To better address the problem of the low prediction accuracy of used car prices under a large number of features and big data and improve the accuracy of existing deep learning models, an iterative framework combining XGBoost and LightGBM is proposed in this paper. First, the relevant data processing is carried out for the initial recognition features. Then, by training the deep residual network, the predicted results are fused with the original features as new features. Finally, the new feature group is input into the iteration framework for training, the iteration is stopped, and the results are output when the performance reaches the highest value. These experimental results show that the combination of the deep residual network and iterative framework has a better prediction accuracy than the random forest and deep residual network. At the same time, by combining the existing mainstream methods with the iterative framework, it is verified that the iterative framework proposed in this paper can be applied to other models and greatly improve the prediction performance of other models.

Graph neural networks (GNNs) have shown significant performance in various practical applications due to their strong learning capabilities. Backdoor attacks are a type of attack that can produce hidden attacks on machine learning models. GNNs take backdoor datasets as input to produce an adversary‐specified output on poisoned data but perform normally on clean data, which can have grave implications for applications. Backdoor attacks are under‐researched in the graph domain, and almost existing graph backdoor attacks focus on the graph‐level classification task. To close this gap, we propose a novel graph backdoor attack that uses node features as triggers and does not need knowledge of the GNNs parameters. In the experiments, we find that feature triggers can destroy the feature spaces of the original datasets, resulting in GNNs inability to identify poisoned data and clean data well. An adaptive method is proposed to improve the performance of the backdoor model by adjusting the graph structure. We conducted extensive experiments to validate the effectiveness of our model on three benchmark datasets.

The number of subtrees in a graph is related to the reliability of a network with possible vertex failure and edge failure. It is known that networks with larger number of subtrees would be more reliable. Therefore, for given families of graphs, determining the graphs with maximum number of subtrees within the family becomes important. For a tree T of n vertices, let $F\left(T\right)$ denote the number of all subtrees in T. Yan and Yeh gave a linear-time algorithm to count the number of subtrees in T and determined the tree of diameter d and order n with the maximum number of subtrees. In this paper, we present two recursive relations to count the number of subtrees of trees. We also characterize all trees of n vertices with $5+n+2^{n-3}\le F\left(T\right)\le 2^{n-1}+n-1$.

Graph neural networks (GNNs) have shown powerful capabilities in modeling and representing graph structural data across various graph learning tasks as an emerging deep learning approach. However, most existing GNNs focus on single-relational graphs and fail to fully utilize the rich and diverse relational information present in real-world graph data. In addition, deeper GNNs tend to suffer from overfitting and oversmoothing issues, leading to degraded model performance. To deeply excavate the multi-relational features in graph data and strengthen the modeling and representation abilities of GNNs, this paper proposes a multi-channel deep graph convolutional neural network method called DeepMCGCN. It constructs multiple relational subgraphs and adopts multiple GCN channels to learn the characteristics of different relational subgraphs separately. Cross-channel connections are utilized to obtain interactions between different relational subgraphs, which can learn node embeddings richer and more discriminative than single-channel GNNs. Meanwhile, it alleviates overfitting issues of deep models by optimizing convolution functions and adding residual connections between and within channels. The DeepMCGCN method is evaluated on three real-world datasets, and the experimental results show that its node classification performance outperforms that of single-channel GCN and other benchmark models, which improves the modeling and representation capabilities of the model.

The dual-channel graph convolutional neural networks based on hybrid features jointly model the different features of networks, so that the features can learn each other and improve the performance of various subsequent machine learning tasks. However, current dual-channel graph convolutional neural networks are limited by the number of convolution layers, which hinders the performance improvement of the models. Graph convolutional neural networks superimpose multi-layer graph convolution operations, which would occur in smoothing phenomena, resulting in performance decreasing as the increasing number of graph convolutional layers. Inspired by the success of residual connections on convolutional neural networks, this paper applies residual connections to dual-channel graph convolutional neural networks, and increases the depth of dual-channel graph convolutional neural networks. Thus, a dual-channel deep graph convolutional neural network (D2GCN) is proposed, which can effectively avoid over-smoothing and improve model performance. D2GCN is verified on CiteSeer, DBLP, and SDBLP datasets, the results show that D2GCN performs better than the comparison algorithms used in node classification tasks.

In this paper, we analyze the diffusion patterns of cascading failure, which happen in the express hypernetwork and electronic hypernetwork respectively. The cascading failure of the express hypernetwork is diffused by the node, and the cascading failure of the electronic hypernetwork is diffused by the hyper-edge. According to hyper-graph theory, we propose two methods to characterize these cascading failures, which are 2-section graph analytical method and line-graph analytical method. We analyze the characteristics of the cascading failures based on node by using the 2-section graph analytical method and based on hyper-edge by using line-graph analytical method, respectively. We construct a k uniform scale-free hypernetwork and analyze the cascading failure process of this hypernetwork based on the couple map lattice according to our methods. The simulation results show that the scale-free hypernetworks are both robust and vulnerable for attack. It is found that the cascading failure based on the node of k uniform scale-free hypernetwork is associated with the hyper-degree distribution of nodes, and the scale-free hypernetwork is robust for random attack and vulnerable for deliberate attack. The more nodes a hyper-edge has, the better robustness the hypernetwork has.The cascading failure based on the hyper-edge is different from the cascading failure based on the node. The cascading failure based on the hyper-edge is associated with the hyper-edge degree distribution. The hyper-edge degree distribution of the scale-free hypernetwork is not entirely the power-low distribution. When the cascading failure is diffused by the hyper-edge, the hypernetwork is vulnerable for random attack and robustness for deliberate attack if there are 3 or 5 nodes in a hyper-edge. Moreover, the hypernetwork becomes robust for the random attack if there are 7 nodes in a hyper-edge. Furthermore, the k uniform scale-free hypernetwork is more robust than the same size Barabasi-Albert scale-free network for the same attack. The cascading failure process based on the hyper-edge is slower than based on the node. We find that the edge number is another influential factor of robustness. The network is more robust if it has more edges for fixed node number. The line-graph has more edges than the 2-section graph in the same size scale-free hypernetwork, so the cascading failure of node is slower than that of hyper-edge.