabeled samples (black circles) gradually separating from a uniform distribution.

[0049] Key details in the image: (1) Boundary sample analysis Figure 9 (c) ): Boundary point 35 ( Figure 8 The black-framed mark indicates a membership degree of [0.5951, 0.4049, 0], which is a non-one-hot encoding form, reflecting the membership degree allocation of fuzzy clustering to boundary points; (2) Semi-supervisory mechanism Figure 11 (a)-(c)): Labeled samples (purple circular markers) always maintain one-hot encoding; unlabeled samples are gradually separated under the guidance of labeled samples, and the distance between heterogeneous samples increases with iteration; (3) The effect of divergent regularization ( Figure 10 vs Figure 11 (c) : Without this regularization term, the labeled samples deviate from one-hot encoding. Figure 10 This leads to weakened supervision information; the complete model maintains the discriminative power of labeled samples through regularization constraints. Figure 11 (c)) to ensure the effective dissemination of the label.

[0050] The technical value of the illustrations: (1) Figure 9 (a)-(c) / Figure 11 (a)-(c) Dual-view verification: Simultaneously demonstrating membership convergence and representation space evolution, proving the effectiveness of end-to-end optimization; (2) Figure 10 Ablation Comparison: The Key Role of Divergent Regularization in Maintaining the Monitoring Signal (Empirical Evidence) (3) Boundary point quantification analysis: reveals the model’s processing mechanism for fuzzy samples and supports the characteristics of “boundary fuzzy membership assignment”.

[0051] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. An adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field, characterized in that: Includes the following steps: The acquired raw medical image data is preprocessed to form an image feature matrix X; A LAGFC objective function f is established using Fenchel conjugate transformation. The loss function of the LAGFC objective function f is to maximize the objective function f which includes the data matrix X, the basis matrix W, the Laplacian matrix L, the discretization regularization matrix G, the clustering indicator matrix F, the label constraint matrix A, the similarity graph matrix S, the first dynamic weight p, and the second dynamic weight b. The parameters in the loss function of the LAGFC objective function f are iteratively optimized and updated until convergence or the maximum number of iterations is reached. Read the position of the maximum value in the clustering indicator matrix F to obtain the cluster label.

2. The adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field according to claim 1, characterized in that: The acquired raw medical image data is preprocessed to form an image feature matrix X, including: Image data from medical imaging equipment is collected, uniformly adjusted to a fixed resolution, and the images are flattened into column vector form to form an image feature matrix X. The parameters include the image feature dimension and the number of image samples. The image feature matrix X is normalized using a standardization process.

3. The adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field according to claim 1, characterized in that: The LAGFC objective function f transformed using the Fenchel conjugation technique is specifically as follows: In the formula, W is the basis matrix, initialized with all zeros; F is the clustering indicator matrix, initialized with one-hot encoding for labeled samples and with uniform distribution for unlabeled samples; S is the similarity graph matrix, initialized with all zeros. ; p represents the first dynamic weight, b represents the second dynamic weight; A is the label constraint matrix, with 1 for labeled sample positions and 0 for the rest. A and L are Laplace matrices. =diag(sum( + ) / 2))-( + ) / 2); G is the discretization regularization matrix, = - , It is the identity matrix. α is a vector with all elements equal to 1; α is the noise resistance strength, and γ is the label constraint strength. , , The Gaussian kernel bandwidth represents the matrix factorization terms. The Gaussian kernel bandwidth represents the self-expression term, and n represents the number of samples; The loss function of the LAGFC objective function f is specifically as follows: In the formula, β is the graph learning intensity. Represents the sparse constraints on the learned graph / 2 is the strength value of the sparsity constraint; the larger the value, the sparser the learned S.

4. The adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field according to claim 3, characterized in that: The step of iteratively optimizing and updating the parameters in the loss function of the LAGFC objective function f until convergence or the maximum number of iterations is reached includes: Calculate the first dynamic weight p and the second dynamic weight b; Update the similarity graph and clustering indicator matrix; Update the base matrix.

5. The adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field according to claim 4, characterized in that: The calculation of the first dynamic weight p and the second dynamic weight b includes: In the formula, t represents the current iteration number.

6. The adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field according to claim 5, characterized in that: The update of the similarity map and clustering indicator matrix includes: Calculate the Lagrange daily number and extrapolation weights: (1) Calculate Lipschitz from the variable values ​​in the current iteration to form the variable similarity graph for the next iteration. and clustering indicator matrix Prepare for the update: Where B = diag(b), P = diag(p), and Lg represents Lg = A(L − γG)A⊤; (2) Take the maximum value between the calculated Lipschitz constant and the set constant value to prevent the Lipschitz constant from being too small, which would result in a large gradient: (3) Update the extrapolated weights using the calculated Lipschitz constant to accelerate variable updates: In the formula, This represents the maximum value of the extrapolated weights in the current iteration. Indicates a by The sequence determined by =1, This represents the extrapolation weight of the current iteration S. Indicates the extrapolation weights of the current iteration F; This indicates the strength of the learning effect of extrapolation weights. <1; Calculate similar graphs and clustering indicator matrix The median value: Update similar images and clustering indicator matrix : Update the similarity graph using gradient descent. : Update the clustering indicator matrix using gradient descent. : ； Test whether the gradient descent occurs with the extrapolation weights applied: If the intermediate values ​​of the similarity graph S and clustering indicator matrix F, calculated more quickly through extrapolation weights, result in no overall improvement in the transformed loss function of the objective function f, then let: And return to update similar images and clustering indicator matrix The steps.

7. The adaptive graph learning fuzzy clustering method based on low-rank matrix factorization in the medical field according to claim 6, characterized in that: The updated base matrix includes: Singular Value Decomposition: Where P = diag(p); and They are respectively for The left and right singular matrices for singular value decomposition. It is a singular value matrix; Update the basis matrix : 。

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