A three-dimensional automatic breast ultrasound image clustering method

Abstract

A method for automatic breast ultrasound image clustering belongs to the field of machine learning technology. By considering a subspace clustering algorithm for biological data clustering and an iterative optimization algorithm for solving the algorithm, as well as the practical application of CAD systems, the present invention can provide a more effective, rapid, and economically feasible early breast cancer screening solution using three-dimensional ABUS imaging. The present invention proposes an image representation method that encapsulates the local structure of the data and applies non-negative constraints to the features to account for both the global and local structural characteristics of the data. A manifold regularizer is incorporated into the image representation to account for the manifold structure of the data, thereby obtaining a GLSR algorithm framework. An efficient iterative algorithm is then developed based on the ADMM iterative method to ensure that the proposed GLSR algorithm obtains a local optimal solution and converges.

Description

Technical Field

[0001] The present invention belongs to the technical field of machine learning, and in particular relates to a three-dimensional automatic breast ultrasound image clustering method. Background Art

[0002] Breast cancer is one of the most common malignancies affecting women, and its incidence continues to rise worldwide. Timely screening can provide patients with faster and more effective interventions. Automated breast ultrasound (ABUS), a breast imaging technique, has become a common technique for early breast cancer screening due to its high resolution, reproducible results, and high objectivity. However, manual observation of three-dimensional ABUS images for early breast cancer screening is cumbersome and laborious, and carries the risk of missed diagnoses.

[0003] Therefore, seeking an efficient and accurate three-dimensional ABUS image screening method is an urgent issue to optimize the early diagnosis process of breast cancer.

[0004] Incorporating computer-aided diagnosis (CAD) systems uses sophisticated algorithms and machine learning techniques to help healthcare professionals automatically classify and interpret breast images, laboratory data, or clinical information. This improves the speed, accuracy, and uniformity of image analysis, thereby facilitating early screening and diagnosis workflows for breast cancer.

[0005] Graph Regularized Least Squares Regression (GLSR) is a subspace clustering (SC) method suitable for clustering biological data and is applicable to CAD systems. SC is a class of clustering algorithms in the field of machine learning. The advantage of this type of algorithm is that it can classify data points into their respective subspaces without the need for labels, and the resulting models are characterized by high construction efficiency, low cost, and excellent overall performance. Graph Regularized Least Squares Regression (GLSR) encodes the intrinsic geometric structure of the data into a least squares regression framework to account for both local and global data structures. Furthermore, the GLSR framework incorporates the manifold structure of features and imposes non-negative constraints on them, making the resulting affinity matrix more accurate and providing a clearer physical meaning for the similarity relationships between samples.

[0006] By applying the Alternating Direction Method of Multipliers (ADMM) to solve GLSR, we can ensure that the GLSR model reaches a local optimum and converges. ADMM is an iterative algorithm framework for solving separable convex optimization problems. By combining the dual decomposition method and the augmented Lagrange multiplier method, the algorithm is decomposable while ensuring good convergence and processing speed.

[0007] The present invention proposes a more effective, rapid and economically feasible three-dimensional ABUS imaging early breast cancer screening solution by considering a subspace clustering algorithm for biological data clustering and an iterative optimization algorithm for solving the algorithm, as well as focusing on the practical application of the CAD system. Summary of the Invention

[0008] In response to the above-mentioned problems existing in the prior art, the purpose of the present invention is to provide a three-dimensional automatic breast ultrasound image clustering method. By incorporating a graph structure regularizer into the GLSR algorithm of the least squares regression algorithm and its iterative optimization algorithm, a preferred breast cancer early screening technology based on three-dimensional automatic breast ultrasound images is provided, which can optimize the breast cancer early screening diagnosis process and improve resource utilization and economic benefits.

[0009] The present invention provides the following technical solutions:

[0010] An automatic breast ultrasound image clustering method comprises the following steps:

[0011] Step 1: Acquire three-dimensional breast ultrasound image data;

[0012] Step 2: Process the obtained three-dimensional images into two-dimensional vectors one by one as samples for subsequent processing;

[0013] Step 3: Considering the manifold structure of the sample space, we obtain the similarity matrix between samples and obtain the smooth representation of any two features from the similarity matrix.

[0014] Step 4: Create a representation graph and apply non-negativity constraints to the features;

[0015] Step 5: Integrate the manifold regularizer and the representation graph, and introduce the sparsity error to obtain the graph regularized least squares regression GLSR objective function;

[0016] Step 6: Based on the alternating direction multiplier method ADMM solution, two auxiliary variables W and Q are introduced to solve the graph regularized least squares regression GLSR objective function to obtain the clustering results.

[0017] Further, the specific process of step 3 is as follows:

[0018] Step 3.1: Build a nearest neighbor graph with N nodes on the total samples, where each node represents a similar sample x belonging to the nearest neighbor graph. i , for each sample x i You can find its k nearest neighbors, x in the graph i and its k nearest neighbors are connected by k edges, so any two samples x i and x j The similarity matrix S ij ;

[0019] Step 3.2: Further calculate the smoothness of the two features through the similarity matrix and the correlation features between samples.

[0020] Furthermore, in step 4, the representation graph encapsulates the local structure and global structure of the data, and the specific process is as follows:

[0021] Step 4.1: For all samples, calculate the sum of the product of the L2 norm square of the residual matrix of each sample data and the inter-sample features, and take the minimum value of all sums as the optimization constraint of the local structure;

[0022] Step 4.2: Multiply the square of the Frobenius norm of the global feature matrix by a positive penalty parameter to obtain the global relationship information between nodes;

[0023] Step 4.3: Integrate the optimization constraints of the local structure with the global relationship information parameter equation and impose a non-negative constraint on the A matrix. The function formula for integrating the optimization constraints of the local structure with the global relationship information parameter equation and impose a non-negative constraint on the parameter matrix A is as follows:

[0024]

[0025] stX=XA,A≥0

[0026] Among them, x i 、x j Represents any two samples i and j, a ij is the associated feature of samples i and j, m is the dimension of the sample, and A is a vector a i The matrix is ​​composed of , λ1 is a positive penalty parameter, is a data matrix containing n samples, ||.|| F It represents the Frobenius norm of the matrix. The first term of the function formula is the function factor considering the local structure, and the second term is the function factor considering the global information of the sample.

[0027] Furthermore, the specific process of step 5 is as follows:

[0028] Step 5.1: Merge the manifold regularizer of step 3 into the representation graph of step 4 to obtain a clustering function model that comprehensively considers the manifold structure, local structure, and global structure of the sample;

[0029] Step 5.2: Introduce the sparse error term λ3||E||1 into the clustering function model, where λ3 is a positive regularization parameter and E represents the error.

[0030] Step 5.3: Add the constraints A1=1, diag(A)=0 to the coefficient matrix A so that the sum of the elements in each row or column is 1.

[0031] Furthermore, the specific process of step 6 is as follows:

[0032] Step 6.1. Add new parameter variables W and Q to distinguish the parameter matrix A in each factor, construct the augmented Lagrangian function and simplify it.

[0033] Step 6.2, solve the augmented Lagrangian function;

[0034] Step 6.3: Calculate the affinity matrix and obtain K clustering results by using the spectral clustering algorithm. By adopting the above technology, compared with the existing technology, the beneficial effects of the present invention are as follows:

[0035] 1) This paper proposes an image representation method that encapsulates the local structure of the data and applies non-negative constraints to the features, thereby taking into account both the global and local structural characteristics of the data. A manifold regularizer is also incorporated into the image representation to account for the manifold structure of the data, thereby obtaining a graph-regularized least squares regression (GLSR) algorithm framework. An efficient iterative algorithm based on the alternating direction multiplier method (ADMM) is then developed to ensure that the proposed graph-regularized least squares regression (GLSR) algorithm obtains a local optimal solution and guarantees convergence.

[0036] 2) In this invention, a subspace clustering machine learning algorithm is used to solve the problem of automatic breast ultrasound image clustering, which greatly reduces the cost of computer-aided diagnosis systems for early diagnosis of breast cancer;

[0037] 3) The graph regularized least squares regression (GLSR) algorithm proposed in this paper takes into account both the local and global structures of the image while considering the manifold structure of the image data, thereby improving the graph clustering performance of the subspace clustering algorithm on automatic ultrasound breast images.

[0038] 4) In the present invention, the graph regularized least squares regression (GLSR) algorithm is iterated based on the alternating direction multiplier method (ADMM) optimization algorithm, thereby improving the efficiency of the GLSR algorithm solution process. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 2 is a framework diagram of the graph regularized least squares regression (GLSR) algorithm of the present invention;

[0040] Figure 2 The present invention implements a flowchart for solving the optimal convergence of the graph regularized least squares regression GLSR algorithm. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0042] On the contrary, the present invention covers any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention as defined by the claims. Furthermore, to facilitate a better understanding of the present invention, certain specific details are described in detail below in the detailed description of the present invention. Those skilled in the art will be able to fully understand the present invention without these details.

[0043] See also Figure 1-2 , an automatic breast ultrasound image clustering method, comprising the following steps:

[0044] Step 1: Acquire three-dimensional breast ultrasound image data using the Invenia automatic breast ultrasound diagnostic system, and perform cleaning and normalization on the acquired data as samples for subsequent processing;

[0045] Step 2: Consider the manifold structure of the sample space, obtain the similarity matrix between samples, and obtain the smooth representation of any two features from the similarity matrix. The specific steps are as follows:

[0046] Step 2.1: Build a nearest neighbor graph with N nodes on the total samples, where each node represents a similar sample x belonging to the nearest neighbor graph. i , for each sample x i You can find its k nearest neighbors, x in the graph i and its k nearest neighbors are connected by k edges, so any two samples x i and x j The similarity matrix S ij , the similarity matrix calculation formula is as follows:

[0047]

[0048] Where ||.||2 represents the L2 norm of the matrix; σ represents the width of the Gaussian kernel function, which affects the calculation of the similarity;

[0049] Step 2.2: Further calculate the smoothness of the two features through the similarity matrix and the correlation features between the samples. The smoothness calculation formula of the features is:

[0050] Tr(A T LA)

[0051] Among them A TRepresents the transpose of matrix A; L represents the Laplacian matrix of the sample graph, which is obtained by subtracting the degree matrix D and the similarity matrix S of the graph; Tr represents the trace of the matrix; this factor can ensure the smoothness of similar samples.

[0052] Step 3: Create a representation graph that encapsulates the local and global structures of the data and applies non-negative constraints to the features. The specific steps are as follows:

[0053] Step 3.1: For all samples, find the sum of the product of the L2 norm square of the residual matrix of each sample data and the inter-sample features, and take the minimum value of all sums as the optimization constraint of the local structure;

[0054] Step 3.2: Multiply the square of the Frobenius norm of the global feature matrix by a positive penalty parameter to obtain the global relationship information between nodes;

[0055] Step 3.3: Integrate the optimization constraints of the local structure with the global relationship information parameter equation and impose a non-negative constraint on the A matrix. The function formula for integrating the optimization constraints of the local structure with the global relationship information parameter equation and impose a non-negative constraint on the parameter matrix A is as follows:

[0056]

[0057] stX=XA,A≥0

[0058] Where λ1 is a positive penalty parameter, is a data matrix containing n samples, ||.|| F It represents the Frobenius norm of the matrix. The first term of the function formula is the function factor considering the local structure, and the second term is the function factor considering the global information of the sample.

[0059] Step 4: Integrate the manifold regularizer and the representation graph, and introduce the sparse error to obtain the GLSR objective function. The specific steps include:

[0060] Step 4.1: Merge the manifold regularizer of step 2 into the representation graph of step 3 to obtain a clustering function model that comprehensively considers the manifold structure, local structure, and global structure of the sample;

[0061] Step 4.2: Introduce the sparse error term λ3||E||1 into the clustering function model, where λ3 is a positive regularization parameter and E represents the error;

[0062] Step 4.3: Add the constraints A1=1, diag(A)=0 to the coefficient matrix A so that the sum of the elements in each row or column is 1. After introducing the constraints A1=1, diag(A)=0, the complete graph regularized least squares GLSR algorithm function equation is as follows:

[0063]

[0064] stX=XA+E, A1=1, diag(A)=0, A≥0.

[0065] Step 5: Solve the graph regularized least squares GLSR algorithm based on the alternating direction multiplier method ADMM optimization algorithm to obtain the clustering results. The steps are as follows:

[0066] Step 5.1. Add new parameter variables W and Q to distinguish the parameter matrix A in the various factors of the function mentioned in step 5.3. Since the three variables A, W, and Q are separable, the augmented Lagrangian function is as follows:

[0067]

[0068] Where Y1, Y2 and Y3 represent Lagrange multipliers, μ>0 is the penalty parameter, and further simplifying the function yields the following formula:

[0069]

[0070] Step 5.2: Solve the augmented Lagrangian function and update the parameters W, Q, A, E, Y1, Y2, Y3, and μ according to the following rules until the function converges:

[0071] The update of parameter W follows the following rules:

[0072] Fixing the other parameters and considering W alone, we can get the following formula by rewriting it:

[0073]

[0074] stW1=1,diag(W)=0,W≥0

[0075] The rewritten factor is equivalent to:

[0076]

[0077] Among them, w i 、v i 、r i are the i-th row of W, V, and R respectively. In order to solve this factor, the following Lagrangian function is defined:

[0078]

[0079] where u i =(v i -r i / μ), η i and α i ≥0 is the Lagrange multiplier, take L for wi The partial derivative of and set it to 0 can be obtained:

[0080]

[0081] Using KKT conditions w i α i =0, we can get w i The optimal solution is:

[0082]

[0083] in Represents a column vector whose i-th element is 0 and the other elements are 1. Since w i 1=1 constraint, η i It can be calculated as:

[0084] η i =(1-u i 1) / (n-1)

[0085] The update of parameter Q follows the following rules:

[0086] By fixing the other parameters and considering Q alone, we can get the following formula:

[0087]

[0088] The solution of this formula belongs to the problem of solving smooth convex programming. Assuming its derivative with respect to Q is 0, the optimal solution of Q is:

[0089] Q=μ(λ2L+μI) -1 (A+Y3 / μ)

[0090] The update of parameter A follows the following rules:

[0091] Fixing the other parameters and considering A alone, we can get the following formula:

[0092]

[0093] This formula can be regarded as an extended LSR model with a closed solution. Let its derivative with respect to A be 0, then its optimal solution is obtained by the following formula:

[0094] A=μ(λ1I+2μI+μX T X) -1 (H1+H2+H3)

[0095] Where H1=X T (X-E+Y1 / μ), H2=W-Y2 / μ, H3=Q-Y3 / μ, I represents an n×n identity matrix;

[0096] The update of parameter E follows the following rules:

[0097] Fixing the other parameters and considering E alone, we can get the following formula:

[0098]

[0099] The closed-form solution of E can be expressed as:

[0100]

[0101] Here, Φ is the shrinkage operator mentioned in the paper titled “Data mining techniques: to predict and resolve breast cancer survivabilit” by Dr. Vikas Chaurasia and Saurabh Pal.

[0102] The update of parameters Y1, Y2, and Y3 can be performed according to the following three equations:

[0103] Y1=Y1+μ(X-XA-E)

[0104] Y2=Y2+μ(AW)

[0105] Y3=Y3+μ(AQ)

[0106] The update of parameter μ follows the following rules:

[0107] μ=min(ρμ,u max )

[0108] where ρ and u max are two given constants;

[0109] Step 5.3: Use the coefficient matrix A to calculate the affinity matrix. The formula is C = (A T +A) / 2, and obtain K clustering results through the spectral clustering algorithm.

[0110] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An automatic breast ultrasound image clustering method, characterized in that: The following steps are involved: Step 1: Acquire three-dimensional breast ultrasound image data; Step 2: Process the obtained three-dimensional images into two-dimensional vectors one by one as samples for subsequent processing; Step 3: Considering the manifold structure of the sample space, we obtain the similarity matrix between samples and obtain the smooth representation of any two features from the similarity matrix. Step 4: Create a representation graph and apply non-negativity constraints to the features; Step 5: Integrate the manifold regularizer and the representation graph, and introduce the sparse error to obtain the graph regularized least squares regression GLSR objective function; the specific process of step 5 is as follows: Step 5.1: Merge the manifold regularizer of step 3 into the representation graph of step 4 to obtain a clustering function model that comprehensively considers the manifold structure, local structure, and global structure of the sample; Step 5.2: Introduce the sparse error term λ3||E||1 into the clustering function model, where λ3 is a positive regularization parameter and E represents the error. Step 5.3: Add the constraints A1=1, diag(A)=0 to the coefficient matrix A so that the sum of the elements in each row or column is 1. Step 6: Based on the alternating direction multiplier method ADMM solution, two auxiliary variables W and Q are introduced to solve the graph regularized least squares regression GLSR objective function to obtain the clustering result; the specific process of step 6 is as follows: Step 6.

1. Add new parameter variables W and Q to distinguish the parameter matrix A in each factor, construct the augmented Lagrangian function and simplify it. Step 6.2, solve the augmented Lagrangian function; Step 6.3: Calculate the affinity matrix and obtain K clustering results through the spectral clustering algorithm.

2. The automatic breast ultrasound image clustering method according to claim 1, characterized in that: The specific process of step 3 is as follows: Step 3.1: Build a nearest neighbor graph with N nodes on the total samples, where each node represents a similar sample x belonging to the nearest neighbor graph. i , for each sample x i You can find its k nearest neighbors, x in the graph i and its k nearest neighbors are connected by k edges, so any two samples x i and x j The similarity matrix S ij ; Step 3.2: Further calculate the smoothness of the two features through the similarity matrix and the correlation features between samples.

3. The automatic breast ultrasound image clustering method according to claim 2, characterized in that: In step 4, the representation graph encapsulates the local and global structures of the data. The specific process is as follows: Step 4.1: For all samples, calculate the sum of the product of the L2 norm square of the residual matrix of each sample data and the inter-sample features, and take the minimum value of all sums as the optimization constraint of the local structure; Step 4.2: Multiply the square of the Frobenius norm of the global feature matrix by a positive penalty parameter to obtain the global relationship information between nodes; Step 4.3: Integrate the optimization constraints of the local structure with the global relationship information parameter equation and impose a non-negative constraint on the A matrix. The function formula for integrating the optimization constraints of the local structure with the global relationship information parameter equation and impose a non-negative constraint on the parameter matrix A is as follows: stX=XA,A≥0 Among them, x i 、x j Represents any two samples i and j, a ij is the associated feature of samples i and j, m is the dimension of the sample, and A is a vector a i The matrix is ​​composed of , λ1 is a positive penalty parameter, is a data matrix containing n samples, ||.|| F It represents the Frobenius norm of the matrix. The first term of the function formula is the function factor considering the local structure, and the second term is the function factor considering the global information of the sample.

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