Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the affinity between data points. This paper proposes a reachable distance function for KNN classification. The reachable distance function is not a geometric direct-line distance between two data points. It gives a consideration to the class attribute of a training dataset when measuring the affinity between data points. Concretely speaking, the reachable distance between data points includes their class center distance and real distance. Its shape looks like “Z,” and we also call it a Z distance function. In this way, the affinity between data points in the same class is always stronger than that in different classes. Or, the intraclass data points are always closer than those interclass data points. We evaluated the reachable distance with experiments, and demonstrated that the proposed distance function achieved better performance in KNN classification.

Graph convolutional networks (GCN) have been widely used in processing graphs and networks data. However, some recent research experiments show that the existing graph convolutional networks have isseus when integrating node features and topology structure. In order to remedy the weakness, we propose a new GCN architecture. Firstly, the proposed architecture introduces the cross-stitch networks into GCN with improved cross-stitch units. Cross-stitch networks spread information/knowledge between node features and topology structure, and obtains consistent learned representation by integrating information of node features and topology structure at the same time. Therefore, the proposed model can capture various channel information in all images through multiple channels. Secondly, an attention mechanism is to further extract the most relevant information between channel embeddings. Experiments on six benchmark datasets shows that our method outperforms all comparison methods on different evaluation indicators.

Hierarchical graph pooling has shown great potential for capturing high-quality graph representations through the node cluster selection mechanism. However, the current node cluster selection methods have inadequate clustering issues, and their scoring methods rely too much on the node representation, resulting in excessive graph structure information loss during pooling. In this paper, a local capsule pooling network (LCPN) is proposed to alleviate the above issues. Specifically, (i) a local capsule pooling (LCP) is proposed to alleviate the issue of insufficient clustering; (ii) a task-aware readout (TAR) mechanism is proposed to obtain a more expressive graph representation; (iii) a pooling information loss (PIL) term is proposed to further alleviate the information loss caused by pooling during training. Experimental results on the graph classification task, the graph reconstruction task, and the pooled graph adjacency visualization task show the superior performance of the proposed LCPN and demonstrate its effectiveness and efficiency.