Method for joint prediction of multiple clinical indicators of breast cancer based on non-negative matrix factorization

Abstract

The application provides a method for jointly predicting multiple clinical indexes of breast cancer based on non-negative matrix factorization, first, image data and clinical data of breast cancer cases are collected, and pre-processing is performed to obtain a clinical index matrix and an image feature matrix; second, the data set is divided into a training set and a test set; then, a multiplication update rule is used to iteratively solve a target function to obtain an optimized feature weight matrix, and the feature weight is sorted according to the corresponding label to select the optimal K features; finally, the performance of the method is verified by using the clinical index matrix and the feature matrix in the test set. The application reasonably extracts shared features between labels and features related to independent labels, and effectively improves the prediction effect of multiple clinical indexes.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bioinformatics, and particularly relates to a method for jointly predicting multiple clinical indexes of breast cancer based on non-negative matrix factorization. BACKGROUND

[0002] Breast cancer is a malignant tumor with high heterogeneity, and its type needs to be divided by multiple clinical indexes to determine the prognosis effect and assist in formulating a treatment plan. Common clinical indexes include human epidermal growth factor receptor 2 (HER2), cell proliferation marker Ki67, and histological grading. HER2 is involved in the regulation of cell growth and differentiation, and is lowly expressed in normal breast tissue and highly expressed in breast cancer tissue. Ki67 can reflect the cell proliferation activity of breast malignant tumors, and the high or low value of Ki67 indicates the speed of breast cancer tumor growth. The histological grading of breast cancer is closely related to the survival of patients, and high-grade breast cancer is more likely to recur and has poor prognosis, so it needs to be followed up in time. Therefore, these indexes are crucial for the diagnosis, development and prognosis of breast cancer, and it is of great significance to study how to improve the prediction results of these indexes for breast cancer patients.

[0003] With the development of computer technology, machine learning as an effective class prediction method has been gradually applied to the prediction of breast cancer and its corresponding clinical indexes. Ma et al. used LASSO regression method to select the image group features of DCE-MRI, and then used support vector machine based on Gaussian kernel for classification and prediction of the high or low value of Ki67 expression. Lu and Yin used the same machine learning method to predict the state of HER2. Lagree et al. first used deep convolutional neural network to extract image features of pathological sections, and then used 5 common machine learning methods such as K-nearest neighbor to predict the class label of tissue grading. Song et al. selected 8 common machine learning methods such as random forest based on multi-parameter MRI image features to predict the high or low value of Ki67 expression and tissue grading. Fan et al. used multi-task learning model based on DCE-MRI and DWI images to jointly predict the high or low value of Ki67 expression and tissue grading.

[0004] The existing methods still have some deficiencies: only a single index is predicted, or multiple indexes are decomposed into multiple single indexes for separate prediction, ignoring the information of mutual correlation between multiple indexes, resulting in poor prediction effect. SUMMARY

[0005] Therefore, the purpose of the present application is to provide a method for jointly predicting multiple clinical indexes of breast cancer based on non-negative matrix factorization, which can consider the correlation between multiple clinical indexes, extract features shared by multiple indexes and features related to each index itself, thereby improving the prediction effect.

[0006] The application is implemented by the following scheme: a method for jointly predicting multiple clinical indicators of breast cancer based on non-negative matrix decomposition, specifically comprising the following steps:

[0007] Step 1: data acquisition and preprocessing. Screening of the predicted clinical indicators to construct the label matrix Y of tumor samples and multiple clinical labels a . Performing tumor segmentation on the images of breast cancer patients and extracting the image features of the tumor to construct the feature matrix X of tumor samples and image features a .

[0008] Step 2: dividing the data set into a training set {X, Y} and a test set {X t tY t}.

[0009] Step 3: using the label matrix Y of the training set and the feature matrix X of the training set to construct a least squares regression model to obtain the feature selection weight matrix W related to each label.

[0010] Step 4: using the coupling non-negative matrix decomposition method to reduce the dimension of the label matrix Y of the training set and the feature matrix X to obtain the latent label matrix Z. The loss function of the coupling matrix decomposition is so that the latent label matrix Z can simultaneously embed the information of the label and the information of the feature.

[0011] Step 5: using the latent label matrix Z and the feature matrix X of the training set to construct a least squares regression model to obtain the feature selection weight matrix Q shared by multiple labels.

[0012] Step 6: using L 2t1 norm regularization to constrain the feature selection weight matrix Q shared by multiple labels. Through row sparsity constraint, the weights in Q are concentrated on individual rows, and other rows tend to zero, so as to select a few important features related to multiple labels.

[0013] Step 7: using graph Laplacian constraint to promote the consistency of the features on Q and W in the local geometric structure of different label spaces, and realizing the fusion of shared features and label independent features. Q and W change dynamically in the optimization process, so the corresponding constraint is a dynamic graph Laplacian constraint, and the calculation method is:

[0014] Tr(W T L Q W)

[0015] Wherein, Tr(*) is the trace of the matrix, L Q =P Q -SQ is the graph Laplacian matrix of Q. S Q is the nearest neighbor matrix with the kernel function as the distance, P Q is the degree matrix, is S Q is the diagonal matrix whose elements are the sum of all column elements in each row of Q.

[0016]

[0017] where, N p (Q *j ) represents the set of p nearest neighbors of Q *j

[0018] Step 8: Considering the target items of steps 3 to 7 comprehensively, the total objective function is constructed as:

[0019]

[0020] s.t. W≥0, Q≥0, Z≥0, A≥0, B≥0

[0021] Step 9: Initialize the variable matrix of the objective function.

[0022] Step 10: Take the partial derivative of the objective function with respect to each variable to obtain the multiplication update formula for each variable:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] where, is the Hadamard product of matrices, v is a column vector of all 1s. R = {(Ω) + (Ω T ) + 2(∑)}⊙S Q , WW T =∑, Ω=WW T ⊙I, I is the identity matrix,

[0029] Step 11: Determine whether the stopping condition is met. If it is met, execute step 12, otherwise update each variable according to step 10.

[0030] Step 12: Sort the weight values corresponding to each label according to the feature selection weight matrix W obtained by optimization, and output the set of K optimal features corresponding to each label.

[0031] ​Step 13: According to the selected optimal features, the training set is used to train the logistic regression classifier, and then the test set is used to evaluate the model results.

[0032] Compared with the prior art, the present application has the following beneficial effects:

[0033] 1、The present application realizes joint prediction of multiple clinical indicators of breast cancer, not only uses independent features corresponding to multiple clinical indicators of breast cancer, but also uses shared features related to multiple clinical indicators of breast cancer, realizes complementary features, and improves the prediction performance. Experiments show that compared with existing methods, the present application improves the prediction performance of multiple clinical indicators of breast cancer.

[0034] 2、The present application proposes a method of coupling non-negative matrix factorization based on dynamic graph constraint, which better meets the non-negative nature of real data, has stronger interpretability, makes the system have better robustness through dimension reduction, couples the information between data and features, and dynamically maintains the consistency of local geometric structure between features in the original space and low-dimensional space, so that the independent features in the original space can better learn the information of the shared features in the low-dimensional space.

[0035] 3、The present application is a non-invasive diagnostic method, which greatly reduces the burden on patients. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The present application is a method of the present application.

[0037] Figure 2 The present application is a method of the present application. DETAILED DESCRIPTION

[0038] The technical solutions of the present application will be further described in detail below with specific examples and in combination with the drawings.

[0039] Example 1

[0040] As shown in the drawings, the embodiment of the present application specifically includes the following steps: Figure 1

[0041] Step 1: Data acquisition and preprocessing. Screening of the predicted clinical indicators to construct the label matrix Y of the tumor sample and multiple clinical labels a . The image of the breast cancer patient is segmented, and the imageomic features of the tumor are extracted to construct the feature matrix X of the tumor sample and the image features a .

[0042] ​In the implementation, the relevant clinical information in the cases of breast cancer patients is statistically analyzed, and the patient samples with Her2, Ki67 and histological grading clinical information are screened out, and the number of samples is 203. The image features of the tumor region on the DCE-MRI are extracted by the PyRadiomics package, and the number of features is 106.

[0043] Step 2: Divide the data set into training set {X, Y} and test set {X t , Y t}.

[0044] In the implementation, the data set is randomly stratified sampled according to the ratio of 7:3 for each label to obtain the training set and the test set, the number of samples of the training set is 142, and the number of samples of the test set is 61.

[0045] Step 3: Use the label matrix Y of the training set and the feature matrix X of the training set to construct a least squares regression model to obtain the feature selection weight matrix W related to each label.

[0046] In the implementation, the rows of the matrix W correspond to the features, and the columns correspond to the clinical indicators, and the dimension is 142*3.

[0047] Step 4: Use the coupled non-negative matrix decomposition method to reduce the dimension of the label matrix Y of the training set and the feature matrix X to obtain the latent label matrix Z. The loss function of the coupled matrix decomposition is so that the latent label matrix Z can simultaneously embed the information of the label and the information of the feature.

[0048] In the implementation, the label dimension of the label matrix Y of the training set is 3, and the label dimension of the latent label matrix Z after dimension reduction is 2.

[0049] Step 5: Use the latent label matrix Z and the feature matrix X of the training set to construct a least squares regression model to obtain the feature selection weight matrix shared by multiple labels.

[0050] In the implementation, the rows of the matrix correspond to the features, and the columns correspond to the latent clinical indicators, and the dimension is 142*2.

[0051] Step 6: Use the L 2，1 norm regularization to constrain the feature selection weight matrix Q shared by multiple labels. Through row sparse constraint, the weights in Q are concentrated on individual rows, and other rows tend to zero, so as to select a few important features related to multiple labels.

[0052] In the implementation, since the L 2，1 norm of Q is not derivable, the derivable matrix form is used for approximation: ||Q||2，1 = tr [Q T DQ].

[0053] where D is a diagonal matrix whose diagonal elements are

[0054] Step 7: Utilize the graph Laplacian constraint to promote the consistency of the local geometric structure of the features on Q and W in different label spaces, and realize the fusion of shared features and label independent features. W is dynamically changed in the optimization process, so the corresponding constraint is a dynamic graph Laplacian constraint, and the calculation method is:

[0055] Tr(W T L Q W)

[0056] where Tr(*) is the trace of the matrix, L Q = P Q -S Q is the graph Laplacian matrix of Q. S Q is the nearest neighbor matrix with the heat kernel function as the distance, P Q is the degree matrix, which is a diagonal matrix composed of the sum of all column elements in each row of S Q .

[0057]

[0058] where N p (Q *j ) represents the set of the p nearest neighbors of Q *j .

[0059] In specific implementation, the size of the nearest neighbor set is p = 10, and the bandwidth of the heat kernel function is σ = 1.

[0060] Step 8: Considering the objective terms of steps 3 to 7, the total objective function is constructed as:

[0061]

[0062] s.t. W ≥ 0, Q ≥ 0, Z ≥ 0, A ≥ 0, B ≥ 0

[0063] In specific implementation, the regularization term coefficients θ, a, b, g, d, e ∈ {0.01, 0.1, 1.0, 10, 100}, microAUC is used as the performance evaluation index, and the parameters that make the average micro AUC on the validation set optimal are selected as the model parameters through 5-fold cross-validation method. Experiments show that: when θ = 0.01, a = 1, b = 100, g = 1, d = 1, e = 1, the performance is optimal.

[0064] Step 9: Initialize each variable matrix of the objective function.

[0065] In specific implementation, the elements in each variable matrix of the objective function are randomly generated subject to uniform distribution on the interval (0, 1).

[0066] Step 10: Partial derivatives of each variable of the objective function are calculated, and the multiplication update formula of each variable is obtained as follows:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] wherein is the Hadamard product of matrices, v is a column vector of all 1s, R = {(Ω) + (Ω T ) + 2(∑)}⊙S Q , WW T =∑, Ω=WW T ⊙I, I is the identity matrix,

[0073] In specific implementation, the multiplication update rule is derived by the Lagrange multiplier method and KKT conditions (Karush-Kuhn-Tucker conditions). During the update of each variable, the other variables remain unchanged.

[0074] Step 11: Determine whether the stopping condition is met. If the stopping condition is met, execute step 12, otherwise update each variable according to step 10.

[0075] In specific implementation, the stopping condition is that the number of iterations reaches the set maximum number of iterations, and the maximum number of iterations is 300.

[0076] Step 12: Sort the weight values corresponding to each label according to the feature selection weight matrix W obtained by optimization, and output the set of K optimal features corresponding to each label.

[0077] In specific implementation, the number of optimal features K = 21.

[0078] Step 13: According to the selected optimal features, train the logistic regression classifier using the training set, and then use the test set to evaluate the model results.

[0079] In specific implementation, the comprehensive micro AUC of multiple indicators and the AUC of each indicator are used as evaluation criteria.

[0080] The effectiveness of the present application is verified by the following simulation:

[0081] The prediction performance of the method ISCMFS proposed in the present application and the existing five multi-label classification methods on the multi-clinical indicator data of breast cancer is compared. The comprehensive performance of various methods on multiple indicators is evaluated by micro AUC, and the experimental results are shown in Table 1. Figure 2 The greater the micro AUC value, the better the prediction performance. The experimental results show that the micro AUC obtained by the method ISCMFS proposed in the present application is 0.804, which is greater than all other methods. At the same time, by analyzing the AUC on the prediction task of each clinical indicator, and the 95% confidence interval, sensitivity, specificity and other parameters, the method ISCMFS proposed in the present application and the other five methods are compared in more detail, and the experimental results are shown in Table 1.

[0082] Table 1 Comparison results of the method proposed in the present application and several methods in the prior art on each clinical indicator prediction task

[0083]

[0084]

[0085] The experimental results show that on each prediction task, the AUC obtained by the method ISCMFS proposed in the present application is 0.823, 0.691, 0.776, which is better than the method Lasso and RFE based on independent feature selection, and also better than the method MIFS, CMFS and SCMFS based on shared feature selection. Overall, the present application proposes a method for predicting multiple clinical indicators of breast cancer based on non-negative matrix factorization, which not only has better comprehensive performance than other methods, but also has better prediction performance on each specific clinical indicator than other methods.

Claims

1.A method for jointly predicting multiple clinical indicators of breast cancer based on non-negative matrix factorization, specifically comprising the following steps: Step 1: data acquisition and preprocessing; screening the clinical indicators to be predicted, constructing the label matrix Y of tumor samples and multiple clinical labels a ; tumor segmentation was performed on the images of breast cancer patients, and the image features of the tumor were extracted to construct the feature matrix X of tumor samples and image features a ; Step 2: Split the dataset into training set {X, Y} and test set {X t , Y t} Step 3: constructing a least square regression model using the label matrix Y of the training set and the feature matrix X of the training set to obtain a feature selection weight matrix W related to each label itself; Step 4: Dimensionality reduction is performed on the labels and features of the label matrix Y and the feature matrix X of the training set by using the coupled non-negative matrix factorization method to obtain a latent label matrix Z; the loss function of the coupled matrix factorization is The latent label matrix Z can simultaneously embed the information of the labels and the information of the features. Step 5: Constructing a least square regression model with the latent label matrix Z and the feature matrix X of the training set to obtain a plurality of label-shared feature selection weight matrices Q; Step 6: Utilizing L 2，1 The norm regularization constrains the feature selection weight matrix Q shared by multiple labels; through the row sparsity constraint, the weights in Q are concentrated on individual rows, and other rows tend to zero, thereby selecting a few important features related to multiple labels. Step 7: Utilize the graph Laplacian constraint to promote the local geometric structure of the features on Q and W to be consistent in different label spaces, and realize the fusion of shared features and label-independent features; Q and W are dynamically changed in the optimization process, so the corresponding constraint is a dynamic graph Laplacian constraint, and the calculation method is: Tr(W T L Q W) where Tr(*) is the trace of a matrix, L Q = P Q - S Q is the graph Laplacian of Q; S Q is a proximity matrix with the kernel function as distance, P Q is the degree matrix, which is a diagonal matrix consisting of the sum of all column elements of each row in S Q . where N p (Q *j ) denotes the set of the p neighbors of Q *j 's nearest neighbors. Step 8: Considering the objective terms of steps 3 to 7, the total objective function is constructed as: s.t.W≥0,Q≥0,Z≥0,A≥0,B≥0 Step 9: Initialize the variable matrix of the objective function; Step 10: Take the partial derivative of the objective function with respect to each variable to obtain the multiplication update formula for each variable: where is the Hadamard product of matrices, v is a column vector of all ones; R = {(Ω) + (Ω T ) + 2(∑)} ⊙ S Q , WW T = ∑, Ω = WW T ⊙ I, I is the identity matrix, D = [D ij ], Step 11: Determine whether the stopping condition is met, if yes, execute step 12, otherwise, update each variable according to step 10; Step 12: According to the feature selection weight matrix w obtained by optimization, sort the weight values corresponding to each label and output the set of K optimal features corresponding to each label; Step 13: According to the selected optimal features, train the logistic regression classifier using the training set, and then use the test set to evaluate the model results.

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