Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning

Abstract

Graph convolutional networks gain remarkable success in semi-supervised learning on graph-structured data. The key to graph-based semisupervised learning is capturing the smoothness of labels or features over nodes exerted by graph structure. Previous methods, spectral methods and spatial methods, devote to defining graph convolution as a weighted average over neighboring nodes, and then learn graph convolution kernels to leverage the smoothness to improve the performance of graph-based semi-supervised learning. One open challenge is how to determine appropriate neighborhood that reflects relevant information of smoothness manifested in graph structure. In this paper, we propose GraphHeat, leveraging heat kernel to enhance low-frequency filters and enforce smoothness in the signal variation on the graph. GraphHeat leverages the local structure of target node under heat diffusion to determine its neighboring nodes flexibly, without the constraint of order suffered by previous methods. GraphHeat achieves state-of-the-art results in the task of graph-based semi-supervised classification across three benchmark datasets: Cora, Citeseer and Pubmed.

MORONET: Multi-omics Integration via Graph Convolutional Networks for Biomedical Data Classification

“…4 is tuned over {1, 2, 5, 10} through cross validation, and the same k value is adopted across all experiments on the same dataset. Although GCN has been widely-utilized in unsupervised [59][60][61][62] and semi-supervised 58,[63][64][65] learning, in this paper, we further extend the use of GCN for supervised classification tasks. For training data X X X tr ∈ R n tr ×d , the corresponding adjacency matrix…”

Adaptive Graph Convolution Using Heat Kernel for Attributed Graph Clustering

“…We propose a novel graph convolution model based on heat kernel to enhance low-frequency signals and suppress high-frequency signals, which can capture the smoothness of node features or labels sufficiently [13]. The heat kernel is defined as…”

“…Figure 1 depicted by the Graph Signal Processing toolbox [14] illustrates that the range of heat diffusion controlled by the scaling parameter s becomes larger as s increases. Different from the graph convolution methods in Section 2.2, which constrain neighboring nodes via the shortest path distance, graph convolution based on heat kernel leverages a continuous manner to determine the neighborhood, which can utilize high-order neighbor nodes sufficiently and discard some irrelevant low-order neighbor nodes [13]. Compared with the linear frequency response function g λ q = 1 − 1 2 λ q proposed in AGC [7], we leverage the exponential frequency function g λ q = 1 + e −sλ q based on heat kernel, which highlights low-frequency signals exponentially to make the graph smoother.…”

Deep Multi-type Objects Muli-view Multi-instance Multi-label Learning

“…(ii) DeepM4L not only guarantees the label consistency between the bag and instance levels; it also pursues the label consistency of bags across views by fusing multiview bag-label score tensors. (iii) Experimental results on benchmark datasets show that DeepM4L outperforms the representative M3L solutions (M3Lcmf [3], M2IL [20] and ICM2L [21] ), data fusion solutions (MFDF [8] , SelDFMF [10] and M4L-JMF [15]) based on matrix factorization, and network embedding methods (metapath2vec [22] and GraphHeat [23]) for diverse M4L tasks.…”