A machine learning-based method and electronic device for predicting patient extubation outcomes

Abstract

This invention discloses a machine learning-based method and electronic device for predicting patient extubation outcomes. The method involves fusing features from multi-source heterogeneous medical data from different devices to obtain a feature vector set. This feature vector set is then input into a first extubation outcome prediction model corresponding to successful extubation and a second extubation outcome prediction model corresponding to failed extubation, yielding the probabilities of successful and failed extubation. The probabilities of successful and failed extubation are compared, and the category with the higher probability value is output as the predicted extubation outcome. This invention not only improves prediction results by fusing multi-source heterogeneous data features but also, by combining a Hidden Markov Model with a t-Gaussian mixture distribution capable of handling sequential data, avoids information loss in sequential data and addresses the heavy-tailed distribution of continuous observations, further improving the model's prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of patient extubation outcome prediction, and more particularly to a machine learning-based method and electronic device for predicting patient extubation outcomes. Background Technology

[0002] Extubation is a crucial step in the treatment of mechanically ventilated patients, and its success directly impacts patient recovery and subsequent treatment. However, extubation failure may lead to re-extubation, increasing the risk of complications such as airway injury and ventilator-associated pneumonia. Therefore, accurately predicting extubation success or failure is of great importance for clinical decision-making.

[0003] With the widespread application of artificial intelligence algorithms in medical intelligent decision-making, significant progress has been made in using intelligent decision-making algorithms to predict extubation outcomes. Among these achievements, the paper titled "A Machine Learning decision-making tool for extubation in Intensive Care Unit patients" in *Comput Methods Programs Biomed* utilizes data from ICU patients' clinical information systems, patient demographics, medical records, and respiratory event logs. Based on classic machine learning algorithms such as SVM (Support Vector Machine), XGBoost (Extreme Gradient Boosting), and Logistic Regression, a model was built to predict patient extubation outcomes, achieving an accuracy of 94.5%. However, the following limitations exist:

[0004] (1) The medical data of the predictor is usually multi-source heterogeneous data from different devices. Compared with a single data source, multi-source heterogeneous data contains more information about the predictor. If multi-source heterogeneous data can be used as input data for the extubation outcome prediction model, the accuracy of the extubation outcome prediction model will inevitably be higher. However, commonly used algorithms such as LogisticRegression, XGBoost, and SVM can only process data with a fixed structure. Usually, the input data of non-neural network machine learning models is feature vectors, while the input data of neural network machine learning models can be a multi-dimensional structure. Therefore, it is not feasible to directly input multi-source heterogeneous data into the machine learning model.

[0005] (2) Commonly used machine learning models are adapted to cross-sectional data. When processing sequence data, they need to be fused into cross-sectional data first before processing, which will result in the loss of sequence data information;

[0006] (3) Using empirical methods or grid search methods to obtain model hyperparameters, although simple, often leads to hyperparameters getting trapped in local optima. Summary of the Invention

[0007] To address the aforementioned issues, embodiments of the present invention provide a method and electronic device for predicting patient extubation outcomes based on machine learning.

[0008] The specific technical solution is as follows:

[0009] In a first aspect, embodiments of the present invention provide a method for predicting patient extubation outcomes based on machine learning, comprising the following steps:

[0010] Feature fusion is performed on multi-source heterogeneous medical data from different devices to predictors, and the resulting feature vector set is mapped to obtain the fused multi-source heterogeneous medical data; wherein, the feature vector set contains feature vectors of multi-source heterogeneous data fusion at T time points;

[0011] The feature vector set is input into the first extubation outcome prediction model corresponding to the successful extubation category and the second extubation outcome prediction model corresponding to the failed extubation category, respectively, to obtain the probability of the successful extubation category and the probability of the failed extubation category; wherein, the first extubation outcome prediction model is obtained by training and testing a Hidden Markov Model with t-Gaussian mixture distribution based on the successful extubation sample set, and the second extubation outcome prediction model is obtained by training and testing a Hidden Markov Model with t-Gaussian mixture distribution based on the failed extubation sample set;

[0012] Compare the probabilities of successful extubation with those of failed extubation, and output the category with the higher probability as the predicted extubation outcome.

[0013] Preferably, the step of fusing features from multi-source heterogeneous medical data from different devices to obtain a feature vector set after fusing the multi-source heterogeneous medical data includes the following steps:

[0014] Vectorizing various data types in multi-source heterogeneous medical data, specifically including:

[0015] Vectorization of tabular data, in order to... The tabular data at each time point is a tabular data vector. ;in, ;

[0016] Vectorization of time-series data is performed using Newton's interpolation method to obtain the vectorization results for each time-series data point at the [missing information - likely a specific time series]. The observations at each time point are then used to analyze each time series data at the 1st time point. A vector is formed from the observations at each time point. ;

[0017] For 2D grayscale, 3D color, and 4D video data, the actually observed 2D grayscale, 3D color, and 4D video data are first mapped into 2D grayscale data vectors respectively. 3D color data vector and four-dimensional video data vector Then, the vector of two-dimensional grayscale data... 3D color data vector Vector of four-dimensional video data Using Newton interpolation, we obtain the first... Vector of two-dimensional grayscale data at each time point Vector of three-dimensional color data and vectors of four-dimensional video data ;

[0018] Concatenating vectors after vectorization of various data types, specifically including:

[0019] The vector of table data at the i-th time point The vector of time series data at the i-th time point A vector of two-dimensional grayscale data at the i-th time point The vector of three-dimensional color data at the i-th time point The vector of four-dimensional video data at the i-th time point By splicing, we can obtain the first Feature vector obtained by fusing multi-source heterogeneous data at each time point.

[0020] Preferably, the step of mapping the actually observed two-dimensional grayscale, three-dimensional color, and four-dimensional video data into two-dimensional grayscale data vectors respectively. 3D color data vector and four-dimensional video data vector By mapping two-dimensional grayscale data, three-dimensional color data, and four-dimensional video data into three-dimensional color data vectors respectively. The implementation includes the following steps:

[0021] Let the length, width, and number of channels of the 3D color data be respectively... and Randomly select a channel, which is a two-dimensional rectangle with a length and width of [missing information]. and ;

[0022] The custom sliding window has a length and width of respectively and The lengths of a single step slide in the length and width directions are respectively and Then the channel can be divided into A sliding window; where the ceil function is a floor function, and the portion of the sliding window that exceeds the channel is assigned a value of 0;

[0023] Randomly select a sliding window and use the discrete cosine transform (DCT) method to transform the channel data from the time domain to the frequency domain. The DCT formula is:

[0024]

[0025]

[0026] in, Represents time-domain window coordinates The time domain value at that point; Represents the frequency domain window coordinates Frequency domain value at; ;

[0027] Will Fill the window with the coordinates to obtain the frequency domain matrix. for:

[0028]

[0029] For signal F in the sliding window M The frequencies are arranged from low to high to form a Z-path, and the first vector is obtained by scanning along the Z-path. ,in ;

[0030] Used The number of and the first vector The ratio of lengths ultimately yields the second vector. ,in, floor represents the function for rounding down;

[0031] Will The second vector corresponding to each sliding window The vectors corresponding to each channel are concatenated to form a vector. Then, the vectors corresponding to the N3 channels are concatenated to form a vector corresponding to the three-dimensional data, resulting in a three-dimensional color data vector. Vector of two-dimensional grayscale data A vector of 3D color data when the number of channels N3 equals 1; a vector of 4D video data. The vector is obtained by concatenating the three-dimensional color data vectors at each timestamp.

[0032] Preferably, the extubation outcome prediction model obtained by training and testing a Hidden Markov Model with a t-Gaussian mixture distribution includes the following steps:

[0033] Collect a large amount of multi-source heterogeneous medical data of patients with clear extubation outcomes as samples. After feature fusion of each sample, classify them according to the extubation outcome category to obtain a successful extubation sample set and a failed extubation sample set including the feature vector set of each sample. Divide the successful extubation sample set and the failed extubation sample set into training set and test set according to the training requirements ratio.

[0034] For each category, a Hidden Markov Model with a t-Gaussian mixture distribution capable of handling continuously distributed observations is constructed. Based on the successful extubation sample set and the failed extubation sample set, the Hidden Markov Model with a t-Gaussian mixture distribution for the corresponding category is trained and tested to obtain the first extubation outcome prediction model and the second extubation outcome prediction model.

[0035] Preferably, the step of constructing a Hidden Markov Model with a t-Gaussian mixture distribution capable of handling continuously distributed observations for each category, and training and testing the corresponding Hidden Markov Model with a t-Gaussian mixture distribution based on the successful extubation sample set and the failed extubation sample set to obtain the first extubation outcome prediction model and the second extubation outcome prediction model, includes the following steps:

[0036] Solve for the t-Gaussian mixture distribution; where the formula for the t-Gaussian mixture distribution is:

[0037]

[0038] The constraints of the above equation are: This represents the weight of the k-th multivariate Gaussian distribution relative to the t-Gaussian mixture distribution; Let represent the mean vector of the k-th multivariate Gaussian distribution; Let represent the covariance of the k-th multivariate Gaussian distribution; K is a hyperparameter indicating that the t-Gaussian mixture distribution contains K multivariate Gaussian distributions. The weight of the m-th multivariate t-distribution outweighs the weight of the t-Gaussian mixture distribution; M is a hyperparameter indicating that the t-Gaussian mixture distribution contains M multivariate t-distributions; Let represent the mean vector of the m-th multivariate t-distribution; Let represent the covariance of the m-th multivariate t-distribution;

[0039] The formula for the multivariate Gaussian distribution is:

[0040]

[0041] Where d represents the length of the feature vector x obtained after the sample features are fused.

[0042] The formula for the multivariate t-distribution is:

[0043]

[0044] in, This represents the total number of samples in the training set used for training. Represents the gamma function;

[0045] The probability density function of the samples is obtained through iterative training using the expectation-maximization method. Iteratively, by maximizing the expectation and the maximum likelihood estimate, we can obtain... ;Depend on The probability density of the multivariate variable x can be calculated;

[0046] Construct a Hidden Markov Model (HMM); where the HMM includes stochastic state transitions and stochastic observable events at specific states; the state transition matrix A is:

[0047]

[0048] in, is a hyperparameter representing the number of categorical variables in the Hidden Markov Model. Size; Indicates the first The state transition of the first category to the second... The probability of each category state; let The corresponding state probability is ; The corresponding state probability is Then we have:

[0049]

[0050] The state probabilities at each time point are normalized, and the normalized probability distribution is as follows:

[0051]

[0052] in, Indicates the number of time points; Indicates the first The first time point The probability of the nth category state; according to the nth Probability distribution at each time point Sampling yields category state sequences For time point 1 It follows an equal probability distribution, and has ;

[0053] Based on the known feature vector set as the observed output sequence and the already determined Solve for the probability density of the multivariate variable x. ;

[0054] Define the loop structures for the forward algorithm and the backward algorithm; where:

[0055] The forward algorithm loop structure is as follows:

[0056] initialization:

[0057] Forward algorithm loop structure:

[0058] Output: in, It is the final probability corresponding to a sample;

[0059] The specific structure of the backward algorithm is as follows:

[0060] initialization:

[0061] Backward algorithm loop structure:

[0062] Output: in, , is the final probability corresponding to a sample;

[0063] Calculate the forward and backward The parameters of the hidden Markov model with a t-Gaussian mixture distribution are calculated using the expectation-maximization algorithm.

[0064] Preferably, the step of calculating the parameters of the hidden Markov model with a t-Gaussian mixture distribution using the expectation-maximization algorithm includes the following steps:

[0065] Calculate the probability of a single state; let the model parameters be... The feature vector set of a single sample is Indicates the first Feature vectors at each time point; given a model Given the feature vector set X, at time points The first The probabilities of each category state are:

[0066]

[0067] Using the definitions of forward probability and backward probability, we know that:

[0068]

[0069] Therefore:

[0070]

[0071] Calculate the joint probability of two states; given... and In this case, at the time point Category status is And at the time series point Category status is The probability is:

[0072]

[0073] in, ;

[0074] Solve using the expected maximum method When the training set is numbered The specific values ​​of the sample feature vector set are:

[0075]

[0076] The number is The expression for the probability distribution of the occurrence of the sample is:

[0077]

[0078] in,

[0079] According to the expected maximum method, the expected value expression can be directly written as:

[0080]

[0081] Where Q represents the total number of samples used for training; This represents the parameter to be determined in the current iteration; This represents the parameters obtained in the previous iteration; then, the maximum likelihood estimation method is used to solve for... The maximum value;

[0082] make It can be obtained The value is:

[0083]

[0084]

[0085] if If it continues to increase, then it will value assigned to Continue with the next iteration until... The training of the Hidden Markov Model with the t-Gaussian mixture distribution is completed until convergence.

[0086] Preferably, it also includes using a genetic algorithm to optimize hyperparameters. The optimization process includes the following steps:

[0087] Genetic algorithm initialization; setting population size Individuals; each individual is express Normalization; express Normalization; express Normalization; The values ​​are initialized using a uniform distribution of 0 to 1; the crossover probability and mutation probability are set as follows: and The evolutionary generation is set as ;

[0088] Performing fitness calculations and individual selection; specifically including:

[0089] Calculate the fitness at each generation of evolution; the fitness function is:

[0090]

[0091] in, This indicates the number of test sets specific to the genetic algorithm. Each test set is drawn from a subset of the training set; each individual will receive a corresponding fitness score. Based on the fitness values ​​of all individuals, obtain the individual population in the current group. The probability of being selected is:

[0092]

[0093] in, This represents the fitness value of the j-th individual in the current population; after calculating the fitness values ​​of all individuals, the individual with the highest fitness is saved; then, based on the probability distribution of the individuals... Randomly select from the current group Individuals form a new group for the next iteration; after all evolutionary generations are completed, the fitness values ​​retained from each iteration are compared again, and the individual with the highest fitness is selected as the optimal solution;

[0094] Perform crossover and variation on individuals; where:

[0095] Individual crossover specifically involves: for a new group, randomly pair up individuals in pairs; if U is odd, the remaining individual is not paired; for a successfully paired group, exchange elements between them at random, equal positions. You can randomly swap 1 to 3 elements at their current positions, but you cannot swap 4 elements at their current positions.

[0096] The mutation specifically involves: for the crossover individuals, randomly sampling 1 to 4 elements using a Gaussian method; for the elements... Sampling, the corresponding Gaussian distribution is The value after sampling is Finally use Replace ;

[0097] After all evolutionary generations are completed, the optimal individual is obtained as follows: Correspondingly , , and The optimal solution is:

[0098]

[0099]

[0100]

[0101] .

[0102] In a second aspect, embodiments of the present invention also provide an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the machine learning-based patient extubation outcome prediction method described in the first aspect.

[0103] The present invention provides a method and electronic device for predicting patient extubation outcomes based on machine learning, which has the following effective technical effects:

[0104] (1) This invention proposes a feature fusion method for multi-source heterogeneous medical data, which enables the extubation outcome prediction model to process multi-source heterogeneous data simultaneously. This not only improves the accuracy of the prediction results, but also has the ability to denoise during feature fusion, which can improve the robustness of the model.

[0105] (2) The Hidden Markov Model with t-Gaussian Mixture Distribution proposed in this invention is not only good at processing sequential data and can obtain dynamic information of the data, avoiding the loss of sequential data information, but also can fit the heavy-tailed distribution of continuous observations, thereby improving the accuracy of model prediction.

[0106] (3) This invention proposes to use a novel genetic algorithm to optimize model hyperparameters, which can obtain the global optimal solution of model hyperparameters.

[0107] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings.

[0108] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0109] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0110] Figure 1 A flowchart illustrating a machine learning-based method for predicting patient extubation outcomes is provided in this embodiment of the invention.

[0111] Figure 2 This is a schematic diagram of the Z-shaped path of a signal from low frequency to high frequency provided in an embodiment of the present invention;

[0112] Figure 3 A schematic diagram of a hidden Markov method with a t-Gaussian mixture distribution provided in an embodiment of the present invention;

[0113] Figure 4 A schematic diagram of the forward and backward algorithm loop structure provided in an embodiment of the present invention;

[0114] Figure 5 This is a schematic diagram illustrating the iterative determination of hyperparameters using a genetic algorithm, as provided in an embodiment of the present invention.

[0115] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0116] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0117] like Figure 1 As shown in the figure, this application provides a method for predicting patient extubation outcomes based on machine learning. The method includes the following steps:

[0118] Step S100: Perform feature fusion on the multi-source heterogeneous medical data from different devices of the predictor to obtain a feature vector set after medical data fusion; the feature vector set contains feature vectors after multi-source heterogeneous data fusion at T time points, each feature vector is a continuous value and its distribution has a heavy-tail problem.

[0119] The most crucial step in fusing multi-source heterogeneous data is first vectorizing the various data types within the medical data, and then concatenating them. This specifically includes:

[0120] 1. Vectorize various data types in medical data.

[0121] (1) For tabular data, which is usually data such as gender, ethnicity, and culture that do not change over time, then the first... The tabular data at each time point is a vector. ;

[0122] (2) For time-series data, this type of data usually includes data such as heart rate, respiratory rate, and pulse that change over time. In the embodiments of this application, Newton interpolation is used to obtain the time-series data at the [number]th [time]. The observations at the nth time point, and then the nth time point A vector is formed from the observed values ​​of heart rate, respiratory rate, pulse, etc., obtained by Newton interpolation at each time point. ;

[0123] (3) For two-dimensional grayscale, three-dimensional color, and four-dimensional video data, this type of data is in the 0~ Within the time period of each time point, samples are taken once or multiple times. If the Newton interpolation algorithm is first used, the samples are taken at the 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, 12th, 13th, 14th, 15th, 16th, 17th, 18th, 19th, 19th, Generating corresponding two-dimensional grayscale, three-dimensional color, and four-dimensional video data at each time point results in large errors and severe image distortion. Therefore, this invention first maps the actually observed two-dimensional grayscale, three-dimensional color, and four-dimensional video data into two-dimensional grayscale data vectors respectively. 3D color data vector and four-dimensional video data vector .

[0124] A single observation of 2D grayscale data has 1 channel, a special case of 3D color data observation; a single observation of 3D color data has more than 1 channel. A single observation of 4D video data contains 3D data at multiple timestamps. Stacking these 3D data along the channel direction eliminates the time axis of the 4D observation, resulting in 3D color data. Therefore, 2D grayscale data, 3D color data, and 4D video data can all use a modeling architecture that maps 3D color data to vectors, thus improving the versatility of multi-dimensional data feature fusion methods. Therefore, the actually observed 2D grayscale data, 3D color data, and 4D video data are mapped to... , and This can be achieved by mapping two-dimensional grayscale data, three-dimensional color data, and four-dimensional video data into three-dimensional color data vectors respectively. get , and Specifically, it includes the following steps:

[0125] Let the length, width, and number of channels of the 3D color data be respectively... and Randomly select a channel, which is a two-dimensional rectangle with a length and width of [missing information]. and ;

[0126] The custom sliding window has a length and width of respectively and The lengths of a single step slide in the length and width directions are respectively and Then the channel can be divided into A sliding window; where the ceil function is a floor function, and the portion of the sliding window that exceeds the channel is assigned a value of 0;

[0127] Randomly select a sliding window and use the Discrete Cosine Transform (DCT) method to transform the data of this channel from the time domain to the frequency domain. This transformation is lossless. The DCT formula is:

[0128]

[0129]

[0130] in, Represents time-domain window coordinates The time domain value at that point; Represents the frequency domain window coordinates Frequency domain value at; ;

[0131] Will Fill the window with the coordinates to obtain the frequency domain matrix. for:

[0132]

[0133] Depend on of It can be seen that, The larger, The higher the frequency of the signal, the more detailed the multidimensional data (including two-dimensional grayscale data, three-dimensional color data, and four-dimensional video data) it provides. This multidimensional data detail includes not only useful information such as texture and illumination, but also electronic noise, signal transmission noise, quantum noise, gradient magnetic field switching noise, radio frequency pulse noise, patient micro-motion noise, and external environmental noise. These noises are typically high-frequency signals. If the useful information from the details outweighs the contribution of the noise, it will improve the model's predictive performance; conversely, it will hinder the model's predictive performance. Furthermore, excessive pursuit of detail can easily lead to model overfitting. Therefore, more detailed image information is not necessarily better; its level of detail depends on the model's predictive results.

[0134] Considering the noise error in high-frequency signals, this embodiment first arranges the converted frequency domain data in the order of a Z-shaped path, and then removes the high-frequency signals according to a certain proportion (the specific proportion is set as required). This reduces the computational load and noise interference, and improves the robustness of the model. Figure 2 This is a schematic diagram of the Z-path of the signal arranged from low frequency to high frequency in a sliding window. For ease of explanation, the length and width of the sliding window are both set to 8. If the length and width of the sliding window are not the same, the shorter side is extended to be equal to the longer side, and then... Figure 2 The path scan yields a vector, which is then stripped of values ​​belonging to the extension to obtain the first vector. .

[0135] To avoid model overfitting and noise interference from high-frequency signals, this invention proposes hyperparameters. It is used The number of and the first vector The ratio of lengths ultimately yields the second vector. ; where floor represents the function for rounding down.

[0136] Will The second vector corresponding to each sliding window By concatenating these vectors into a single channel, and then concatenating the vector sets corresponding to the N3 channels into a vector corresponding to the 3D data, we can obtain the 3D color data vector. Vector of two-dimensional grayscale data A vector of 3D color data when the number of channels N3 equals 1; a vector of 4D video data. The vector obtained by concatenating the three-dimensional color data vectors at each timestamp;

[0137] Then, the three-dimensional color data vector Vector of two-dimensional grayscale data Vector of four-dimensional video data Using Newton interpolation, we obtain the first... Vector of two-dimensional grayscale data at each time point Vector of three-dimensional color data and vectors of four-dimensional video data .

[0138] 2. Concatenate vectors after vectorization of various data types.

[0139] The vector of table data at the i-th time point The vector of time series data at the i-th time point A vector of two-dimensional grayscale data at the i-th time point The vector of three-dimensional color data at the i-th time point The vector of four-dimensional video data at the i-th time point By splicing them together, we can obtain the first one. Feature vector obtained by fusing multi-source heterogeneous data at each time point.

[0140] Step S200: Input the feature vector set after medical data fusion into the first extubation outcome prediction model corresponding to the successful extubation category and the second extubation outcome prediction model corresponding to the failed extubation category, respectively, to obtain the probability of the successful extubation category and the probability of the failed extubation category; wherein, the first extubation outcome prediction model is obtained by training and testing a Hidden Markov Model with t-Gaussian mixture distribution based on the successful extubation sample set, and the second extubation outcome prediction model is obtained by training and testing a Hidden Markov Model with t-Gaussian mixture distribution based on the failed extubation sample set.

[0141] Step S300: Compare the probabilities of successful extubation and unsuccessful extubation, and output the category with the larger probability value as the extubation outcome prediction result.

[0142] In this embodiment of the application, the extubation outcome prediction model obtained by training and testing a Hidden Markov Model with a t-Gaussian mixture distribution includes the following steps:

[0143] Step S201: Collect a large amount of multi-source heterogeneous medical data of patients with clear extubation outcomes as samples. After feature fusion of each sample, classify them according to the extubation outcome category to obtain a successful extubation sample set and a failed extubation sample set including the feature vector set of each sample. Divide the successful extubation sample set and the failed extubation sample set into a training set and a test set according to the training requirements ratio.

[0144] Step S202: Construct a Hidden Markov Model with t-Gaussian Mixture Distribution for each category, capable of handling continuously distributed observations. Train and test the Hidden Markov Model with t-Gaussian Mixture Distribution for the corresponding category based on the successful extubation sample set and the failed extubation sample set, respectively, to obtain the first extubation outcome prediction model and the second extubation outcome prediction model.

[0145] In the feature vector set of the predictor's medical data obtained after fusion in this invention, the sample data of each feature vector is continuously distributed, while Hidden Markov Models (HMMs) are most commonly used for discretely distributed observations. To process continuous observations based on HMMs, this invention makes corresponding improvements to the HMM, specifically by using a Gaussian mixture model to calculate the probability of the observations. However, Gaussian mixture models have drawbacks. For the problem of heavy-tailed data in the samples of this invention, using only a Gaussian distribution will lead to large prediction bias. The t-distribution can effectively compensate for the bias caused by heavy-tailed data. Therefore, this invention constructs a HMM with a t-Gaussian mixture distribution. Therefore, step S202 of this embodiment includes the following steps:

[0146] Solve for the t-Gaussian mixture distribution; where the formula for the t-Gaussian mixture distribution is:

[0147]

[0148] The constraints of the above equation are: This represents the weight of the k-th multivariate Gaussian distribution relative to the t-Gaussian mixture distribution; Let represent the mean vector of the k-th multivariate Gaussian distribution; Let represent the covariance of the k-th multivariate Gaussian distribution; K is a hyperparameter indicating that the t-Gaussian mixture distribution contains K multivariate Gaussian distributions. The weight of the m-th multivariate t-distribution outweighs the weight of the t-Gaussian mixture distribution; M is a hyperparameter indicating that the t-Gaussian mixture distribution contains M multivariate t-distributions; Let represent the mean vector of the m-th multivariate t-distribution; Let represent the covariance of the m-th multivariate t-distribution;

[0149] The formula for the multivariate Gaussian distribution is:

[0150]

[0151] Where d represents the length of the feature vector x obtained after the sample features are fused.

[0152] The formula for the multivariate t-distribution is:

[0153]

[0154] in, This represents the total number of samples in the training set used for training. This represents the gamma function.

[0155] The probability density function of the samples is obtained through iterative training using the expectation-maximization method. The expectation-maximization method is an existing algorithm that can be iteratively obtained by maximizing the expectation and the maximum likelihood estimate. Thus, by The probability density of the multivariate variable x can be calculated.

[0156] After solving for the t-Gaussian mixture distribution, we can then model the Hidden Markov Model (HMM). The basic structure of the HMM is as follows: Figure 3 As shown. A Hidden Markov Model (HMM) contains two types of randomness: the model state transitions and the randomness of observable events in a specific state. The state transition matrix A is:

[0157]

[0158] in, is a hyperparameter representing the number of categorical variables in the Hidden Markov Model. Size; Indicates the first The state transition of the first category to the second... The probability of each category state; let The corresponding state probability is ; The corresponding state probability is Then we have:

[0159]

[0160] To obtain the hidden state sequence, the state probabilities at each time point need to be normalized. The normalized probability distribution is as follows:

[0161]

[0162] in, Indicates the number of time points; Indicates the first The first time point The probability of each category state. According to the... Probability distribution at each time point Sampling yields category state sequences Note that for time point 1... The distribution can be customized, typically an equal probability distribution, and has... .

[0163] For the randomness of observable events under specific conditions, this invention studies the probability density of continuous multivariate variables (feature vectors). In the sample set after feature fusion, the feature vector set of each sample contains the feature vectors of the sample at time point 1 to time point T. The ascending order of the time points is usually used to express the temporal and spatial acquisition order of sample features. This invention uses the feature data at each time point to complete the pattern recognition of the samples. Since the task of this invention is to complete the pattern recognition of samples, Figure 3 The observed output sequence (feature vector set) is known in advance, as mentioned above. Since it has been determined, the probability density of the multivariate variable x is... It can be solved directly.

[0164] If the state transition matrix A and the initial state probability distribution can be inferred solely from the feature vector set of the samples, then the t-Gaussian mixture distribution Hidden Markov Model (HMM) is successfully trained. For multi-class machine learning, a t-Gaussian mixture distribution HMM is trained for each class using the corresponding class sample set. Then, the test samples are fed into the first and second extubation outcome prediction models, respectively, and the probabilities are calculated using the forward algorithm. The class corresponding to the highest probability is then determined, and that class is the class to which the sample belongs. Before training the t-Gaussian mixture distribution HMM, a loop structure of the forward and backward algorithms is introduced (…). Figure 4 ).

[0165] The forward algorithm loop structure is as follows:

[0166] (1) Initialization:

[0167] (2) Forward algorithm loop structure:

[0168] (3) Output:

[0169] It is the final probability corresponding to a sample.

[0170] The specific structure of the backward algorithm is as follows:

[0171] (1) Initialization:

[0172] (2) Backward algorithm loop structure:

[0173] (3) Output:

[0174] It is also the final probability corresponding to a sample.

[0175] Calculate the forward and backward Then, the expectation-maximization algorithm can be used to calculate the parameters of the hidden Markov model with the t-Gaussian mixture distribution. The specific steps are as follows:

[0176] (1) Calculate the probability of a single state;

[0177] Let the model parameters be The feature vector set of a single sample is Indicates the first Feature vectors at each time point. In a given model Given the feature vector set X, at time points The first The probabilities of each category state are:

[0178]

[0179] Using the definitions of forward probability and backward probability, we know that:

[0180]

[0181] Therefore:

[0182]

[0183] (2) Calculate the joint probability of the two states;

[0184] In a given and In this case, at the time point Category status is And at the time series point Category status is The probability is:

[0185]

[0186] in, .

[0187] (3) Solve using the expected maximum method ;

[0188] When the training set is numbered The specific values ​​of the sample feature vector set are:

[0189]

[0190] The number is The expression for the probability distribution of the occurrence of the sample is:

[0191]

[0192] in,

[0193] According to the expected maximum method, the expected value expression can be directly written as:

[0194]

[0195] Where Q represents the total number of samples used for training; This represents the parameter to be determined in the current iteration; This represents the parameters solved in the previous iteration. Then, the maximum likelihood estimation method is used to solve for... The maximum value.

[0196] make It can be obtained The value is:

[0197]

[0198]

[0199] if If it continues to increase, then it will value assigned to Continue with the next iteration until... Until convergence. After convergence, the Hidden Markov Model (HMM) with a t-Gaussian mixture distribution is trained. In multi-class machine learning tasks, the sample set for each class is split into a training set and a test set, and HMMs with t-Gaussian mixture distributions are trained independently using their respective training sets. During testing, a test case is randomly selected from the test set and fed into the extubation outcome prediction model for each class. (in The category corresponding to the largest predicted extubation outcome (representing the test cases used for model performance evaluation) is the result of the extubation outcome prediction.

[0200] Genetic algorithms are search heuristic algorithms that simulate the mechanisms of natural selection and genetics. They draw on the genetic mechanisms in biological evolution to solve optimization and search problems by simulating the natural evolutionary process.

[0201] In this embodiment of the invention, the hyperparameters include:

[0202]

[0203]

[0204]

[0205] ;

[0206] This invention uses a genetic algorithm to optimize the above hyperparameters, including the following steps:

[0207] (1) Initialization of the genetic algorithm;

[0208] Define the group to include Individuals; each individual is express Normalization; express Normalization; express Normalization; The values ​​are initialized using a uniform distribution of 0 to 1. The crossover probability and mutation probability are set as follows: and The evolutionary generation is set as .

[0209] (2) Fitness calculation and individual selection;

[0210] Fitness is obtained during each generation of evolution. The fitness function of this invention is:

[0211]

[0212] in, This indicates the number of test sets specific to the genetic algorithm. Each test set is drawn from a subset of the training set; each individual will receive a corresponding fitness score. Based on the fitness values ​​of all individuals, obtain the individual population in the current group. The probability of being selected is:

[0213]

[0214] in, This represents the fitness value of the j-th individual in the current population. After calculating the fitness values ​​of all individuals, the individual with the highest fitness is saved. Then, based on the probability distribution of the individuals... Randomly select from the current group Individuals form a new population for the next iteration. After all evolutionary generations are completed, the fitness values ​​retained from each iteration are compared, and the individual with the highest fitness is selected as the optimal solution.

[0215] (3) Individual crossover and variation;

[0216] Individual crossover specifically involves: for a new group, randomly pairing individuals into two groups; if U is odd, the remaining group is not paired. Successfully paired groups then randomly swap elements at equal positions. You can randomly swap 1 to 3 elements at their positions, but you cannot swap 4 elements at their positions. If you swap 4 elements, it is equivalent to no overlap.

[0217] The mutation specifically involves: for each crossover individual, randomly sampling 1 to 4 elements using a Gaussian method. (The sentence is incomplete and requires further context to be fully translated.) Taking sampling as an example, the corresponding Gaussian distribution is: The value after sampling is Finally use Replace .

[0218] The advantage of genetic algorithms is that they can obtain the global optimum, while conventional grid search easily gets trapped in local optima. After all generations, the optimal individual is obtained. Correspondingly , , and The optimal solution is:

[0219]

[0220]

[0221]

[0222]

[0223] This invention transforms multi-source heterogeneous medical data from different devices into the frequency domain using the Discrete Cosine Transform (DCT) algorithm, a lossless transformation process. Considering the noise and error inherent in high-frequency signals, the transformed frequency domain data is first arranged in a Z-shaped path order, and then high-frequency signals are removed at a certain ratio. This reduces computational load and noise interference while improving model robustness. After feature fusion, the multi-source heterogeneous data of the samples is finally mapped into a feature vector set containing feature vectors at T time points. Each feature vector is a continuous value with a heavy-tailed distribution. Traditional Hidden Markov Algorithms (HMAs) lack effective methods to address the heavy-tailed nature of continuous observations. Therefore, this invention proposes using a HMA with a t-Gaussian mixture distribution to calculate the probability of continuous observations with heavy-tailed distributions, with significant results. Multiple hyperparameters exist in feature fusion and the construction of the continuously distributed HMA. Using a grid search method can easily lead to local optima. Therefore, this invention also uses a genetic algorithm to determine the optimal solution for the hyperparameters. In the model development phase, this invention pre-creates successful and failed extubation sample sets for different extubation outcome categories through feature fusion. Then, the dataset for each category is split into training and test sets in an 8:2 ratio. When optimizing model parameters using a genetic algorithm, only a subset of the training set is used for hyperparameter optimization. After the Hidden Markov Models (HMMs) for each category are trained on their respective sample sets, the trained HMMs for all categories are tested using test cases from the test sets for each category. The class corresponding to the HMM with the highest probability value is the predicted extubation outcome for that test case, thus achieving the goal of predicting the extubation outcome.

[0224] The present invention will be further illustrated below with specific application examples.

[0225] (1) Introduction to the dataset

[0226] The training set for this invention comes from MIMIC-III, and the inclusion criteria are 5,213 patients aged ≥65 years, with a first ICU stay of more than 24 hours and a clear extubation success or failure outcome label between 2001 and 2012. The MIMIC (Medical Information Mart for Intensive Care) database contains data such as laboratory test data, demographic characteristics, microbiological test results, inpatient transfers, treatment processes, and fluid intake and output.

[0227] The test set for this embodiment was from MIMIC-IV. The inclusion criteria were 3,203 patients aged ≥65 years, with a first ICU stay of more than 24 hours, and with a clear extubation success or failure outcome label between 2013 and 2018.

[0228] The third-party validation set in this embodiment comes from a top-tier hospital in Beijing. The inclusion criteria are 500 patients aged ≥65 years who were admitted to the ICU for the first time between 2019 and 2023, had a first-time ICU stay of more than 24 hours, and had a clear extubation success or failure outcome label.

[0229] Each patient corresponds to one sample. Successful or unsuccessful extubation occurred 24 hours after ICU admission. Each sample has... Each sample has a feature vector, meaning it has one feature vector per hour after admission to the ICU. The multi-source heterogeneous data for each sample includes two-dimensional chest X-ray data, which is scaled down to... The corresponding sliding window size is set to Because it is a two-dimensional image, .

[0230] (2) Genetic algorithm to determine hyperparameters.

[0231] Set population size Crossover probability Probability of mutation Number of iterations .

[0232] Finally determined The maximum likelihood value obtained by the model is The genetic algorithm iterated 100 times, and the trends of the hyperparameters and the likelihood P(*) are as follows. Figure 5 As shown.

[0233] (3) Model performance evaluation

[0234] Table 1. Performance evaluation results of various models using different machine learning algorithms.

[0235]

[0236] To test the performance of the extubation outcome prediction model provided by the invention, the prediction performance of extubation outcome prediction models based on LightGBM, Random Forest, XGBoost, Logistic Regression, SVM, and DecisionTree were also tested. The datasets and testing environments used for each model were identical. Specific evaluation results are shown in Table 1. Clearly, the Hidden Markov Algorithm with t-Gaussian Mixture Distribution (HMM) exhibits high AUCs on both the external validation set (MIMIC-IV dataset) and the third-party validation set (dataset from a top-tier hospital in Beijing), with AUCs of 0.983 and 0.967, respectively. Furthermore, the HMM with t-Gaussian Mixture Distribution also achieved higher sensitivity and specificity than other models on both the external and third-party validation sets, with sensitivity and specificity of 0.895 and 0.933, and 0.884 and 0.932, respectively. Therefore, the extubation prediction model proposed in this invention has superior prediction performance and can be considered a preferred intelligent decision-making algorithm for extubation prediction.

[0237] and Figure 1 Corresponding to the embodiments shown, this invention also provides an electronic device, see [link to previous document]. Figure 6 Specifically, it includes one or more processors and memory, taking a processor 200 and memory 100 as an example. The processor 200 and memory 100 can be connected via a bus or other means, such as connecting via a bus.

[0238] The memory 100, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs, such as a machine learning-based patient extubation outcome prediction method in this embodiment. The processor 200 implements the machine learning-based patient extubation outcome prediction method described above in this embodiment by running the non-transitory software program and instructions stored in the memory 100.

[0239] The memory 100 may include a program storage area and a data storage area. The program storage area may store applications required for operating the device and at least one function; the data storage area may store data required for executing a machine learning-based patient extubation outcome prediction method as described in the above embodiments. Furthermore, the memory 100 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the terminal via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0240] The non-transient software program and instructions required to implement the machine learning-based patient extubation outcome prediction method in the above embodiments are stored in memory. When executed by one or more processors, the machine learning-based patient extubation outcome prediction method in the above embodiments is executed, for example, the method described above is executed. Figure 1 The method steps S100 to S300.

[0241] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for predicting patient extubation outcomes based on machine learning, characterized in that, Includes the following steps: Feature fusion is performed on multi-source heterogeneous medical data from different devices to predictors, and the resulting feature vector set is mapped to obtain the fused multi-source heterogeneous medical data; wherein, the feature vector set contains feature vectors of multi-source heterogeneous data fusion at T time points; The feature vector set is input into the first extubation outcome prediction model corresponding to the successful extubation category and the second extubation outcome prediction model corresponding to the failed extubation category, respectively, to obtain the probability of the successful extubation category and the probability of the failed extubation category; wherein, the first extubation outcome prediction model is obtained by training and testing a Hidden Markov Model with t-Gaussian mixture distribution based on the successful extubation sample set, and the second extubation outcome prediction model is obtained by training and testing a Hidden Markov Model with t-Gaussian mixture distribution based on the failed extubation sample set; Compare the probabilities of successful extubation with those of unsuccessful extubation, and output the category with the higher probability value as the predicted extubation outcome. The step of fusing features from multi-source heterogeneous medical data from different devices to obtain a feature vector set after fusion of multi-source heterogeneous medical data includes the following steps: Vectorizing various data types in multi-source heterogeneous medical data, specifically including: Vectorization of tabular data, in order to... The tabular data at each time point is a tabular data vector. ;in, ; Vectorization of time-series data is performed using Newton's interpolation method to obtain the vectorization results for each time-series data point at the [missing information - likely a specific time series]. The observations at each time point are then used to analyze each time series data at the 1st time point. A vector is formed from the observations at each time point. ; For 2D grayscale, 3D color, and 4D video data, the actually observed 2D grayscale, 3D color, and 4D video data are first mapped into 2D grayscale data vectors respectively. 3D color data vector and four-dimensional video data vector Then, the vector of two-dimensional grayscale data... 3D color data vector Vector of four-dimensional video data Using Newton interpolation, we obtain the first... Vector of two-dimensional grayscale data at each time point Vector of three-dimensional color data and vectors of four-dimensional video data ; Concatenating vectors after vectorization of various data types, specifically including: The vector of table data at the i-th time point The vector of time series data at the i-th time point A vector of two-dimensional grayscale data at the i-th time point The vector of three-dimensional color data at the i-th time point The vector of four-dimensional video data at the i-th time point By splicing, we can obtain the first Feature vector obtained by fusing multi-source heterogeneous data at each time point.

2. The method according to claim 1, characterized in that, The process involves mapping the observed two-dimensional grayscale, three-dimensional color, and four-dimensional video data into two-dimensional grayscale data vectors, respectively. 3D color data vector and four-dimensional video data vector By mapping two-dimensional grayscale data, three-dimensional color data, and four-dimensional video data into three-dimensional color data vectors respectively. The implementation includes the following steps: Let the length, width, and number of channels of the 3D color data be respectively... and Randomly select a channel, which is a two-dimensional rectangle with a length and width of [missing information]. and ; The custom sliding window has a length and width of respectively and The lengths of a single step slide in the length and width directions are respectively and Then the channel can be divided into A sliding window; where the ceil function is a floor function, and the portion of the sliding window that exceeds the channel is assigned a value of 0; Randomly select a sliding window and use the discrete cosine transform (DCT) method to transform the channel data from the time domain to the frequency domain. The DCT formula is: in, Represents time-domain window coordinates The time domain value at that point; Represents the frequency domain window coordinates Frequency domain value at; ; Will Fill the window with the coordinates to obtain the frequency domain matrix. for: For signal F in the sliding window M The frequencies are arranged from low to high to form a Z-path, and the first vector is obtained by scanning along the Z-path. ,in ; Used The number of and the first vector The ratio of lengths ultimately yields the second vector. ,in, floor represents the function for rounding down; Will The second vector corresponding to each sliding window The vectors corresponding to each channel are concatenated to form a vector. Then, the vectors corresponding to the N3 channels are concatenated to form a vector corresponding to the three-dimensional data, resulting in a three-dimensional color data vector. Vector of two-dimensional grayscale data A vector of 3D color data when the number of channels N3 equals 1; a vector of 4D video data. The vector is obtained by concatenating the three-dimensional color data vectors at each timestamp.

3. The method according to claim 2, characterized in that, The extubation outcome prediction model obtained by training and testing a Hidden Markov Model with a t-Gaussian mixture distribution includes the following steps: Collect a large amount of multi-source heterogeneous medical data of patients with clear extubation outcomes as samples. After feature fusion of each sample, classify them according to the extubation outcome category to obtain a successful extubation sample set and a failed extubation sample set including the feature vector set of each sample. Divide the successful extubation sample set and the failed extubation sample set into training set and test set according to the training requirements ratio. For each category, a Hidden Markov Model with a t-Gaussian mixture distribution capable of handling continuously distributed observations is constructed. Based on the successful extubation sample set and the failed extubation sample set, the Hidden Markov Model with a t-Gaussian mixture distribution for the corresponding category is trained and tested to obtain the first extubation outcome prediction model and the second extubation outcome prediction model.

4. The method according to claim 3, characterized in that, The method involves constructing a Hidden Markov Model (HMM) with a t-Gaussian mixture distribution for each category, capable of handling continuously distributed observations. Based on successful and failed extubation sample sets, the HMMs with t-Gaussian mixture distributions for the corresponding categories are trained and tested to obtain a first extubation outcome prediction model and a second extubation outcome prediction model. Includes the following steps: Solve for the t-Gaussian mixture distribution; where the formula for the t-Gaussian mixture distribution is: The constraints of the above equation are: This represents the weight of the k-th multivariate Gaussian distribution relative to the t-Gaussian mixture distribution; Let represent the mean vector of the k-th multivariate Gaussian distribution; Let represent the covariance of the k-th multivariate Gaussian distribution; K is a hyperparameter indicating that the t-Gaussian mixture distribution contains K multivariate Gaussian distributions. The weight of the m-th multivariate t-distribution outweighs the weight of the t-Gaussian mixture distribution; M is a hyperparameter indicating that the t-Gaussian mixture distribution contains M multivariate t-distributions; Let represent the mean vector of the m-th multivariate t-distribution; Let represent the covariance of the m-th multivariate t-distribution; The formula for the multivariate Gaussian distribution is: Where d represents the length of the feature vector x obtained after the sample features are fused; The formula for the multivariate t-distribution is: in, This represents the total number of samples in the training set used for training. Represents the gamma function; The probability density function of the samples is obtained through iterative training using the expectation-maximization method. Iteratively, by maximizing the expectation and the maximum likelihood estimate, we can obtain... ;Depend on The probability density of the multivariate variable x can be calculated; Construct a Hidden Markov Model (HMM); where the HMM includes stochastic state transitions and stochastic observable events at specific states; the state transition matrix A is: in, is a hyperparameter representing the number of categorical variables in the Hidden Markov Model. Size; Indicates the first The state transition of the first category to the second... The probability of each category state; let The corresponding state probability is ; The corresponding state probability is Then we have: The state probabilities at each time point are normalized, and the normalized probability distribution is as follows: in, Indicates the number of time points; Indicates the first The first time point The probability of the nth category state; according to the nth Probability distribution at each time point Sampling yields category state sequences For time point 1 It follows an equal probability distribution, and has... ; Based on the known feature vector set as the observed output sequence and the already determined Solve for the probability density of the multivariate variable x. ; Define the loop structures for the forward algorithm and the backward algorithm; where: The forward algorithm loop structure is as follows: initialization: Forward algorithm loop structure: Output: in, It is the final probability corresponding to a sample; The specific structure of the backward algorithm is as follows: initialization: Backward algorithm loop structure: Output: in, , is the final probability corresponding to a sample; Calculate the forward and backward The parameters of the hidden Markov model with a t-Gaussian mixture distribution are calculated using the expectation-maximization algorithm.

5. The method according to claim 4, characterized in that, The calculation of parameters for a hidden Markov model with a t-Gaussian mixture distribution using the expectation-maximization algorithm includes the following steps: Calculate the probability of a single state; let the model parameters be... The feature vector set of a single sample is Indicates the first Feature vectors at each time point; given a model Given the feature vector set X, at time points The first The probabilities of each category state are: Using the definitions of forward probability and backward probability, we know that: Therefore: Calculate the joint probability of two states; given... and In this case, at the time point Category status is And at the time series point Category status is The probability is: in, ; Solve using the expected maximum method When the training set is numbered The specific values ​​of the sample feature vector set are: The number is The expression for the probability distribution of the occurrence of the sample is: in, According to the expected maximum method, the expected value expression can be directly written as: Where Q represents the total number of samples used for training; This represents the parameter to be determined in the current iteration; This represents the parameters obtained in the previous iteration; then, the maximum likelihood estimation method is used to solve for... The maximum value; make It can be obtained The value is: if If it continues to increase, then it will The value assigned to Continue with the next iteration until... The training of the Hidden Markov Model with the t-Gaussian mixture distribution is completed until convergence.

6. The method according to claim 5, characterized in that, It also includes using genetic algorithms to optimize hyperparameters. The optimization process includes the following steps: Genetic algorithm initialization; setting population size Individuals; each individual is express Normalization; express Normalization; express Normalization; The values ​​are initialized using a uniform distribution of 0 to 1; the crossover probability and mutation probability are set as follows: and The evolutionary generation is set as ; Performing fitness calculations and individual selection; specifically including: Calculate the fitness at each generation of evolution; the fitness function is: in, This indicates the number of test sets specific to the genetic algorithm. Each test set is drawn from a subset of the training set; each individual will receive a corresponding fitness score. Based on the fitness values ​​of all individuals, obtain the individual population in the current group. The probability of being selected is: in, This represents the fitness value of the j-th individual in the current population; after calculating the fitness values ​​of all individuals, the individual with the highest fitness is saved; then, based on the probability distribution of the individuals... Randomly select from the current group Individuals form a new group for the next iteration; after all evolutionary generations are completed, the fitness values ​​retained from each iteration are compared again, and the individual with the highest fitness is selected as the optimal solution; Perform crossover and variation on individuals; where: Individual crossover specifically involves: for a new group, randomly pair up individuals in pairs; if U is odd, the remaining individual is not paired; for a successfully paired group, exchange elements between them at random, equal positions. You can randomly swap 1 to 3 elements at their current positions, but you cannot swap 4 elements at their current positions. The mutation specifically involves: for the crossover individuals, randomly sampling 1 to 4 elements using a Gaussian method; for the elements... Sampling, the corresponding Gaussian distribution is The value after sampling is Finally use Replace ; After all evolutionary generations are completed, the optimal individual is obtained as follows: Correspondingly , , and The optimal solution is: 。 7. An electronic device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the computer program, implements the steps of the method according to any one of claims 1 to 6.

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