A fully interpretable staging prediction method, device and medium for small sample rectal cancer MR images

Abstract

The present invention relates to the field of image recognition, and in particular to a fully interpretable staging prediction method, device and medium for small sample rectal cancer MR images; the co-occurrence matrix of the preprocessed rectal cancer MR images is calculated to extract the physical features of each image, and the real label is also used as the physical feature; K clusters are determined according to the image and the real label to characterize the staging stage of rectal cancer; the relevant information of the K clusters is obtained by using a fuzzy C-means algorithm for the physical features; a TSK fuzzy system is trained according to the relevant information of the K clusters to obtain an initial rectal cancer staging prediction model; the rectal cancer MR images and the real labels are input into the model to output the staging prediction value; the objective function of the fuzzy rule weight in the model is constructed by using the prediction error, the output variance and the improved feature distribution loss; the objective function is solved in the form of an analytical solution to obtain the optimized rule weight and the rectal cancer staging prediction model, so as to realize fully interpretable staging prediction based on a small number of rectal cancer MR images.

Description

Technical Field

[0001] The present invention relates to the technical field of image recognition, and in particular to a fully interpretable staging prediction method, device and medium for small sample rectal cancer MR images. Background Art

[0002] Magnetic resonance (MR) images of the rectum can provide detailed images of the rectum with high soft tissue contrast, which enables medical staff to more accurately assess the stage of rectal cancer, thus providing an important basis for formulating effective treatment plans. Generally speaking, for rectal cancer in stages T1 and T2, medical staff usually do not recommend preoperative treatment, but directly perform surgery. However, for rectal cancer in stages T3 and T4, according to the current rectal cancer treatment guidelines, preoperative chemoradiotherapy is generally regarded as the standard treatment method. Because preoperative chemoradiotherapy may cause irreversible damage to the body and is expensive, accurate prediction of the stage of rectal cancer in stages T2 and T3 has become a key link in rectal cancer staging prediction and subsequent treatment. Traditional staging prediction methods for rectal cancer MR images rely on manually extracted features, such as vascular structure or local plaque features. However, extracting these features usually requires rich professional knowledge and experience of medical staff in this field, with high labor costs and slow staging prediction.

[0003] In recent years, with the continuous development of artificial intelligence technology in medical research, more and more machine learning models have been applied to the prediction task of rectal cancer MR images. However, most studies inevitably face the following two dilemmas: (1) Lack of interpretability, including lack of model-based interpretability and lack of result-based interpretability. Most existing rectal cancer prediction and staging models are based on deep neural networks, but deep neural networks themselves are black box models. Due to their abstract input features and unexplainable structures, they lack interpretability for results or models; (2) Small sample learning problem. Due to patient privacy and security issues, researchers usually cannot obtain a sufficient number of rectal cancer MR images. Therefore, small sample learning is a challenge often faced by machine learning models in medical research. It often leads to problems such as insufficient model fitting, poor generalization ability, and unstable classifiers. Although some existing small sample learning methods based on data level such as data enhancement, data synthesis, or algorithm level such as L1, L2 and other regularization techniques have been used for medical image prediction tasks, they have problems such as lack of interpretability, overfitting risk, or high computational complexity.

[0004] Therefore, a method that can achieve fully interpretable rectal cancer staging prediction on a small number of rectal cancer MR images and has high staging prediction efficiency is urgently needed. Summary of the invention

[0005] To this end, the technical problem to be solved by the present invention is to overcome the problem in the prior art that it is difficult to achieve fully interpretable rectal cancer staging prediction on small sample rectal cancer MR images and to ensure a high staging prediction efficiency.

[0006] To solve the above technical problems, the present invention provides a fully interpretable staging prediction method for small sample rectal cancer MR images, comprising the following steps:

[0007] Preprocessing of rectal cancer MR images;

[0008] The co-occurrence matrix of the pre-processed rectal cancer MR image is calculated and the D-dimensional physical features of the pre-processed rectal cancer MR image are extracted through the co-occurrence matrix. The true label of the pre-processed rectal cancer MR image is used as the D+1-dimensional physical feature, so there are a total of D+1-dimensional physical features;

[0009] Determine K clusters based on the preprocessed rectal cancer MR images and their true labels, and the clusters represent the staging of rectal cancer; use the fuzzy C-means algorithm on the D+1-dimensional physical features of all preprocessed rectal cancer MR images to output the relevant information of the K clusters, where the relevant information includes the mean and variance of the d-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster, and the covariance matrix of the k-th cluster; where k=1, 2,..., K; d=1, 2,..., D+1;

[0010] The TSK fuzzy system is trained with the relevant information of K clusters to obtain an initial rectal cancer staging prediction model; the preprocessed rectal cancer MR images and their true labels are input into the initial rectal cancer staging prediction model, and the staging prediction value of the preprocessed rectal cancer MR images is output;

[0011] According to the staging prediction value of the preprocessed rectal cancer MR image, the convex optimization objective function of the rule weight of the fuzzy rule in the initial rectal cancer staging prediction model is constructed with the prediction error, output variance and improved feature distribution loss of the preprocessed rectal cancer MR image; wherein the improved feature distribution loss includes Taylor expansion of the feature distribution loss and discarding all items higher than twice;

[0012] Combined with the D+1-dimensional physical characteristics of the preprocessed rectal cancer MR images, the convex optimization objective function is solved in the form of an analytical solution to obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model, thereby obtaining the optimized rectal cancer staging prediction model.

[0013] Preferably, preprocessing the rectal cancer MR image includes: intensity normalization and histogram equalization preprocessing.

[0014] Preferably, the D+1-dimensional physical features specifically include: energy, contrast, correlation, entropy, homogeneity, and true labels; wherein the D+1-dimensional physical features characterize the texture and structural information of the rectal cancer MR image.

[0015] Preferably, the covariance matrix of the kth cluster is , the expression is as follows:

[0016] ,

[0017] in, represents the kth cluster of all preprocessed rectal cancer MR images i Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ;

[0018] represents the kth cluster of all preprocessed rectal cancer MR images j Dimensional features and D +1-dimensional features composed of covariance D ×1 vector;

[0019] represents the kth cluster of all preprocessed rectal cancer MR images D +1-dimensional features and j The covariance between the dimensional features is composed of 1× D A vector of

[0020] represents the kth cluster of all preprocessed rectal cancer MR images D +1-dimensional features and D + Covariance of 1-dimensional features;

[0021] Covariance matrix of the kth cluster The inverse matrix , the expression is as follows:

[0022] ,

[0023] in, express The matrix consists of the elements in the first D rows and the first D columns; express A vector consisting of the elements of the first D rows in the D+1th column; express The vector consisting of the first D columns of the D+1th row; express The element at the D+1th row and the D+1th column in .

[0024] Preferably, the TSK fuzzy system is trained with the relevant information of K clusters to obtain an initial rectal cancer staging prediction model including:

[0025] According to K clusters, K first-order fuzzy rules are defined, where and They represent the antecedent mean parameter and antecedent variance parameter of the kth fuzzy rule respectively; where k=1,2,…,K, represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, d=1,2,...,D; represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster;

[0026] , k=1,2,…,K represents the consequent constant parameter of the corresponding kth fuzzy rule, represents the coefficient of the consequent polynomial of the corresponding k-th fuzzy rule; represents all preprocessed rectal cancer MR images under the kth cluster D + the mean of the 1-dimensional feature, represents a column vector consisting of the mean of each dimension of features of all preprocessed rectal cancer MR images under the kth cluster.

[0027] Preferably, the improved feature distribution loss is expressed as follows:

[0028] ,

[0029] in, Represents the column vector consisting of the rule weights of each fuzzy rule, represents the rule weight of the kth fuzzy rule, where k=1, 2, ..., K; express The transpose of is a K×1 column vector, where the kth element is determined by the antecedent parameter of the kth fuzzy rule: ;

[0030] in, represents the normal density distribution function of the D-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster; Represents the nth preprocessed rectal cancer MR image D dimensional features, represents the kth cluster of all preprocessed rectal cancer MR imagesi Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ; represents a column vector consisting of the mean of each dimension of all preprocessed rectal cancer MR images under the kth cluster; express The transpose of ; N represents the number of preprocessed rectal cancer MR images;

[0031] The convex optimization objective function of the rule weights of the fuzzy rules in the initial rectal cancer staging prediction model is expressed as follows:

[0032] ,

[0033] ,

[0034] in, represents the prediction error of the preprocessed rectal cancer MR image, represents the output variance of the preprocessed rectal cancer MR image, Represents the improved feature distribution loss of preprocessed rectal cancer MR images; represents the staging prediction value of the nth preprocessed rectal cancer MR image, is the true label corresponding to the nth preprocessed rectal cancer MR image, and Represents the preset positive hyperparameter, and its value range is and ;

[0035] represents a K×1 column vector; the kth element It is determined by multiplying the antecedent parameter and consequent parameter of the kth fuzzy rule:

[0036] ,

[0037] in, represents the normal density distribution function of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster; represents the d-th dimension feature of the n-th rectal cancer MR image; represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster; express of pseudo-rebellion; represents all preprocessed rectal cancer MR images under the kth cluster D +The mean of 1-dimensional features;

[0038] represents a K×1 column vector, where the kth element The calculation formula is as follows:

[0039] .

[0040] Preferably, solving the convex optimization objective function in the form of an analytical solution to obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model includes: using a convex optimization technique to directly solve the convex optimization objective function to obtain the rule weights The analytical solution is the global optimal solution, and the normalized rule weights The analytical solution is to normalize the rule weights The analytical solution is used as the rule weight of the fuzzy rules in the optimized initial rectal cancer staging prediction model.

[0041] Preferably, the rule weight The analytical solution is as follows:

[0042] ,

[0043] in, is a K×1 column vector, and the kth element is determined by the antecedent parameter of the kth fuzzy rule: ; express The transpose of represents the normal density distribution function of the D-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster, where Represents the nth preprocessed rectal cancer MR image D Column vector of dimensional features; is the true label corresponding to the nth preprocessed rectal cancer MR image; represents the kth cluster of all preprocessed rectal cancer MR images i Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ; represents a column vector consisting of the mean of each dimension feature of all preprocessed rectal cancer MR images under the kth cluster; N represents the number of preprocessed rectal cancer MR images;

[0044] represents a K×1 column vector; the kth element It is determined by multiplying the antecedent parameter and consequent parameter of the kth fuzzy rule:

[0045] ,

[0046] in, represents the normal density distribution function of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster; represents the d-th dimension feature of the n-th rectal cancer MR image; represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster; express of pseudo-rebellion; represents all preprocessed rectal cancer MR images under the kth cluster D +The mean of 1-dimensional features;

[0047] represents a K×1 column vector, where k Elements The calculation formula is as follows:

[0048] ,

[0049] in, and Represents the preset positive hyperparameter, and its value range is and , Indicates The covariance matrix of the clusters, express The vector consisting of the first D columns of the D+1th row; Indicates The covariance matrix of the clusters The inverse matrix of express The element at the D+1th row and the D+1th column in .

[0050] The present invention also provides a fully interpretable staging prediction device for small sample rectal cancer MR images, comprising:

[0051] A preprocessing module, used for preprocessing rectal cancer MR images;

[0052] A feature extraction module is used to calculate the co-occurrence matrix of the pre-processed rectal cancer MR image and extract the D-dimensional physical features of the pre-processed rectal cancer MR image through the co-occurrence matrix, and take the true label of the pre-processed rectal cancer MR image as the D+1-dimensional physical feature, so there are D+1-dimensional physical features in total;

[0053] A clustering module is used to determine K clusters based on the preprocessed rectal cancer MR images and their true labels, and the clusters represent the staging of rectal cancer; the fuzzy C-means algorithm is used for the D+1-dimensional physical features of the preprocessed rectal cancer MR images to output the relevant information of the K clusters, wherein the relevant information includes the mean and variance of the d-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster, and the covariance matrix of the k-th cluster; wherein k=1, 2,..., K; d=1, 2,..., D+1;

[0054] Generate an initial model module, which is used to train the TSK fuzzy system with relevant information of K clusters to obtain an initial rectal cancer staging prediction model; input the preprocessed rectal cancer MR image and its true label into the initial rectal cancer staging prediction model, and output the staging prediction value of the preprocessed rectal cancer MR image;

[0055] Constructing a convex optimization objective function module, which is used to construct a convex optimization objective function of the rule weight of the fuzzy rule in the initial rectal cancer staging prediction model according to the staging prediction value of the preprocessed rectal cancer MR image, the prediction error of the preprocessed rectal cancer MR image, the output variance and the improved feature distribution loss; wherein the improved feature distribution loss includes Taylor expansion of the feature distribution loss and discarding all terms higher than twice;

[0056] The optimization model module is used to combine the D+1-dimensional physical characteristics of the preprocessed rectal cancer MR images, solve the convex optimization objective function in the form of an analytical solution, obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model, and thus obtain the optimized rectal cancer staging prediction model.

[0057] The present invention also provides a computer-readable storage medium for fully interpretable staging prediction of small sample rectal cancer MR images, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned method for fully interpretable staging prediction of small sample rectal cancer MR images are implemented.

[0058] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0059] The present invention discloses a fully interpretable staging prediction method for a small sample rectal cancer MR image. First, the co-occurrence matrix of the pre-processed rectal cancer MR image is calculated and the physical features of the pre-processed rectal cancer MR image are extracted through the co-occurrence matrix. These physical features characterize the texture and structural information of the rectal cancer MR image, such as the texture and structural differences between the diseased tissue and the normal tissue, which helps doctors to make a diagnosis based on these features. Secondly, K clusters are determined based on the pre-processed rectal cancer MR image and its true label, and each cluster characterizes a different stage of rectal cancer staging; the fuzzy C-means algorithm is used for the physical features of the pre-processed rectal cancer MR image to output the relevant information of the K clusters; K fuzzy rules are defined based on the K clusters, and the relevant information of the K clusters is used to train the TSK fuzzy system, so that the parameters of the antecedent part and the consequent part of the K fuzzy rules can be determined to obtain an initial rectal cancer staging prediction model; through the relevant information of the K clusters, the model can learn how to predict and assign appropriate cancer staging based on the features of the rectal cancer MR image. Then, the feature distribution loss is Taylor expanded and all terms higher than quadratic are discarded as the improved feature distribution loss, which balances the complexity and accuracy of the calculation during actual prediction and can support the prediction of small sample rectal cancer MR images; the convex optimization objective function of the rule weights of the fuzzy rules in the initial rectal cancer staging prediction model is constructed using the training error, output variance and improved feature distribution loss, which simplifies the optimization process, reduces the risk of overfitting of rectal cancer MR images, and improves the generalization ability of the rectal cancer staging model; combined with the D+1-dimensional physical characteristics of the preprocessed rectal cancer MR images, the convex optimization objective function is solved in the form of an analytical solution, which ensures the rapidity and efficiency of the rectal cancer staging prediction training process, and obtains the optimized rule weights, thereby obtaining the optimized rectal cancer staging prediction model.

[0060] Since the optimized rectal cancer staging prediction model is based on the TSK fuzzy system, the rectal cancer staging rules therein are readable, intuitive and easy to understand, so that each rectal cancer staging rule can clearly explain the basis of the prediction results. The method of the present invention provides a more intuitive and easy-to-understand decision-making process than many "black box" models (such as deep learning models), thereby enhancing the interpretability of the rectal cancer staging prediction model and helping medical personnel analyze and understand the meaning of rectal cancer MR images. At the same time, the method of the present invention improves the accuracy of staging prediction on small sample rectal cancer MR images. Experimental results show that the method of the present invention is superior to other methods in terms of test performance, training time and interpretability. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0062] Figure 1 It is an overall flow chart of a fully interpretable staging prediction method for small sample rectal cancer MR images of the present invention;

[0063] Figure 2 It is an experimental flow chart of a fully interpretable staging prediction method of a small sample rectal cancer MR image of the present invention;

[0064] Figure 3 It is the overall framework of a fully interpretable staging prediction method for small sample rectal cancer MR images on training samples of the present invention;

[0065] Figure 4 This is the testing process of the fully interpretable staging prediction method of small sample rectal cancer MR images on the test sample. DETAILED DESCRIPTION

[0066] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0067] Example 1

[0068] Reference Figure 1 FIG. 1 is an overall flow chart of a fully interpretable staging prediction method for small sample rectal cancer MR images of the present invention, which specifically includes the following steps:

[0069] S1: Preprocessing of rectal cancer MR images by intensity normalization and histogram equalization;

[0070] S2: Calculate the co-occurrence matrix of the preprocessed rectal cancer MR image and extract the D-dimensional physical features of the preprocessed rectal cancer MR image through the co-occurrence matrix, and use the true label of the preprocessed rectal cancer MR image as the D+1-dimensional physical feature, then there are D+1-dimensional physical features in total; the D+1-dimensional physical features specifically include: energy, contrast, correlation, entropy, homogeneity, and true label; wherein the D+1-dimensional physical features characterize the texture and structural information of the rectal cancer MR image.

[0071] S3: Determine K clusters based on the preprocessed rectal cancer MR images and their true labels, and the clusters represent the staging of rectal cancer; use the fuzzy C-means algorithm on the D+1-dimensional physical features of the preprocessed rectal cancer MR images to output the relevant information of the K clusters, where the relevant information includes the mean and variance of the d-th (d=1, 2, ..., D+1)-th dimensional features of all preprocessed rectal cancer MR images under the k-th cluster (k=1, 2, ..., K) and the covariance matrix of the k-th cluster (k=1, 2, ..., K);

[0072] ①The covariance matrix of the kth cluster , the expression is as follows:

[0073] ,

[0074] in, represents the kth cluster of all preprocessed rectal cancer MR images i Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ;

[0075] represents the kth cluster of all preprocessed rectal cancer MR images j Dimensional features and D +1-dimensional features composed of covariance D ×1 vector;

[0076] represents the kth cluster of all preprocessed rectal cancer MR images D +1-dimensional features and j The covariance between the dimensional features is composed of 1× D A vector of

[0077] represents the kth cluster of all preprocessed rectal cancer MR images D +1-dimensional features and D + Covariance of 1-dimensional features;

[0078] ②The covariance matrix of the kth cluster The inverse matrix , the expression is as follows:

[0079] ,

[0080] in, express The matrix consists of the elements in the first D rows and the first D columns; express A vector consisting of the elements of the first D rows in the D+1th column; express The vector consisting of the first D columns of the D+1th row; express The element at the D+1th row and the D+1th column in .

[0081] S4: training the TSK fuzzy system with the relevant information of the K clusters to obtain an initial rectal cancer staging prediction model; inputting the preprocessed rectal cancer MR image and its true label into the initial rectal cancer staging prediction model, and outputting the staging prediction value of the preprocessed rectal cancer MR image; said training the TSK fuzzy system with the relevant information of the K clusters to obtain the initial rectal cancer staging prediction model includes:

[0082] ① Define K first-order fuzzy rules based on K clusters, where and They represent the antecedent mean parameter and antecedent variance parameter of the kth fuzzy rule respectively; where k=1,2,…,K, represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, d=1,2,...,D; represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster;

[0083] ② , k=1,2,…,K represents the consequent constant parameter of the corresponding kth fuzzy rule, represents the coefficient of the consequent polynomial of the corresponding k-th fuzzy rule; represents all preprocessed rectal cancer MR images under the kth cluster D + the mean of the 1-dimensional feature, represents a column vector consisting of the mean of each dimension of features of all preprocessed rectal cancer MR images under the kth cluster.

[0084] S5: According to the staging prediction value of the preprocessed rectal cancer MR image, the prediction error, output variance and improved feature distribution loss of the preprocessed rectal cancer MR image are used to construct a convex optimization objective function of the rule weight of the fuzzy rule in the initial rectal cancer staging prediction model; wherein the improved feature distribution loss includes Taylor expansion of the feature distribution loss and discarding all terms higher than twice;

[0085] ① Improved feature distribution loss, the expression is as follows:

[0086] ,

[0087] Among them, the specially designed and improved feature distribution loss, i.e. the regularization term, is used to enhance the generalization ability of the model in the case of small sample learning; Represents the column vector consisting of the rule weights of each fuzzy rule, represents the rule weight of the kth fuzzy rule, where k=1, 2, ..., K; express The transpose of is a K×1 column vector, where the kth element is determined by the antecedent parameter of the kth fuzzy rule:

[0088] ,

[0089] in, represents the normal density distribution function of the D-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster; Represents the nth preprocessed rectal cancer MR image D dimensional features, represents the kth cluster of all preprocessed rectal cancer MR images i Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ; represents a column vector consisting of the mean of each dimension of all preprocessed rectal cancer MR images under the kth cluster; express The transpose of ; N represents the number of preprocessed rectal cancer MR images;

[0090] ② The convex optimization objective function of the rule weights of the fuzzy rules in the initial rectal cancer staging prediction model is expressed as follows:

[0091] ,

[0092] ,

[0093] in, represents the prediction error of the preprocessed rectal cancer MR image, represents the output variance of the preprocessed rectal cancer MR image, Represents the improved feature distribution loss of preprocessed rectal cancer MR images; represents the staging prediction value of the nth preprocessed rectal cancer MR image, is the true label corresponding to the nth preprocessed rectal cancer MR image, and Represents the preset positive hyperparameter, and its value range is and ;

[0094] represents a K×1 column vector; the kth element It is determined by multiplying the antecedent parameter and consequent parameter of the kth fuzzy rule:

[0095] ,

[0096] in, represents the normal density distribution function of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster; represents the d-th dimension feature of the n-th rectal cancer MR image; represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster; express of pseudo-rebellion; represents all preprocessed rectal cancer MR images under the kth cluster D +The mean of 1-dimensional features;

[0097] represents a K×1 column vector, where the kth element The calculation formula is as follows:

[0098] .

[0099] S6: Combined with the D+1-dimensional physical characteristics of the preprocessed rectal cancer MR images, the convex optimization objective function is solved in the form of an analytical solution to obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model, thereby obtaining the optimized rectal cancer staging prediction model.

[0100] ① Solve the convex optimization objective function in the form of analytical solution to obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model, including: directly solve the convex optimization objective function using convex optimization technology to obtain the rule weights The analytical solution is the global optimal solution. This method ensures fast training of the model.

[0101] Normalized rule weights The analytical solution is to normalize the rule weights The analytical solution of is used as the rule weight of the fuzzy rules in the optimized initial rectal cancer staging prediction model, where the rule weight of each fuzzy rule after normalization can be interpreted as the prior probability of each first-order fuzzy rule.

[0102] ②Rule weight The analytical solution is as follows:

[0103] ,

[0104] in, is a K×1 column vector, and the kth element is determined by the antecedent parameter of the kth fuzzy rule: ; express The transpose of represents the normal density distribution function of the D-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster, where Represents the nth preprocessed rectal cancer MR image D Column vector of dimensional features; is the true label corresponding to the nth preprocessed rectal cancer MR image; represents the kth cluster of all preprocessed rectal cancer MR images i Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ; represents a column vector consisting of the mean of each dimension feature of all preprocessed rectal cancer MR images under the kth cluster; N represents the number of preprocessed rectal cancer MR images;

[0105] represents a K×1 column vector; the kth element It is determined by multiplying the antecedent parameter and consequent parameter of the kth fuzzy rule:

[0106] ,

[0107] in, represents the normal density distribution function of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster; represents the d-th dimension feature of the n-th rectal cancer MR image; represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster; express of pseudo-rebellion; represents all preprocessed rectal cancer MR images under the kth cluster D +The mean of 1-dimensional features;

[0108] represents a K×1 column vector, where k Elements The calculation formula is as follows:

[0109] ,

[0110] in, and Represents the preset positive hyperparameter, and its value range is and , Indicates The covariance matrix of the clusters, express The vector consisting of the first D columns of the D+1th row; Indicates The covariance matrix of the clusters The inverse matrix of express The element at the D+1th row and the D+1th column in .

[0111] In summary, the K fuzzy rules of the optimized rectal cancer staging prediction model are fully interpretable, including: an interpretable antecedent part, an understandable consequent part, i.e., output, and the rule weight of each fuzzy rule, i.e., prior probability, which can help medical personnel analyze and understand the practical significance of rectal cancer MR images based on the prediction results of the model.

[0112] Example 2

[0113] Based on Example 1, the small sample rectal cancer MR image dataset of the method of the present invention is used as the experimental dataset. The download link of the dataset is http: / / ieee-dataport.org / documents / rectal-cancer. The use of this dataset has been approved by the Medical Ethics Committee of Jiangnan University (JNU202403RB138). The small sample dataset contains 190 MR images, including 56 T2 stage MR images and 134 T3 stage MR images. In the experiment, the T2 stage MR image is specified as the negative class, that is, the training label is "-1"; the T3 stage MR image is specified as the positive class, that is, the training label is "1". In the experiment, two five-fold cross validations were used to determine the parameters and conduct the experiment. Reference Figure 2 , which is an experimental flow chart of a fully interpretable staging prediction method for small sample rectal cancer MR images of the present invention.

[0114] The specific experimental steps are as follows Figure 3 As shown, including:

[0115] (1) Image preprocessing. Image intensity normalization and histogram equalization were performed on the rectal cancer MR images used for training and testing, respectively. Figure 3 , is the overall architecture of a fully interpretable staging prediction method for small sample rectal cancer MR images on training samples of the present invention; refer to Figure 4, is a testing process of a fully interpretable staging prediction method of a small sample rectal cancer MR image on a test sample of the present invention;

[0116] (2) Obtain training and test samples. Use the CoM co-occurrence matrix method to extract the D-dimensional features of the preprocessed rectal cancer MR images used for training and testing, respectively, and map the features to the range of [0, 1] to obtain training and test samples.

[0117] (3) Model training and parameter range adjustment. Grid search is used to determine the optimal parameter combination on the non-public small sample rectal cancer MR image dataset used. The optimal parameters are found from the given parameter optimization range through two five-fold cross-validations, and the optimal parameter combination is obtained by continuously updating the current optimal parameters until the iteration ends. In the above dataset, the relevant parameters of the algorithm during optimization are shown in Table 1:

[0118] Table 1:

[0119]

[0120] (4) Retraining: Use grid optimization to find the optimal hyperparameters to retrain the model.

[0121] (5) Model testing: Input the test samples into the trained model, observe and record the test results.

[0122] (6) Evaluation indicators. Determine the evaluation indicators for this experiment and calculate the multiple evaluation indicator values ​​corresponding to the test results output by the model. The evaluation indicators used in this experiment are accuracy, sensitivity and precision.

[0123] This embodiment compares a fully interpretable staging prediction method for small sample rectal cancer MR images provided by the method of the present invention with existing deep learning methods and related fuzzy system methods for rectal cancer staging prediction. The deep learning-based comparison algorithms include: Inception-Seg [J.Kim et al. 2019], ResNet-18 [D.Sarwinda et al. 2021], ResNet-50 [D.Sarwinda et al. 2021] and RectalNet [S.Sun et al. 2023]. The comparison algorithms of related fuzzy systems include: TSK-FCM [Zhou et al. 2023], FIMG-TSK [Zhou et al. 2023] and FIMG-TSK-FoS. Among them, FIMG-TSK-FoS uses the first-order statistics (FoS) as a feature extraction method to extract interpretable features for training and testing, and the other structures are consistent with the fully interpretable staging prediction method for small sample rectal cancer MR images described in the present invention. As shown in Table 2, the means and standard deviations of the three classification evaluation indicators of these algorithms under two five-fold cross validations are recorded (for the convenience of observing the results, all results are retained to 4 decimal places):

[0124] Table 2:

[0125]

[0126] Comprehensively comparing the three indicators, the fully interpretable staging prediction method for small sample rectal cancer MR images described in the present invention shows the best test performance among all fuzzy-based comparison methods, which shows the effectiveness of the method of the present invention when facing the small sample rectal cancer staging prediction task. Due to the additional consideration of the regularization term specially designed for small sample learning, the average test performance of the prediction method of the present invention is better than FIMG-TSK. Although FoS extracts more features (a total of 19 dimensions) from the preprocessed MR images, this feature extraction method is not suitable for the rectal cancer staging prediction task. In addition, the test performance of the prediction method of the present invention is comparable to that of Inception-Seg, and is better than ResNet-18 and ResNet-50, which shows that even in the face of deep learning-based comparison algorithms, the prediction method of the present invention is still competitive. Although the overall test performance of RectalNet is better than the prediction method of the present invention, RectalNet is essentially a black box model and is not fully interpretable. In addition, considering the interpretability of the method, the rule complexity comparison of the four fuzzy system-based TSK-FCM, FIMG-TSK, FIMG-TSK-FoS and a fully interpretable staging prediction method for small sample rectal cancer MR images provided by the method of the present invention is shown in Table 3:

[0127] Table 3:

[0128]

[0129] As can be seen from Table 3, the interpretability of the fully interpretable staging prediction method for small sample rectal cancer MR images provided by FIMG-TSK and the method of the present invention is higher than that of TSK-FCM and FIMG-TSK-FoS. This is because the subsequent part of the fully interpretable staging prediction method for small sample rectal cancer MR images provided by the method of the present invention does not require additional training.

[0130] In summary, the fully interpretable staging prediction method for small sample rectal cancer MR images provided by the method of the present invention not only maintains competitive classification performance, but also has better interpretability. In addition, considering the training time of the method, the average training time comparison of the four fuzzy system-based methods of TSK-FCM, FIMG-TSK, FIMG-TSK-FoS and the fully interpretable staging prediction method for small sample rectal cancer MR images provided by the method of the present invention is shown in Table 4:

[0131] Table 4:

[0132]

[0133] The average training time consumed by the fully interpretable staging prediction method for small sample rectal cancer MR images and FIMG-TSK provided by the method of the present invention is the shortest. This is because the parameters of the subsequent part in the fully interpretable staging prediction method for small sample rectal cancer MR images and FIMG-TSK provided by the method of the present invention do not require any training and can be directly calculated.

[0134] In addition, through the hyperparameter analysis of a fully interpretable staging prediction method for a small sample of rectal cancer MR images provided by the method of the present invention, the classification performance of the method of the present invention is more sensitive to the number of rules of the fuzzy system, and the number of fuzzy rules also determines the interpretability of the method of the present invention. In practical applications, medical staff have very high requirements for the accuracy and interpretability of rectal cancer MR image staging prediction, so the relative balance between performance and interpretability can be pursued by flexibly adjusting the number of fuzzy rules according to actual needs.

[0135] Example 3

[0136] Based on Example 1, this example provides a fully interpretable staging prediction device for small sample rectal cancer MR images, comprising:

[0137] A preprocessing module, used for preprocessing rectal cancer MR images;

[0138] A feature extraction module is used to calculate the co-occurrence matrix of the pre-processed rectal cancer MR image and extract the D-dimensional physical features of the pre-processed rectal cancer MR image through the co-occurrence matrix, and take the true label of the pre-processed rectal cancer MR image as the D+1-dimensional physical feature, so there are D+1-dimensional physical features in total;

[0139] A clustering module is used to determine K clusters based on the preprocessed rectal cancer MR images and their true labels, and the clusters represent the staging of rectal cancer; the fuzzy C-means algorithm is used for the D+1-dimensional physical features of the preprocessed rectal cancer MR images to output the relevant information of the K clusters, wherein the relevant information includes the mean and variance of the d-th (d=1, 2, ..., D+1)-th dimensional features of all preprocessed rectal cancer MR images under the k-th cluster (k=1, 2, ..., K) and the covariance matrix of the k-th cluster (k=1, 2, ..., K);

[0140] Generate an initial model module, which is used to train the TSK fuzzy system with relevant information of K clusters to obtain an initial rectal cancer staging prediction model; input the preprocessed rectal cancer MR image and its true label into the initial rectal cancer staging prediction model, and output the staging prediction value of the preprocessed rectal cancer MR image;

[0141] Constructing a convex optimization objective function module, which is used to construct a convex optimization objective function of the rule weight of the fuzzy rule in the initial rectal cancer staging prediction model according to the staging prediction value of the preprocessed rectal cancer MR image, the prediction error of the preprocessed rectal cancer MR image, the output variance and the improved feature distribution loss; wherein the improved feature distribution loss includes Taylor expansion of the feature distribution loss and discarding all terms higher than twice;

[0142] The optimization model module is used to combine the D+1-dimensional physical characteristics of the preprocessed rectal cancer MR images, solve the convex optimization objective function in the form of an analytical solution, obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model, and thus obtain the optimized rectal cancer staging prediction model.

[0143] Example 4

[0144] Based on Example 1, this embodiment provides a computer-readable storage medium for fully interpretable staging prediction of small sample rectal cancer MR images, including:

[0145] The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above-mentioned fully interpretable staging prediction method for small sample rectal cancer MR images are implemented.

[0146] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0147] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0148] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0149] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0150] Obviously, the above embodiments are merely examples for the purpose of clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A fully interpretable staging prediction method for small sample rectal cancer MR images, characterized in that: The following steps are involved: Preprocessing of rectal cancer MR images; The co-occurrence matrix of the pre-processed rectal cancer MR image is calculated and the D-dimensional physical features of the pre-processed rectal cancer MR image are extracted through the co-occurrence matrix. The true label of the pre-processed rectal cancer MR image is used as the D+1-dimensional physical feature, so there are a total of D+1-dimensional physical features; Determine K clusters based on the preprocessed rectal cancer MR images and their true labels, and the clusters represent the staging of rectal cancer; use the fuzzy C-means algorithm on the D+1-dimensional physical features of all preprocessed rectal cancer MR images to output the relevant information of the K clusters, where the relevant information includes the mean and variance of the d-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster, and the covariance matrix of the k-th cluster; where k=1, 2,..., K; d=1, 2,..., D+1; The TSK fuzzy system is trained with the relevant information of K clusters to obtain an initial rectal cancer staging prediction model; the preprocessed rectal cancer MR images and their true labels are input into the initial rectal cancer staging prediction model, and the staging prediction value of the preprocessed rectal cancer MR images is output; According to the staging prediction value of the preprocessed rectal cancer MR image, the convex optimization objective function of the rule weight of the fuzzy rule in the initial rectal cancer staging prediction model is constructed with the prediction error, output variance and improved feature distribution loss of the preprocessed rectal cancer MR image; wherein the improved feature distribution loss includes Taylor expansion of the feature distribution loss and discarding all items higher than twice; Combined with the D+1-dimensional physical characteristics of the preprocessed rectal cancer MR images, the convex optimization objective function is solved in the form of an analytical solution to obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model, thereby obtaining the optimized rectal cancer staging prediction model.

2. A fully interpretable staging prediction method for small sample rectal cancer MR images according to claim 1, characterized in that: Preprocessing of rectal cancer MR images includes: intensity normalization and histogram equalization preprocessing.

3. The fully interpretable staging prediction method for small sample rectal cancer MR images according to claim 1, characterized in that: The D+1-dimensional physical features specifically include: energy, contrast, correlation, entropy, homogeneity, and true labels; among them, the D+1-dimensional physical features characterize the texture and structural information of rectal cancer MR images.

4. The fully interpretable staging prediction method for small sample rectal cancer MR images according to claim 1, characterized in that: Covariance matrix of the kth cluster , the expression is as follows: ， in, represents the kth cluster of all preprocessed rectal cancer MR images i Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ; represents the kth cluster of all preprocessed rectal cancer MR images j Dimensional features and D +1-dimensional features composed of covariance D ×1 vector; represents the kth cluster of all preprocessed rectal cancer MR images D +1-dimensional features and j The covariance between the dimensional features is composed of 1× D A vector of represents the kth cluster of all preprocessed rectal cancer MR images D +1-dimensional features and D + Covariance of 1-dimensional features; Covariance matrix of the kth cluster The inverse matrix , the expression is as follows: ， in, express The matrix consists of the elements in the first D rows and the first D columns; express A vector consisting of the elements of the first D rows in the D+1th column; express The vector consisting of the first D columns of the D+1th row; express The element at the D+1th row and the D+1th column in .

5. The fully interpretable staging prediction method for small sample rectal cancer MR images according to claim 4, characterized in that: The TSK fuzzy system is trained with the relevant information of K clusters, and the initial rectal cancer staging prediction model is obtained, including: According to K clusters, K first-order fuzzy rules are defined, where and They represent the antecedent mean parameter and antecedent variance parameter of the kth fuzzy rule respectively; where k=1,2,…,K, represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, d=1,2,...,D; represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster; , k=1,2,…,K represents the consequent constant parameter of the corresponding kth fuzzy rule, represents the coefficient of the consequent polynomial of the corresponding k-th fuzzy rule; represents all preprocessed rectal cancer MR images under the kth cluster D + the mean of the 1-dimensional feature, represents a column vector consisting of the mean of each dimension of features of all preprocessed rectal cancer MR images under the kth cluster.

6. The fully interpretable staging prediction method for small sample rectal cancer MR images according to claim 4, characterized in that: The improved feature distribution loss is expressed as follows: ， in, Represents the column vector consisting of the rule weights of each fuzzy rule, represents the rule weight of the kth fuzzy rule, where k=1, 2, ..., K; express The transpose of is a K×1 column vector, where the kth element is determined by the antecedent parameter of the kth fuzzy rule: ; in, represents the normal density distribution function of the D-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster; Represents the nth preprocessed rectal cancer MR image D dimensional features, represents the kth cluster of all preprocessed rectal cancer MR images i Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ; represents a column vector consisting of the mean of each dimension feature of all preprocessed rectal cancer MR images under the kth cluster; express The transpose of ; N represents the number of preprocessed rectal cancer MR images; The convex optimization objective function of the rule weights of the fuzzy rules in the initial rectal cancer staging prediction model is expressed as follows: ， ， in, represents the prediction error of the preprocessed rectal cancer MR image, represents the output variance of the preprocessed rectal cancer MR image, Represents the improved feature distribution loss of preprocessed rectal cancer MR images; represents the staging prediction value of the nth preprocessed rectal cancer MR image, is the true label corresponding to the nth preprocessed rectal cancer MR image, and Represents the preset positive hyperparameter, and its value range is and ; represents a K×1 column vector; the kth element It is determined by multiplying the antecedent parameter and consequent parameter of the kth fuzzy rule: ， in, represents the normal density distribution function of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster; represents the d-th dimension feature of the n-th rectal cancer MR image; represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster; express of pseudo-rebellion; represents all preprocessed rectal cancer MR images under the kth cluster D +The mean of 1-dimensional features; represents a K×1 column vector, where the kth element The calculation formula is as follows: 。 7. The fully interpretable staging prediction method for small sample rectal cancer MR images according to claim 1, characterized in that: The convex optimization objective function is solved in the form of an analytical solution to obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model, including: using the convex optimization technology to directly solve the convex optimization objective function to obtain the rule weights The analytical solution is the global optimal solution, and the normalized rule weights The analytical solution of The analytical solution is used as the rule weight of the fuzzy rules in the optimized initial rectal cancer staging prediction model.

8. The fully interpretable staging prediction method for small sample rectal cancer MR images according to claim 7, characterized in that: Rule Weight The analytical solution is as follows: ， in, is a K×1 column vector, and the kth element is determined by the antecedent parameter of the kth fuzzy rule: ; express The transpose of represents the normal density distribution function of the D-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster, where Represents the nth preprocessed rectal cancer MR image D Column vector of dimensional features; is the true label corresponding to the nth preprocessed rectal cancer MR image; represents the kth cluster of all preprocessed rectal cancer MR images i Dimensional features and j The covariance between the dimensional features is composed of D × D The matrix of i , j =1,2,…, D ; represents a column vector consisting of the mean of each dimension feature of all preprocessed rectal cancer MR images under the kth cluster; N represents the number of preprocessed rectal cancer MR images; represents a K×1 column vector; the kth element It is determined by multiplying the antecedent parameter and consequent parameter of the kth fuzzy rule: ， in, represents the normal density distribution function of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster; represents the d-th dimension feature of the n-th rectal cancer MR image; represents the mean of the d-th dimension features of all preprocessed rectal cancer MR images under the k-th cluster, represents the d-th dimension feature and the variance of the d-th dimension feature of all preprocessed rectal cancer MR images under the k-th cluster; express of pseudo-rebellion; represents all preprocessed rectal cancer MR images under the kth cluster D +The mean of 1-dimensional features; represents a K×1 column vector, where k Elements The calculation formula is as follows: ， in, and Represents the preset positive hyperparameter, and its value range is and , Indicates The covariance matrix of the clusters, express The vector consisting of the first D columns of the D+1th row; Indicates The covariance matrix of the clusters The inverse matrix of express The element at the D+1th row and the D+1th column in .

9. A fully interpretable staging prediction device for small sample rectal cancer MR images, characterized in that: include: A preprocessing module, used for preprocessing rectal cancer MR images; A feature extraction module is used to calculate the co-occurrence matrix of the pre-processed rectal cancer MR image and extract the D-dimensional physical features of the pre-processed rectal cancer MR image through the co-occurrence matrix, and take the true label of the pre-processed rectal cancer MR image as the D+1-dimensional physical feature, so there are D+1-dimensional physical features in total; A clustering module is used to determine K clusters based on the preprocessed rectal cancer MR images and their true labels, and the clusters represent the staging stages of rectal cancer; The fuzzy C-means algorithm is used for the D+1-dimensional physical features of the preprocessed rectal cancer MR images to output the relevant information of K clusters, wherein the relevant information includes the mean and variance of the d-dimensional features of all preprocessed rectal cancer MR images under the k-th cluster and the covariance matrix of the k-th cluster; wherein k=1, 2, ..., K; d=1, 2, ..., D+1; Generate an initial model module, which is used to train the TSK fuzzy system with relevant information of K clusters to obtain an initial rectal cancer staging prediction model; input the preprocessed rectal cancer MR image and its true label into the initial rectal cancer staging prediction model, and output the staging prediction value of the preprocessed rectal cancer MR image; Constructing a convex optimization objective function module, which is used to construct a convex optimization objective function of the rule weight of the fuzzy rule in the initial rectal cancer staging prediction model according to the staging prediction value of the preprocessed rectal cancer MR image, the prediction error of the preprocessed rectal cancer MR image, the output variance and the improved feature distribution loss; wherein the improved feature distribution loss includes Taylor expansion of the feature distribution loss and discarding all terms higher than twice; The optimization model module is used to combine the D+1-dimensional physical characteristics of the preprocessed rectal cancer MR images, solve the convex optimization objective function in the form of an analytical solution, obtain the rule weights of the fuzzy rules in the optimized rectal cancer staging prediction model, and thus obtain the optimized rectal cancer staging prediction model.

10. A computer-readable storage medium for fully interpretable staging prediction of small sample rectal cancer MR images, characterized in that: include: The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a fully interpretable staging prediction method for small sample rectal cancer MR images as claimed in any one of claims 1 to 8.

Images