## 3 Materials and Methods
### Methods
#### 3.2.3 Semi-Supervised  
As unsupervised learning, semi-supervised learning aims to learn a generic feature representation for downstream tasks. In the classification task, we cannot determine the class of unlabeled samples. However, based on common sense, we can assume that the following basic assumptions hold for most tasks:  
1. Smoothness assumption: If two samples, \(x_{1}\) and \(x_{2}\), are similar, their corresponding output representations, \(y_{1}\) and \(y_{2}\), should also be close to each other. Conversely, if the two samples, \(x_{1}\) and \(x_{2}\), are different, their corresponding output representations, \(y_{1}\) and \(y_{2}\), should also be far apart. 2. Clustering hypothesis and low-density hypothesis: The sample data should be clustered into clusters, and each cluster of samples corresponds to a subclass. In other words, similar samples are always densely clustered in one area, and the boundary line of classification is always located at the place where the sample density is low. Therefore, it can be assumed that if two samples, \(x_{1}\) and \(x_{2}\), are very similar, they are of the same kind, and the classification boundary will not be located between them. 3. The stream shape assumption: The input control consists of multiple low-dimensional stream shapes, all samples are located in a stream shape, and the data points located on the same stream shape have the same classification labels. In this paper, we use two semi-supervised learning methods:  
1. Agent labeling-based semi-supervised learning method. Proxy labels are high-confidence labels derived from the classification of the model itself, which are mixed into the labeled samples to provide additional information to assist in the subsequent training steps. However, these proxy labels are usually noisy and not fully accurate. Further, semi-supervised learning methods based on agent labels can be subdivided into self-supervised learning methods and multi-view learning methods. The self-supervised learning method first uses the labeled data to train the model, then uses the trained model to classify the unlabeled samples, removes the part of the classification confidence above a certain threshold, adds it to the labeled samples, then retrains the model and repeats this step until all the unlabeled samples have been added to the labeled samples. Figure 8: The structure of the classification model. The multi-view learning approach involves training several models with different parameters, each with a higher confidence level of unlabeled samples classified by other models in addition to the labeled dataset. The classical methods are the Co-training and Tri-training. Co-training divides the labeled dataset into two and trains the two classification models separately. Each classification model adds its own unlabeled samples with confidence higher than a certain threshold to the training set of the other classification model and then repeats the training until all unlabeled samples have been added to both training sets. Tri-training is performed by taking three training sets from the originally labeled samples with put-back sampling, and training three models separately, and then each model adds the unlabeled samples judged by the other two models to its own training set, and then repeats the training until all the unlabeled samples have been added to the three training sets. 2. Consistency-based semi-supervised learning method. The consistency-based semi-supervised learning method mainly utilizes the clustering assumption/low-density assumption, i.e., two extremely similar samples belong to the same class, regardless of the possibility that the classification boundary may cross the high-density region between them. Thus, for sample \(x\), a certain perturbation can be made to produce \(x^{\prime}\), and it is assumed that \(x\) and \(x^{\prime}\) must belong to the same classification.