A multi-classification learning technique for partially missing data stream scenarios of labels

Abstract

The application discloses a kind of multi-classification learning technology for label partial missing data stream scene, which combines the idea of propensity score and online learning, extends PU learning to multi-class scene, especially solves the problem that sample does not satisfy complete random missing hypothesis.This algorithm predicts the probability of positive class sample with label by constructing propensity score estimation module based on multilayer perceptron, and adjusts sample weight using weighting strategy.At the same time, using rolling training strategy and online gradient descent method, the real-time update of model parameters is realized, so that the model can adapt to large-scale dynamic data stream environment.The core idea of the method is to introduce propensity score weighting mechanism to correct the bias caused by uneven distribution of positive sample labels, and use robust non-convex loss function to achieve higher accuracy in classification tasks.

Description

Technical Field

[0001] This invention relates to a data analysis technique, and more particularly to a multi-classification learning method for data streams with partially missing labels. Background Technology

[0002] In the real world, multi-classification problems are very common. For example, in text classification, articles need to be divided into different categories, such as news classification and sentiment analysis; in image classification, images need to be divided into different categories, such as disease classification in medical images. Traditional supervised classification algorithms can be trained on labeled data to predict and classify new data samples. However, obtaining large amounts of labeled datasets is both time-consuming and expensive. In reality, the available datasets often contain only a small amount of labeled data, with most data being unlabeled. Furthermore, whether data is labeled is often not random; data with certain characteristics are more or less likely to be labeled. Therefore, how to effectively classify this unlabeled data has become a problem worthy of research.

[0003] MPU learning, or Multi-Positive Unlabeled Learning, is an evolution of PU learning. Some researchers have attempted to extend binary classification problems to multi-class problems. Regarding MPU learning, in 2017, Y. Xu et al. first proposed this classification problem in their paper "Multi-Positive and Unlabeled Learning," defining it as the MPU problem. They used a two-step strategy-like approach, selecting reliable negative examples and positive samples to co-train the classifier. In 2020, S. Shu et al. in their paper...

[0004] The paper "Learning from Multi-Class Positive and Unlabeled Data" proposes a method called UREA, which constructs an unbiased estimator using direct empirical risk minimization. This estimator is used for estimating the original classification risk in multi-class PU learning, but it suffers from overfitting. Building upon UREA, this paper uses an alternative loss function to obtain a method called AREA with a clear lower bound on the estimation error, reducing overfitting and improving classification performance. In 2022, Racanati et al. published...

[0005] The ProtoMPUL framework developed in "Dealing with multipositive unlabeled learning combining metric learning and deep clustering" innovatively combines prototype networks with contrastive clustering strategies, optimizing inter-class distance through metric learning, and showing significant advantages in small-sample scenarios. Regarding patents related to PU learning, in 2019, Huang Shengjun et al. applied active learning to the classification problem of positive unlabeled data in "An Active Learning Method for Positive and Unlabeled Data Classification," effectively improving the performance of the PU classification algorithm with relatively low labeling costs (Publication No.: CN109299162A). In 2021, Huang Qingming et al. proposed an iterative deep PU learning and class prior estimation framework in "Data Classification Method and System Based on Deep PU Learning and Class Prior Estimation." This framework can simultaneously estimate class priors and use the obtained priors to estimate deep models without needing to know the true prior distribution of the data (Publication No.: CN114417975A).

[0006] Although MPU learning has made initial progress, the related work is still relatively superficial compared with PU learning research. Existing MPU methods have the following limitations: First, current research is limited to the completely random missing data hypothesis (SCAR) and ignores the label distribution bias in real-world scenarios. Scholars have not considered building models with label missing mechanisms and lack systematic research on data distribution bias. Second, traditional methods mostly use batch training, which is difficult to adapt to dynamic data flow environments and ignores the fact that the sample distribution in real-world scenarios changes continuously with arrival time. The online multi-positive class unlabeled classification algorithm proposed in this invention has the following distinguishing technical features compared with traditional and other existing methods: (1) Unlike the traditional method of training a classifier for every two classes, the number of classifiers trained in this invention is equal to the number of sample classes, reducing the number of classifiers trained and improving model training efficiency. (2) Unlike the traditional batch processing method for solving multi-class classification, this invention designs an online learning method and uses the sliding window method for online updates, which can update model parameters in real time. (3) This invention introduces a propensity score weighting mechanism to adjust the data label distribution by predicting the propensity score of positive samples, thereby correcting the bias caused by label imbalance in the original data. Existing methods usually assume that the propensity score model is a linear function or use a fixed function form to estimate the propensity score. However, propensity scores are usually complex and nonlinear, which makes it impossible for linear models to effectively capture the characteristics of the data. This invention uses a multilayer perceptron (MLP) model, which can capture more complex nonlinear relationships and provide more accurate propensity score estimates. Summary of the Invention

[0007] The MLP used in this invention includes two structures: a single-hidden-layer perceptron and a double-hidden-layer perceptron, which can be found in the appendix. Figure 1 For a single-hidden-layer perceptron, the hidden layer uses the ReLU activation function, and the output layer uses the Sigmoid activation function for prediction. The structure is shown in the appendix. Figure 1 -a, the MLP structure containing two hidden layers is shown in the appendix. Figure 1 -b.

[0008] This invention addresses the problem of data not satisfying the completely random missing labels hypothesis in multi-class classification problems, reducing the cost of manual labeling. It uses an MLP (Multi-Level Processing) algorithm to estimate propensity scores to handle this issue. By combining online learning with mini-batch sample estimation to update the MLP model weights, and employing gradient descent to optimize the classifier, the invention further optimizes the classifier. Finally, a classifier is used to predict sample labels. A flowchart of this method can be found in the appendix. Figure 2 This invention not only solves the problem of high labeling costs in multi-class classification problems, but also demonstrates high-precision classification capabilities for data that do not meet the SCAR hypothesis.

[0009] The disclosed method mainly includes the following steps:

[0010] S1. Data preprocessing: Convert each feature of the data into numerical data, remove redundant features, normalize the data, and convert the label values.

[0011] S2. Let the preprocessed training samples be... Where T is the total number of training samples, x t ∈R d Let y be a d-dimensional feature of the data. t =i(i=1,2,3…,k) is x t The corresponding labels are y = 1, 2, ..., k-1, representing positive class samples and y = k, representing negative class samples. The MLP outputs predicted values, and the binary cross-entropy loss function, in the following form, is minimized:

[0012]

[0013] Where y represents the real label. The value is the propensity score prediction obtained using MLP, and n is the number of samples used to calculate the cross-entropy loss.

[0014] S3. Use the gradient descent algorithm to update the network weights and biases.

[0015] S4. For labeled samples, it is necessary to calculate the propensity score. For unlabeled samples, the loss is calculated directly, and the instantaneous loss is as follows, which is then minimized:

[0016]

[0017] Where, x t ∈R d The d-dimensional sample received at time t, y t =i(i=1,2,3…,k) is x t The corresponding label, sign{y t =i} in y t =1 when i, 0 otherwise. γ represents the proportion of positive samples (i.e., labeled samples) to the total sample. The loss function l(·) is a non-convex loss function, and a linear discriminant function is chosen. f(x) t )= <B,x t > is a linear classifier. This is an estimate of the prior probability, where m and ∈ are weighting parameters, and this invention sets default values. And ∈ = 0.01.

[0018] S5. Use the traditional gradient descent algorithm to find the weight parameters that minimize the online instantaneous loss. in At time t, when B = B t The gradient value taken at instantaneous loss.

[0019] S6. Train the classifier based on parameter B. Used to classify samples into the correct category.

[0020] Detailed explanation of each step

[0021] S1. Data Normalization: The various features of the sample are processed by translation and scaling to make the numerical distribution of the features have the statistical characteristics of zero mean and unit variance, so as to avoid some features having too much influence on the model training process and improve the generalization ability of the model.

[0022] S2. Selecting a suitable loss function l(z) is the key technology of this invention. Since non-convex loss functions have more complex shapes and exhibit robustness to outliers and noise, to ensure that the expected loss is unbiased and the loss function is smooth under random missing values, this invention considers a family of loss functions l(z) with the following properties:

[0023] (1)l: It is monotonically decreasing;

[0024] (2) The function satisfies l(z) + l(-z) = 1;

[0025] (3) l in It is continuously differentiable and Lipschitz continuous, with the Lipschitz constant being L.

[0026] |l(z1)-l(z2)|≤L|z1-z2|

[0027] This allows us to verify the non-convex sigmoid loss function. In this invention, σ = 1, provided the above conditions are met. Figure 3 The graph of the function and its derivative is shown.

[0028] S3. Update the MLP model parameters using the gradient descent algorithm. To achieve a fully online multi-class classification algorithm, this invention uses the sliding window method, introducing a parameter Z to represent the maximum number of samples for training the MLP. Z samples are input each time to train the propensity score model. In addition, parameters t0, t1, and t2 are set to control the forward scrolling of the sliding window. (Appendix) Figure 4 The diagram illustrates the settings for a sliding window. The current sliding window size is set to Z, the sliding step size is Γ, and the starting and ending points of the window are t0 and t1, respectively. The starting point for classifier updates is denoted by t2. For t∈[t0,t1], the corresponding samples are selected from the data stream. And shuffled into m mini-batches {b1, b2, ..., b m For each batch, calculate the binary cross-entropy loss:

[0029]

[0030] n is the number of samples in a batch, and then the weights and biases of the MLP model are updated:

[0031]

[0032] Where W and b are the network weights and biases in the MLP model, η is the learning rate, and L is the calculated cross-entropy loss.

[0033] S4. For t∈[t2,t1], the true label y of the received sample t Determine whether the sample is labeled. If it is labeled, calculate the propensity score using the updated MLP model. If the sample is unlabeled, no calculation is required. Then, calculate the online instantaneous loss of B at time t, and derive the gradient by taking its derivative:

[0034]

[0035] wherein, represents the partial derivative of the base loss function with respect to the component b in the parameter matrix B v , and the update rule of the parameter matrix is:

[0036]

[0037] where γ1 is the learning rate.

[0038] Algorithm 1. Online Multi-class Learning Algorithm

[0039] Input: Data stream: (x1,y1),...,(x T ,y T ), learning rate γ1, category k, number of training samples Z, large batch Γ

[0040] Output: f T (x t )=<B T ,x t >

[0041] Step 1. Initialization: Parameter matrix B ← B0; θ in the propensity score model is set to θ0; training frame start point t0=1; training frame end point t1=t0+Γ; prediction start point t2=1

[0042] Step 2. Online Iteration

[0043] (1) for: t=1,2,…,T

[0044] (2) When t0<T:

[0045] t1=min(t1,T)

[0046] For t∈[t0,t1]:

[0047] Shuffle the dataset Divide into m mini-batches {b1,b2,...,b m}

[0048] For each batch:

[0049] Calculate the binary cross-entropy loss, and update the model weights using the gradient descent method

[0050] For t∈[t2,t1]:

[0051] Calculate f t (x t )=<B t ,x t >

[0052] Receive the true label y of the sample tDetermine whether the sample has a label (if there is no label, let y t =k)

[0053] If x t For labeled samples:

[0054] Obtain propensity score Calculate the instantaneous loss L(x) t )

[0055] If x t Unlabeled samples:

[0056] Calculate the instantaneous loss L(x) t )

[0057] (3) Calculation

[0058] (4) Update:

[0059] (5) Update: t2←t1

[0060] If t1 ≥ T, then stop the loop.

[0061] Update: t0←t0+Γ

[0062] t1←t1+Γ

[0063] If t0 ≥ T, then stop the loop.

[0064] Step 3, return to f T (x t )= T ,x t >

[0065] S5. Obtain the classifier based on training. Classify the samples into the correct categories. The specific discrimination rule is as follows: if all f i If all values ​​of (x) are less than or equal to 0, the sample is classified as class k; otherwise, the sample is classified as class f with the largest component. i The category i corresponding to (x). The discrimination rule can be expressed as:

[0066]

[0067] Compared with the prior art, the beneficial effects of the present invention are:

[0068] 1. Effectively solves the MPU problem. Currently, the application of MPU learning in multi-class classification problems is still in the exploratory stage. This invention combines the ideas of propensity score and online learning to extend PU learning to multi-class scenarios. On multiple datasets, the method of this invention demonstrates superior classification performance compared to other existing methods. ​

[0069] 2. Highly efficient online learning capability. The algorithm of this invention possesses powerful online learning capabilities, enabling it to adapt to continuously arriving data streams in a dynamically changing environment and promptly capture changes in data distribution. It can quickly update model parameters without reprocessing the entire dataset, achieving efficient processing of large-scale dynamic MPU data and demonstrating high practical application value.

[0070] 3. Robust multi-class classification learning algorithm. The method of this invention adjusts the data label distribution by predicting the propensity score of positive samples, thereby correcting the bias caused by the imbalance of labels in the original data, making the algorithm more robust even when the labels of positive samples do not satisfy the completely random missing label hypothesis. Attached Figure Description

[0071] Figure 1 The diagram shows the structure of the single-hidden-layer perceptron and the double-hidden-layer perceptron used in this invention.

[0072] Figure 2 The flowchart below illustrates the multi-class unlabeled online learning method disclosed in this invention. As data streams are input and parameters are initialized, the MLP model and classifier are trained. The algorithm updates parameters using gradient descent and ultimately outputs a parameter matrix B. T According to the classifier f(x) t )= <B,x t Give each component f i (x t The value of ) is used to identify the category to which the sample belongs, based on the magnitude of each component value.

[0073] Figure 3 The non-convex sigmoid loss function proposed in this invention The graph of its derivative function.

[0074] Figure 4 The sliding window method used in this invention refers to the maximum number of samples for training the MLP, where Z samples are input each time to train the propensity score model. A parameter Γ is introduced to represent the batch size used for each classifier update. The start and end points of the window are t0 and t1, respectively, and the starting point for the classifier update is represented by t2.

[0075] Figure 5 This is a distribution map of the original data and the processed MPU data of the artificial dataset generated by this invention. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0077] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0078] The experiment was mainly divided into tests under the conditions that the samples met and did not meet the SCAR assumption. The following is a brief introduction to the datasets used. First, there was a man-made dataset, which generated 2500 samples based on a normal distribution by setting three cluster centers. Each sample contained two features. (Appendix) Figure 5 This shows the data distribution of the artificial dataset; the original data distribution is shown in the appendix. Figure 5 -a. To test the algorithm's performance without satisfying the completely random missing label assumption, MPU data was constructed by randomly selecting samples from subsets of Category 1 and Category 2 and performing label missing labeling. See Appendix. Figure 5 -b.

[0079] Next is the Peptide Identification Dataset (PSM). The peptide identification process generally follows this procedure: In biological specimens, samples containing complex proteins are first broken down into peptide chains using specific enzymes; then, the mass spectrometry data of these peptides are measured using a high-performance mass spectrometer (HPLC); finally, the amino acid sequence of the peptide is determined by matching the observed mass spectra with theoretical or known mass spectra in a database. However, a large portion of the peptide sequence matching results generated by this method are incorrect. To improve identification accuracy, researchers often employ a strategy called "target-decoy," which involves deliberately adding non-existent fake peptide sequences to the database. These matching results with fake sequences are naturally incorrect and can be considered as known positive samples. Other matching results, including correct and incorrect matches, are treated as unlabeled samples. Thus, the problem is transformed into an HPLC learning task, with the goal of identifying the correct peptide sequence matches from these unlabeled samples. This invention was tested on four real PSM datasets, which are binary classification datasets. Basic information is shown in Table 1.

[0080] Table 1 Basic Information of PSM Dataset

[0081]

[0082] Due to the unique nature of PSM data, the true labels of unlabeled samples cannot be accurately determined. Therefore, classification accuracy cannot be directly used as a metric to evaluate model performance. Against this backdrop, this invention introduces two key metrics, α1 and α2, to measure classification effectiveness:

[0083]

[0084] in, and They represent samples x respectively i PSM samples are predicted as either positive or negative, where P represents the positive sample dataset and U represents the unlabeled sample dataset. The metric α1 reflects the proportion of positive samples correctly identified by the classifier, while α2 measures the proportion of negative samples correctly identified by the classifier in the unlabeled sample dataset. Therefore, in evaluating the classifier... Ideally, the model should achieve a high α1 and not too low α2, which means that the classifier can not only accurately identify positive samples, but also effectively distinguish negative samples.

[0085] Finally, there are the UCI datasets, which consist of four numerical datasets, all of which are multi-class datasets. Pendigits is a handwritten digit dataset; Drybeans is a dried lentil dataset; Students is a student information dataset; and Car is a car dataset. Detailed features of each dataset are shown in Table 2.

[0086] Table 2 Basic Information Table of UCI Dataset

[0087]

[0088] This invention mainly compares the following methods:

[0089] (1) MPU: A multi-positive class unlabeled method that learns the discriminant function by constructing different convex loss functions to achieve one-step classification; and proves that its generalization error upper bound is comparable to that of traditional supervised multi-class classification methods.

[0090] (2)UREA: Unbiased Risk Estimator, which constructs an unbiased estimator by minimizing empirical risk, is used for the original classification risk estimation in multi-class PU learning, but it has a certain overfitting problem.

[0091] (3) AREA: Alternative Risk Estimator. Based on UREA, it uses an alternative loss function to obtain a method with a clear lower bound on the estimation error, which reduces overfitting and improves classification performance.

[0092] (4) OPUDH A baseline online PU classifier based on a linear kernel, with the base loss using the Double Hinge loss function.

[0093] Neither the artificially created dataset nor the peptide profiling dataset satisfies the SCAR hypothesis; however, for the UCI dataset, this invention designs two settings. The first setting satisfies the SCAR hypothesis, i.e., the bias score is assumed to be a constant value; the second setting does not satisfy the SCAR hypothesis, i.e., according to specific rules, a subset of labels is manually selected from each positive class for label missing. The specific steps are as follows: First, a logistic regression model is used to pre-classify the dataset according to the correct labels. Each sample is processed by the discriminant function f(x) = ax + b, resulting in a k-dimensional vector f. Based on the k-th component f... k Samples with labels in the first k-1 classes are selected as the positive class, and the remaining samples are considered as the negative class with missing labels. The specific selection criteria are as follows: calculate the label score for each sample using the following formula:

[0094] η(x)=1-(1+exp(-f k )) -1

[0095] Where η(x) is the label score of the sample, f k This represents the k-th component of the vector f obtained using the discriminant function. A larger value for f... k The smaller the score, the higher the probability that the sample will be labeled. Then, samples are taken based on the label score; the higher the label score, the more likely the sample is to be labeled.

[0096] In the experiment, the first k-1 classes of all datasets were considered positive samples, and the k-th class was considered negative samples. Under the assumption of completely random missing data, the propensity score of each positive sample was the same and constant. Samples with a proportion of r (r = 0.2, 0.3, 0.4, 0.5, 0.6) were randomly drawn from each positive class. N q represents the number of positive class samples with missing labels, and N represents the total number of positive class samples. The extracted samples and all negative class samples are considered as samples with missing labels, and the remaining samples are considered as samples with intact labels. 80% of the samples are randomly selected from each dataset as the training set, and the remaining 20% ​​as the test set. Prior probabilities are estimated using the ratio of the number of samples in each class to the total number of samples. All features are standardized to the range [-1, 1]. In each experiment, training is first performed on the training set, and then independently repeated ten times on the test set to obtain the final average accuracy and standard deviation of the algorithm. Accuracy represents the proportion of correctly classified samples out of the total number of samples.

[0097] First, the performance of the algorithm of this invention was tested on the UCI dataset under the condition that the samples satisfy the SCAR assumption. Table 3 lists the classification accuracy and standard deviation of the method of this invention and other methods for MPU, AREA and UREA on the UCI dataset.

[0098] Table 3. Classification accuracy and standard deviation of the UCI dataset under the SCAR hypothesis.

[0099]

[0100] The results show that the method of this invention exhibits superior accuracy at higher missing proportions (r = 0.5, 0.6); however, at missing proportions r = 0.2, 0.3, its performance is slightly worse than the AREA method. This indicates that the method of this invention performs better at high missing proportions. Overall, the method of this invention achieves better prediction results when the samples satisfy the assumption of completely random missing data.

[0101] Most theoretical analyses of MPU classification are based on the assumption of completely random missing values, but this is not necessarily the case in real-world problems. This invention tests the classification performance of the algorithm under conditions where the SCAR assumption is not satisfied. Experiments were conducted on the aforementioned UCI dataset, a two-dimensional artificial dataset, and a peptide recognition dataset.

[0102] The first experiment was conducted on an artificial dataset. Since the propensity scores of the samples were known, the method of this invention directly used the known propensity scores to weight the loss function. The results are shown in Table 4, with the optimal classification accuracy highlighted in bold black. Experimental results show that the method of this invention has a stable classification accuracy under different missing proportions. In contrast, the classification accuracy of other comparative methods decreases significantly with increasing missing proportions. Moreover, the standard deviation of the method of this invention is relatively small, ranging from 0.001 to 0.006, while the standard deviations of AREA, UREA, and MPU are between 0.002 and 0.078, slightly larger than that of the method of this invention.

[0103] Table 4. Classification accuracy and standard deviation of the artificial dataset under conditions where the SCAR assumption is not satisfied.

[0104]

[0105] Then, the present invention was tested on four real-world binary classification PSM datasets. Three MLP models were set up: "1LP-64" represents a perceptron with one hidden layer and 64 neurons; "1LP-32" represents a perceptron with one hidden layer and 32 neurons; and "2LP-128-64" represents a two-hidden-layer perceptron with 128 neurons in the first hidden layer and 64 neurons in the second hidden layer. Experiments were conducted on each dataset under all three settings. Table 5 shows the mean accuracy and standard deviation of the method of the present invention, which are the experimental results for each dataset under the optimal multilayer perceptron settings. The optimal α2 value is shown in bold. To compare the effect of α2, α1 was controlled above 0.975 accuracy. Experimental results show that the method of the present invention can accurately identify positive samples while identifying as many negative samples as possible, demonstrating a certain advantage.

[0106] Table 5. Identification results of the peptide dataset.

[0107]

[0108] After setting up MPU data that does not satisfy the SCAR hypothesis, this invention conducted experiments on the UCI dataset with different missing proportions. The mean accuracy and standard deviation corresponding to the method of this invention in the table are also the experimental results of each dataset on the multilayer perceptron setting with the best classification performance. Table 6 shows the classification performance of the method of this invention and the comparison methods, where the optimal classification accuracy is highlighted in bold.

[0109] Table 6. Classification accuracy and standard deviation of the UCI dataset without satisfying the SCAR assumption.

[0110]

[0111] The results show that: (1) On the Pendigits and Car datasets, the method of this invention significantly outperforms other methods. (2) On the Drybeans dataset, the method of this invention exhibits the best classification performance when the missing proportion is small; while when the missing proportion increases to 0.4, 0.5, and 0.6, the UREA method shows the best performance. (3) On the Students dataset, the method of this invention performs well when the missing proportion is 0.2, 0.4, 0.5, and 0.6, and the classification accuracy is relatively stable. Overall, in scenarios where the samples do not meet the SCAR hypothesis, the method of this invention has a small standard deviation, showing strong robustness.

[0112] The above description, in conjunction with the diagrams, illustrates specific embodiments of the present invention, but is not intended to limit the scope of protection of the present invention. Various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A multi-classification learning technique for data streams with partially missing labels, characterized in that, comprising the following steps: S1. Data preprocessing: standardize all features to the range of [-1, 1] to ensure different features have the same scale; S2. Select a smooth non-convex loss function as the base loss function, which satisfies the following properties: (1) It is monotonically decreasing. (2) The function satisfies l(z)+l(-z)=1 (3) l in It is continuously differentiable and Lipschitz continuous, i.e. |l(z1)-l(z2)|≤L|z1-z2|; This allows us to verify the non-convex sigmoid function. In this invention, the sigmoid loss function is set to σ = 1, provided that the above conditions are met. S3. Train a propensity score model using a Multi-Layer Perceptron (MLP), and update model parameters by calculating the binary cross-entropy loss; S4. Use the gradient descent method to minimize the instantaneous loss of the algorithm at time t: Where, x t ∈R d The d-dimensional sample received at time t, y t =i(i=1,2,3…,k) is x t The corresponding label, sign{y t =i} in y t The value is 1 when i = 0, and 0 in other cases. The updated MLP model calculates the propensity score, γ represents the proportion of positive samples (i.e., labeled samples) to the total sample, and the loss function l(·) is a non-convex loss function. A linear discriminant function is used, f(x) t )= <B,x t > is a linear classifier. This is an estimate of the prior probability, where m and ∈ are weighting parameters, and this invention sets default values. And ∈ = 0.01; S5. Obtain the classifier based on training. Classify the samples into the correct categories. The discrimination rule can be expressed as: The specific discrimination rule is as follows: If all f i If all values ​​of (x) are less than or equal to 0, the sample is classified as class k; otherwise, the sample is classified as class f with the largest component. i The category i corresponding to (x).

2. The multi-classification learning method for data streams with partially missing labels as described in claim 1, characterized in that, Step S3 updates the MLP model by calculating the binary cross-entropy loss. A sliding window method is used, with parameter Z representing the maximum number of samples for training the MLP. Each time, Z samples are input, and the MLP is used to train the propensity score model. Furthermore, parameters t0, t1, and t2 are set to control the forward scrolling of the sliding window. The size of the existing sliding window is set to Z, the step size is Γ, and the starting and ending points of the window are t0 and t1, respectively. The starting point for classifier updates is represented by t2. For t∈[t0,t1], the corresponding samples are selected from the data stream. And shuffled into m mini-batches {b1, b2, ..., b m For each batch, calculate the binary cross-entropy loss: Where y represents the real label. The propensity score prediction is obtained using MLP, where n is the number of samples in a batch; Use the gradient descent algorithm to update the weights and biases of the MLP network: Where W and b are the network weights and biases in the MLP model, η is the learning rate, and L is the calculated cross-entropy loss.

3. The multi-classification learning method for data streams with partially missing labels as described in claim 1, characterized in that, Step S4 is to solve for minimizing the online instantaneous loss, and the specific solving steps are as follows: S41. Initialization: parameter matrix B←B0; θ in the propensity score model is set as θ=θ0; the start point of the training window t0=1; the end point of the training window t1=t0+Γ; the prediction start point t2=1; set the learning rate γ1 S42. Online iteration S421 for: t=1,2,…,T S422 receives samples <x t ,y t > S423 When t0<T: t1=min(t1,T) For t∈[t0,t1]: Shuffle the dataset Divided into m mini-batches {b1, b2, ..., b m } For each batch: Calculate the binary cross-entropy loss, perform gradient descent using Adam, and update the model weights For t∈[t2,t1]: Calculate f t (x t )= t ,x t >​ The true label y of the received sample t Determine whether the sample has a label (if there is no label, let...). y t=k) If x t For labeled samples: Obtain propensity score Calculate the instantaneous loss L(x) j ) If x t Unlabeled samples: Calculate the instantaneous loss L(x) j ) S424 calculation S425 Update: S426 Update: t2←t1 If t1≥T, stop the loop Update: t0←t0+Γ t1←t1+Γ If t0 ≥ T, then stop loop S43 and return f. T (x t )= T ,x t >​

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