UPN-GCN: Update Positive-Negative Graph Convolution Neural Network in Non-Euclidean Structured Data

Graph Convolutional neural Networks (GCNs) demonstrate exceptional effectiveness when working with data that have non-Euclidean structures. In recent years, numerous researchers have utilized GCNs for data with Euclidean structures. such as image data and language data, and achieved good results, expanding the application scope of GCN. Although there are numerous methods for handling non-Euclidean structured data, there are few studies that approach non-Euclidean structured data from a graph perspective. Constructing non-Euclidean data structures using classical measurement methods results in significant information loss. Therefore, it hinders the generalization of GCN in non-Euclidean structure data. Some researchers have proposed to construct an intuitive fuzzy relationship, namely the positive-negative relationship, in non-Euclidean data, and explained the physical meaning of this relationship. Based on the positive-negative relationship, a graph convolutional neural network model PN-GCN was constructed. However, this positive-negative relationship does not accurately reflect the differences and similarities between data, thereby reducing the accuracy of node classification. Therefore, we have designed a new convolutional neural network model UPN-GCN based on updating positive and negative graphs. When using the adjacency matrix obtained from positive and negative relationships to perform GCN operations on data, the feature representations obtained from each iteration are continuously updated to optimize the adjacency matrix of positive and negative relationships, making the representation of data differences and similarities more accurate. Finally, we validated the accuracy and robustness of this adjacency matrix update operation based on positive and negative relationships through experimental comparisons.