| With the development of intelligent technology,semi-supervised learning has been utilized in many application scenarios,which can effectively expand sample space to solve the shortcomings caused by manual sample labeling.According to the loss function and model structure,semi-supervised learning can be divided into generative,consistent regularization,graph-based,pseudo-labeling,and mixed methods.The label propagation method is based on graphs and pseudo labels,which has simple operations and low complexity.Nowadays,it has been widely used in virtual community mining and other fields.However,some limitations exist:(1)Localization problem: The label propagation method only utilizes Euclidean distance to measure the similarity between the samples,ignoring the complete structural information of sample data.(2)Instability issues: In the process of label propagation,if the maximum number of neighbors of a node is more than one,a random select strategy will be utilized to obtain its label.(3)Label relevance problem: In a multi-label scenario,multi-label learning is straightforwardly transformed into single-label learning,which ignores the correlation between labels.To address these issues,label propagation approaches that combine with group optimization are proposed for single-label and multi-label scenarios.The main contents are as follows:(1)To solve the instability issue of propagation results caused by excessive localization and randomness in the graph construction,a label propagation algorithm for single-label data based on hierarchical weighting method is proposed.During the initialization phase,hierarchical weighting is employed for attribute aggregation and attribute update to predict the initial label embedding vector for each node.Then,in the label propagation process,for each unlabeled node,the label owned by its neighborhood node with the highest similarity in each iteration is selected to update its label information to avoid arbitrary label propagation.And then,the optimal voting strategy in group optimization is utilized to fuse the obtained label results to reduce the error rate of the results,so as to improve the robustness of the model and the stability of the results.Finally,the proposed method is compared with the existing classical algorithms LP,Heter LP,ILP,and SPCT on iris,wine,glass,cmc,robot,ionosphere,sonar,and wdg.Experiment results show that the proposed method can effectively solve the localization and stability problems in single-label datasets.Furthermore,statistical measures are utilized to evaluate the degree of difference between different methods,and the results show that the proposed method has better performance.(2)To solve the problem of label relevance and instability in multi-label scenarios,a label propagation algorithm based on ranking weighting strategy is proposed.Firstly,the fuzzy Cmeans approach is adopted to construct the similarity matrix to measure the correlation between labels.On this basis,the ranking weighting strategy in group optimization is introduced to improve the stability of the model.The stability of the propagation results will be enhanced with the increase in the number of iterations,and the weight given also gradually increases.And then,the probability is calculated based on the obtained weights to acquire the label information of each sample in the multi-label space.Finally,the proposed method is compared with LP,Transductive MLP,and MLk NN algorithms on yeast,scene,enron,flag,cla500,emotions,and birds.The experimental results show that the proposed method performs better under different evaluations,which can help to solve the stability and label correlation problems in multi-label datasets.Moreover,statistical analysis results show that the proposed method performs better than other algorithms. |